Answer:
We accept H₀ we don´t have evidence of differences between the two toothbrushes
Step-by-step explanation:
Toothbrushes A
Sample mean μₐ = 119,7
Standard deviation sₐ = 1,74
Sample size nₐ = 18
Toothbrushes B
Sample mean μ₀ = 120,6
Standard deviation s₀ = 1,72
Sample size n₀ = 15
With CI = 90 % CI = ( -1,93 ; 0,13 ) that s the acceptance region for H₀
Test hypothesis is
H₀ μₐ = μ₀
Hₐ μₐ ≠ μ₀
We need to calculate t(s) as
t(s) = ( μₐ - μ₀ ) /Sₓ * √ (1/nₐ) + 81/n₀)
and see if it is insde CI
Sₓ = (nₐ - 1 ) * sₐ² + ( n₀ - 1 ) * s₀² / nₐ + n₀ - 2
Sₓ = 17*3,03 + 14*2,96 / 31
Sₓ = (51,51 + 41,44 )/ 31
Sₓ = 2,998
t(s) = 0,9 / 2,998*√(1/18) + (1/15)
t(s) = 0,9 / 1,04
t(s) = 0,87
In a bag, the ratio of red beads to blue beads is 3∶ 5. Beads are added to the bag, but the ratio of red beads to blue beads remains the same.
In this question, we use the ratio given to complete the table.
Doing this, the completed table is:
3 - 5 - 8
6 - 10 - 16
9 - 15 - 24
12 - 20 - 32
60 - 100 - 160
75 - 125 - 200
In a bag, the ratio of red beads to blue beads is 3∶5.
This means, that for each 3 beads, there are 5 blue beads, and for each 8 beads, there are 3 red and 5 blue.
Third line:
15 blue, the amount of red is 3/5 of this, so:
[tex]\frac{3}{5}(15) = 3(3) = 9[/tex]
Thus, there are 9 red, 9 + 15 = 24, and thus, the third line is:
9 - 15 - 24
Fourth line:
32, 3/8 are red and 5/8 are blue, so:
[tex]\frac{3}{8}(32) = 3(4) = 12[/tex]
[tex]\frac{5}{8}(32) = 5(4) = 20[/tex]
Thus, the fourth line is:
12 - 20 - 32
Fifth line:
100 blue, the amount of red is 3/5 of this, so:
[tex]\frac{3}{5}(100) = 3(20) = 60[/tex]
60 + 100 = 160
Thus, the fifth line is:
60 - 100 - 160
Sixth line:
75 red, the amount of blue is 5/3 of this, so:
[tex]\frac{5}{3}(75) = 5(25) = 125[/tex]
75 + 125 = 200.
Thus, the sixth line is:
75 - 125 - 200
The complete table is:
3 - 5 - 8
6 - 10 - 16
9 - 15 - 24
12 - 20 - 32
60 - 100 - 160
75 - 125 - 200
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PLEASE HELP!!!!!! I AM BEING TIMED!!!!
A garden hose fills a 2 gallon bucket in five seconds the number of gallons G is the proportional to the number of seconds T that the water is running select all the equations that represent the relationship between G and T
Answer:
A and E
Step-by-step explanation:
um for some reason my answer was deleted…
anyways, I think its A and E because the equation should be g = 2/5t and 0.4 is equal to 2/5 so that means that E is also correct.
Find the value of the following expression:
(28 ⋅ 3−5 ⋅ 60)−2 ⋅ 3 to the power of negative 2 over 2 to the power of 3, whole to the power of 4 ⋅ 228 (5 points)
Write your answer in simplified form. Show all of your steps.
Answer:
9Step-by-step explanation:
(2⁸ ⋅ 3⁻⁵ ⋅ 6⁰)⁻² ⋅ (3⁻²/2³)⁴ ⋅ 2²⁸ =2⁻¹⁶·3¹⁰·3⁻⁸·2⁻¹²·2²⁸ =2⁻¹⁶⁻¹⁰⁺²⁸ · 3¹⁰⁻⁸ =2⁰ · 3² =1 · 9 =9Which expression is equivalent to StartFraction 1 Over sine (2 x) EndFraction minus StartFraction cosine (2 x) Over sine (2 x) EndFraction?
tan(x)
–tan(x)
StartFraction 1 Over cosine (x) EndFraction
Negative StartFraction 1 Over cosine (x) EndFraction
Answer:
Tan(x)
Step-by-step explanation:
JUST TOOK THE TEST
tan(x) is equivalent to 1/sin2x - cos2x/sin2x. Option a is correct.
To determine equivalent 1/sin2x - cos2x/sin2x.
tan(x) is tangent of x here, tan is trigonometric operator.
