when bonding teeth, orthodontists must maintain a dry field. a new bonding adhesive has been developed to eliminate the necessity of a dry field. however, there is concern that the new bonding adhesive is not as strong as the current standard, a composite adhesive. tests on a sample of extracted teeth bonded with the new adhesive resulted in a mean breaking strength (after 24 hours) of mpa and a standard deviation of s mpa. orthodontists want to know if the true mean breaking strength is less than mpa, the mean breaking strength of the
Answers
When we compare the p-value and the significance level is given \(\alpha=0.01\), we can see that \(p_v < \alpha\), so we can conclude that we have enough evidence to reject the null hypothesis, which is less than 5.7 Mpa at 1% significance.
Given:
\(\bar{X}=5.07\) display the sample means = 0.46 represent the standard deviation of the samplen = 10 size of the sample\(\mu_o=5.7\) represent the value under consideration\(\alpha=0.01\) represent the hypothesis test's significance levelThe statistic would be represented by t. (variable of interest)\(p_v\) represent the test's p-value (variable of interest)Identify the null and alternative hypotheses.
We need to test a hypothesis to see if the true mean is less than 5.7 Mpa; the hypothesis system would be:
Null hypothesis: \(\mu \geq 5.7\)Alternative hypothesis: \(\mu < 5.7\)If the sample size is 30 and we don't know the population deviation, we should use a t-test to compare the actual mean to the reference value, and the statistic is given by:
\(t=\frac{X-\mu_0}{\frac{s}{\sqrt{n}}}\) ......(1)The t-test: "Is one of the most common tests for determining whether the mean is (higher, lower, or not equal) to a specified value."
Determine the statistic
We can substitute the following information in formula (1):
\(t=\frac{5.07-5.7}{\frac{11.40}{\sqrt{30}}}=-4.33\)P-value:
The first step is to compute the degrees of freedom, which in this case are:
\(d f=n-1=10-1=9\)Because this is a one-sided lower-tailed test, the p-value would be:
\(p_v=P\left(t_{(9)} < -4.33\right)=0.00095\)Therefore, when we compare the p-value and the significance level given \(\alpha=0.01\), we can see that \(p_v < \alpha\), so we can conclude that we have enough evidence to reject the null hypothesis, which is less than 5.7 Mpa at 1% significance.
Know more about the null hypothesis here:
https://brainly.com/question/23413408
#SPJ4
The complete question is given below:
When bonding teeth, orthodontists must maintain a dry field. A new bonding adhesive (called "Smartbond") has been developed to eliminate the necessity of a dry field. However, there is concern that the new bonding adhesive is not as strong as the current standard, a composite adhesive. ( Trends in Biomaterials & Artificial Organs, Jan. 2003.) Tests on a sample of 10 extracted teeth bonded with the new adhesive resulted in a mean breaking strength (after 24 hours) of x = 5.07 Mpa and a standard deviation of s = 0.46 Mpa, where Mpa = megapascal, a measure of force per unit area. Orthodontists want to know if the true mean breaking strength of the new bonding adhesive is less than 5.70 Mpa, the mean breaking strength of the composite adhesive. Conduct the appropriate analysis for the orthodontists. Use alpha= 0.01. What is the p-value?
Related Questions
Help please!
Area= ______in^2
Answers
Therefore, the area of the trapezoid is 6 square inches.
What is area?Area is a measure of the size of a two-dimensional surface or shape, such as a square, rectangle, circle, triangle, or any other polygon. It is usually measured in square units, such as square inches, square feet, square meters, or square centimeters. The area of a shape is calculated by multiplying the length of one side of the shape by the length of an adjacent side.
Here,
The formula for the area of a trapezoid is:
Area = (1/2) x (sum of parallel sides) x height
In this case, the parallel sides are 1.1 inches and 2.9 inches, and the height is 3 inches. So we can substitute these values into the formula and calculate the area:
Area = (1/2) x (1.1 + 2.9) x 3
Area = (1/2) x 4 x 3
Area = 6 square inches
To know more about area,
https://brainly.com/question/13194650
#SPJ1
Elwood invested $5,000 in a money market account and has been tracking its progress. He found that after 3 years, the account held $7,100 and after 8 years, the account held $10,350.
