a) If μ₁ is the average learning rate of the 6th graders without background noise level and μ₂ is the average learning rate of the 6th graders with the background noise level
The Null Hypothesis is that the learning rate of the 6th graders is not affected by the background noise level.
The null hypothesis, H₀: μ₁ = μ₂
b) The Alternative Hypothesis is that the learning rate of the 6th graders is affected by the background noise level.
An alternative hypothesis, Hа: μ₁ ≠ μ₂
c) Assumptions that must be met about the data before she can correctly use an independent t-test
There must be a random selection of the 6th graders
That the two groups are normally similar in their learning abilities
The division of students into the two groups should be at random
d) She has to make these assumptions to prevent bias and inaccuracy of results. If these assumptions are not made, the outcome of the experiment may not reflect the true effect of background noise on the learning of the 6th graders.
She can still get accurate results if she includes some bias in the selection to prove a particular result.
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math. is 1.096 x 10 ^4 the right answer?
Work Shown:
[tex]1.04 \cdot 10^4 + 5.6 \cdot 10^2\\\\10,400 + 560\\\\10,960\\\\1.096 \cdot 10^4\\\\[/tex]
Note: Something like [tex]5.6 \cdot 10^2[/tex] means we move the decimal point two spots to the right to get to 560. If the exponent was negative, then we move that many spaces to the left.
The FBI wants to determine the effectiveness of their 10 Most Wanted list. To do so, they need to find out the fraction of people who appear on the list that are actually caught. In an earlier study, the population proportion was estimated to be 0.26. How large a sample would be required in order to estimate the fraction of people who are captured after appearing on the 10 Most Wanted list at the 98% confidence level with an error of at most 0.04?
The sample size required to estimate the fraction of people who are captured after appearing on the 10 most wanted list is 228.
Given standard deviation of 0.26 ,margin of error of 0.04, and confidence interval of 98%.
We have to determine the sample size required to estimate the fraction of people who are captured after appearing on the 10 ost wanted list.
We can find the sample size with the help of margin of error.
Margin of error is the difference between the calculated values and real values.
Margin of error=z*σ/[tex]\sqrt{n}[/tex]
where σ is standard deviation,
n is sample size and z is critial z value.
We have to find the z value for 98% confidence level from z table.
z value=2.326.
Put the values in the formula of margin of error.
0.04=2.326*0.26/[tex]\sqrt{n}[/tex]
[tex]\sqrt{n}[/tex]=2.326*0.26/0.04
[tex]\sqrt{n}[/tex]=15.119
squaring both sides we get
n=228.58
By rounding we get
n=228.
Hence the sample size needed is 228.
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Over which interval are the exponential and linear function approximately the same?
hard to tell but from 0.75 to 1
In the formula d = startroot (x 2 minus x 1) squared (y 2 minus y 1) squared endroot, how does each subtraction expression relate to the pythagorean theorem?
Each subtraction expression, in relation with the Pythagoras Theorem, represents the length of one side of a right-angled triangle with a hypotenuse of length d.
What is Pythagoras Theorem?
The Pythagoras Theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the remaining two sides in a right-angled triangle.
The formula for Pythagoras Theorem is given by,
[tex]h^{2}=a^{2} +b^{2}[/tex]
Here, h is the hypotenuse, a and b are the two legs of the right-angled triangle.
Each Subtraction in view of Pythagoras Theorem
It is is given that,
[tex]d =\sqrt{(x_{2} - x_{1} )^{2}+(y_{2} -y_{1} )^{2} }[/tex]
or [tex]d^{2} =(x_{2} - x_{1} )^{2}+(y_{2} -y_{1} )^{2}[/tex]
Therefore, d is the hypotenuse and each subtraction term represents one leg of the right-angled triangle in accordance with the Pythagoras Theorem.
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Try It #4
For the function f (x) = | 2x − 1 | − 3, find the values of x such that f(x) = 0.
Answer:
x=2 or x= -1
Step-by-step explanation:
when f(x) = 0
⇒| 2x-1 | =3
case(i) (x>1/2)
2x-1=3
x=2
case(ii) (x<1/2)
-(2x-1)=3
2x-1=-3
x=-1
case(iii) (x=1/2)
[tex]0=3[/tex] absurd.
2. If (300) (30,000) = 9 x 10m, then m =
The height of a cone is twice the radius of its base.
2x
X
What expression represents the volume of the cone, in
cubic units?
O 2x³
O 47x³
Answer: O253
Step-by-step explanation:
The correct expression which represents the volume of the cone is,
V = 2x³π/3
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
The height of a cone is twice the radius of its base.
