A random sample of n = 12 individuals is selected from a population with
µ = 70 and a treatment is administered to each individual in the sample. After treatment the sample mean is found to be M = 74.5 with S = 5.20. Based on the sample data, the treatment has a significant effect as per the deduced test statistic. Following are the statements for Null and the Alternate Hypotheses,
H₀: The treatment does not have a significant effect
Hₐ: The treatment has a significant effect
According to the given information,
Size of the sample, n = 12
Population Mean, μ = 70
Sample Mean, M = 74.5
Standard Deviation, S = 5.20
The Null hypothesis is given by,
H₀: The treatment does not have a significant effect (μ = 70)
The Alternate hypothesis is given by,
Hₐ: The treatment has a significant effect (μ ≠ 70)
Since the population standard deviation is unknown, we will use one-sample t-test here.
Test statistic, TS = (M-μ) / (s/√n)
Substituting the given values of M, μ, S, and n, we get,
TS = (74.5-70) / (5.20/√12)
TS = 4.5 / 1.5
TS ≈ 3
The t table now provides critical values of -2.131 and 2.131 at 15 degrees of freedom for a two-tailed test using α = 0.05 (significance level).
Since our test statistic, TS does not fall in the range of the critical values, it falls in the rejection region. Thus, we can reject the null hypothesis and say that the treatment has a significant effect.
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Cual es la sucesión aritmética de 3,8,13,18,23
Equation [1] : a(n) = 3 + (n - 1)5 represents the step where he made the mistake.
We have,
A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have a student who used the explicit formula a[n] = 5+3(n-1) for the sequence 3,8,13,18,23,...to find the 12th term.
The given sequence is -
3 , 8 , 13 , 18 , 23, ..
Here -
d = 8 - 3 = 13 - 8 = 5
a = 3
a(n) = a + (n - 1)d {for arithmetic sequence}
a(n) = 3 + (n - 1)5 ...Eq[1]
a(n) = 3 + 5n - 5
a(n) = 5n - 2
Therefore, Equation [1] : a(n) = 3 + (n - 1)5 represents the step where he made the mistake.
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complete question:
A student uses the explicit formula an= 5+3(n-1) for the sequence 3,8,13,18,23,...to find the 12th term. Explain the error the student made.
3. In a cooking class, Martin pours 500 milliliters
of broth into a pot. He then adds 1,500 milliliters
of water to the broth. How much total liquid is in
the pot?
A. 1 liter
B.
2 liters
C.
3 liters
D. 5 liters
C
Answer:The correct answer is C. 3 liters.
Step-by-step explanation:
To determine the total amount of liquid in the pot, we need to add the volume of the broth and the volume of the water.
The broth has a volume of 500 milliliters, and the water has a volume of 1,500 milliliters. Adding these together, we get:
500 mL + 1,500 mL = 2,000 mL
Since there are 1,000 milliliters in a liter, we can convert the volume to liters:
2,000 mL ÷ 1,000 = 2 liters
Therefore, the total amount of liquid in the pot is 2 liters.
A woodworker wants to build a jewelry box in the shape of a rectangular prism with a total volume of 61.3 cubic inches. The woodworker is going to use a very expensive exotic wood to build the box. He wants to choose the dimensions of the box so that the bases of the prism are squares and the box's surface area is minimized. What dimensions should he choose for the box? Round answers to 4 decimal places
Answer: the woodworker should choose the dimensions of the box to be approximately 3.825 inches by 3.825 inches by 1.603 inches, with a total surface area of approximately 33.512 square inches.
Step-by-step explanation:
Let the side length of the square base be x, and the height of the prism be h. Then the volume of the prism is:
V = x^2h
We're given that V = 61.3 cubic inches, so:
x^2h = 61.3
We want to minimize the surface area of the box, which consists of the area of the two square bases (2x^2) plus the area of the four rectangular faces (4xh). So the total surface area is:
A = 2x^2 + 4xh
We can solve the first equation for h:
h = 61.3/x^2
Substituting this into the equation for A, we get:
A = 2x^2 + 4x(61.3/x^2)
A = 2x^2 + 245.2/x
To minimize A, we take the derivative and set it equal to zero:
dA/dx = 4x - 245.2/x^2 = 0
4x = 245.2/x^2
x^3 = 61.3
x = (61.3)^(1/3)
x ≈ 3.825
So the length of each side of the square base should be approximately 3.825 inches. We can use the equation for h to find the height:
h = 61.3/x^2
h ≈ 1.603
So the height of the prism should be approximately 1.603 inches.