Answers
Answer:
The percent of interest is 12.3% per year
Step-by-step explanation:
According to the question Elwood invested 5000 $ in market account
The market account gives the compound interest annually
let p be the interest per year then
At the end of 1st year
amount =(1+0.p) x 5000 = 1.p x 5000
similarly at the end of 2nd year
amount =(1+0.p) x(1+0.p)x 5000 = \((1.p)^{2}\) x 5000
similarly at the end of 3rd year
amount = 7100 $ = \((1.p)^3\) x 5000
⇒ \(\frac{71}{50}\) = \((1.p)^3\)
1.392 = \((1.p)^3\)
on further solving we get
1.p = \((1.42)^{1/3}\) = 1.123
thus 1.p = 1 + 0.p = 1.123
thus p = 0.123
thus the percent of interest is 12.3% per year
Answer:
drop down 1 a slower rate per year
drop down 2 670
Step-by-step explanation:
as in three years you get $7100
you take that and subtract it by your starting amount (5000)
7100-5000= 2100
then divide 2100 by the number of years (3)
to get your annual rate of 700$
then you take the 8 year total and subtract it from your 3 year total
10350-7100= 3250
Then divide that by 5 because that how many years it has been
to get the annual rate of 650
making the 5 year rate slower.
The to find the average rate over all 8 year you take 10350 and subtract it from your starting number 5000
10350-5000= 5350
then take 5350 and divide it by the number of years (8)
you then get you average rate of 668.75
668.75=670
Hope this helps!
FIRST ANSWER GETS BRAINLIEST! (WILL ONLY COUNT IF YOU ANSWER CORRECTLY)
You are purchasing a car for $12,465.00 plus 5.65% sales tax. You make a $1,300.00 down payment and have a fair credit score. If you improved your credit score to good and paid $1,500 on your purchase, how much interest could you save in the first month?
Secured Unsecured
Credit APR (%) APR (%)
Excellent 4.75 5.50
Good 5.00 5.90
Average 5.85 6.75
Fair 6.40 7.25
Poor 7.50 8.40
A) $14.68
B) $13.25
C) $25.69
Answers
Answer:
A
Step-by-step explanation:
A store owner wants to develop a new snack mix by mixing chocolate and trail mix. how many pounds of chocolate costing $20.10 per pound should be mixed with 25 pounds of trail mix costing $2.80 per pound to create a mixture worth $8.41 per pound.
Answers
If a store owner wants to develop a new snack mix by mixing chocolate and trail mix, then the number of pounds of chocolate costing $20.10 per pound that should be mixed with 25 pounds of trail mix costing $2.80 per pound to create a mixture worth $8.41 per pound is equal to 11.99.
The pounds of chocolate needed to create a mixture worth $8.41 per pound can be calculated using an algebraic expression.
An algebraic expression can be defined as an expression consisting of both numbers and letters.
If x = the unknown pounds of chocolate
An algebraic expression can be given as,
20.10x + 2.80(25) = 8.41(x + 25)
Solving for x,
20.10x + 70 = 8.41x + 210.25
Rearranging,
20.10x - 8.41x = 210.25 - 70
11.69x = 140.25
x = 140.25 ÷ 11.69
x = 11.99
Hence, 11.99 pounds of chocolate costing $20.10 per pound should be mixed with 25 pounds of trail mix costing $2.80 per pound to create a mixture worth $8.41 per pound.
To learn more about algebraic expressions, click here:
https://brainly.com/question/4344214
#SPJ4
The image of the point (8,1) under a translation is (9,2). Find the coordinates of
the image of the point (5,5) under the same translation.
