Answer:
5.9 years.
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].
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]
In this question:
Mean of the population is [tex]\mu = 5.9[/tex]
If a sampling distribution is created using samples of the ages at which 69 children begin reading, what would be the mean of the sampling distribution of sample means?
By the Central Limit Theorem, the same population mean, of 5.9 years.
6.Write the equation of the line that goes through (4, –6) and (1, 2). Put your answer in Slope–Intercept Form.
Answer:
Step-by-step explanation:
y ≈ -2.667x + 4.667
A one pound bag of skittles contains 300 pieces of which 28% are red. How many skittles were red?
Answer:84
Step-by-step explanation:
iv)
The sum of
four numbers in G.P. is 80 and the A.M. between the
first and the last is 28. Show that the numbers are 2, 6, 18, 54.
Answer:
Step-by-step explanation:
Given numbers : 2 , 6, 18, 54
Since common ration between numbers,
[tex]common \ ratio \ in \ GP , \ r = \frac{a_n}{a_{n-1}} = \frac{6}{2} = 3[/tex]
So the numbers are in GP.
Now Sum of the numbers = 2 + 6 + 18 + 54 = 80
AM, arithmetic mean between first and last number :
[tex]\frac{54+2}{2} = \frac{56}{2} =28[/tex]
All the conditions are true.
he function a = –2x2 + 8x + 5 models the altitude a in feet of a ball thrown in the air and the horizontal distance in feet that the ball travels. Which is the vertex form of the function? (i just need part b answer)
Answer:
for part b the vertex is (2, 13)
Step-by-step explanation:
no (ice)
Answer:
It could be (2, 13)..
Step-by-step explanation:
Please :/ 38 in scientific notation
Answer:
3.8 x [tex]10^{1}[/tex]
What is the length of the line segment?
Answer:
SQRT(8-1)^2+(3-7)^2
sqrt49+16= sqrt65
Step-by-step explanation:
Find the area of the regular polygon. Round to the nearest tenth.
Answer:
3462.8 squared unit
Step-by-step explanation:
Applying,
A = nh²tan(360/n)......... equation 1
Where A = area of the regular polygon, n = number of sides of the polygon, h = length of the apothem.
From the question,
Give; n = 5 sides, h = 15
Substitute these values into equation 1
A = 5×15²×tan(360/5)
A = 1125×tan72
A = 1125×3.078
A = 3462.75
A = 3462.8 squared unit
I would appreciate if someone could answer this question:)
Answer:
x = 1
Step-by-step explanation:
Recall: adjacent angles supplementary
Therefore,
65x + 115° = 180°
Subtract 115° from each side
65x + 115° - 115° = 180° - 115°
65x = 65
Divide both sides by 65
65x/65 = 65/65
x = 1
choose the best selection for the quadrilateral with vertices at the following points: (-3,0), (3-, -3), (0, -3), (0,0)
Answer:
B. Square
Step-by-step explanation:
If cotangent of theta is < 0, in which quadrant(s) could the terminal side of
angle theta lie?
Q2 and Q4
02 and 03
Q3 only
04 only
Answer:
Q2 and Q4
Step-by-step explanation:
Trigonometric functions and quadrants:
In x is in the first quadrant, cos(x) > 0 and sin(x) > 0.
In x is in the second quadrant, cos(x) < 0 and sin(x) > 0.
In x is in the third quadrant, cos(x) < 0 and sin(x) < 0.
In x is in the fourth quadrant, cos(x) > 0 and sin(x) < 0.
Cotangent:
The cotangent is the cosine divided by the sine.
Cotangent negative, which quadrants?
It is negative when sine and cosine have opposite signals. So in the second and the fourth quadrant, that is, Q2 and Q4.
Triangle DEF measures as shown below. What is x in the diagram?
E
50"
1050
F
D
Answer:
option D
Step-by-step explanation:
Exterior angle = sum of interior
105 = 50 + x
105 - 50 = x
55° = x
solution to 3/x + 2/(x+1) = 3/5x?
9514 1404 393
Answer:
x = -6/11
Step-by-step explanation:
We assume you want the solution to ...
3/x +2/(x+1) = 3/(5x)
Subtracting the term on the right, we get the form f(x) = 0.
[tex]\displaystyle\frac{3}{x}+\frac{2}{x+1}-\frac{3}{5x}=0\\\\\frac{15-3}{5x}+\frac{2}{x+1}=0\\\\\frac{12(x+1)+10x}{5x(x+1)}=0\\\\22x+12=0\quad\text{numerator must be zero}\\\\x+\frac{6}{11}=0\quad\text{divide by 22, simplify}\\\\\boxed{x=-\frac{6}{11}}[/tex]
_____
If you really intend 3/x +2/(x+1) = (3/5)x as you have written, the solution is 3 irrational values for x. I find a graphing calculator a convenient way to find them.
