The 99% confidence interval for the decrease in the defective rate after the reconfiguration is (-0.018, 0.086).
How to find Confidence Intervals?Let the random variable & parameters be;
x1 : Number of successes from group 1
x2 : Number of successes from group 2
p1: Proportion of successes in group 1
p2: Proportion of successes in group 2
n1 : number of trial in group 1
n2: number of trial in group 2
We are given;
x1 = 260
n1 =985
x2 = 194
n2 = 842
Thus;
p1 = 260/985
p1 =0.2640
p2 = 194/842
p2 = 0.2304
Constructing a (1 - α)100% confidence interval for proportion from the formula;
(p₁ - p₂) - z√[((p₁(1 - p₁)/n₁) + p₂(1 - p₂)/n₂)]
plugging in z = 2.576 and the values of p₁, p₂, n₁ and n₂, we have the confidence interval as;
(-0.0184631, 0.0855743)
Therefore the 99% confidence interval for the decrease in the defective rate after the reconfiguration is (-0.018, 0.086).
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Hodaya is drawing a map of the trails in the canyon near her house. she knows that the distance from the first creek crossing to the second creek crossing is 1.8 miles. if every 3 inches on the map represents 0.75 of a mile, how far apart will the two creek crossings be on the map, to the nearest tenth of an inch? 2.3 4.1 5.4 7.2
The correct answer is 7.2 inch.
What is meant by distance?The length of the path joining two points determines their distance from one another.The entire journey that an object has taken can be used to define distance. An illustration. If an automobile drives 5 km east, then turns and drives 8 km further north, the total distance driven by the car is 13 km.'Distance' can be a verb or a noun, as was said above. He set himself apart from the remarks made by several of his coworkers. Thirty miles separate Peterborough from the nearest point. He had pledged to complete this duty but fell short of his commitment.The length of the line segment connecting any two points is referred to as their distance. In coordinate geometry, the distance between two points can be computed by measuring the length of the line segment connecting the two points.The nearest tenth of a 7inch.
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Find the volume of the triangular prism below if B = 12 cm, h = 8 cm, and L = 27 cm.
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{Formula \rightarrow \dfrac{1}{2} \times \bold{b}ase\times\bold{h}eight\times \bold{l}ength}[/tex]
[tex]\mathsf{Your\ equation\ should\ look\ like\rightarrow \dfrac{1}{2}\times12\times8\times27}[/tex]
[tex]\mathsf{Solving\rightarrow \dfrac{1}{2}\times12\times8\times27}[/tex]
[tex]\mathsf{ \dfrac{1}{2}\times12\times8\times27}[/tex]
[tex]\mathsf{= \dfrac{1}{2}\times\dfrac{12}{1}\times\dfrac{8}{1}\times\dfrac{27}{1}}[/tex]
[tex]\mathsf{= \dfrac{1\times12\times8\times27}{2\times1\times1\times1}}[/tex]
[tex]\mathsf{= \dfrac{12\times8\times27}{2\times1\times1}}[/tex]
[tex]\mathsf{= \dfrac{96\times27}{2\times1}}[/tex]
[tex]\mathsf{= \dfrac{2,592}{2}}[/tex]
[tex]\mathsf{= 2.592\div2}[/tex]
[tex]\mathsf{= 1,296}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{Option\ C.\ }\frak{1,296\ cm^3}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]A binomial distribution has a mean of = 12 for a sample of n = 60. what is the value of p?
Value of p is 0.5.
Given
Mean of a binomial distribution np = 12
Sample n = 60
The binomial distribution is the discrete probability distribution that gives only two possible results in an experiment, either success or failure.
To calculate the mean of a binomial distribution B(n, p) we need to multiply the number of trials n by the probability of successes p,
mean = n × p .
Value of p:
np = 12
(60) p = 12
p = 12/60
p = 1/2
p = 0.5
Value of p is 0.5.
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Question 2 of 10 Based only on the information given in the diagram, it is guaranteed that PQR~ STU.
A. True B. False
please!? thanks!
The given statement is false because the triangles may not be identical if their corresponding angles are genuinely different.
What is the triangle?Three sides, three vertices, and three angles make up a triangle. A triangle's three interior angles are always added up to 180 degrees. A triangle's two longest sides are always longer than its third side. A triangle with the vertices P, Q, and R symbol is △PQR.Based only on the information given in the diagram, it is guaranteed that PQR~ STU:
Two right triangles, ΔPQR and ΔSTU—are shown in the illustration with their right angles at ∠P and ∠S, respectively.