Therefore, the woodworker should choose the dimensions of the box to be approximately 3.825 inches by 3.825 inches by 1.603 inches, with a total surface area of approximately 33.512 square inches.
Consider the function f(x)=x^3+16x^2+60x+40. If there is a remainder of −5 when the function is divided by (x−a), what is the value of a?
The value of "a" is approximately -3.784 when the function f(x) is divided by (x - a) and leaves a remainder of -5.
To find the value of "a" when the function f(x) = x^3 + 16x^2 + 60x + 40 is divided by (x - a) and leaves a remainder of -5, we can use the Remainder Theorem.
According to the Remainder Theorem, if a polynomial f(x) is divided by (x - a), the remainder is equal to f(a).
In this case, the remainder is -5, so we have f(a) = -5.
Substituting a into the function, we get:
f(a) = a^3 + 16a^2 + 60a + 40 = -5
Now, we need to solve this equation to find the value of "a."
a^3 + 16a^2 + 60a + 40 = -5
Rearranging the equation:
a^3 + 16a^2 + 60a + 45 = 0
To find the exact value of "a," we can use numerical methods such as factoring, synthetic division, or using a graphing calculator. Unfortunately, the solution to this equation is not straightforward and requires numerical approximations.
Using numerical methods or a graphing calculator, we find that the value of "a" is approximately -3.784.
Therefore, the value of "a" is approximately -3.784 when the function f(x) is divided by (x - a) and leaves a remainder of -5.
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Which equation is the inverse of y = x² - 36?
Oy=± √√x +6
Oy=+√√x+36
O y=+√√x +36
Oy=+√√x²+36
Answer:
Step-by-step explanation:
Answer: B y = ±[tex]\sqrt{x+36}[/tex]
Step-by-step explanation:
To find the inverse of any equation. Switch the x and the y then solve for y.
y = x² - 36 >switch variables
x = y² - 36 >add 36 to both sides
x+36=y² >take square root of both sides
y = ±[tex]\sqrt{x+36}[/tex]
B
Find k so the product of the roots is -4 if 3x² + 5x + 3k = 0
Answer:
k = - 4
Step-by-step explanation:
given a quadratic equation in standard form
ax² + bx + c = 0 ( a ≠ 0 ) , then the product of the roots is [tex]\frac{c}{a}[/tex]
3x² + 5x + 3k = 0 ← is in standard form
with a = 3 and c = 3k , then
[tex]\frac{c}{a}[/tex] = - 4 , that is
[tex]\frac{3k}{3}[/tex] = - 4 ( multiply both sides by 3 to clear the fraction )
3k = - 12 ( divide both sides by 3 )
k = - 4
How many different ways can president, vice president, and secretary be chosen from a group of 24 individuals?
The number of ways to choose a president, vice president and secretary from a set of 24 individuals is given as follows:
12,144 ways.
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
The permutation formula is used when the order in which the elements are chosen is important, which is the case for this problem. The order is important as there are different roles, that is, president, vice president and secretary.
For this problem, 3 people are chosen from a set of 24, hence the number of ways is given as follows:
P(24,3) = 24!/21! = 12144.
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Can someone please answer and provide an explanation for these problems?
The values of x for the tangent segments to the circles are: (25). x = 2 and (26). x = 4
What are the segments tangent to the circleA theorem of tangents to a circle states that if from one exterior point, two tangents are drawn to a circle then they have equal tangent segments.
(25). 2x - 1 = x + 1 {equal tangent segments}
2x - x = 1 + 1 {collect like terms}
x = 2
(26). 2x - 4 = x {equal tangent segments}
2x - x = 4 {collect like terms}
x = 4
Therefore, the values of x for the tangent segments to the circles are: (25). x = 2 and (26). x = 4
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Which expressionis equivalent to 60m-2n6/5m-4n-2 for all values of m and n where the expression is defined?
