Answer:
The correct option is (b) 0.3333.
Step-by-step explanation:
The standard deviation of the sampling distribution of sample mean [tex](\bar x)[/tex] is known as the standard error [tex](\sigma_{\bar x})[/tex].
The standard error is given as follows:
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
The information provided is:
[tex]\mu=8\\\\\sigma=2\\\\n=36[/tex]
Compute the standard deviation of the sample mean as follows:
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
[tex]=\frac{2}{\sqrt{36}}\\\\=\frac{2}{6}\\\\=\frac{1}{3}\\\\=0.3333[/tex]
Thus, the standard deviation of the sample mean is 0.3333.
A signal light is green for 4 minutes, yellow for 10 seconds, and red for 3 minutes. If you drive up to this light, what is the probability that it will be green when you reach the intersection? Round your answer to two decimal places.
Answer:
0.56 is the required probability.
Step-by-step explanation:
Time for which signal shows green light = 4 minutes
Time for which signal shows yellow light = 10 seconds
Time for which signal shows red light = 3 minutes
To find:
Probability that the signal will show green light when you reach the destination = ?
Solution:
First of all, let us convert each time to same unit before doing any calculations.
Time for which signal shows green light = 4 minutes = 4 [tex]\times[/tex] 60 seconds = 240 seconds
Time for which signal shows yellow light = 10 seconds
Time for which signal shows red light = 3 minutes = 3 [tex]\times[/tex] 60 seconds = 180 seconds
Now, let us have a look at the formula for probability of an event E:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
Here, E is the event that green light is shown by the signal.
Number of favorable cases mean the time for which green light is shown and Total number of cases is the total time (Time for which green light is shown + Time for which Yellow light is shown + Time for which red light is shown)
So, the required probability is:
[tex]P(E) = \dfrac{240}{240+10+180}\\\Rightarrow P(E) = \dfrac{240}{430}\\\Rightarrow \bold{P(E) \approx 0.56 }[/tex]
The area of the circle x² + y2 - 6x-4y +9 = 0 is
Answer:
Your answer is here.Enjoy dude
Answer:
12.56 unit²
Step-by-step explanation:
Given:x² + y² - 6x - 4y + 9 = 0To find:The area of circleSolution:The form of the circle is:
(x- h)² + (y-k)² = r²Let's bring the given to the form of a circle as above:
x² + y² - 6x - 4y + 9 = 0x² - 6x + y²- 4y + 9 = 0 ⇒ combining like terms and completing squarex² - 6x + 9 + y²- 4y + 4 = 4 ⇒ adding 4 to both sides(x-3)² + (y - 2)² = 2² ⇒ got the form of this circleAs per the form, we got r² = 2², so the radius of circle is 2 units.
The area of circle:
A= πr² = 3.14×2² = 12.56 unit²10/7p+13/8+15/2p=909/56 i NEED THiS solving multi step equations w fractions and #8 PLEASE
Answer:
P= 2
Step-by-step explanation:
10/7p+13/8+15/2p=-909/56
Combine like terms
10/7p+15/2p=-909/56-13/8
20p+105p/14=-909-13*7/56
125/14p=-909-91/56
125/14p= -1000/56
125/14p*14/125= -1000/56*14/125
simplify
P= 8/4=2
And for #8 n =1 I answered this question it
Search
The equation below is written in words. x plus ten equals two. What's the value of x?
Answer:
x+10 =2
x = -8
Step-by-step explanation:
plus means add
x+10 =2
Subtract 10 from each side
x+10-10 =2-10
x = -8
3.24 (4 being repeated) to a fraction
Answer:
146/45
Step-by-step explanation:
Let x represent the value of the number of interest. Then we can do the following math to find its representation as a fraction.
