Answer:
c. As sample size increases, standard error decreases.
Step-by-step explanation:
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].
Thus:
The standard error is inversely proportional to the square root of the sample size, that is, as the sample size increases, the standard error decreases, and the correct answer is given by option c.
What value can you add in the blank in the expression x^2 + 6x + 7 +__ to complete the
square?
Answer:
2
Proof:
x^2 + 6x + 7 + 2 = x^2 + 6x + 9 = x^2 + 6x + 3^2 = (x + 3)^2
The value can you add in the blank in the expression [tex]x^2 + 6x + 7 +\textunderscore\textunderscore[/tex] to complete the square is 2
What is trinomial?"It is a polynomial which consists of three terms."
What is square trinomial?"A trinomial with degree 2"The general form of square trinomial is [tex]ax^{2} +bx+c[/tex] where a ≠ 0What is perfect square trinomial?"A square trinomial is a perfect square, if and only if it satisfies the condition b² = 4ac"
For given question,
We have been given a square trinomial.
[tex]x^2 + 6x + 7 +\textunderscore\textunderscore[/tex]
We need to find the number in the blank space, so that the given trinomial would be complete square.
Let 'm' be the required number.
So, the trinomial would be [tex]x^2 + 6x + (7 +m)[/tex]
Comparing above square trinomial with [tex]ax^{2} +bx+c[/tex],
we have a = 1, b = 6, c = 7 + m
We know, a square trinomial is a perfect square, if and only if it satisfies the condition b² = 4ac
⇒ b² = 4ac
⇒ 6² = 4 × 1 × (7 + m)
⇒ 36 = 4 × (7 + m)
⇒ 9 = 7 + m
⇒ m = 2
This means, we need to add 2 in the blank space.
So, the square trinomial would be,
[tex]x^2 + 6x + 7 + \underline {2}\\\\= x^2 + 6x + 9\\\\= (x + 3)^2[/tex]
Therefore, the value can you add in the blank in the expression [tex]x^2 + 6x + 7 +\textunderscore\textunderscore[/tex] to complete the square is 2
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Question 13
Find the volume of the prism.
Answer:
[tex]\boxed {\boxed {\sf B. \ 324 \ cm^3}}[/tex]
Step-by-step explanation:
The volume of a triangular prism is the product of the area of the triangular cross-section (B) and the height (h).
[tex]V= B*h[/tex]First, let's find the area of the triangular cross-section/the end of the triangle. The area of a triangle is:
[tex]B= \frac{1}{2} b*h[/tex]
The base of the triangle base (not the prism) is 6 centimeters and the height is 9 centimeters.
b= 6 cm h= 9 cm[tex]B= \frac{1}{2} (6 \ cm)(9 \ cm)[/tex]
Multiply the numbers in parentheses.
[tex]B= \frac{1}{2}(54 \ cm^2)[/tex]
Multiply by 1/2 or divide by 2.
[tex]B= 27 \ cm^2[/tex]
Now we know the area of the cross-section or base is 27 square inches. The height of the prism is 12 centimeters.
B= 27 cm²h= 12 cmSubstitute the values into the volume formula for a triangular prism.
[tex]V= 27 \ cm^2 * 12 \ cm[/tex]
Multiply.
[tex]V= 324 \ cm^3[/tex]
The volume of the prism is 324 cubic centimeters and choice B is correct.
The volume of the triangular prism is 324 cubic centimeters, and choice B is correct.
The volume of a triangular prism is determined by multiplying the area of the triangular cross-section (B) by the height (h). In this case, the base (b) of the triangular cross-section is given as 6 centimeters, and the height (h) is given as 9 centimeters.
To find the area of the triangular cross-section (B), we can use the formula for the area of a triangle: B = (1/2) * base * height.
Substituting the values:
B = (1/2) * 6 * 9 = 27 square centimeters.
Next, we multiply the area of the cross-section (B) by the height (h) to find the volume (V) of the prism:
V = B * h = 27 * 12 = 324 cubic centimeters.
Therefore, the volume of the triangular prism is 324 cubic centimeters, and choice B is correct.
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Find the area
96 sq meters
144 sq meters
84 sq meters
102 sq meters
Answer:
the answer is 84.... .....
A certain country has 586.08 million acres of forest. Every year, the country loses 7.92 million acres of forest mainly due to deforestation for farming purposes. If this situation continues at this pace, how many years later will the country have only 237.6 million acres of forest left? (Use an equation to solve this problem.)
Answer:
At this pace the country will have only 237.6 million acres of forest left in 44 years.