Answers
1-2-3-4-5-6-7-8-9-10
0.10)/%
simplify
(8p^6)^1/3
simplifyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy
Answers
Answer:
\(2p^2\)
Step-by-step explanation:
Step 1: Apply the exponentiation property:
\((8p^6)^\frac{1}{3} = 8^\frac{1}{3} * (p^6)^\frac{1}{3}\)
Step 2: Simplify the cube root of 8:
The cube root of 8 is 2:
\(8^\frac{1}{3} =2\)
Step 3: Simplify the cube root of \((p^6)\):
The cube root of \((p^6)\) is \(p^\frac{6}{3} =p^2\)
Step 4: Combine the simplified terms:
\(2 * p^2\)
So, the simplified expression is \(2p^2\).
If the population of the small town is currently 8,500 people, how many years will it take for the population to reach 5,500 people
Answers
If the population of the small town is currently 8,500 people, then 4.06 years will it take for the population to reach 5,500 people.
To find the number of years it will take for the population of the small town to reach 5,500 people from the current 8,500 people, we can use the formula for exponential decay which is:
P(t) = P₀e^(kt)
Where:
P₀ = initial population
P(t) = population after time t
k = growth/decay constant
To solve for the number of years it will take for the population to reach 5,500 people, we need to use the exponential decay formula and solve for t when P(t) = 5,500, P₀ = 8,500, and k is negative since the population is decreasing.
P(t) = P₀e^(kt)
5500 = 8500e^(kt)
Divide both sides by 8500.5500/8500 = e^(kt)
Take the natural logarithm of both sides to isolate k.
ln(5500/8500) = ln(e^(kt))
ln(5500/8500) = kt
Divide both sides by k.
ln(5500/8500)/k = t
Approximately, t ≈ 4.06
Therefore, it will take approximately 4.06 years for the population of the small town to reach 5,500 people.
To learn more about population: https://brainly.com/question/29885712
#SPJ11
l = [?] ft
9 ft
4ft
PLEASE HELP MEMEMEMEME
![l = [?] ft9 ft4ftPLEASE HELP MEMEMEMEME](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/Ziuw24pcx3neMWY8i7kFigk4DiBA4BLK.png)
Answers
Click an item in the list of groups of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place.
What is the equation of the exponential graph shown
Answers
An equation is formed of two equal expressions. The equation of the exponential graph is A=100(0.5)ˣ.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The equation of an exponential function is given by the formula,
y = A (B)ˣ
Now as per the graph, there are two points (1, 50) and (2, 25).
50 = A (B)¹
50 = AB
A = 50/B
Substitute another point in the equation,.
25 = A (B)²
25 = (50/B) (B)²
25 = 50B
B = 0.5
Substitute the value of B,
A = 50/0.5 = 100
Hence, the equation of the exponential graph is A=100(0.5)ˣ.
Learn more about Equation:
https://brainly.com/question/2263981
#SPJ1
How do I solve this?
x^2 + 8x - 4 = 0
Answers
Answer: -2(2 + sqrt(5)) and -2(2 - sqrt(5))
Step-by-step explanation:
We'd want to use the quadratic formula, because there's no two numbers that add to 8 and multiply to equal -4.
Recall that the quadratic formula is:
\(x=\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)
Each letter corresponds to:
ax^2 + bx + c
So, if we were to put in the values corresponding into the function, it would look like:
\(\frac{-8 \pm \sqrt{64 +16}}{2}\)
This should give us the answer of:
-2(2 + sqrt(5)) and -2(2 - sqrt(5))
find the greatest common factor
Answers
HELP! 7th grade math! GIVE CORRECT ANSWER AND YOU WILL GET BRAINLIEST!!
Answers
Answer:
ED = 4 units
Step-by-step explanation:
Observing the figure given to us, we can deduce the following:
=>CE = EA (because point E is the midpoint of CA)
Therefore, if CE = EA = x unit, CA = 2x
=>Also, CD = DB (because point D is the midpoint of CB)
Therefore, if CD = DB = y, CB = 2y
Thus, CA/CE = CB/CD = 2 (2x/x = 2y/y)
Going by the above ration we got comparing the ratio of the corresponding sides of ∆CAB and ∆CED (2:1), we can conclude that ∆CAB ~ ∆CED
Using the ratio of the corresponding sides of ∆CAB to ∆CED = (2:1), measure of segment ED is calculated below:
AB/ED = 2/1
8/ED = 2/1
Cross multiply
8 × 1 = 2 × ED
Divide both sides by 2
8/2 = ED
ED = 4 units
Pierre has more money than alex.
if Pierre gave Alex £20 they would have the same amount.
if Alex gave Pierre £22, the Pierre would have twice as much as Alex.