Here,
= 1/sin2x - cos2x/sin2x
= (1-cos2x)/sin2x
= (2sin²x)/2sinxcosx
= sin(x)/cos(x)
= tan(x)
Thus, tan(x) is equivalent to 1/sin2x - cos2x/sin2x.
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BRAINLIST ASAP
san was charged $1,050 in interest on a loan with a 2.5% interest rate. what was the original amount of the loan if he took 5 years to pay it?
What is the quotient of the rational expressions shown below? Make sure
your answer is in reduced form.
x2 + 5x +6/x-6/x^2-9/2x-12
Picture of the right answers
Hence, the quotient of the rational expression given below is x-3.
How to solve?
To solve the division we will use basic properties of rational numbers here.
The first step is to factor numerator/denominator if possible.
To divide the expressions follow the following steps
1.leave the first fraction as it is
2. Convert division to multiplication
3.Turn the second fraction upside down
([tex]x^{2}[/tex]+5x+6)/x-6 / ([tex]x^{2}[/tex]-9)/2x-12
=([tex]x^{2}[/tex]+5x+6)(2(x-6))/([tex]x^{2}[/tex]-9)(x-6)
=2([tex]x^{2}[/tex]+5x+6)/[tex]x^{2}[/tex]-9
By splitting the quadratic equation into factors we get,
[tex]x^{2}[/tex]+5x+6=(x+2)(x+3)
and using the formula [tex]a^{2}[/tex]-[tex]b^{2}[/tex]=(a-b)(a+b) we get [tex]x^{2}[/tex]-9=(x-3)(x+3)
=2(x+3)(x+2)/(x+3)(x-3)
=2(x+2)/(x-3)
hence, the quotient of the given ration expression is x-3.
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Stephen imports cars from the USA. He sells them in the UK. He has just bought a car in the USA costing $24 000. It cost him £900 to import the car to the UK. The exchange rate is £1 = $1.45. Stephen needs to make a profit of 20% on his total costs.
Work out the least amount that Stephen must sell the car for in the UK. Give your answer in pounds.
Answer:
£20942.04
Step-by-step explanation:
The total cost of the car includes its purchasing price and the cost of importing it into the UK.
Cost of the car in pounds = 24000/1.45 = £16,551.7
Total cost of the car = £16,551.7 + £900 = £17,451.7
If the profit made is 20%
Then;
Profit % = selling price - cost price/cost price * 100/1
Let selling price = SP
Cost price = CP
20 = SP - CP/CP * 100/1
20 = SP - 17,451.7/17,451.7 * 100/1
17,451.7 (20) = 100(SP - 17,451.7)
349034 = 100SP - 1745170
349034 + 1745170 = 100SP
2094204 = 100SP
SP = £20942.04
Hmmm , can someone help with this one?
Answer:
answer choice c
Step-by-step explanation:
V = 2s^3
If s = 3.5 units, what is the value of V? The photo shows the answers available.
Answer:
21.0 Cubic Units
Step-by-step explanation:
2 times 3.5 = 7
7 times 3 = 21
You wonder if one's age is independent of whether or not one's willingness to wear masks in public. You ask 100 people whether they are wearing masks in public or not and whether they are under 20 years old, between 20 and 39, between 40 and 59, or 60 or above. Using your data, you calculate a test statistic of 16.5. Using a critical value of 7.82, what is your statistical conclusion
Answer:
One's age is not independent of one's willingness to wear masks in public.
Step-by-step explanation:
The hypothesis for the study can be defined as follows:
H₀: One's age is independent of one's willingness to wear masks in public.
Hₐ: One's age is not independent of one's willingness to wear masks in public.
It is provided that the test statistic value is, t = 16.5.
And the critical value of the test is, c = 7.82.
t = 16.5 > c = 7.82
Since the test statistic value is more than the critical value, the null hypothesis will be rejected.
Thus, concluding that one's age is not independent of one's willingness to wear masks in public.
John believes that height is related to leadership and specifically hypothesizes that the taller one is, the more other people look to that person as a leader. To test this hypothesis, he randomly selects a sample of 50 people, and measures their height and perceived leadership potential (both quantitative measures). This is a ______ hypothesis and will result in a(n) _______ -tailed test
Answer:
This is a __simple____ hypothesis and will result in a(n) _______one-tailed test.
Step-by-step explanation:
The Simple Hypothesis predicts the relationship between two variables, in this case, height and leadership. The one-tailed test will be performed to determine whether to reject the null hypothesis. This is why the null and alternative hypotheses must be established before the statistic test is carried out. If the null hypothesis is rejected, this simply results in the acceptance of the alternative hypothesis.
I need help please but if you can give me the step by step it would be helpful thank you
Answer: (x^2 -6x +10)(x - 2)
All the steps are shown in the picture below:
Solve the proportion.