Step-by-step explanation:
Given that a certain country has 586.08 million acres of forest, and every year, the country loses 7.92 million acres of forest mainly due to deforestation for farming purposes, to determine, if this situation continues at this pace, how many years later will the country have only 237.6 million acres of forest left, the following calculation must be performed:
Current amount - (amount lost per year x number of years) = 237.6
586.08 - (7.92 x X) = 237.6
586.08 - 7.92X = 237.6
-7.92X = 237.6 - 586.08
-7.92X = -348.48
X = -348.48 / -7.92
X = 44
Therefore, at this pace the country will have only 237.6 million acres of forest left in 44 years.
What is an equation of the line that passes through the point (-2, -3) and is
parallel to the line 5x + 2y =14?
Answer:
The equation of the parallel line will be y = -2.5x - 8.
Step-by-step explanation:
First things first, let's rearrange the line equation provided into a more standard form:
[tex]5x + 2y = 14[/tex]
[tex]5x - 14 = -2y[/tex]
[tex]\frac{5x - 14}{-2} = y[/tex]
[tex]y = -2.5x + 7[/tex]
Therefore, we can see that this line has a slope (the coefficient preceding x) of -2.5. The parallel line must therefore also have a slope of -2.5.
Now, let us set the y-intercept of the parallel line to be (0, a) (since it must be on the y-axis).
If we factor in all of this, we get the equation:
[tex]\frac{a-(-3)}{0-(-2)} = -2.5[/tex]
Remember, the slope is found by dividing the vertical difference with the horizontal difference.
[tex]a - (-3) = -2.5(0+2)[/tex]
[tex]a + 3 = -5[/tex]
[tex]a = -8[/tex]
Hence, the equation of the parallel line will be y = -2.5x - 8.
Hope this helped!
I need help with this question.
Có 6 quyển sách và 7 quyển vở. Hỏi có bao nhiêu cách chọn
một trong các quyển nói trên?
Answer:
eeeeeee
Step-by-step explanation:
xdddddddudjdjdjdjdjdjsjsjsjsjsjsjsjjsjsjsjsjsjsjsjsjsjsjjs
HELP ASAP PLEASE!!!
Answer:
the function g because the graphs the graphs of f and g are symmetrical about the line y=x
Step-by-step explanation:
Inverse functions are symmetrical to each other about the line y=x. This means that if you flip a function over y=x, that will be its inverse function. It makes sense because inverse functions turn the input of the original function (x) into the output of the inverse function (y), so y=x and x=y. Take the point (-6,0) on f, it becomes (0,-6) on g.
Im Struggling i could use some help pls!!
Answer:
option4 : 0.4
Step-by-step explanation:
[tex]Sin N = \frac{Opposite}{hypotenuse}[/tex]
[tex]sin 7 = \frac{x}{3.4}\\\\3.4 \times sin 7 = x \\\\3.4 \times 0.122 = x \\x = 0.41[/tex]
Find the volume of the solid generated by revolving the region bounded by the x-axis, the curve y = 3x^4 , and the lines x = 1 and x = -1 about the x-axis.
Answer:
Let's define A as the area given by the integral:
[tex]\int\limits^1_{-1} {3x^4} \, dx[/tex]
Which is the area between the curve y = 3*x^4 and the x-axis between x = -1 and x = 1
To find the volume of a revolution around the x-axis, we need to multiply the area by 2*pi (a complete revolution)
where pi = 3.14
First, let's solve the integral:
[tex]\int\limits^1_{-1} {3x^4} \, dx = \frac{3}{5}(1^5 - (-1)^5) = \frac{3*2}{5} = \frac{6}{5}[/tex]
Then the volume of the solid is just:
V = (6/5)*2*3.14 = 7.536
1. The Graduate Management Admission Test (GMAT) is a standardized exam used by many universities as part of the assessment for admission to graduate study in business. The average GMAT score is 547 (Magoosh website). Assume that GMAT scores are bell-shaped with a standard deviation of 100. What percentage of GMAT scores are 647 or higher
Answer:
16% of GMAT scores are 647 or higher.
Step-by-step explanation:
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.
The average GMAT score is 547 (Magoosh website). Assume that GMAT scores are bell-shaped with a standard deviation of 100.
This means that [tex]\mu = 547, \sigma = 100[/tex]
What percentage of GMAT scores are 647 or higher?
The proportion is 1 subtracted by the p-value of Z when X = 647. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{647 - 547}{100}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a p-value of 0.84.