How much does each one actually have?
Answers
Answer:
p = 2a-22
a= p-20
these will help you find the actual value
Step-by-step explanation:
this is not for the actual value
pierre = p
alex = a
p = a+20
p-20 = a
p+22 = 2a
p = 2a-22
If x/y + y/x = -1 , find the value of x^3 - y^3
Answers
Answer:
0
Step-by-step explanation:
Multiplying the first equation by xy, we have ...
x^2 +y^2 = -xy
Factoring the expression of interest, we have ...
x^3 -y^3 = (x -y)(x^2 +xy +y^2)
Substituting for xy using the first expression we found, this is ...
x^3 -y^3 = (x -y)(x^2 -(x^2 +y^2) +y^2) = (x -y)(0) = 0
The value of x^3 -y^3 is 0.
Evaluate the expression −x^2 + 2x-7 when X=-4
Answers
-(-4)^2+2(-4)-7
-16-8-7
=-31
I took this today and just want to know how to do it next time I get a problem like this
Answers
In the given figure,
In triangle DEF,
\(\tan 45^{\circ}=\frac{12}{EF}\Rightarrow EF=12\)\(\sin 45^{\circ}=\frac{12}{DF}\Rightarrow\frac{1}{\sqrt[]{2}}=\frac{12}{DF}=DF=12\sqrt[]{2}\)The length of DF is
\(12\sqrt[]{2}\)Now in triangle DFG,
\(\tan 45^{\circ}=\frac{DF}{FG}=\frac{12\sqrt[]{2}}{FG}\)\(FG=12\sqrt[]{2}\)The length of FG is
\(12\sqrt[]{2}\)Now apply Pythagoras theorem to determine DG,
\(DG^2=(12\sqrt[]{2})^2+(12\sqrt[]{2})^2\)\(DG^2=288+288=576\)\(DG=\sqrt[]{576}=24\)The length of DG is 24.
need asap solve for x
Answers
Answer:
answer is 25
Step-by-step explanation:
x+2+153=180
x+155=180
x=180-155
x=25
hope this helps :)
Which function is represented by this graph?
Answers
Answer:
the 2nd one
Step-by-step explanation:
Answer:
the 2nd One
Step-by-step explanation:
I'm not sure if I'm right
this is due in a few hours send help
Rewrite each equation in standard form.
2. y = 6x - 4
3. y -2=-(x + 7)
Answers
Hi I Know the 2 Number Only So Here is that amswer
6x-y=4
What value of x is in the solution set of 8x – 6 > 12 + 2x?
(answer choices are -1, 0, 3, 5)
Answers
Answer:
\(Given:\)
\(8x-6 > 12 + 2x\)
\(8x-2x>12+6\)
\(6x>18\)
\(x>18/6\)
\(x>3\)
\(5>3\)
\(ANSWER: D)\:5\)
------------------------
Hope it helps...
Have a great day!!
will mark branliest!
A sand dune stands 5 feet above sea level. The hill is eroding at a rate of 1 foot per 20 years. Let y represent the height of the sand dune after x years. Which equation represents the situation?
a. y=-1/20x-5
b.y=-1/20x+5
c.-20x-5
d.y=-20x+5
Answers
Answer:
The given 5 feet above sea level could be taken as the y-intercept, while the rate of -1 foot per 20 years could be taken as the slope. The height y is a function of time. Using y-intercept slope form of a line: Y = (-1/20)t + 5
Step-by-step explanation:
magic
The equation for height of the sand dune is y = -1/20 x + 5.
Thus, option B. y = -1/20 x + 5 is correct.
Given,
Height of sand dune = 5 feet above sea level
Erosion rate = 1 foot / 20 years
Let y represent the height of the sand dune after x years.
Here, the erosion rate shows the rate of change or slope.