The expression that is equivalent to [tex]\\\\\frac{60m^-2n^6\\}{5m^-4 n^-2}[/tex] for all values of m and n where the 5m-4n-2 expression is defined is [tex]12m^{2} n^{8}[/tex]
How can the expression be known?In mathematics, an expression or mathematical expression can be described as the finite combination of symbols which is been analyzed and well-formed according by following some set of rules which could be varies base on the kind of the symbol as ll as the operation that are involved in the expression and it s been done depending on the context so that another expression can be gotten.
This is given as [tex]\\\\\frac{60m^-2n^6\\}{5m^-4 n^-2}[/tex]
Then we have it defined by; [tex]12m^{2} n^{8}[/tex]
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The first shelf of one bookcase is 2 inches off the ground. The second shelf is 1’5” above the first the third shelf is 1’3” above the second and the fourth shelf is 1’2” above the third. The top shelf is 1’4” above the fourth how high off the ground is the top shelf.
answer: 5'6"
step by step: 1'5"+2"=1'7"+1'3"=3'0"+1'2"=4'2"+1'4"=5'6"
Please help urgent thank you
If he wants an average of 84, he needs to get at least 93 points.
What score does he need to get in the next test?Remember that the average value between 3 values A, B, and C is:
(A + B + C)/3
Here we know that the first two scores are 76 and 83 points, let's say that the third score is x, if we want to have an average of 84 or more, then we need to solve:
(76 + 83 + x)/3 = 84
159 + x = 252
x = 252 - 159
x = 93
So he needs to get at least 93 points in the next exam.
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Can someone help me? Write a rule for nth term of the arithmetic sequence with a1=7 and the common difference is 3
Answer:
[tex]a_n=3n+4[/tex]
Step-by-step explanation:
If the common difference is d=3 and the first term is a₁=7, then we can create an arithmetic sequence:
[tex]a_n=a_1+(n-1)d\\a_n=7+(n-1)(3)\\a_n=7+3n-3\\a_n=3n+4[/tex]
AABC is similar to ADEF.
Find x.
D
A
6
B
8
PADEF = 60
[?]
X =
We can solve for x by equating the two ratios:
a/b = 6/8 = 3/4
We can conclude that x is equal to 3/4.
To find the value of x in the given scenario, where triangles AABC and ADEF are similar, we can use the concept of corresponding sides in similar triangles.
From the given information, we know that the lengths of sides AB and DE are in proportion with each other, as the triangles are similar. Let's denote the length of AB as a and the length of DE as b. Similarly, let's denote the length of BC as c and the length of EF as d.
Since the corresponding sides are in proportion, we can set up the following equation:
AB/DE = BC/EF
Substituting the given values, we have:
a/b = 6/8
To find the value of x, we need to determine the ratio of the corresponding side lengths. Dividing both sides of the equation by 6, we get:
a/6 = b/8
Cross-multiplying, we have:
8a = 6b
Now, we can solve for x by equating the two ratios:
a/b = 6/8 = 3/4
We can conclude that x is equal to 3/4.
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evaluate 6a +4b -3c when a=4 , b=7 , and c=-2 (a) 26 (b) 16 (c) 46) (d) 58
Answer:
(d) 58
Step-by-step explanation:
Let's start with the equation:
6a+4b-3c
Now, since we got the values of a, b, and c, we can just plug them into the equation:
6(4)+4(7)-3(-2)
24+28+6=58
So the answer is d) 58
you and a friend have created a carnival game for your classmates. you plan to charge $1 for each time a student plays, and the payout for a win is $5. according to your calculations, the probability of a win is .05 what is your expected value for this game?
Answer:
The expected value for this game is -$0.75, indicating that, on average, players would expect to lose $0.75 per game.
Step-by-step explanation:
Expected Value = (Probability of Winning * Payout for Win) - Cost of Playing
In this case:
Probability of Winning = 0.05
Payout for Win = $5
Cost of Playing = $1
Expected Value = (0.05 * $5) - $1
Expected Value = $0.25 - $1
Expected Value = -$0.75
A student is establishing the A.A criterion for the similarity of triangles [MN and [QR. The student writes LMLN ~ ZQLR What other information can the student use to establish the AA criterion?
