Answer:23
Step-by-step explanation:
Suppose a large shipment of televisions contained 9% defectives. If a sample of size 393 is selected, what is the probability that the sample proportion will differ from the population proportion by less than 3%
Answer:
0.9624 = 96.24% probability that the sample proportion will differ from the population proportion by less than 3%
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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Suppose a large shipment of televisions contained 9% defectives
This means that [tex]p = 0.09[/tex]
Sample of size 393
This means that [tex]n = 393[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.09[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.09*0.91}{393}} = 0.0144[/tex]
What is the probability that the sample proportion will differ from the population proportion by less than 3%?
Proportion between 0.09 - 0.03 = 0.06 and 0.09 + 0.03 = 0.12, which is the p-value of Z when X = 0.12 subtracted by the p-value of Z when X = 0.06.
X = 0.12
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.12 - 0.09}{0.0144}[/tex]
[tex]Z = 2.08[/tex]
[tex]Z = 2.08[/tex] has a p-value of 0.9812
X = 0.06
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.06 - 0.09}{0.0144}[/tex]
[tex]Z = -2.08[/tex]
[tex]Z = -2.08[/tex] has a p-value of 0.0188
0.9812 - 0.0188 = 0.9624
0.9624 = 96.24% probability that the sample proportion will differ from the population proportion by less than 3%
log2(6x) – log2 (x)-2
Answer:
xlog(64)−xlog(2)−2
Step-by-step explanation:
Simplify 6log(2) by moving 6 inside the logarithm.
log(2^6)x − log(2)x − 2
Raise 2 to the power of 6.
log(64)x − log(2)x − 2
Reorder factors in log(64)x − log(2)x −2.
24
4
3+
2+
2
1
-3
-
-1
1
1
2
3
4
-1+
-2 +
-3+
4
What is the slope of the line?
Answer:
1.5/2
Step-by-step explanation:
slope formula = y2-y1/ x2 - x1
point one (2,0)
point 2 (0, 1.5)
you dont really need to subtract anything because the intercepts, so the slope is 1.5/2
(slope or m = 1.5 - 0 / 2 - 0 )
x intercept = value of x when y is 0
y intercept = value of y when x is 0
7. What is given in the problem?
A. Radius of 80m C. Radius of 80 ft.
B. Diameter of 40 ft. D. Diameter of 40 m paki sagot
Answer:
radius of 80cm is the answer
On a coordinate plane, 2 triangles are shown. The first triangle has points A (negative 1, negative 2), B (negative 4, negative 2), C (negative 1, negative 4). The second triangle has points A prime (1, 2), B prime (4, 2), C prime (1, 4). What rule describes the rotation about the origin? (x, y) → How many degrees was the figure rotated about the origin?
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Answer:
(x, y) ⇒ (-x, -y)180°Step-by-step explanation:
Each image point has its signs reversed from the pre-image point.
(x, y) ⇒ (-x, -y) . . . . describes the rotation
Rotation from the third quadrant (A) to the first quadrant (A') is a rotation of 180°.
Answer:
3rd and 2nd option
Step-by-step explanation:
class 7th chapter: Simple Equation
The solution of the equation p-1 =20 is -------- *
a) 19
b) 20
c) 21
Answer:
C
Step-by-step explanation:
p=20+1
Why is underfind the square root of a negative number?
Answer:
The square root of a negative number is undefined, because anything times itself will give a positive (or zero) result. Note: Zero has only one square root (itself). Zero is considered neither positive nor negative
Answer:
sjshzhshshdhdgdgdhdhdgshshshshshwywhwhw
Joan has raised $306 by selling 34 equally priced boxes of chocolate for the team fund-raiser. Which of the following equations can be used to find the price, n, of each box of chocolate?
n ÷ 34 = 306
34n = 306
n − 34 = 306
n + 34 = 306
Answer:
34n=306
Step-by-step explanation:
Use inverse operation to find it, 306÷34= 9, check again 34(9)=306, so it's correct!
y + x + z =762500
z : x = 15/9 : 2
y : x = 1 : 3/4
Step-by-step explanation:
true
Hannah ran 12 laps for 8 days. How many laps did she run in total if she take a break of 1 complete day and 1 half day.
Answer:
The correct answer would be - 9.75 laps (if runs 12 laps in 8 days) or 78 laps (if 12 laps each day for 8 days)
Step-by-step explanation:
Given:
a) Laps covered in 8 days = 12
interval = 1 and half day
total laps = ?
Solution:
To know the total laps with intervals we need to calculate the laps run each day :
= 12/8 laps per day
= 3/2 laps per day
Now multiply the daily run with days
= (3/2)*6.5 (due to 8 - 1.5 = 6,5 days)
= 9.75 laps
B) Given:
Laps covered in 8 days = 12*8 =96
interval = 1 and half day
total laps = ?