A density curve for all the possible weights between 0 pounds and 10 pounds is in the shape of a rectangle. What is the height of the rectangle in this density curve? O A. 0.01 OB. 0.001 O c. 0.1 O D. 0.0001 SUBMIT
Answer:
0.1
Step-by-step explanation:
For a density curve, total area = 1
Probability lies in between 0 and 1
The Area of rectangle :
Area = Length * width
Length = 0 - 10 = 10
Area = 1
Hence,
Area = Length * width
1 = 10 * w
1 = 10w
w = 1 /10
w = 0.1
BRAINIEST AND 10 POINTS
Answer:
1 kilometer
Step-by-step explanation:
Answer:
5,000 meters
Step-by-step explanation:
5,000 meters is the greatest measure of length because when compared to the rest it is the highest. Hope this helps :)
A quadratic function y=f(x)y=f(x) is plotted on a graph and the vertex of the resulting parabola is (3, -6)(3,−6). What is the vertex of the function defined as g(x)=f(x)+2g(x)=f(x)+2?
Explanation:
The vertex of f(x) is (3,-6)
The vertex of g(x) is (3,-4). We keep the x coordinate the same, but add 2 to the y coordinate. This shifts the vertex 2 units up.
UI is uecreasing. (16 ---
Water is poured into a right circular cylinder of radius 8 cm at the rate of 18
cu.cm/min. Find the rate at which the level of water is rising in the cylinder.
of 24 cu.cm/min. The
what is the slope of a line between (-4,14) and (-16,8)
Answer:
[tex] \frac{1}{2} [/tex]
Step-by-step explanation:
slope :
[tex]slope \: = \: \frac{y2 - y1}{x2 - x1} = \frac{8 - 14}{ - 16 - - 4} = \frac{ - 6}{ - 12} = \frac{1}{2} [/tex] = 0.5
Find all Values of b that will make the polynomial a perfect square trinomial.
25z^2+bz+36
Please write out how to do this so I can see the steps of what I am doing wrong. thank you!
Answer:
There are two solutions for [tex]b[/tex]: [tex]b = + 30\cdot z[/tex], [tex]b = -30\cdot z[/tex]
Step-by-step explanation:
By Algebra, we know that a polynomial is a perfect square trinomial if it is of the form:
[tex]a^{2} + 2\cdot a \cdot c + c^{2} = (a + c)^{2}[/tex] (1)
By direct comparison, we have the following system:
[tex]a^{2} = 25\cdot z^{2}[/tex], [tex]c^{2} = 36[/tex], [tex]2\cdot a \cdot c = b[/tex].
There are two possible solutions for [tex]b[/tex]:
1) [tex]a = \pm 5\cdot z[/tex], [tex]c = \pm 6[/tex], [tex]b = + 30\cdot z[/tex]
2) [tex]a = \pm 5\cdot z[/tex], [tex]c = \mp 6[/tex], [tex]b = -30\cdot z[/tex]
given the slope intercept form of the equation identified the slope y=3/4x-3
were there leftovers?
Answer:
Yes, if you didn't eat all 5 of your pizzas young man.
Step-by-step explanation:
(x + 3)^2 = 12 ? need answers ASAP
Answer:
option c is the correct answer
help with this please
Answer:
I think the answer to this would be 93.40
Statisticians prefer large samples. Describe briefly the effect of increasing the size of a sample (or the number of subjects in an experiment) on each of the following:
1. Increases
2. Decreases
3. Unaffected
A. The margin of error of a 95% confidence interval.
B. The P-value of a test, when H0 is false and all facts about the population remain unchanged as n increases.
C. The power of a fixed level test when the alternative hypothesis, and all facts about the population remain unchanged.
Answer:
Margin of Error decreases
Pvalue decreases
Power increases
Step-by-step explanation:
The margin of error decreases as sample size increases given the same level of confidence, hence, the interval gets narrower.
The margin of error = (Zcritical * σ/√n) ; where, n is the denominator, as the denomination increases, the obtained value will decrease, hence, the margin of error.
When we have a false H0, then we expect a statistical result which will reject H0, with all facts remaining unchanged , increase in sample size n, will lead to decrease in Pvalue, because a lower P value increases the significance of statistical test needed to reject H0.
The power of a fixed level test when the null hypothesis is true, higher power is required to reject the null , increasing n will increase the probability of rejecting H0, by increasing the power of a fixed level test.
To prove that AVWZ - AYXZ by the SAS similarity
theorem, which other sides or angles should be used?
