Answer:
Type II error occurred
Step-by-step explanation:
It is given that a new shampoo is being tested to determine whether the hair grows faster by using this shampoo.
It is known that hair grow at 0.5 inches per month at average.
The hypothesis are,
Null hypothesis, [tex]$H_0: \mu=0.5$[/tex]
Alternate hypothesis, [tex]$H_1: \mu>0.5$[/tex]
But it is known that :
Type [tex]$I$[/tex] error occurs when rejecting the null hypothesis when the null hypothesis is true actually.
Type [tex]$II$[/tex] error occurs [tex]\text{when we fail reject the null hypothesis}[/tex] when the null hypothesis is actually false.
Now here since the null hypothesis is not been rejected, type [tex]$II$[/tex] error had occurred.
When sample size increases:____.
A. Standard deviation of the sample mean increases.
B. Confidence interval remains the same.
C. Confidence interval increases.
D. Confidence interval decreases.
Answer:
D. Confidence interval 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].
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]
When sample size increases:
The standard deviation of the sample mean is:
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
That is, it is inversely proportional to the sample size, so if the sample size incerases, the standard deviation decreases, and so does the confidence interval.
This means that the correct answer is given by option D.
If AJKL * AMNP, which statement must be true?
Write an expression to represent the perimeter of a rectangle with a length of 4x+14 and a width of 2x-9. Simplify your answer.
Answer:
[tex]{ \boxed{ \bf{formular : } \: \tt{perimeter = 2(length + width)}}} \\ perimeter = 2((4x + 14) + (2x - 9)) \\ perimeter = 2(6x + 5) \\ perimeter = 12x + 10 \\ \\ { \tt{expression : 12x + 10}} \\ \\ { \underline{ \blue{ \tt{becker \: jnr}}}}[/tex]
Adirondack Savings Bank (ASB) has $5 million in new funds that must be allocated to home loans, personal loans, and automobile loans. The annual rates of return for the three types of loans are 7% for home loans, 12% for personal loans, and 9% for automobile loans. The bank's planning committee has decided that at least 40% of the new funds must be allocated to home loans. In addition, the planning committee has specified that the amount allocated to personal loans cannot exceed 60% of the amount allocated to automobile loans.(a) Formulate a linear programming model that can be used to determine the amount of funds ASB should allocate to each type of loan to maximize the total annual return for the new funds.(b) How much (in dollars) should be allocated to each type of loan? 1) What is the total annual return (in dollars)?2) What is the annual percentage return?
The graph below shows a proportional relationship between x and y. What is the constant of proportionality,
y/x?
Answer:
0.5
Step-by-step explanation:
you just need see at one point. i see at point (1, 0.5)
PLEASE HELP!!!please >_
Answer:
x =56 (corresponding angles are equal)
Answer:
56°
Step-by-step explanation:
Since these two lines are parallel, and these two angles are at the corresponding position, the required angle measure is 56
If the width of the rectangle increases by 4 and the length decreases by 3, by how much will the area change? Express the difference as a simplified expression (View attachment)
Answer:
this might be the answer..
Step-by-step explanation:
m²+6m+9
if three-fourth of a number is added to 14 gives result less than or equal to 20 .find the number,hense illustrate your answer on a number line
Answer:
x≤8
Step-by-step explanation:
let the number be x
¾x+14≤20
LCM=4
3x+56≤80
3x≤80-56
3x≤24
x≤8
I am unable to add number line here
tan^2theta - Sin^2theta = tan^2theta. sin^2theta
explain this step
tan²(θ) - sin²(θ) = sin²(θ)/cos²(θ) - sin²(θ)
-- because tan(θ) = sin(θ)/cos(θ) by definition of tangent --
… = sin²(θ) (1/cos²(θ) - 1)
-- we pull out the common factor of sin²(θ) from both terms --
… = sin²(θ) (1/cos²(θ) - cos²(θ)/cos²(θ))
-- because x/x = 1 (so long as x ≠ 0) --
… = sin²(θ) ((1 - cos²(θ))/cos²(θ))
-- we simply combine the fractions, which we can do because of the common denominator of cos²(θ) --
… = sin²(θ) (sin²(θ)/cos²(θ))
-- due to the Pythagorean identity, sin²(θ) + cos²(θ) = 1 --
… = sin²(θ) tan²(θ)
-- again, by definition of tan(θ) --
What is the formula of a palindrome?
Answer:
For example, 6(1001) + 3(110) = 6006 + 330 = 6336 is a palindrome. Since 11 is a factor of both 1001 and 110, we conclude that all four digit palindromes are divisible by 11.
Tasha needs 75 liters of a 40% solution of alcohol. She has a 20% and a 50% solution available. How many liters of the 20% and how many liters of the 50% solutions should she mix to make the 40% solution?
Answer:
25 liters of 20%
50 liters of 50%
Step-by-step explanation:
x = liters of 50%
75 - x = liters of 20%
50x + 20(75 - x) = 40(75)
50x + 1500 - 20x = 3000
30x = 1500
x = 50
75 - x = 25
Which one is it I need to know quick and I’ll mark you Brainly
Answer: i think
the corrcect answer is 0.5*10^-1
Step-by-step explanation:
hope this helps
If someone can pls give the answer with steps that would be greatly appreciated :)
Answer:
D
C
Step-by-step explanation:
One equation must have a slope that is the negative reciprocal of the other equation's slope.