Solution:
To know the total laps with intervals we need to calculate the laps run each day :
= 96/8 laps per day
= 12laps per day
Now multiply the daily run with days
= 12*6.5 (due to 8 - 1.5 = 6,5 days)
= 78 laps
5. In 2015, Texas led the nation in the percentage of people who lacked health insurance (21.6% of the population). It is known that, nationally, 5% of patients account for 50% of the costs of healthcare. These are the “high cost” patients Assume* that: Being a high cost patient and being uninsured are independent characteristics Insured and uninsured people become “patients” at the same rate The uninsured and high cost patients in Texas are evenly distributed across the state, and that high cost patients are evenly distributed across insured and uninsured patient populations a. What is the probability that a patient in a Texas healthcare facility will be a high cost patient who is uninsured?
Answer: 0.108
Step-by-step explanation:
Since the probability of the uninsured is 21.6% of the population, then the probability of insured will be:
= 1 - 21.6%
= 78.4%
The probability of high cost patients is 5%. Therefore, the probability that a patient in a Texas healthcare facility will be a high cost patient who is uninsured will be:
= 5% × 21.6%
= 0.05 × 0.216
= 0.108
If f(x) = 4x and gx) = 2x- 1, what is g(f(-2))?
-17
-13
-8
-5
Answer:
-17
Step-by-step explanation:
We are given these following functions:
[tex]f(x) = 4x[/tex]
[tex]g(x) = 2x - 1[/tex]
g(f(-2))
First we find f when x = -2, then we find g for this value(f when x = -2). So
[tex]f(-2) = 4(-2) = -8[/tex]
[tex]g(f(-2)) = g(-8) = 2(-8) - 1 = -16 - 1 = -17[/tex]
Thus -17 is the answer.
two angles are complementary. The measure of one angle is 15° more than one-half of the measure of the other. Find the measure of each angle.
Answer:
Step-by-step explanation:
First you have to know two definitions. Well, you only have to know one for this problem, but you should probably learn the 2nd just to be thorough.
Definition 1: Complementary angles are two angles whose sum is 90 degrees.
Definition 2: Supplementary angles are two angles whose sum is 180 degrees.
For this problem, we'll work with the definition that says two complementary angles have a sum of 90 degrees.
Soooo, here are the facts from your problem: if one angle is 15 degree more than 2 times the other.find the measure of two angles.
Let's let the larger angle equal this: 15 + 2(x) (<--See how it is 15 degrees MORE than 2 times the other?)
Let's let the smaller angle equal: x
SO now our total equation is:
15 + 2(x) + x = 90
3x + 15 = 90 (combined like terms)
3x = 75 (subtracted 15 from both sides)
x = 25 (divided both sides by 3)
Now we know that one angle is 25. The other angle must add to 25 to make 90 degrees, so 90 - 25 = 65.
Therefore, your two angles are 25 and 65 degrees.
Does this check out? Let's see...
First: 25 + 65 = 90 Therefore, this checks out.
Second: The angle that is 65 degrees must be 15 degrees more than twice the other. So, let's take twice the other...... 25 * 2 = 50. And, let's add 15....50 + 15 = 65. Therefore YES, the 2nd angle is 15 more than 2 times the angle that was 25 degrees.
I hope this is helpful. :-)
Will give brainliest answer
Answer:
A
Step-by-step explanation:
the proof of the answer is shown above
Explain how to divide a decimal by a decimal
Answer:
To divide a decimal by another decimal:
Move the decimal point in the divisor to the right until it is a whole number.
Move the decimal point in the dividend to the right by the same number of places as the decimal point was moved to make the divisor a whole number.
Then divide the new dividend by the new divisor
Step-by-step explanation:
see in the example
Which would result in a lower price to first discount an item by 10% and then by a further 15%, OR to first discount an item by 15% and then by a further 10%. Justify your reasoning.
Answer:
Neither one. They will both result in the same price.
Step-by-step explanation:
To discount an item 10%, you charge 90% of the price of the item. To find 90% of a price, you multiply the price by 0.9.
To discount an item 15%, you charge 85% of the price of the item. To find 85% of a price, you multiply the price by 0.85.
Since multiplication is commutative, multiplying a number by 0.9 and then by 0.85 is the same as multiplying the number by 0.85 first and then by 0.9.
Let's say the item costs x.
Take off the 10% discount first: 0.9x
Now take off the 15% discount: 0.85 * (0.9x)
Now do it the other way.