47/39 = b/2
A: 94/39
B: 78/47
C: 47/78
D: 39/94
Answer:
94/39 is the correct answer
Answer:
The answer above is correct! A. 94/39
Step-by-step explanation:
E2020!
Write the given expression as a single trigonometric function.
StartStartFraction tangent (StartFraction 3 pi Over 7 EndFraction) minus tangent (StartFraction 2 pi Over 5 EndFraction) OverOver 1 + tangent StartFraction 3 pi Over 7 EndFraction) tangent (StartFraction 2 pi Over 5 EndFraction) EndEndFraction
Answer:
tan (pi/35)
Step-by-step explanation:
edge 2020
The expression [tan (3π/7) - tan (2π/5)] / [1 + tan (3π/7) × tan (2π/5)] as a single trigonometric function will be tan (29π / 35).
What is trigonometry?Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The trigonometric function is given below.
⇒ [tan (3π/7) - tan (2π/5)] / [1 + tan (3π/7) × tan (2π/5)]
We know that the formula,
tan (a + b) = [tan a - tan b] / [1 + tan a) × tan b]
Then the expression is written as,
⇒ [tan (3π/7) - tan (2π/5)] / [1 + tan (3π/7) × tan (2π/5)]
⇒ tan [(3π/7) + (2π/5)]
⇒ tan (29π / 35)
The expression [tan (3π/7) - tan (2π/5)] / [1 + tan (3π/7) × tan (2π/5)] as a single trigonometric function will be tan (29π / 35).
More about the trigonometry link is given below.
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Does anyone know this?
Answer:
its first one
Step-by-step explanation:
37.5/15=2.5
42.5/17=2.5
52.5/21=2.5
What are the first three terms of the Arithmetic Sequence an = 12 – 2(n – 1)?
Group of answer choices
11, 10, 9
12, 10, 8
0, 10, 20
1, 2, 3
Answer:
The first 3 choices are:
12, 10, 8
Step-by-step explanation:
n represents a variable, in which you start at 1 and increase by 1.
So, we first start at 1.
12 - 2(1 - 1) = 12 - 2(0) = 12
Now, 2.
12 - 2(2 - 1) = 12 - 2(1) = 10
Now, 3.
12 - 2(3 - 1) = 12 - 2(2) = 8
So, we result in 12, 10, and 8.
#teamtrees #WAP (Water And Plant)
Answer:
B
Step-by-step explanation:
an = 12 - 2(n - 1)
a1 = 12 - 2(0)
a1 = 12
==============
a2 = 12 - 2(2 - 1)
a2 = 12 - 2
a2 = 10
==============
a3 = 12 - 2(3-1)
a3 = 12 - 2*2
a3 = 8
I think B must be the correct answer. I don't think you can start with n = 0 but the question should qualify that.
In parallelogram MNPT, MZM - (6x + 10% and m2N - (5x + 10.5. How many
degrees is ZT?
True or False? A circle could be circumscribed about the quadrilateral below.
OA. True
OB. False
Answer:
True
Step-by-step explanation:
The solution is, OA. True, A circle could be circumscribed about the quadrilateral below.
What is circle?A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “centre”. The perimeter around the circle is known as the circumference.
here, we have,
from the given diagram, we get,
the angles of each side = 90 degree
and, as per shape, it is a rectangle.
now, we know that,
If opposite angles of a quadrilateral add to 180 then it is called a cyclic quadrilateral and a circle can be inscribed in it.
now, we get,
Here, the opposite sides are 90 and 90 (=180),
so, we have,
which means that it is true that a circle can be circumscribed about the quadrilateral above.
Hence, The solution is, OA. True, A circle could be circumscribed about the quadrilateral below.
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what was josquin des prez 3 favorite pieces?
Answer:
While in Ferrara, Josquin wrote some of his most famous compositions, including the austere, Savonarola-influenced Miserere, which became one of the most widely distributed motets of the 16th century; the utterly contrasting, virtuoso motet Virgo salutiferi; and possibly the Missa Hercules Dux Ferrariae, which is ...
Step-by-step explanation:
fill in the blank pls i need help
Answer:
x=5
y=30
y=15
Step-by-step explanation:
Many track runners believe that they have a better chance of winning if they start in the inside lane that is closest to the field. For the data below, the lane closest to the field is Lane 1, the next lane is Lane 2, and so on until the outermost lane, Lane 6. The data lists the number of wins for track runners in the different starting positions. Calculate the chi-square test statistic to test the claim that the number of wins is uniformly distributed (equally likely) across the different starting positions. The results are based on 240 races.