1 - 0.84 = 0.16
0.16*100% = 16%
16% of GMAT scores are 647 or higher.
Suppose you have a score that puts you 1.1 standard deviations below the mean. What is your percentile score?
Answer:
200000%
Step-by-step explanation:
.
một hộp đựng 11 tấm thẻ được đánh số từ 1 đến 11. tính số cách lấy ra 4 tấm thẻ từ hộp đó để tổng các số ghi trên 4 tấm thẻ ấy là một số lẻ
Answer:
16/33
Step-by-step explanation:
Tổng của cả 4 tấm thẻ là một số lẻ khi:
Có 1 thẻ là lẻ, 3 thẻ còn lại là chẵn, có: 6C1.5C3=60 cách
Có 3 thẻ là lẻ, 1 thẻ là chẵn, có: 5C1.6C3=100 cách
Suy ra có 160/11C4=16/33 cách
Question 11
Find the volume.
Answer:
volume of the cube=15×15×15
=3375 in³
volume of the cylinder=πr²h
=π×7²×14
=686π
volume of the figure=3375+686π
the answer is first option
please help me please!!! I'll give brainlest for correct answer
Answer:
why you just don't put the question up
Step-by-step explanation:
There were 436 tickets purchased for a major league baseball game. The general admission tickets cost $6.50 and the upper reserved tickets cost $8.00. The total amount of money spent was $3284.00. How many of each kind of ticket were purchased?
How many general admission tickets were purchased? ____
How many upper reserved tickets we purchased? ___
Answer:
136 general admission tickets were purchased, and 300 upper reserved tickets were purchased.
Step-by-step explanation:
This question is solved using a system of equations.
I am going to say that:
x is the number of general admission tickets purchased.
y is the number of reserved tickets purchased.
There were 436 tickets purchased for a major league baseball game.
This means that [tex]x + y = 436[/tex], or also, [tex]x = 436-y[/tex]
The general admission tickets cost $6.50 and the upper reserved tickets cost $8.00. The total amount of money spent was $3284.00.
This means that [tex]6.5x + 8y = 3284[/tex]. Since [tex]x = 436-y[/tex]
[tex]6.5(436-y) + 8y = 3284[/tex]
[tex]1.5y = 450[/tex]
[tex]y = \frac{450}{1.5}[/tex]
[tex]y = 300[/tex]
And:
[tex]x = 436 - y = 436 - 300 = 136[/tex]
136 general admission tickets were purchased, and 300 upper reserved tickets were purchased.
Can y’all help me on question 15?!
Answer:
297
Step-by-step explanation:
5.5x4.5x12=297
Rewrite as a simplified fraction .16 repeating
Answer:
1/6
Step-by-step explanation:
10x = 1.6666....
100x =16.6666...
90x = 16.6666... - 1.6666...
90x = 15
x = 15/90
x = 1/6
someone help please I'm stuck and frustrated,?????
Answer:
The area of the circle in terms of π is:
9/64 π in^2Step-by-step explanation:
To find the area of that circle, you can use the equation:
Area of a circle = [tex]\pi * \frac{D^{2}}{4}[/tex]Where:
D = Diameter (3/4 in)Now, we can replace the given measurement in the equation:
Area of a circle = [tex]\pi * \frac{(\frac{3}{4}in) ^{2}}{4}[/tex]Area of a circle = [tex]\pi * \frac{\frac{9}{16}in ^{2}}{4}[/tex]Area of a circle = [tex]\pi * \frac{9}{64} in^{2}[/tex]That result is the same that to write:
Area of a circle = [tex]\frac{9}{64}\pi in^{2}[/tex]By this reason, the result is 9/64 π in^2, giving the result in terms of π.