Let radius of cone = x
Then, The height of cone = 2x
Hence, The volume of cone is,
V = 1/3πr²h
V = 1/3 × π × x² × 2x
V = 2x³π/3
Thus, The correct expression which represents the volume of the cone is,
V = 2x³π/3
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The school tuck-shop has milk in 700mL and 1L cartons. If there are 60 cartons and 48L of milk in total, how many 700 mL cartons are there?
60 × 48 = 2880 L
2880 ÷ 700 = 4
Answer:
20 1 Liter Cartons
40 700 ml Cartons
Step-by-step explanation:
Let A be the number of 700ml cartons.
Let B be the number of 1 L cartons
We are told that A + B = 60 cartons total
Rearrange to isolate A: A = 60 - B
700ml is 0.700L
Total volume of milk is 48L
Total volume (in liters) of the 700 ml cartons is from (0.70 L)A
Total volume from the 1L cartons is (1 L)B
Total = (0.70)A + 1B = 48 L
Now use the rearranged equation for A in the above espression:
(0.70)A + 1B = 48 L
(0.70)(60-B) + 1B = 48 L
42 - 0.70B + B = 48
0.30B = 6
B = 20
A is 60 - B or 40
=============
CHECK:
B: 20*(1 L) = 20 L
A: 40*(0.70 L) = 28 L
Total = 48 L YES
Comparing Domain and Range
Which sets of values belong to the domain and range of a relation?
Domain
Quick
Chock
output values
values for the independent variable
input values
values for the dependent variable
Range
write the equation for a polynomial of least degree with integer coefficients given the following zeros: -2, -6, -10i. leave your answer in factored form, but make sure there are no irrational or imaginary numbers
The equation of the polynomial in factored form is (x+2)(x+6)(x-10) = 0
What is a polynomial?A polynomial is an algebraic equation with at least the power of its variable 3.
Analysis:
if -2, -6, -10i are the zeroes of the polynomial, it means x = -2, x = -6, x = -10i
if x = -2, (x+2) is a factor, (x+6) is a factor.
convert x = -10i to a real number,
i = [tex]\sqrt{-1}[/tex]
-10[tex]\sqrt{-1}[/tex] = 10[tex]\sqrt{- -1}[/tex] = 10[tex]\sqrt{1}[/tex] = 10
x = 10, so (x-10) is a factor.
Therefore equation of the polynomial in factored form is (x+2)(x+6)(x-10) = 0
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A boat can travel 408 miles on 204 gallons of gasoline how far can it travel on 169 gallons
Answer:
338 milesStep-by-step explanation:
If a boat can travel 408 miles on 204 gallons, this means that for every 2 miles, it requires 1 gallon.
So, for 169 gallons, there are 2 miles for every gallon.
So, multiply 169 * 2.
The answer is 338
Hope this helps!
In a class of 40 students, 20% are females. How many males are in the class?
Answer:
In a class of 40 students, 20% are females. How many males are in the class?
ANSWER
= 32
if in a class of 40 students 20% are females that means 80% of the class are males...
Please answer with everything needed i appreciate everyones help:)0)
Answer:
1/3
Step-by-step explanation:
please mark brainliest if correct
A tablet at a local electronics store is in high demand and will only be available to customers for a limited time. The store initially has 4 cases of the tablet on hand. The store manager receives new supplies of the tablet each week. At the beginning of week 1, the store manager receives an additional order from the distributor of 5 cases of tablets. At the beginning of week 6, the manager receives another order of 10 cases. Which of the following equations best models the scenario for how many cases of the tablet the store can expect to receive each week?
Answer:
y = x + 4
Explanation:
Initially (at week 0) = 4 cases
now (at week 1) = 5 cases
now (at week 6) = 10 cases
turn them into points:
(0, 4), (1, 5), (6, 10)Find slope:
[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
[tex]\rightarrow \sf slope \ (m) : \dfrac{5-4}{1- 0 } = 1[/tex]
Find equation:
[tex]\sf y - y_1 = m(x - x_1)[/tex]
[tex]\sf \rightarrow y-4 =1(x -0)[/tex]
[tex]\sf \rightarrow y = x +4[/tex]
How much simple interest is earned on an investment of 1,250 if the money is invested for 5 years at an annual interest rate of 4.5%
Work Shown:
i = P*r*t
i = 1250*0.045*5
i = 281.25
How to find the answer to0.291×0.34
Answer:
0.291×0.34=0.09894
Answer: 0.09894
We are going to use long division:
Simplify.