The other information can the student use to establish the AA criterion is Angle LMN congruent angle LQR or angle LMN congruent angle LRQ
The student can use the following information to establish the AA criterion:
Angle MLN congruent angle QLR (already given)Angle LMN congruent angle LQR or angle LMN congruent angle LRQ (either one will work)These two angles correspond to the two angles in the other triangle (LQR or LRQ) that are not congruent to the angle already known to be congruent (angle QLR).
Therefore, the AA congruent for similarity can be congruent .
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8 +[13-(2+1] =
20
18
-3
Answer: false
Step-by-step explanation:
What is the value of i 20+1
1
-1
i
-i
A square piece of sheet metal (24 in x 24 in)
is used to make an open box (no lid). Equal
squares are cut out of each corner, and the
edges are folded up to make the box.
What is the maximum volume, V, of the box?
The maximum volume of the box is 864 cubic inches.
Let side length of the square cut from each corner is x inches.
After cutting the squares from each corner, the remaining dimensions of the sheet metal will be:
Length: 24 - 2x inches
Width: 24 - 2x inches
Height: x inches
So, the volume of the box
V = (24 - 2x) (24 - 2x) x
V = x(24 - 2x)²
To find the maximum volume, we can take the derivative of V with respect to x, set it to zero, and solve for x:
dV/dx = (24 - 2x)² - 2x(24 - 2x) = 0
4x² - 96x + 576 = 0
Solving the quadratic equation,
x = 6 and x = 12.
We can substitute x = 6 into the volume equation to find the maximum volume:
V = 6(24 - 2(6))²
V = 6(12)²
V = 6 x 144
V = 864 cubic inches
Therefore, the maximum volume of the box is 864 cubic inches.
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factorise fully:
1) 2014² - 2013²
please explain and help
The distribution of monthly charges for cellphone plans in the United States is approximately normal with a mean of $62 and a standard deviation of $18. What percentage of plans have charges that are less than $83.60?
About 88.49% of cellphone plans have charges that are less than $83.60.
How to determine the percentage of plans have charges that are less than $83.60?To determine the percentage of plans that have charges less than $83.60, we need to find the z-score (z) using the given mean and standard deviation, and then look up the corresponding area under the normal distribution curve.
z = (x – μ) / σ
where x = 83.60, mean, μ = 62 and standard deviation, σ = 18
Thus, the z-score of $83.60 is:
z = (83.60 - 62) / 18 = 1.2
Using a standard normal distribution table, we can find that the area to the left of z = 1.20 is 0.8849 or 88.49% (check image attached).
Therefore, about 88.49% of cellphone plans have charges that are less than $83.60.
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What is x? Because I don’t know g how to work it out
Answer:
45 degrees
Step-by-step explanation:
The 4 angles of a quadrilateral will add to 360.
We know 1 of them (angle B) is 90 degrees.
We can set up an equation to solve the others.
2x+3x+x+90 = 360
Now solve for x.
Start by combining the x terms together.
6x+90 = 360
6x = 360-90
6x = 270
(6x/6) = 270/6
x = 45 degrees
Check back to see if that makes sense and if the equation equals 360 when x is 45:
2x+3x+x+90 = 360
2(45)+3(45)+45+90=360.
Which function has a greater output value for x = 10? Explain your reasoning.
The function that has a greater output value for x = 10 is table B
How to determine which function has a greater output value for x = 10?From the question, we have the following parameters that can be used in our computation:
The table of values
The table A is a linear function with
A(x) = 1 + 0.3x
The table B is an exponential function with the equation
B(x) = 1.3ˣ
When x = 10, we have
A(10) = 1 + 0.3 * 10 = 4
B(10) = 1.3¹⁰ = 13.79
13.79 is greater than 4
Hence, the function that has a greater output value for x = 10 is table B
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D
(x+2)(x+6)=0
In the problem shown, to conclude that x+2=0 orx+6=0, one must use the:
O zero product property
O division property
O transitive property
O multiplication property
H
OI
Answer:
zero product property
Step-by-step explanation:
To conclude that x+2=0 or x+6=0 from the equation (x+2)(x+6)=0, one must use the zero product property.