Use Newton’s method to approximate the indicated root of the equation correct to six decimal places. The positive root of 3 sin x = x
Answer:
[tex]x \approx 2.278863[/tex]
Step-by-step explanation:
Required
The positive root of [tex]3\sin(x) = x[/tex]
Equate to 0
[tex]0 = x -3\sin(x)[/tex]
So, we have our function to be:
[tex]h(x) = x -3\sin(x)[/tex]
Differentiate the above function:
[tex]h'(x) = 1 -3\cos(x)[/tex]
Using Newton's method of approximation, we have:
[tex]x_{n+1} = x_n - \frac{h(x_n)}{h'(x_n)}[/tex]
Plot the graph of [tex]h(x) = x -3\sin(x)[/tex] to get [tex]x_1[/tex] --- see attachment for graph
From the attached graph, the first value of x is at 2.2; so:
[tex]x_1 = 2.2[/tex]
So, we have:
[tex]x_{n+1} = x_n - \frac{h(x_n)}{h'(x_n)}[/tex]
[tex]x_{1+1} = x_1 - \frac{h(x_1)}{h'(x_1)}[/tex]
[tex]x_{2} = 2.2 - \frac{2.2 -3\sin(2.2)}{1 -3\cos(2.2)} = 2.28153641[/tex]
The process will be repeated until the digit in the 6th decimal place remains unchanged
[tex]x_{3} = 2.28153641 - \frac{2.28153641 -3\sin(2.28153641)}{1 -3\cos(2.28153641)} = 2.2788654[/tex]
[tex]x_{4} = 2.2788654 - \frac{2.2788654 -3\sin(2.2788654)}{1 -3\cos(2.2788654)} = 2.2788627[/tex]
[tex]x_{5} = 2.2788627 - \frac{2.2788627-3\sin(2.2788627)}{1 -3\cos(2.2788627)} = 2.2788627[/tex]
Hence:
[tex]x \approx 2.278863[/tex]
IN DESPERATE NEED OF HELP! PLEASE ANSWER!! Which of the following represents the synthetic division form of the long division problem below? (x^2+9x-2)÷(x-4)
Answer:its d
Step-by-step explanation:
12
There are 81 counters in a bag.
32 of the counters are green.
The rest of the counters are orange.
One of the counters is taken at random.
Find the probability that the counter is orange.
helpppp pls
Answer:
49
81
Step-by-step explanation:
Probability = number of possible outcome.
number of total outcome.
= orange counters = 81 - 32 = 49
49
81
Please help me please
Answer:
1. Paralleogram
2. Trapeziod
3. Square
4. Rhombus
5. Rectangle
6. I don't know
7. Rectangle
8. can't see it
9. Trapeziod
Find f(0) if f (x) = log base 10 of 10 + 9^x + (x - 2)(x - 1)
Answer:
Step-by-step explanation:
Five times the sum of twice a number and 12 is -55. Find the number
Find the value for the side marked below.
Round your answer to the nearest tenth.
61°
135
y
y = = [?]
Answer:
[tex]65.4[/tex]
Step-by-step explanation:
In any right triangle, the cosine of an angle is equal to its adjacent side divided by the hypotenuse, or longest side, of the triangle.
Therefore, we have:
[tex]\cos 61^{\circ}=\frac{y}{135},\\t=135\cos 61^{\circ}=65.4492987333\approx \boxed{65.4}[/tex]
Hello, here's the question :D
"Use three different values of n to demonstrate that 2n + 3n is equivalent to 5n."
Answer:
(examples) n = 2
n = 3
n = 4
Step-by-step explanation:
to demonstrate, all you do is select a number to represent 'n' and plug it in.
so for example, n = 2:
2(2) + 3(2) = 5(2)
4 + 6 = 10, which is true.
Suppose that a dart board is given by a circle of radius 1 in R², centered at (0,0). You throw a dart at the dart board, and the position that it lands is given by a pair of random variables, (X,Y).
a. Suppose that the probability of a "Bull's Eye" is zero; that is, P(X = 0, y = 0) = 0.
b. Prove that there must be some integer n > 0 such that P (√X^2 +Y^2 > 1/2) > 0.
Answer:
Answer B
Step-by-step explanation:
where is EF to the nearest tenth??
Answer:
37.7
Step-by-step explanation:
EF and ED define the Tangent of D
Tan(37) = side opposite D / side adjacent to D
Opposite means a line (FE) that is not connected to the angle. It is never the longest line (hypotenuse) in a Right Triangle
Adjacent means the leg that is connected to the angle, but is not the hypotenuse.
Tan(D) = opposite over adjacent
Opposite = x
Adjacent = 50
Tan(37) = 0.7536 rounded to 4 places, but I've kept the exact value in my calculator.
0.7536 = x / 50 Multiply both sides by 50
0.7536*50 = x
x = 37.6777
The nearest 1/10 is 37.7
Last year, nine employees of an electronics company retired. Their ages at retirement are listed below in years. Find the mean retirement age.56 65 62 53 68 58 65 52 56
Answer:
59.44
Step-by-step explanation:
Nine employees If an electronic company retired last year
The retirement ages are listed below
56, 65, 62, 53, 68, 58, 65, 52, 56
The mean retirement age can be calculated as follows
= 56+65+62+53+68+58+65+52+56/9
= 535/9
= 59.44
Hence the mean retirement age is 59.44