It is also demonstrated that TU = 12 units and QR = 6 units.
Because we only provided one set of congruent angles, we are unable to apply the A postulate of similarity to it.
Additionally, since there is only one pair of comparable sides, we are unable to determine whether they are proportionate.
The statement "based purely on the information presented in the diagram, it is assumed that triangle PQR triangle STU" is False because the triangles may not be identical if their corresponding angles are genuinely different.
Hence, The given statement is false.
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what is coefficient of x in 5x-3y
Answer:
Hey there!
Step-by-step explanation:
This is ur answer...
The coefficient of 5x-3y is 5.Hope it helps!
Brainliest pls!
Have a good day!^^
❄ Hi there,
the coefficient of a variable is a number multiplied by that variable; it can be any real number.
∴,
[tex]\hfill\stackrel{\textbf{coefficient of x}}{5}[/tex]
[tex]\hfill\stackrel{\textbf{coefficient of y}} {-3}[/tex]
That's it.
❄ [tex]\small\pmb{Frozen \ melody}[/tex]
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer: y ≥ [tex]\frac{3}{2}[/tex]x + 3
Step-by-step explanation:
Since the shaded area is above the line, we will use either > or ≥ for our inequality.
Next, since this is a solid line we will use the ≥ symbol for our inequality. This means the answer is the first option.
One number chosen randomly from the integers 1 to 20. Find the probability of getting a number that is odd and prime.
Answer:
35%
Step-by-step explanation:
All the prime numbers from 1 to 20 are:
2 3 5 7 11 13 17 19
7 / 20 = 35 / 100 = 35%
Verify whether the given differential equation is exact or not. if exact, solve. cosx y/x dx dy
The differential equation [tex]cos(x)dx+\frac{y}{x} dy=0[/tex] is not exact.
For given question,
we have been given a differential equation [tex]cos(x)dx+\frac{y}{x} dy=0[/tex]
We have to determine given differential equation is exact or not.
Compare it with M dx + N dy = 0
⇒ M = cos(x) and N = y/x
Find the derivative of M with respect to y.
[tex]\Rightarrow M_y=-sin(x)[/tex]
Now, find the derivative of N with respect to x.
[tex]\Rightarrow N_x=\frac{-y}{x^{2} }[/tex]
Since [tex]M_y \neq N_x[/tex], given differential equation is not exact.
Therefore, the differential equation [tex]cos(x)dx+\frac{y}{x} dy=0[/tex] is not exact.
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Please helppp!! i will hand brainlist and 19 points aswell thank you :)
I am not sure but when I calculated answer is √52...........
Answer:
[tex]\sqrt{52}[/tex]
Step-by-step explanation:
You would use the Pythagorean Thereon to find the answer.
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex] You can You can draw a right triangle from the two points. One way you could do this is draw a line straight down from N and stop when you get down to N'. Then continue drawing the line horizontally until it gets to N'. Connect N' to N and will have drawn a right triangle.
The vertical height of your triangle would be the difference of you y values and the horizontal distance would be the difference between your x values.
9 - 3 = 6
6 - 2 = 4
[tex]6^{2}[/tex] + [tex]4^{2}[/tex] =[tex]c^{2}[/tex]
36 + 16 = [tex]c^{2}[/tex]
52 = [tex]c^{2}[/tex]
[tex]\sqrt{52}[/tex] = c
Three Algebra 1 students are comparing how fast their social media posts have spread. Their results are shown in the following table:
Student
Amber
Ben
Carter
Description
Amber shared her photo with 3 people. They continued to share it, so the number of shares increases every day, as shown by the function.
Ben shared his post with 2 friends. Each of those friends shares with 3 more every day, so the number of shares triples every day.
Carter shared his post with 10 friends, who each share with only 2 people each day.
Social Media Post Shares
f(x) = 3(4)x
Day
0
1
2
number of shares
2
6
18
Write an exponential function to represent the spread of Carter's social media post.