6a2−4b2+4abc−9b2−4a2+8abc
Answer:
[tex]\huge\boxed{\sf 2a^2-13b^2+12abc}[/tex]
Step-by-step explanation:
Given expression:[tex]=6a^2-4b^2+4abc-9b^2-4a^2+8abc\\\\Combine \ like \ terms\\\\=6a^2-4a^2-4b^2-9b^2+8abc+4abc\\\\=2a^2-13b^2+12abc\\\\\rule[225]{225}{2}[/tex]
Answer:
Hello! The answer is: [tex]2a^2 - 13b^2 + 12abc[/tex]
Step-by-step explanation:
[tex]6a^2 - 4b^2 + 4abc - 9b^2 - 4a^2 + 8abc[/tex]
Rearrange to combine like terms:
[tex]6a^2 - 4a^2 - 4b^2 - 9b^2 + 4abc + 8abc[/tex]
Combine like terms:
[tex]2a^2 - 13b^2 + 12abc[/tex]
A study conducted at a certain college shows that 51% of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that 5 randomly selected graduates all find jobs in their chosen field within a year of graduating. Round to the nearest thousandth if necessary.
Answer:
0.035
Step-by-step explanation:
Since all of them find a job, the probability is
[tex]51\%\times51\%\times51\%\times51\%\times51\%\\\\=(51\%)^5\\\\=0.035[/tex]
(rounded to the nearest thousandth)
A=[37], B =[²7], C = [= ² =8].
Which matrix represents (A - B) - C?
PLEASE HELP THIS IS MY LAST TEST QUESTION!!!14x^5y^4+21x^3y^2/7x^3y
Answer: =2x²y³+3y.
Step-by-step explanation:
[tex]\frac{14x^5y^4+21x^3y^2}{7x^3y} =\frac{7x^3y*(2x^2y^3+3y)}{7x^3y}= 2x^2y^3+3y.[/tex]
increase the number 1.25 by 8/25 of it
Answer: 1.65
Step-by-step explanation:
First, we must find 8/25 of 1.25. This is using multiplication.
1.25 * 8/25 = 0.4
Now, we can increase 1.25 by 8/25 of it. This is using addition.
1.25 + 0.4 = 1.65
The quotient of 7 more than three times a number m and the number 27 less than n
The given statement can be modeled as an algebraic expression (3m+7)/27 < n.
What is an Expression?In mathematics, an expression is a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The statement is given as "The quotient of 7 more than three times a number m and the number 27 less than n" can be modeled as an algebraic expression.
(3m+7)/27 < n
Hence, the given statement can be modeled as an algebraic expression (3m+7)/27 < n.
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Evaluate the expression for x = 6.
12 + 2x -
5
O A. 19
O B. 79
O C. 14
O D. 54
A scientist has 50 grams of a radioactive element. The amount of radioactive element remaining after t days can be
determined using the equation f()-50
50 (1) ³ . After two days the scientist receives a second shipment of 50 grams of the
same element. The equation used to represent the amount of shipment 2 remaining after t days is f(t)-50
(1)- 50 (2)
of the following is an equivalent form of the expression for the amount remaining in shipment 2?
•(9²
5
50.
19
t
50-(³
The option that is the equivalent form of the expression for the amount remaining in shipment 2 is the second option: 50 ([tex]\frac{1}{2} ^ \frac{t}{5} / \frac{1}{2} ^ \frac{2}{5}[/tex])
What is the radioactive element about?Note that:
f(t)= 50 (1/2)^ [tex]\frac{t-2}{5}[/tex]
f(t)= 50 (1/2)^ [tex]\frac{\frac{t}{5} } - {\frac{2}{5} }[/tex]
Note also that in indices, [tex]x^{-y}[/tex] = 1/ [tex]x^{y}[/tex]
Then: 50 ([tex]\frac{1}{2} ^ \frac{t}{5} / \frac{1}{2} ^ \frac{2}{5}[/tex])
([tex]50 \frac {1}{2} ^ \frac{t}{5} / \frac{1}{2} ^ \frac{2}{5}[/tex])
= 50 ([tex]\frac{1}{2} ^ \frac{t}{5} / \frac{1}{2} ^ \frac{2}{5}[/tex])
Therefore, The option that is the equivalent form of the expression for the amount remaining in shipment 2 is the second option: 50 ([tex]\frac{1}{2} ^ \frac{t}{5} / \frac{1}{2} ^ \frac{2}{5}[/tex])
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Simplify
(13x² +10) - 9x²
2 triangles are shown. They have one congruent side. The first triangles has angle measures of 98 degrees and 35 degrees. The second triangle has angle measures of 35 degrees and 47 degrees.
Are the triangles congruent? If so, how do you know?
yes, because all the angles of the triangles are acute
yes, because the triangles have three congruent, corresponding angles
yes, because of ASA or AAS
not enough information given
Answer:
215 is the answer of the 2 triangles
Answer: Yes because of ASA or AAS (C)
Step-by-step explanation:
Got it right on edge ")
с
Instructions: Find the value of the trigonometric ratio. Make sure to simplify the fraction
if needed.