[tex]x=3.2\overline{4}\\10x=32.4\overline{4}\\10x-x=9x=32.4\overline{4}-3.2\overline{4}=29.2\\\\x=\dfrac{29.2}{9}=\boxed{\dfrac{146}{45}}[/tex]
__
Comment on procedure
The power of 10 that we multiply by (10x) is the number of repeated digits. Here, there is a 1-digit repeat, so we multiply by 10^1. If there were a 2-digit repeat, we would compute 10^2x -x = 99x to rationalize the number.
Give the domain and range of each relation using set notation
Answer:
See below.
Step-by-step explanation:
First, recall the meanings of the domain and range.
The domain is the span of x-values covered by the graph.
And the range is the span of y-values covered by the graph.
1)
So, we have here an absolute value function.
As we can see, the domain of the function is all real numbers because the graph stretches left and right infinitely. Therefore, the domain of the function is:
[tex]\{x|x\in\textbb{R}\}[/tex]
(You are correct!)
For the range, notice how the function stops at y=7. The highest point of the function is (-2,7). There graph doesn't and won't ever reach above y=7. Therefore, the range of the graph is all values less than or equal to 7. In set notation, this is:
[tex]\{y|y\leq 7\}[/tex]
2)
We have here an ellipse.
First, for the domain. We can see the the span of x-values covered by the ellipse is from x=-4 to x=6. In other words, the domain is all values in between these two numbers and including them. Therefore, we can write it as such:
[tex]-4\leq x\leq 6[/tex]
So x is all numbers greater than or equal to -4 but less than or equal to 6. This describes the span of x-values. In set notation, this is:
[tex]\{x|-4\leq x\leq 6\}[/tex]
For the range, we can see that the span of x values covered by the ellipse is from y=-5 to y=1. Just like the domain, we can write it like this:
[tex]-5\leq y\leq 1[/tex]
This represents all the y-values between -5 and 1, including -5 and 1.
In set notation, thi is:
[tex]\{y|-5\leq y\leq 1\}[/tex]
Select the correct answer -1/4(12x+8) is less than it equal to -2x+11
Answer:
x ≤ [tex]\frac{9}{5}[/tex]
Step-by-step explanation:
Given
[tex]\frac{1}{4}[/tex](12x + 8) ≤ - 2x + 11 ← distribute parenthesis on left side
3x + 2 ≤ - 2x + 11 ( add 2x to both sides )
5x + 2 ≤ 11 ( subtract 2 from both sides )
5x ≤ 9 ( divide both sides by 5 )
x ≤ [tex]\frac{9}{5}[/tex]
-¼(12x+8) ≤ -2x+11
• Divide by 44X-¼(12x+8) ≤-2x+11
= -12x + 8 ≤ -2x + 11
• Group like terms-12x + 2x ≤ 11 - 8
= -10x/10 ≤ 3/-10
x≤ 3/-10The table shows the height, in meters, of an object that is dropped as time passes until the object hits the ground. A 2-row table with 10 columns. The first row is labeled time (seconds), x with entries 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.6. The second row is labeled height (meters), h with entries 100, 98.8, 95.1, 89.0, 80.4, 69.4, 55.9, 40.0, 21.6, 0. A line of best fit for the data is represented by h = –21.962x + 114.655. Which statement compares the line of best fit with the actual data given by the table? According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground. According to the line of best fit, the object was dropped from a lower height. The line of best fit correctly predicts that the object reaches a height of 40 meters after 3.5 seconds. The line of best fit predicts a height of 4 meters greater than the actual height for any time given in the table.
Answer: A. According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground.
The statement first "According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground" is correct.
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
We have a line of best fit:
h = –21.962x + 114.655
As per the data given and line of best fit, we can say the object would have impacted the ground 0.6 seconds later than it did according to the line of best fit.
Thus, the statement first "According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground" is correct.
Learn more about the line of best fit here:
brainly.com/question/14279419
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An experimental probability is ______ likely to approach the theoretical probability if the number of trials simulated is larger. A. as B. more C. less D. not
Answer:
B. More
Step-by-step explanation:
This is according to the law of large numbers
An experimental probability is more likely to approach the theoretical probability if the number of trials simulated is larger.