The zero product property states that if the product of two factors is equal to zero, then at least one of the factors must be equal to zero. In this case, if (x+2)(x+6)=0, it means that the product of (x+2) and (x+6) is zero. Therefore, we can conclude that either (x+2) = 0 or (x+6) = 0, based on the zero product property.
Suppose it is known that 879 of young Americans earn a hig of 1600 young Americans is selected.
a) Describe the distribution of the proportion of people in t high school diploma.
chool diploma. A random sample
same who have earned their
b) What is the probability that at least 88% of the sample of 1600 young Americans will have earned their high school diploma?
(a) The distribution of the proportion of people in t high school diploma = 0.0158.
(b) the probability that at least 88% of the sample of 1600 young Americans will have earned their high school diploma is extremely small.
Given that,
(a) Based on the central limit theorem, the normal distribution may be used to approximate the fraction of persons in the sample who have a high school diploma.
The mean proportion of individuals in the population who have earned their high school diploma can be estimated as
⇒ 879/1600 = 0.5494.
The standard deviation can be estimated as the square root of (0.5494*(1-0.5494)/1600)
=0.0158
b) To find the probability that at least 88% of the sample of 1600 young Americans will have earned their high school diploma,
We need to use the normal distribution with a mean of 0.5494 and a standard deviation of 0.0158.
We can standardize the value of 88% to the corresponding z-score:
z = (0.88 - 0.5494) / 0.0158
= 20.99
Using a standard normal distribution table or calculator, we find that the probability of a z-score this large or larger is essentially zero,
So the probability that at least 88% of the sample will have earned their high school diploma is extremely small.
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Haru recorded how long his bus ride to school took for `16` days.
Here are the values of the quartiles.
About how many rides would you expect to be less than `6.5` minutes long?
The number of rides that one would expect to be less than `6.5` minutes long is 4 rides.
How to determine the number of ridesTo determine the number of rides, we will first begin by classifying the quartiles. There are 4 quartiles that each constitute 25% of the ride timing.
The number of rides that one would expect to be less than 6.5 minutes can be gotten by finding 25% of 16, the total days recorded. This is 1/4 * 16 = 4. So, the number of rides that will be less than 6.5 minutes will be 4 rides.
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when y is directly proportional to x. When x= 2.5, y=20. what is the value of y when x= 22?
What is the value of x *
7+5x
47°
Answer: X = 8
Step-by-step explanation:
47 - 7 = 40
40 / 5 = 8
x = 8
What is the length of this circle?
The length of arc length s is 1152π² or 11358.26.
We have,
The arc length of a circle can be calculated using the formula:
Arc Length = 2πrθ/360
Where:
π is a mathematical constant approximately equal to 3.14159.
r is the radius of the circle.
θ is the central angle subtended by the arc, measured in degrees.
The arc length of a circle can be written as:
s = angles/360 x 2πr _______(1)
Now,
r = 4 cm
Angle = (2/5)π
Now,
Substitute in (1).
s = angles/360 x 2πr
s = (2/5)π/360 x 2π x 4
s = 2π x 72 x 2π x 4
s = 4π² x 288
s = 1152π²
or
s = 11358.26
Thus,
The length of arc length s is 1152π² or 11358.26.
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A rectangle has an area of 114cm squared and a perimeter of 50 cm. What are its dimensions
Answer:
width = 6
length = 9
Step-by-step explanation:
Perimeter = 2(length + width) or P = 2(l + w)
2(l + w) = 50
l + w = 25
l = 25 - w
Area = length x width or A = lw
lw = 114
Substitute l = 25 - w into the lw = 114
(25 - w)w = 114
25w - w^2 = 114
-w^2 + 25w - 114 = 0
=> w^2 - 25w + 114 = 0
we have x = [-b ± √(b^2 - 4ac)] / 2a
w = [-(-25) ± √((-25)^2 - 4(1)(114)))] / 2(1)
w = [25 ± √(625 - 456)] / 2
w = [25 ± √(169)]/2
w = [25 ± 13]/2
w = [25 + 13]/2 = 38/2 = 14
or
w = [25 - 13]/2 = 12/2 = 6
if width = 14, length = 25 - 14 = 11
then area = 14 x 11 = 154, this is incorrect answer
if width = 6, length = 25 - 6 = 19
then area = 6 x 19 = 114, this is correct answer