Tan A
Check
50
30
A
40
B
Using relations in a right triangle, it is found that:
tan(A) = 3/4 = 0.75.
What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.In this triangle:
The adjacent side to A has length 40.The opposite side to A has length 30.Hence the tangent of A is:
tan(A) = 30/40 = 3/4 = 0.75.
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Clara did not want to tell Carl how old she was. All she said was that every year on her birthday, her Mom puts as many coins in her money box as how old she turned that day. Carl roughly estimated the number of coins in the box as not less that 110 but not more than 130 coins. How old is Clara?
Clara is 15 years old, and there are 120 coins on the box.
How old is Clara?Each year her mom puts as many coins in her money box as how old she turns that day.
So on her first birthday, 1 coin is put in the box.
On her second birthday, 2 coins are put in the box
And so on.
So we have the simple summation:
[tex]\sum_{n = 1} n[/tex]
We know that the outcome of that summation is a number in the interval [110, 130]
If we know that the sum goes from n = 1 to n = N (N is the age of Clara) then we can rewrite the summation as:
[tex]N*(N + 1)/2[/tex]
Now we can solve:
[tex]N*(N + 1)/2 = 110\\\\N^2 + N = 220\\\\N^2 + N - 220 = 0[/tex]
The two solutions of the quadratic equation are:
[tex]N = \frac{-1 \pm \sqrt{1^2 - 4*1*(-220)} }{2} \\\\N = (-1 \pm 29.7) /2[/tex]
If we take only the positive solution:
N = (-1 + 29.7)/2 = 14.35
Now, notice that we got this number by taking the smallest possible number of coins (110) So we can round this to the next whole number, which is 15.
If N = 15, then the number of coins in the box is:
15*(15 + 1)/2 = 120
Which lies on the wanted interval.
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Suppose a large shipment of televisions contained 19% defectives. If a sample of size 479 is selected, what is the probability that the sample proportion will be greater than 17%
The value is P(p'-p > 0.17) = 0.09
From the question we are told that
The population proportion is p=0.19
The sample size is n = 479
Generally given that the sample size is large enough , i.e n > 30 then the mean of this sampling distribution is mathematically represent
[tex]u_{x} =p=0.19[/tex]
Generally the standard deviation is mathematically represented as
σ[tex]=\sqrt{ \frac{p(1-p)}{n}[/tex]
σ= [tex]\sqrt{ \frac{0.19(1-0.19)}{479}[/tex]
σ=0.017
Generally the the probability that the sample proportion will differ from the population proportion by greater than 17% is mathematically represented as
[tex]P(p'-p > 0.17) =P (z > \frac{0.17}{0.017} )[/tex]
[tex]P(p'-p > 0.17) =P (z > 10 )[/tex]
[tex]P(p'-p > 0.17) =P (z > 10 ) - P (z > -10 )[/tex]
From the z table the area under the normal curve to the left corresponding to 10 and - 10 is
[tex]P(p'-p > 0.17) = 0.97042 - 0.87450\\P(p'-p > 0.17) = 0.09[/tex]
So, the value of probability is greater than 17% is P(p'-p > 0.17) = 0.09
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The probability that the sample proportion will be greater than 17% is 0.8677 or 86.77%.
The true proportion of the sample or the mean of the sample = 19%, that is, μ = 19% or 0.19.
The sample size (n) = 479.
The sample proportion is to be calculated at the point 17% or 0.17.
The standard error (s) = √{μ(1 - μ)/n} = √{0.19(1 - 0.19)/479} = 0.0179.
We are asked to calculate the probability that the sample proportion is greater that 17% or 0.17.
This is written as P(X > 0.17) = P(Z > {(0.17-0.19)/0.0179}) = P(Z > -1.1173) = 1 - P(Z ≤ -1.1173) = 1 - 0.1304 = 0.8696 or 86.96%.
To calculate this using the calculator, we use the calculator function:
Normalcdf(0.17,10000000,0.19,0.0179) = 0.8677 or 86.77%.
Thus, the probability that the sample proportion will be greater than 17% is 0.8677 or 86.77%.
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Simplify the expression completely.
The solution of the given expression [tex]\sqrt{7xy^7}\sqrt{21x^5y^5}[/tex]will be 7x³y⁶√3.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The given expression will be solved as follows:-
E = [tex]\sqrt{7xy^7}\sqrt{21x^5y^5}[/tex]
E = [tex]\sqrt{7\times 7\times 3\times xy^7\times x^5y^5[/tex]
E=[tex]\sqrt{7\times 7\times 3\times x^6y^{12}[/tex]
E = 7x³y⁶√3.
Therefore the solution of the given expression [tex]\sqrt{7xy^7}\sqrt{21x^5y^5}[/tex]will be 7x³y⁶√3.
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