What is an experimental probability and theoretical probability?Experimental probability is an experimental outcome whereas theoretical probability is a possible or expected outcome.
An experimental probability is more likely to approach the theoretical probability if the number of trials increased because of the law of large numbers which states that the average of the results obtained from a large number of trials should be close to the expected value and tends to become closer to the expected value as more trials are performed
Thus using the concept of the law of large numbers we can say that an experimental probability is more likely to approach the theoretical probability.
Learn more about probability here:
https://brainly.com/question/9627169
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At the age of 10, Edgar received an inheritance of $10,000. His father wants to invest the money in an account that will double in value in 8 years. Approximately what interest rate does the father need to find in order to reach his goal?
Answer:
9%
Step-by-step explanation:
Use the rule of 72. If you want the money to double in 8 years, it will need to be at 9 percent interest rate to reach this goal.
Brian needs to paint a logo using two right triangles. The dimensions of the logo are shown below. What is the difference between the area of the large triangle and the area of the small triangle?
Answer:
7.5 cm²
Step-by-step explanation:
Dimensions of the large ∆:
[tex] base (b) = 3cm, height (h) = 9cm [/tex]
[tex] Area = 0.5*b*h = 0.5*3*9 = 13.5 cm^2 [/tex]
Dimensions of the small ∆:
[tex] base (b) = 2cm, height (h) = 6cm [/tex]
[tex] Area = 0.5*b*h = 0.5*2*6 = 6 cm^2 [/tex]
Difference between the area of the large and the small ∆ = 13.5 - 6 = 7.5 cm²
A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in feet. (If an answer does not exist, enter DNE.) f(t) = t3 − 8t2 + 27t
The question is not clear, but it is possible to obtain distance, s, from the given function. This, I would show.
Answer:
s = 17 units
Step-by-step explanation:
Given f(t) = t³ - 8t² + 27t
Differentiating f(t), we have
f'(t) = 3t² - 16 t + 27
At t = 0
f'(t) = 27
This is the required obtainaible distance, s.
On a coordinate plane, 2 lines are shown. Line A B has points (negative 4, negative 2) and (4, 4). Line C D has points (0, negative 3) and (4, 0). Which statement best explains the relationship between lines AB and CD? They are parallel because their slopes are equal. They are parallel because their slopes are negative reciprocals. They are not parallel because their slopes are not equal. They are not parallel because their slopes are negative reciprocals.
Answer:
A. they are parallel because their slopes are equal.
Step-by-step explanation:
edge 2020
Answer:
its A in egde
Step-by-step explanation:
Word phrase for algebraic expression 15-1.5/d
Answer: 1.5 less than 15 is divided by a number d.
Step-by-step explanation:
I need help will rate you branliest
Answer:
[tex] {x}^{2} + 5x + 10[/tex]
Answer:
[tex]\large \boxed{x^2 +5x+10}[/tex]
Step-by-step explanation:
A polynomial is an expression that has variables, coefficients, and constants.
An example of a polynomial can be x² - 6x + 2.
The probability density function for random variable W is given as follows: Let x be the 100pth percentile of W and y be the 100(1 – p)th percentile of W, where 0
Answer:
Step-by-step explanation:
A probability density function (pdf) is used for continuous random variables. That is why p is between 0 and 1 (the two extremes - 0 and 1 - exclusive).
X = 100pth percentile of W
Y = 100(1-p)th percentile of W
Expressing Y as a function of X;
Y = 100(1-p)th = 100th - 100pth
Recall that 100pth is same as X, so substitute;
Y = 100th - X
where 100th = hundredth percentile of W and X = 100pth percentile of W
if f(x)=3x-3 and g(x)=-x2+4,then f(2)-g(-2)=
Answer:
3
Step-by-step explanation:
f(x)=3x-3
g(x)=-x^2+4,
f(2) = 3(2) -3 = 6-3 =3
g(-2) = -(-2)^2+4 = -4+4 = 0
f(2)-g(-2)= = 3-0 = 3
Explain how to perform a two-sample z-test for the difference between two population means using independent samples with known.