Take off the 15% discount first: 0.85x
Now take off the 10% discount: 0.9 * (0.85x)
Since 0.85 * 0.9 * x = 0.9 * 0.85 * x, the results are the same.
Answer: neither
Determine the domain of the function graphed above.
Answer:
the domain of given f is (-2,4)
4b^2+300=0 this is a quadratic equation that I am trying to solve including any solutions with imaginary numbers I will include a picture
Answer:
b= 5i square root of 3
b = -5i square root of 3
Step-by-step explanation:
4b^2+300=0
4b^2 = -300
b^2 = -75
b = square root of -75
b = -75^1/2
^1/2 means square root
b = 25^1/2 * 3^1/2 * i
b= 5i square root of 3
b = -5i square root of 3
I’ll mark u plz help
Answer:
D is the answer
Step-by-step explanation:
all sides and angles are equal
hope it helps!! let me know if it does
for a science fair project javier is recording the amount of water that evaporate from a bucket in a month he creates a table like this i will give point for the best answer
week 1 2/16 inch
week 2 1/16 inch
week 3 3/16 inch
week 4 2/16 inch
how much water had evaported from the bucket at the end of week 2
what was the total amount of water that evaported in the four weeks
if javier orignally put 4 inches of water in the bucket how many inches of water were left after the experment was completed
Answer: [tex]\dfrac{3}{16},\ \dfrac{1}{2}, \dfrac{7}{2}\ \text{inch}[/tex]
Step-by-step explanation:
Given
Javier created a table for the amount of water evaporated in each week
After two weeks, the amount of water evaporated is
[tex]\Rightarrow \dfrac{2}{16}+\dfrac{1}{16}\\\\\Rightarrow \dfrac{2+1}{16}=\dfrac{3}{16}\ \text{inch}[/tex]
Total amount of water evaporated in four weeks is
[tex]\Rightarrow \dfrac{2}{16}+\dfrac{1}{16}+\dfrac{3}{16}+\dfrac{2}{16}\\\\\Rightarrow \dfrac{2+1+3+2}{16}=\dfrac{8}{16}\\\Rightarrow \dfrac{1}{2}\ \text{inch}[/tex]
If Javier originally puts 4 inches of water, amount of water left in the bucket
[tex]\Rightarrow 4-\dfrac{1}{2}\\\\\Rightarrow \dfrac{4\times 2}{2}-\dfrac{1}{2}\\\\\Rightarrow \dfrac{8-1}{2}=\dfrac{7}{2}\ \text{inch}[/tex]
The perimeter of a square and rectangle is the same. The width of the rectangle is 6cm and it's area is 16cmsquare less than the area of the square. Find the area of the square
Answer:
Area of square = 100 square cm
Step-by-step explanation:
Let the sides of a square be = a
Perimeter of a square = 4a
Let area of square = [tex]a^2[/tex]
Let the Length of rectangle be = [tex]l[/tex]
Given: width of the rectangle = 6 cm
Area of rectangle = length x breadth
Perimeter of rectangle and square is equal.
That is,
[tex]2(length + width) = 4a\\\\2(l + 6) = 4a\\\\l + 6 = 2a\\\\l = 2a - 6[/tex]
Therefore ,
Area of rectangle
[tex]= Length \times width \\\\= (2a - 6) \times 6\\\\=6(2a - 6)[/tex]
Given area of rectangle is 16 less than area of square.
That is ,
[tex]( 6(2a- 6) ) = a^2 - 16\\\\12a - 36 = a^2 - 16\\\\a^2 - 12a +20= 0\\\\a^2 - 2a -10a + 20 = 0\\\\a(a - 2) - 10(a - 2) = 0\\\\(a -10) ( a-2) = 0\\\\a = 10 , \ a = 2[/tex]
Check which value of 'a ' satisfies the equation:
[tex]\underline {when \ a = 2 }\\\\Length\ of \ rectangle \ l = 2a - 6 = 2 ( 2 ) - 6 = 4 - 6 = - 2. \\\\Length \ cannot \ be \ negative \ number. \\\\ \underline{ when \ a = 10 }\\\\Length \ of \ rectangle \ , l = 2a - 6 = 2 (10) - 6 = 20 - 6 = 14\\\\satisfies \ the \ conditions. \\\\Therefore , a = 10[/tex]
That is , side of the sqaure = 10
Therefore , area of the square = 10 x 10 = 100 square cm.
The formula for the lateral area of a right cone is LA = pi rs, where is the radius of the base and s is the slant height of the cone.