The exponential model that best represents the data is f(x) = 2(3)x
Exponential equationExponential equations are inverse of logarithmic equation. Exponential equations are written in the form y = ab^x
where
a is the base
x is the exponent
Using the coordinate points (0, 2) and (1, 6)
Substitute
2 = ab^0
6 = ab
Take the ratio
6/2 = ab/a
3 = b
Determine the value of 'a"
Recall that
6 = ab
6 = 3a
Divide both sides by 3
3a/3 = 6/3
a = 2
Hence the exponential model that best represents the data is f(x) = 2(3)x
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There are 61 boxes of pencils in a store there are 14 pencils in each box how many pencils are in the store
Choose the definition for the function.
(-x+ 2 x < 1
x ≥ 1
a. y = x + 1
(-x+ 2
x + 1
b.y = {-x+ 2 x≤1
1
x >
c. y = {-x-
C.
x≤ 1 d. y = { x + 1
(-x+ 2
x > 1
x ≤ 1
x ≥ 1
x < 1
Enter
Answer:
A
Step-by-step explanation:
The answer is negative so that eliminates one
and the greater sign is opposite of b so that makes the answer A!
Triangle ABC is rotated to create the image A'B'C'.
Which rule describes the transformation?
Ty
O (x, y) - (x, -
O (x, y) - (v, x)
O (x, y) - (-x, -y)
B'AL
O (x, y) - (-Y, -x)
Answer-
Step-by-step explanation:
Choose the correct simplification of the expression (8x − 5)(2x2 − 5x − 6). 16x3 − 50x2 − 23x − 30 16x3 − 50x2 − 23x 30 16x3 − 30x2 − 23x 30 16x3 50x2 − 23x 30
The correct simplification of the given expression is (B) [tex]16x^{3} -50x^{2} -23x+30[/tex].
What is an expression?An expression or mathematical expression is a finite combination of symbols that is well-formed according to context-dependent norms.To find the correct simplification of the given expression:
The easiest terms to check are the first (8x)(2x²) = 16x³ and the last (-5)(-6) = 30. This check eliminates the first choice. The remaining choices differ only in the sign and coefficient of the squared term, so that is the one we need to find.The squared term will be the sum of the products of factors whose degrees total 2:[tex](8x)(-5x)+(-5)(2x^{2} )=-40x^{2} -10x^{2} =-50x^{2} =16x^{3} -50x^{2} -23x+30[/tex]Therefore, the correct simplification of the given expression is (B) [tex]16x^{3} -50x^{2} -23x+30[/tex].
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The correct question is given below:
Choose the correct simplification of the expression (8x − 5)(2x2 − 5x − 6). (1 point)
(A) 16x3 − 50x2 − 23x − 30
(B) 16x3 − 50x2 − 23x + 30
(C) 16x3 − 30x2 − 23x + 30
(D) 16x3 + 50x2 − 23x + 30
Which equation represents the explicit formula for a constant velocity arithmetic sequence?
A. xₙ = x₁+(n-1)(v•△t)
B. xₙ = x₁+(n+1)(v/△t)
C. xₙ = x₁+(n+1)(v•△t)
D. xₙ = x₁+(n-1)(v/△t)
The equation which represents the explicit formula for a constant velocity arithmetic sequence is; Choice A; xₙ = x₁+(n-1)(v•△t).
Which equation among the answer choices represents the explicit formula for a constant velocity arithmetic sequence?It follows from convention that an arithmetic sequence is usually defined by an expression of the form;
T(n) = T(1) + (n-1)×d in which case, d = common difference.
Consequently, in the event that the velocity in discuss is constant, it follows that the required expression is; Choice A; xₙ = x₁+(n-1)(v•△t).
Therefore, xₙ = x₁+(n-1)(v•△t) represent the equation for explicit formula for a constant velocity arithmetic sequence.
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what is the equation of a line that has a slope of .8 and passes through the point (-3,1)
Answer:
y = 0.8x + 3.4
Step-by-step explanation:
Substituting into point-slope form and converting to slope-intercept form,
[tex]y-1=0.8(x+3) \\ \\ y-1=0.8x+2.4 \\ \\ y=0.8x+3.4[/tex]
Mr Lim had a bag of sweets. After giving each pupil 7 sweets, he had 4 sweets left. If he had given only 5 sweets to each pupil, he would have 4 sweets left. If he had given only 5 sweets to each pupil, he would have 80 sweets left.
i.How many pupils were there in the class?
ii. How many sweets did Mr Lim have?