The the sentence I've given you is correct, it is probably a little difficult to understand. Let's use an example
y = 1/2 x + 4
The slope of this line = 1/2
Therefore if you want a negative reciprocal, it would - 2 so y=-2x would be perpendicular to y = 1/2x + 4.
Just to be sure you understand, I'll put the graph of these two equations below.
===================================
So to answer your question
8)
is D. All the others have signs that are the same. They are reciprocals but with signs the same.
9) This is a little harder. You have reciprocals in all of them. But the slope must be positive. So that means that only a and c can be true. A does not go through (4,-1). C does.
y = 1/4 * 4 - 2
y = 1 - 2
y = - 1
So the answer is C
What are the odds against choosing a red marble from a bag that contains two blue marbles, one green marble, seven white marbles, and four red marbles?
Answer:
4/14
Step-by-step explanation:
2+1+7+4=14
red marbles are 4/14
Answer:
2/7
Step-by-step explanation:
Probability = Number of ways event can occur/ total number of possible outcomes.
Total number of possible outcomes = 2+1+7+4=14 = 4/14.
And if you break that down, 2 will go into four, twice and into fourteen, seven times = 2/7.
Brainliest?
What is the slope of the line?
I will mark the brainliest!
Answer:
1
Step-by-step explanation:
Slope = change in y over change in x
If you look at the graph as y goes up 1 x goes up 1
So slope = 1/1 or just 1
Answer:
m=1
Step-by-step explanation:
Hi there!
We're given the graph of a line and we need to find the slope of the line
There are many ways to do this, but the easiest is to calculate it from two points
The formula for the slope (m) calculated from 2 points is [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex], where ([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and ([tex]x_{2}[/tex],[tex]y_{2}[/tex]) are points
So we can take 2 points from the graph of the line to find the slope
For example, let's take (-1,0) and (0,1)
Let's label their values to avoid any confusion before we substitute their values into the formula
[tex]x_{1}[/tex]=-1
[tex]y_{1}[/tex]=0
[tex]x_{2}[/tex]=0
[tex]y_{2}[/tex]=1
now substitute into the formula *remember: we have SUBTRACTION in the slope formula
m=[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
substitute
m=[tex]\frac{1-0}{0--1}[/tex]
simplify
m[tex]\frac{1}{0+1}[/tex]
simplify again
m=[tex]\frac{1}{1}[/tex]
divide
m=1
Therefore the slope of the line is 1
Hope this helps! :)
How tall is the average human baby ?
Liner equation with a rapid change over time
Answer:
y=130(2.5) ^(x-1)
Step-by-step explanation:
This should give you an exponential growth curve. I'm assuming this is what you meant by "rapid change over time".
In the figure, ∆AMH ≅ ∆HTA by Side-Side-Side (SSS). Which angles are congruent by CPCTC?
Answer:
it is option a. pls mark me brainliest. hope this helps you
YA is the angle bisector of ZXYZ. If mZXYZ = 52°, what is mZZYA?
Given:
[tex]YA[/tex] is the angle bisector of [tex]\angle XYZ[/tex].
[tex]m\angle XYZ=52^\circ[/tex]
To find:
The measure of [tex]m\angle ZYA[/tex].
Solution:
It is given that [tex]YA[/tex] is the angle bisector of [tex]\angle XYZ[/tex]. It means
[tex]m\angle XYA=m\angle ZYA[/tex] ...(i)
Now,
[tex]m\angle XYA+m\angle ZYA=m\angle XYZ[/tex]
[tex]m\angle ZYA+m\angle ZYA=52^\circ[/tex] [Using (i)]
[tex]2m\angle ZYA=52^\circ[/tex]
Divide both sides by 2.
[tex]m\angle ZYA=\dfrac{52^\circ}{2}[/tex]
[tex]m\angle ZYA=26^\circ[/tex]
Therefore, the required value is [tex]m\angle ZYA=26^\circ[/tex].
Somebody please help asap
Answer:
B. [tex] 4x^2 + \frac{3}{2}x - 7 [/tex]
Step-by-step explanation:
[tex] f(x) = \frac{x}{2} - 3 [/tex]
[tex] g(x) = 4x^2 + x - 4 [/tex]
(f + g)(x) = f(x) - g(x)
= [tex] \frac{x}{2} - 3 + 4x^2 + x - 4 [/tex]
Add like terms
[tex] = 4x^2 + \frac{x}{2} + x - 3 - 4 [/tex]
[tex] = 4x^2 + \frac{3x}{2} - 7 [/tex]
[tex] = 4x^2 + \frac{3}{2}x - 7 [/tex]
At a school, there are two different math classes for children of the same age. The two classes have different teachers. The school principal is interested in gauging the effectiveness of two different teaching methods and asks each teacher to try one of the methods. At the end of the semester both classes are given the same test and the results are compared.
In this experiment, what is the treatment variable?