So, Slope = -1/20.
( the negative sign shows the erosion or decrease in sand.)
Since the initial height of sand dune, b = 5 feet.
Using the slope intercept form formula
\(y= mx + b\)
where m = -1/20 and b = 5 feet.
Substituting the value of m and b in equation y= mx+b as
y = -1/20 x + 5.
Therefore, the required equation is y = -1/20 x + 5.
Learn more about Slope intercept form here:
https://brainly.com/question/29146348
#SPJ7
solve the following heat equation: ut(x, t) = uxx(x, t) u(0, t) = u(1, t) = 0 u(x, 0) = f (x)
Answers
The given heat equation, ut(x, t) = uxx(x, t), subject to boundary conditions u(0, t) = u(1, t) = 0 and initial condition u(x, 0) = f(x), can be solved using separation of variables and Fourier series.
The heat equation is given as ut(x, t) = uxx(x, t), subject to the boundary conditions u(0, t) = u(1, t) = 0 and the initial condition u(x, 0) = f(x).
1. Assume a separable solution: u(x, t) = X(x)T(t), where X(x) represents the spatial component and T(t) represents the temporal component.
2. Substitute the assumed solution into the heat equation:
X(x)T'(t) = X''(x)T(t).
3. Divide both sides of the equation by X(x)T(t) to separate the variables:
T'(t)/T(t) = X''(x)/X(x) = -λ².
4. Solve the temporal equation T'(t)/T(t) = -λ²:
Integrate both sides with respect to t:
∫ (1/T)dT = -λ² ∫ dt.
ln|T(t)| = -λ²t + C₁, where C₁ is a constant of integration.
Exponentiate both sides:
T(t) = C₁exp(-λ²t).
5. Solve the spatial equation X''(x)/X(x) = -λ²:
X''(x) + λ²X(x) = 0.
The boundary conditions u(0, t) = u(1, t) = 0 imply that X(x) must satisfy X(0) = X(1) = 0.
The solutions to the spatial equation are given by X(x) = sin(nπx), where n is a positive integer.
6. Combine the temporal and spatial components to obtain the general solution:
u(x, t) = ΣCₙsin(nπx)exp(-n²π²t), where Σ represents the summation over all positive integers n.
7. To determine the coefficients Cₙ, we use the initial condition u(x, 0) = f(x):
Substitute t = 0 into the general solution:
u(x, 0) = ΣCₙsin(nπx) = f(x).
Compare the Fourier sine series expansion of f(x) with the general solution to find the coefficients Cₙ.
In conclusion, the solution to the given heat equation ut(x, t) = uxx(x, t) with boundary conditions u(0, t) = u(1, t) = 0 and initial condition u(x, 0) = f(x) involves separating the variables, solving the resulting differential equations, and determining the coefficients using the Fourier sine series.
Learn more about heat equation visit
brainly.com/question/28205183
#SPJ11
Since the question is incomplete, so complete question is:
find the value of x,y,z
Answers
Answer:
x y z are all equal to 60 because it on a line
Answer:
Step-by-step explanation:
40 + x + 80 = 180 degree (being linear pair)
120 + x = 180
x = 180 - 120
x = 60 degree
y + 120 = 180 degree (being linear pair)
y = 180 - 120
y = 60 degree
70 + 50 + z = 180 degree (being linear pair)
120 + z = 180
z = 180 - 120
z = 60 degree
x + y + z = 180 degree (being linear pair)
Note : A linear pair is a pair of adjacent angles formed when two lines intersect.
What is the answerrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr
Answers
Answer:
$1559.40
Step-by-step explanation:
1. Find the perimeter of the garden
\(14\frac{2}{3} + 14\frac{2}{3} + 10\frac{1}{3} + 10\frac{1}{3} = 50 yd\)
2. Convert to feet
1 yd = 3ft
50 x 3 = 150
50 yd = 150 ft
3. Divide by 2.5 to find out how many sections are needed
150/2.5 = 60 sections
4. Multiply by 25.99
60 x 25.99 = 1559.4
It will cost $1559.40
what additional information could be used to prove that the triangles are congruent using aas or asa? select three options. angleb ≅ anglep and bc ≅ pq anglea ≅ anglet and ac
Answers
The additional information that could be used to prove congruence using AAS or ASA is: Angle A ≅ Angle T and AC (ASA) Angle A ≅ Angle T and BC ≅ PQ (ASA).