Answer:
The steps 1-7 have been explained
Step-by-step explanation:
The steps are;
1) We will verify that the population standard deviations are known and that the population is normally distributed which means the sample size must be a minimum of 30.
2) We will state the null and alternative hypothesis
3) We will determine the critical values from the relevant tables
4) From the critical values gotten, we will determine it's corresponding region where it can be rejected.
5)We will calculate the value of the test statistic from the formula;
z = [(x1' - x2') - (μ1 - μ2)]/√[((σ1)²/n1) + ((σ2)²/n2)]
6) If the value of the test statistic gotten from step 5 above falls in the region of rejection noted in step 4,then we will reject the null hypothesis
7) After rejection of the null hypothesis, we will now give a decision/conclusion on the claim.
What is the domain of f?
Answer:
-5 ≤x ≤6
Step-by-step explanation:
The domain is the values that x can take
X goes from -5 and includes -5 to x =6 and includes 6
-5 ≤x ≤6
Answer:
See attached!
Step-by-step explanation:
(05.06A LC)
Line segment AB has a length of 4 units. It is translated 1 unit to the right on a coordinate plane to obtain line segment A'B'. What is the length
of A'B'?
1 unit
4 units
5 units
6 units
Answer:
4 units
Step-by-step explanation:
A transformation is the movement of a point from one position to another position. If a shape is transformed all its points are also transformed. Types of transformations are translation, rotation, reflection and dilation.
If a shape is transformed, the length of its sides and shape remains the same, only the position changes.
If Line segment AB has a length of 4 units. It is translated 1 unit to the right on a coordinate plane to obtain line segment A'B, the length of A'B' remains the same which is 4 unit. To prove this:
Let A be at ([tex]x_1,y_1[/tex]) and B be at ([tex]x_2,y_2[/tex]). The length of AB is:
[tex]AB=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
If AB is translated to the right by 1 unit the new points are A' at ([tex]x_1+1,y_1[/tex]) and B' at ([tex]x_2+1,y_2[/tex]). The length of A'B' is:
[tex]A'B'=\sqrt{(y_2-y_1)^2+(x_2+1-(x_1+1))^2}=\sqrt{(y_2-y_1)^2+(x_2+1-x_1-1)^2}\\\\A'B'=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
AB = A'B' = 4 units
Transform the polar equation to a Cartesian (rectangular) equation: r= 4sinθ
options include:
x^2+y^2 = 4y
x^2+y^2 = -4
x^2+y^2 = 4
x^2+y^2 = -4y
Answer:
x^2 +y^2 = 4y
Step-by-step explanation:
Using the usual translation relations, we have ...
r^2 = x^2+y^2
x = r·cos(θ)
y = r·sin(θ)
Substituting for sin(θ) the equation becomes ...
r = 4sin(θ)
r = 4(y/r)
r^2 = 4y
Then, substituting for r^2 we get ...
x^2 +y^2 = 4y . . . . . matches the first choice
Find the reciprocal of the equation in standard form. The selected answer is incorrect.