O WV and XY
O WV and ZY
O
O < VWZ =
Answer:
C. <VZW ≅ <YZX
Step-by-step explanation:
The SAS Similarity theorem says that two triangles are considered similar to each other, when 2 of the corresponding side lengths of the triangles are proportional to each other, and also the included angles in each triangle are congruent.
We are given the two sides of each triangle that corresponds to each other already. So, the next item to be used in order to prove that both triangles are similar is the corresponding included angles that should be congruent to each other. Thus:
The included angle, <VZW in ∆VWZ corresponds to the included angle, <YZX in ∆YXZ.
Therefore:
<VZW ≅ <YZX
where is the vertex located at?
Answer:
The vertex of [tex]f(x) = |x-3| + 6[/tex] is [tex](x,y) = (3, 6)[/tex].
Step-by-step explanation:
The vertex of the absolute value function is the point where [tex]|x-3| = 0[/tex]. Hence, the coordinates of the vertex are, respectively:
[tex]x-3 = 0[/tex]
[tex]x = 3[/tex]
[tex]y = |x-3| + 6[/tex]
[tex]y = |3-3|+6[/tex]
[tex]y = |0|+6[/tex]
[tex]y = 0 + 6[/tex]
[tex]y = 6[/tex]
The vertex of [tex]f(x) = |x-3| + 6[/tex] is [tex](x,y) = (3, 6)[/tex].
024
+2]
Answer to this ?
Answer:
[tex]4 \times \frac{11}{12} [/tex]
also equals 4.9
francis is ten years old. ben is twice as old as francis .what is the age of ben?
Answer:
Collage math (hehe) ... Ben is 20
Step-by-step explanation:
Give me Brainiest Answer Award please and thank you! :D
Arithmetic
If Francis is ten years old, then Ben is twenty.
10x2=20
Solve the equation by factoring. 3x^2-5x-12=0
Answer:
x = 3
[tex]x=-1\frac{1}{3}[/tex] or [tex]x=-\frac{4}{3}[/tex]
Step-by-step explanation:
3x² - 5x - 12 = 0
Method 1: Factoring
3x² + 4x - 9x - 12 = 0
(3x² + 4x) + (- 9x - 12) = 0
x(3x + 4) - 3(3x + 4) = 0
(x - 3)(3x + 4) = 0
Two separate equations
x - 3 = 0
3x + 4 = 0
x - 3 = 0
x - 3 + 3 = 0 + 3
3x + 4 = 0
3x + 4 - 4 = 0 - 4
3x = - 4
[tex]\frac{3x}{3} :-\frac{4}{3}[/tex]
[tex]x=-1\frac{1}{3}[/tex]
Method 2: Quadratic Formula
Ignore the A before the ±, it wouldn't let me type it correctly.
[tex]x=\frac{-b±\sqrt{b^{2} -4ac} }{2a}[/tex]
3x² - 5x - 12 = 0
a = 3
b = - 5
c = - 12
[tex]x=\frac{-(-5)±\sqrt{(-5)^{2} -4((3)(-12))} }{2(3)}[/tex]
[tex]x=\frac{-(-5)±\sqrt{25 -4((3)(-12))} }{2(3)}[/tex]
[tex]x=\frac{-(-5)±\sqrt{25 +144} }{2(3)}[/tex]
[tex]x=\frac{-(-5)±\sqrt{169} }{2(3)}[/tex]
[tex]x=\frac{-(-5)±13}{2(3)}[/tex]
[tex]x=\frac{5±13}{6}[/tex]
Two separate equations
One must have a + (positive) and the other will have a - (negative).
[tex]x=\frac{5+13}{6}[/tex]
[tex]x=\frac{18}{6}[/tex]
x = 18 ÷ 6
x = 3
[tex]x=\frac{5-13}{6}[/tex]
[tex]x=\frac{-8}{6}[/tex]
x = - 8 ÷ 6
[tex]x=-1\frac{1}{3}[/tex]
A box-and-whisker plot titled Move length in minutes is shown. The number line goes from 80 to 400 in increments of 10. The whiskers range from 81 to 138, and the box ranges from 95 to 128. A line divides the box at 108. Describe the shape of the graph. Although the mean cannot be determined from the graph, can an approximation of the mean be determined? Explain.
Answer:
the answer is b
Step-by-step explanation:
Simplify (4x^3)^5 ????
Answer:
1024x^15
Step-by-step explanation:
First, we'll do 4 to the 5th power which results in 1024
Next, we'll multiply the exponents following the laws of exponents, so 3 times 5=15
This results in 1024x^15
Hope I helped :)
Answer:
[tex]1024 {x}^{15} [/tex]
Step-by-step explanation:
[tex](4 {x}^{3} ) ^{5} \\ {4}^{5} \times {x}^{3 \times 5} \\ 1024 {x}^{15} [/tex]
hope this helps you.
Have a nice day!