To prove that two triangles are congruent using the Angle-Angle-Side (AAS) or Angle-Side-Angle (ASA) criteria, we need specific information about the angles and sides of the triangles.
In this case, we are given three options, and we need to determine which combination of angles and sides would be sufficient to prove congruence using AAS or ASA.
To prove congruence using AAS, we need to show that two angles and the side between them in one triangle are congruent to the corresponding angles and side in the other triangle.
For the given options:
Angle B ≅ Angle P and BC ≅ PQ: This information alone is not sufficient to prove congruence using AAS or ASA. We need additional information about another angle or side in order to establish congruence.
Angle A ≅ Angle T and AC: This option provides information about an angle and a side. If we also have additional information about another angle or side, we can use the Angle-Side-Angle (ASA) criterion to prove congruence.
To determine the third option, we need to consider the remaining combinations of angles and sides:
Angle A ≅ Angle T and BC ≅ PQ: This option provides information about an angle and a side. If we also have additional information about another angle or side, we can use the Angle-Side-Angle (ASA) criterion to prove congruence.
In summary, the additional information that could be used to prove congruence using AAS or ASA is:
Angle A ≅ Angle T and AC (ASA)
Angle A ≅ Angle T and BC ≅ PQ (ASA)
Learn more about triangle here:
https://brainly.com/question/2773823
#SPJ11
Which postulate, if any, can be used to prove the triangles congruent.
Answers
Answer:
ASA postulate
Step-by-step explanation:
∠DCE = ∠BAE
CE = AE
∠DEC = ∠BEA
ASA postulate
David then withdrew that money and put it into another bank account with a rate of 5% interest compounded annually. How much money worth of interest did David gain after 4 years?
Answers
David gained approximately $2,155.06 in interest after 4 years.
How to solveBy utilizing the compound interest formula A = P(1 + r/n)^(nt), one can determine the future value of an investment or loan, inclusive of its added interest.
Variables to consider include the initial deposit (P), annual interest rate (r as a decimal), frequency at which it is compounded per year (n) and time (t).
This specific scenario assimilates a principal amount of $10,000 with an annual interest rate of 5% compounded yearly for four years, resulting in an accrued balance of roughly $12,155.06.
Therefore, David gained approximately $2,155.06 in interest after 4 years.
Read more about compound interest here:
https://brainly.com/question/24274034
#SPJ1
If David deposited $10,000 into a bank account with a 5% interest rate compounded annually, how much interest did he gain after 4 years?
16) Find the surface area of a square pyramid: square base is 3 centimeters by 3 centimeters and the slant
height is 4.6 centimeters.
Answers
Answer:
73.2 cm
Step-by-step explanation:
area = 2 bases + 4 sides
area = 2× 3×3 + 4× 3×4.6
area = 2×9 + 4×13.8
area = 18 + 55.2
area = 73.2 cm
QUESTION 3 of 10: You sample a 2 square mile neighborhood and find 20 people in your target demographic. If your trade area has a radius
of 10 miles and the population across the area is similar to your sample neighborhood, how many people in your target demographic live in
your trade area?
a) 1,000
b) 1,760
Oc) 3,140
d) None of the Above
Answers
Answer:3,140
Step-by-step explanation:
Which equation can be used to find the missing angle?
a. X + 90 = 180
b. X + 40 = 90
c. 180 - 40 = x
Answers
Answer:
A, all three angles of a triangle equal 180
Answer:
b. x + 40 = 90
Step-by-step explanation:
This is a right triangle, so we already know one of the angles is 90 degrees. The other angles combine to make the other 90 degrees. So, we have to figure out what the other angle is, as the second one is 40 degrees. To figure that out, use the equation x + 40 = 90. (This is extra, but x is 50, right?)