This question is incomplete, the complete question is;
Many track runners believe that they have a better chance of winning if they start in the inside lane that is closest to the field. For the data below, the lane closest to the field is Lane 1, the next lane is Lane 2, and so on until the outermost lane, Lane 6. The data lists the number of wins for track runners in the different starting positions. Calculate the chi-square test statistic to test the claim that the number of wins is uniformly distributed (equally likely) across the different starting positions. The results are based on 240 races.
starting position: 1 2 3 4 5 6
Number of wins : 44 33 50 32 45 36
options
a) 15.541
b) 9.326
c) 6.750
d) 12.592
Answer:
the chi-square test statistic is 6.75
Option c) 6.750 is the correct answer
Step-by-step explanation:
Given that;
starting position: 1 2 3 4 5 6
Number of wins : 44 33 50 32 45 36
Given that we have 240 races
Using x² test.
we have to calculate the expected frequency
so
E(1) = 240 × 1/6 = 40
E(2) = 240 × 1/6 = 40
E(3) = 240 × 1/6 = 40
E(4) = 240 × 1/6 = 40
E(5) = 240 × 1/6 = 40
E(6) = 240 × 1/6 = 40
Now we know that,
x²_cal = [∑( Oi - Fi)²] / Fi
so
x²_cal = (44-40)²/40 + (33-40)²/40 + (50-40)²/40 + (32-40)²/40 + (45-40)²/40 + (35-40)²/40
= 0.4 + 1.225 + 2.5 + 1.6 + 0.625 + 0.4
= 6.75
Therefore the chi-square test statistic is 6.75
Option c) 6.750 is the correct answer
the unit rate of 55 and 8
Answer:6.875
Step-by-step explanation:
Find the number between 100 and 999 such that
the sum of the three digits is 12.
the hundreds digit equals the sum of the tens digit and the ones digit.
the hundred digit equals one greater than the tens digit.
-4x + 10y
X=5
Y=7
Find the value of the algebraic expression
Answer:
50
Step-by-step explanation:
-20+70=50
Help help help help help
Answer:
Option 1 and the bottom right answer.
Step-by-step explanation:
Use 50% as the percentage amount taken off of 199.99. Please help me
Answer:
199.49
Step-by-step explanation:
Answer:
199.49
Step-by-step explanation:
Hope this helped have an amazing day!
lIf f) = 6x -4, what is f(x) when x= 8?
answer the question in the photo , its the easy one please help me ;((
9514 1404 393
Explanation:
The problem statement tells you what to do.
25^(n-1) +125 -6·5^n = 0 . . . . . subtract 6·5^n
(5^2)^(n-1) -6·5^n +125 = 0 . . . . express 25 as a power of 5
5^(2n-2) -6·5^n +125 = 0 . . . . . eliminate the double layer of exponent
(5^-2)(5^n)^2 -6·5^n +125 = 0 . . . . . use 5^n where possible
(1/25)y^2 -6y +125 = 0 . . . . . . . substitute y = 5^n
y^2 -150n +3125 = 0 . . . . . . . . . multiply by 25
_____
The applicable rules of exponents are ...
(a^b)^c = a^(bc)
(a^b)(a^c) = a^(b+c)
a^-b = 1/a^b
help me on this question please
Answer:
7 6/18
Step-by-step explanation:
Answer:
3.71851851852
Step-by-step explanation:
The average size of single-family homes in the U.S. is 2,390 square feet. A random sample of 100 homes in California yielded the mean of 2,507 square feet and the standard deviation of 257 square feet. Do the sample data provide sufficient evidence to conclude that the mean size of California homes exceeds the national average? Test using significance level of 0.01. (7 Points)
Answer:
The decision rule is
Reject the null hypothesis
The conclusion is
There is sufficient evidence to conclude that the mean size of California homes exceeds the national average
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 2390 \ ft^2[/tex]
The sample size is n = 100
The sample mean is [tex]\= x = 2 507 \ ft^2[/tex]
The standard deviation is [tex]s = 257 \ ft^2[/tex]
The level of significance is [tex]\alpha = 0.01[/tex]
The null hypothesis is [tex]H_o : \mu = 2390[/tex]
The alternative hypothesis is [tex]H_a : \mu > 2390[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{ \= x - \mu }{ \frac{s}{ \sqrt{n} } }[/tex]
=> [tex]z = \frac{2507 - 2390 }{ \frac{ 257 }{ \sqrt{100 } } }[/tex]
=> [tex]z = 4.55[/tex]
From the z table the area under the normal curve to the left corresponding to 4.55 is
[tex]p-value = P( X > 4.55 ) = 0.00[/tex]
From the value obtained we see that [tex]p-value < \alpha[/tex] hence
The decision rule is
Reject the null hypothesis
The conclusion is
There is sufficient evidence to conclude that the mean size of California homes exceeds the national average