Answer:
C
Step-by-step explanation:
reciprocal of z=1/z
[tex]z=2(cos \frac{\pi }{4} +i sin\frac{\pi }{4} )=2e ^{i \frac{\pi } {4}\\\frac{1}{z}=\frac{1}{2e^{i \frac{\pi}{4} } }\\\frac{1}{z} =\frac{1}{2} e^{-i\frac{\pi}{4} } \\\frac{1}{z} (cos\frac{\pi}{4} -isin\frac{\pi}{4} ) \\\frac{1}{z}=\frac{1}{2} (\frac{\sqrt{2} }{2} -\frac{\sqrt{2} }{2} )\\\frac{1}{z} =\frac{\sqrt{2} }{4} -i \frac{\sqrt{2 } }{4}[/tex]
Which expression is equivalent to (jk)l? A. (j + k) + l B. j(kl) C. (2jk)l D. (j + k)l
Answer:
B. j(kl)
Step-by-step explanation:
(jk)l
We can change the order we multiply and still get the same result
j(kl)
Answer:
Step-by-step explanation:
its B i did it
Find the sum of (5x3 + 3x2 - 5x + 4) and (8x3 -5x2 + 8x + 9)
Answer:
(5x³+3x²-5x+4) + (8x³-5x²+8x+9)
= 5x³+3x²-5x+4 +8x³-5x²+8x+9
= 5x³+8x³+3x²-5x²-5x+8x+4+9
= 13x³-2x²+3x+13
Hope this helps
if u have question let me know in comments ^_^
Write "six and thirty-four thousandths" as a decimal
Answer:
6.034
Step-by-step explanation:
6 is a whole number.
.034 because it is 34 thousandths, not 34 hundredths.
what is the distance between the first and third quartiles of a data set called?
Answer:
Interquartile range is the distance between the first and third of a data.
Step-by-step explanation:
Hope it will help you :)
A cabinet door has a perimeter of 76 inches. Its area is 357 square inches. What are the dimensions of the door?
Answer:
17 by 21 inches
Step-by-step explanation:
The perimeter is twice the sum of the dimensions, and the area is their product, so you have ...
L + W = 38
LW = 357
__
Solution:
W(38 -W) = 357 . . . . . substitute for L
-(W^2 -76W) = 357 . . expand on the left
-(W^2 -38 +19^2) = 357 -19^2 . . . . complete the square
(W -19)^2 = 4 . . . . . . . write as a square
W -19 = ±√4 = ±2 . . . take the square root; next, add 19
W = 19 ±2 = {17, 21} . . . . if width is one of these, length is the other
The dimensions are 17 by 21 inches.
f as a function of x is equal to the square root of quantity 4 x plus 6, g as a function of x is equal to the square root of quantity 4 x minus 6 Find (f + g)(x). x times the square root of 8 4x square root of 8 times x The square root of quantity 4 times x plus 6 plus the square root of quantity 4 times x minus 6
Answer:
Last one
Step-by-step explanation:
The function f is:
● f (x)= √(4x+6)
The function g is:
● g(x) = √(4x-6)
Add them together:
● f+g (x)= √(4x+6 )+ √(4x-6)
Answer:
[tex]\large \boxed{{\sqrt{4x+6} + \sqrt{4x-6} }}[/tex]
Step-by-step explanation:
[tex]f(x)=\sqrt{4x+6}[/tex]
[tex]g(x)=\sqrt{4x-6}[/tex]
[tex](f+g)(x)[/tex]
[tex]f(x)+g(x)[/tex]
Add both functions.
[tex](\sqrt{4x+6} )+ (\sqrt{4x-6} )[/tex]
1
1 point
mZABD = 79
D
C
V
(5x + 4)
(8x - 3)
В B.
A
x= type your answer...
2
1 point
Answer:
x = 6
Step-by-step explanation:
∠ DBC + ∠ ABC = ∠ ABD , substitute values
5x - 4 + 8x - 3 = 79
13x + 1 = 79 ( subtract 1 from both sides )
13x = 78 ( divide both sides by 13 )
x = 6
Stock prices used to be quoted using eighths of a dollar. Find the total price of the transaction. 400 shares of national semi at 135 1/2
Answer:
The value is [tex]T = \$54200[/tex]
Step-by-step explanation:
From the question we are told that
The number of shares is n = 400
The rate of each share is [tex]k = 135\frac{1}{2} = 135.5[/tex]
Generally the total price is mathematically represented as
[tex]T = 400 * 135.5[/tex]
[tex]T = \$54200[/tex]