Solving a system of equations we can see that there are 270 sweets and 38 pupils.
How many pupils and sweets are there?
Let's define the variables:
P = number of pupils.
S= number of sweets.
With the given information, we can write:
7*P + 4 = S
5*P + 80 = S
So we have a system of equations, now we can write:
7*P + 4 = S = 5*P + 80
Solving that for P:
7*P + 4 = 5*P + 80
7*P - 5*P = 80 - 4
2*P = 76
P = 76/2 = 38
There are 38 pupils, and the number of sweets is given by:
S = 7*P + 4 = 7*38 + 4 = 270
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If the graph of f(x)=x2, how will the graph be affected if it is changed to f(x)=3x2?
There will be a vertical stretch with a factor of 3.
Pls help with middle school math (2 questions in photo)
Question 8
Part (a)
The gradient is the coefficient of x after isolating y.
[tex]3x+y=15 \\ \\ y=\boxed{-3}x+15 [/tex]
Part (b)
The line crosses the y-axis when x=0. So, the line crosses tne y-axis at (0,15).
By similar logic, the answers to Question 9 are:
(a) -3
(b) (0, -4.5)
construct a quadrilateral
AB=6cm , BC = 5cm, AD = 4CM CD =7cm and BD = 6cm
If a quadrilateral exists as a parallelogram, then opposite sides exist congruent and parallel.
What is quadrilateral?
If a quadrilateral exists as a parallelogram, then opposite sides exist congruent and parallel.
Given: AB = 6cm , BC = 5cm, AD = 4cm, CD = 7cm and BD = 6cm
Draw a line AB with 6cm with A as the center draw an arc of radius 4 cm. And draw another arc of 6cm to cut the previous arc at D with B as the center draw an arc of radius 5cm. And with D draw another arc of 7cm to cut the previous arc at C. Join the lines of the quadrilateral.
Now ABCD exists as a required quadrilateral.
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SinA=√1-x÷√1+X
Find the value of cosA
The value of cos A is √(1 + x²)/ (1 - x²) /√1 + x
Trigonometric ratios
It is important to note that
sin A = opposite/ hypotenuse
cos A = adjacent/ hypotenuse
Then,
opposite = [tex]\sqrt{1} - x[/tex]
Hypotenuse = [tex]\sqrt{1} + x[/tex]
Let's find the adjacent side using the Pythagorean theroem
[tex](\sqrt{1} + x)^2 = (\sqrt{1 -x } )^2 + x^2[/tex]
[tex]1 + x^2 = 1 - x^2 + x^2[/tex]
[tex]x = \sqrt{\frac{1 + x^2}{1 -x^2} }[/tex]
cos A = x/hypotenuse
[tex]cos A = \frac{\sqrt{\frac{1+x^2}{1 -x^2} } }{\sqrt{1} +x}[/tex]
cos A = √(1 + x²)/ (1 - x²) /√1 + x
Thus, the value of cos A is √(1 + x²)/ (1 - x²) /√1 + x
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Consider a function that goes through the two points (0, 5) and (1, 20). Find the formula for the function if(a) the function is linear (of the formf(x) =mx b)
The formula for the linear function which is passing the points (0, 5) and (1, 20) is f(x) = 15x + 5.
According to the given question.
The linear form of the function is
f(x) = mx + b
Also, the function is passing through the points (0, 5) and (1, 20).
So, the given points (0, 5) and (1, 20) must satisfy f(x) = mx + b.
Now,
At (0, 5)
f(0) = m(0) + b
⇒ 5 = 0 + b
⇒ b = 5 ..(i)
Also,
at (1, 20)
f(1) = m(1) + b
⇒ 20 = m + 5 (from i)
⇒ m = 20 - 5
⇒ m = 15
Therefore, the formula for the linear function which is passing the points (0, 5) and (1, 20) is given by
f(x) = 15(x) + 5 (on substituting the vale of m and b in f(x) = mx + b).
⇒ f(x) = 15x + 5
Hemce, the formula of the function is f(x) = 15x + 5.
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two less than y is subtracted from x
Answer: x- (y-2)
Step-by-step explanation:
Two less than y would be y-2,
Then you just subtract it from x
Which equation represents a population of 370 animals that decreases at an annual rate of 11% ?