Answer:
r is the radius of the base and s is the slant height of the cone. From the options given, We can make s the subject of the formula. Hence: Option a) s equals StartFraction L A Over pi r EndFraction
Two equivalent equations are s = LA/πr and r = LA/πs
What is cone?A cone is a shape formed using a series of line segments or lines that connect a common point, called a apex or vertex, to all points on the base of a circle that do not contain a vertex. The distance from the apex of the cone to the base is the height of the cone. A circular base has a measured radius value. And the length from the apex of the cone to any point around the base is the height of the slope. Equations for the surface area and volume of a cone can be derived from these quantities
Volume(V) = ⅓ πr²h cubic units
The total surface area of the cone = πrs + πr²
where, r is radius of the base, s is slant height and h is height of the cone
Given,
Lateral area of cone is denoted by LA
Lateral area of cone = πrs
where r is radius and s is slant height
⇒ LA = πrs
⇒ s = LA/πr
⇒ r = LA/πs
Hence, s = LA/πr and r = LA/πs are two equivalent equations in the given options.
Learn more about cone here:
https://brainly.com/question/16394302
#SPJ7
f(x)=2x1 + 16x2 + 7x3 + 4x4 -> min
Step-by-step explanation:
f(x)=(2x-1)square=0
it can be 0 or greater than 0
Hence,maximum value of (2x- 1)square=0
maximum value of (2x- 1square)+3=0+3=3
The cardinal number of {200, 201, 202, 203, ..., 1099}
Answer:
I have not been able to answer it sorry
Negating conditional statement (a V ~ b) => c
Please show your work and give a proper answer
"p implies q" is equivalent to "(p and q) or not p", which in turn is equivalent to "(p or not p) and (q or not p)". But "p or not p" is always true, so the implication reduces completely to "not p or q". Negating an implication thus gives "not (not p or q)", which is equivalent to "p and not q".
So
not [(a or not b) implies c] <==> (a or not b) and not c
Screenshot of the question
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Answer:
x = 1, x = 7
Step-by-step explanation:
You can see from the graph that the x-intercepts of f(x) are ...
0 = f(-3)
0 = f(3)
To find the corresponding values of x for f(x-4), we can solve ...
0 = f(x -4)
x -4 = -3 ⇒ x = 1
x -4 = 3 ⇒ x = 7
The x-intercepts of the function after translation 4 units right are ...
x = 1, x = 7
__
Your sketch will be the same curve moved 4 units to the right. (Add 4 to every x-value shown.)
Test 21,753 for divisibility by 2,3,5,9 and 10
Answer:
Step-by-step explanation:
21,753
at unit place=3 not an even number,not equal to 5 and not equal to 0
so 21,753 is not divisible by 2,5 and 10
again
2+1+7+5+3=18 divisible by 3 and 9.
so 21,753 is divisible by 3 and 9.
Find the equivalent exponential expression.
(543
Answer:
(5) we have multiple the powers
HELP ASAP I WILL GIVE BRAINLIST
If sin ∅ = -sqrt{3} OVER 2 and π < ∅ < 3π OVER 2, what are the values of cos ∅ and tan ∅? What is ∅ in degrees and radians? Be sure to show and explain all work.
Step-by-step explanation:
sin ∅ = -(√3)/2
Note that
cos²∅ + sin²∅ = 1
cos²∅ = 1 - sin²∅
= 1 - (-√3 / 2)²
= 1 - (-√3)²/ 2²
= 1 - 3/4
= 1/4
cos²∅ = 1/4
Taking square root of both sides
cos∅ = 1/2
Note that tan∅ = sin∅/cos∅
therefore, tan∅ = -(√3)/2 ÷ 1/2
= -(√3)/2 × 2/1
= -√3
tan∅ = -√3
Since sin∅ = -√3 /2
Then ∅ = -60⁰
The value of ∅ for the given range (third quadrant) is 240⁰.
NB: sin∅ = sin(180-∅)
Also, since 180⁰ is π radians, then ∅ = 4π/3
A boy leaves station X on a bearing of 035' to station Y. which is 21km away. He then travels to another station Z on a bearing of 125 degrees . If Z is directly East of X, what is the distance from X to his present position?
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Answer:
36.6 km
Step-by-step explanation:
We assume the initial bearing of the boy is 35°. Then he will make a 90° turn to a heading of 125°. A diagram shows the distance of interest is the hypotenuse of a right triangle in which 35° is the angle opposite the side of length 21 km.
The relevant trig relation is ...
Sin = Opposite/Hypotenuse
sin(35°) = (21 km)/XZ
XZ = (21 km)/sin(35°) ≈ 36.61 km
The distance from X to Z is about 36.61 km.
_____
The attached diagram has the angles measured in the usual way for a Cartesian plane: CCW from the +x axis. This will correspond to bearing measures if we relabel the axes so that +x is North, and +y is East.