Give an example of a variable that could confound the results.
Answer:
Treatment variable = Teaching methods
Confounding variable = Teacher's teaching prowess
Step-by-step explanation:
The treatment variable here is that variable which is applied on the student in other to ovtujba measure of the dependent or response variable, the response variable here is the test score, while the treatment variable is the independent variable, which are the teaching methods.
The confounding variable is that variable which is capable of causing a spurious association in our measurement and also has an effect on the test score. However, this variable isn't taken into account during our experiment. One possible confounding variable could be the Teacher's individual teaching prowess regardless of the teaching method. This could cause the student to get a better grasp of what is being taught by one teacher than the other.
Answer:Treatment variable = Teaching methods
Confounding variable = Teacher's teaching prowess
Step-by-step explanation:
For each of the following, shade the portion of the Venn diagram that illustrates the set. ( A ∩ B ) ∪ ( A ∩ C )
Answer:
Here's what that would look like on a venn diagram
Step-by-step explanation:
2. Tricky Flips sells a coin that promises to land on heads 3 out of every 4 times. If the coin is
flipped 20 times, which of the following is the number of times you should expect it to land
on head
Answer:
15
Step-by-step explanation:
Because 3/4 of 20 or 75% of 20 is 15
1. There are 2 schools. Each school has 3 buildings. Each building has 4 floors. Each floor has 5 classrooms. Each classroom has 6 rows of desks. Each row has 7 desks. How many desks are there in the two schools?
Consider a circle whose equation is x^2+y^2-2x-8=0. Which statements are true? Select three options.
Answer:
The radius of the circle is 3 units
The center of the circle lies on the x-axis.
The radius of this circle is the same as the radius of the circle whose equation is x^2 + y^2 = 9
Step-by-step explanation:
A video store charges $8 per movie, and the fifth movie is free. How much do you actually pay per movie?
Answer:
$6.40 per movie
Step-by-step explanation:
Since the fifth movie is free, find the total cost by multiplying 8 by 4:
8(4)
= 32
Find how much you actually pay per movie by dividing this by 5:
32/5
= 6.4
So, you are actually paying $6.40 per movie
Answer:
$6.40
Step-by-step explanation:
If you buy five movies, but only pay for the first four, then that is the first amount we need to find. Paying $8 for four movies means you are paying $32. If you are paying $32 for five movies, then you are paying $6.40 per movie.
Math:
8 + 8 + 8 + 8 + 0 = 32
32/5 = 6.4
Solve the following system of equations graphically on the set of axes below.
y= x+2
y= -1/2x+8
Hi there!
»»————- ★ ————-««
I believe your answer is:
(4,6)
»»————- ★ ————-««
Here’s why:
I have graphed the two equations in a program. The point of intersection would be the solution to the system.When graphed, the lines intersect at point (4, 6). (4,6) is the solution.⸻⸻⸻⸻
See the graph attached.
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Pls help I don’t understand this one pls
Answer:
15=225
20= 400
Step-by-step explanation:
the small 2 means multiply that number two times :)
Answer:
[tex]15^2\\[/tex] = 225
[tex]20^{2}[/tex] = 400
Step-by-step explanation:
[tex]x^{2}[/tex] = [tex]x[/tex] × [tex]x[/tex]
basically it's the number times itself
15 × 15 = 225
20 × 20 = 400
Mr. Arju wishs to purchase a house . to buy the house he needs to make a down payment of nu.300000 and also pay nu.15000 every quarter for the next 8 years. the interest charge is 9% per year compounded quarterly. what is the price of the house?
Answer:
The price of the house is $ 853,735.05.
Step-by-step explanation:
Since Mr. Arju wishes to purchase a house, and to buy the house he needs to make a down payment of $ 300,000 and also pay $ 15,000 every quarter for the next 8 years, if the interest charge is 9% per year compounded quarterly, to determine what is the price of the house, the following calculation must be performed:
300,000 + (15,000 x 12 x 8) = X
300,000 + (180,000 x 8) = X
300,000 + 1,440,000 = X
1,740,000 = X
X x (1 + 0.09 / 4) ^ 8x4 = 1,740,000
X x (1 + 0.0225) ^ 32 = 1,740,000
X x 1.0225 ^ 32 = 1,740,000
X x 2.0381030257737 = 1,740,000
X = 1,740,000 / 2.03810
X = 853,735.05
Therefore, the price of the house is $ 853,735.05.
Evaluate 64 to the power of 2/3
Answer:
[tex]16[/tex]
Step-by-step explanation:
[tex] {64}^{ \frac{2}{3} } \\ {2}^{6 \times \frac{2}{3} } \\ {2}^{ \frac{12}{3} } \\ {2}^{4} \\ = 16[/tex]
hope this helps you
have a nice day!
Answer:
16
Step-by-step explanation:
Using the rule of exponents/ radicals
[tex]a^{\frac{m}{n} }[/tex] = [tex](\sqrt[n]{a}) ^{m}[/tex] , then
[tex]64^{\frac{2}{3} }[/tex] = [tex](\sqrt[3]{64}) ^{2}[/tex] = 4² = 16