The equation represents a population of 370 animals that decreases at an annual rate of 11% is [tex]p=370(0.89)^{t}[/tex].
What is an exponential function?It is defined as the function that rapidly decreases and the value of the exponential function is always positive. It denotes with exponent y = a^x
where a is a constant and a>1.
Given that,
A population of 370 animals that decreases at an annual rate of 11%
a = 370, r = 11%
p = [tex]a(1-r)^{t}[/tex]
= [tex]370(1-0.11)^{t}[/tex]
p = [tex]370(0.89)^{t}[/tex]
Hence, The equation represents a population of 370 animals that decreases at an annual rate of 11% is [tex]p=370(0.89)^{t}[/tex].
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How do you solve this geometry question?
The statement that <A > <C and <B > <D has been proved
How to prove that <A > <C and <B > <D?In geometry, the side length opposite the largest angle is the longest side.
Similarly, the side length opposite the smallest angle is the shortest side.
From the given figure of quadrilateral, we have the following sides in increasing order:
Side length ABSide length BCSide length ADSide length CDThe angles opposite the side lengths are:
Angle DAngle BAngle CAngle AThis means that:
<A > <C and <B > <D
Hence, the statement that <A > <C and <B > <D has been proved
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Find the area of the shaded region
Step-by-step explanation:
Since the circle is inside the square, we can subtract its area from the squares area.
the squares area can be found by multiplying the height and width
[tex]8^2=64[/tex]
now to find the area of the circle we use
[tex]A=\pi r^2[/tex]
the radius is 4.
assuming pi=3.14
your answer is 50.24.
expressions equivelant to 64^x
[tex]64^{\text{x}} = (8^2)^{\text{x}} = 8^{2\text{x}}[/tex]
The rule used is that [tex](a^b)^c = a^{bc}[/tex] we multiply the exponents b and c.
Or we could say this
[tex]64^{\text{x}} = (4^3)^{\text{x}} = 4^{3\text{x}}[/tex]
Or,
[tex]64^{\text{x}} = (2^6)^{\text{x}} = 2^{6\text{x}}[/tex]
Therefore, we have multiple possible answers.
Pls help I keep getting this wrong
Answer:
x = 8
y = -3
Step-by-step explanation:
Multiply the first equation with (-2)
(-2) * (x - 4y) = 20
-2x + 8y = -40 now find the sum of it with second equation
2x + 5y - 2x + 8y = 1 - 40 add like terms (2x will eliminate -2x)
13y = -39 divide both sides by 13
y = -3
Now we can use this to find the value of x
x - 4y = 20 rewrite the equation using the value we found for y
x - 4(-3) = 20 multiply (-4) and (*3) (product will be positive because we are multiplying two negatives)
x + 12 = 20 subtract 12 from both sides
x = 8
Brianna walks around a triangular park, daily. The longest side of the park measures 75 yards
and the shortest side measures 45 yards. If she walks 3 full laps around the park, how far does she
walk in one day?
She walks 540 yards for 3 full laps around the park per day.
How to determine the distanceFrom the information given;
The longest part of the triangular park = 75 yards
The shortest part = 45 yards
Let's find the other part, using Pythagorean theorem;
a² = b² + c²
75² = 45² + c²
c² = 75² - 45²
Find the squares
c² = 5625 - 2025
c² = 3600
Make 'c' the subject
c = √3600
c = 60 yards
If she walks
75 + 60 + 45 yards per lap
180 yards per lap
For three laps, she walks
= 3 × 180
= 540 yards
Thus, she walks 540 yards for 3 full laps around the park per day.
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How long does it take the wave to travel 6.0 m in the x-direction? 0.13 seconds 0.67 seconds 2.0 seconds 8.0 seconds
It takes the time for the wave to travel 6.0 m in the x-direction of 8s.
What is the wavelength?A wave's wavelength is measured in meters since it is the separation between its two peaks (or troughs). Since waves can be any size or shape, the prefix for meters can vary significantly, from km for radio waves to micrometers for visible light (although it is sometimes stated in nanometers) to picometers for gamma rays..
According to the information:the wavelength is 1.5 m.
λ/2 = 1 s
1.5/2 =1 s
0.75 m in 1 s is travelled by the wave.
To travel 6m , the time required is
= 6/0.75
=8s
Thus,
it takes the time for the wave to travel 6.0 m in the x-direction is 8s.
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