Answer:
21%
Step-by-step explanation:
Percentage reduction is (999.99-789.99)/(999.99)=21%
What is the value of log,1252
PERE
3
5
Ο ΟΟΟ
15
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boat costs $54,000. you pay 10% down and amortize the rest with equal monthly payments over a 15 year period. If you must pay 4.5 % comounded monthly, what is your monthly payment?
3385.8
Step-by-step explanation:
An expression is ???
Answer:
s-6
Step-by-step explanation:
difference means subtract
s-6
I need help with this question.
Answer:
Complement = 15 Degrees
Supplement = 105 Degrees
Step-by-step explanation:
The complement of an angle refers to the measure that will make the angle 90 degrees. So, the complement of 75 would be 15, since 90 - 75 = 15.
The supplement of an angle refers to the measure that will make the angle 180 degrees. So, the supplement of 75 would be 105, since 180-75 = 105.
Cheers.
If a teacher's guide to a popular SAT workbook is to be printed using a special type of paper, the guide must have at most 400 pages. If the publishing company charges 1 cent per page printed, what is the largest price, in dollars, that can be charged to print 20 copies of the workbook using the special paper?
Answer:
$80
Step-by-step explanation:
To find the largest price, assume that all 20 copies of the workbook will have 400 pages.
Since the company charges 1 cent per page, this means each workbook will cost 400 cents. This is equivalent to 4 dollars.
Find the total cost by multiplying this by 20:
20(4)
= 80
So, the largest price to print 20 copies is $80
Billy has x marbles. Write an
expression for the number of
marbles the following have…
a) Charlie has 5 more than Billy
b) Danny has 8 fewer than Billy
c) Eric has three times as many as
Billy
Answer:
[tex]Charlie = 5 + x[/tex]
[tex]Danny = x - 8[/tex]
[tex]Eric = 3x[/tex]
Step-by-step explanation:
Given
Billy's Marble = x
Required
Determine a,b and c
a. Charlie's Marble
"5 more" means 5 + or + 5
Since Billy's Marble is represented with x, then Charlie's Marbles will be
[tex]Charlie = 5 + x[/tex]
b. Danny's Marbles
Having "8 fewer" means we have to subtract 8 from Billy's marble;
Since Billy's Marble is represented with x, then Danny's Marbles will be
[tex]Danny = x - 8[/tex]
c. Eric Marbles
Having "three times as " means we have to multiply Bill's marble by 3;
Since Billy's Marble is represented with x, then Danny's Marbles will be
[tex]Eric = 3 * x[/tex]
[tex]Eric = 3x[/tex]
The difference between two positive integers is 7 and the sum of their squares is 949. What are the numbers?
Answer:
25 and 18
Step-by-step explanation:
Let's say that the first number is x and the second one is y.
First, the difference between them is 7, so x-y=7
Next, the sum of their squares is 949, so x²+y² = 949
We have
x-y=7
x²+y²=949
One thing we can do to solve this problem is to solve for x in the first equation, plug that into the second equation, and go from there
Adding y to both sides in the first equation, we have
x = 7 + y
Plugging that into the second equation for x, we have
(7+y)²+ y² = 949
expand
(7+y)(7+y) + y² = 949
49 + y² + 7y + 7y + y² = 949
combine like terms
2y² +14y + 49 = 949
subtract 949 from both sides to put this in the form of a quadratic equation
2y² + 14y - 900 = 0
divide both sides by 2
y² + 7y - 450 = 0
To factor this, we want to find 2 numbers that add up to 7 and multiply to -450.
The factors of 450 are as follows:
1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, and 450.
Note that we want to find two numbers with a difference of 7, as one will have to be negative for the multiplication to end up at -450. Two numbers that stand out are 18 and 25. To make them add up to 7, 18 can be negative. We therefore have
y² + 25y - 18y - 450 = 0
y(y+25) - 18(y+25) = 0
(y-18)(y+25) = 0
Solving for 0,
y-18 = 0
add 18 to both sides
y=18
y+25 = 0
subtract 25 from both sides
y= -25
As the question states "two positive integers", this means that y must be positive, so y = 18. We know x-y=7, so
x-18 = 7
add 18 to both sides to isolate x
x = 25
Say we decided to expand our study and asked ten more urban homeowners what they pay each month for rent. Assume the sample deviation remains the same. What will happen to our samples standard error
Complete Question
The complete question is shown on the first uploaded image
Answer:
The correct option is C
Step-by-step explanation:
Generally the sample standard error is mathematically represented as
[tex]\sigma_{\= x } = \frac{\sigma }{ \sqrt{n} }[/tex]
Where [tex]\sigma[/tex] is the standard deviation and n is the sample size
Now looking at the formula we see that
[tex]\sigma_{\= x } \ \ \ \alpha \ \ \ \frac{1}{ \sqrt{n} }[/tex]
So at constant [tex]\sigma[/tex] if n increases [tex]\sigma_{\= x }[/tex] decreases
So from the question if ten more urban homeowners are asked the question the samples standard error decreases
An ESP experiment used the "Ten Choice Trainer." This is like the Aquarius, but with 10 targets instead of 4. Suppose that in 1,000 trials, a subject scores 173 correct guesses.
Required:
a. Set up the null hypothesis as a box model.
b. The SD of the box is:_______
c. Make the z-test.
d. What do you conclude?
Answer:
a. The H0 is number of correct guesses is 173
b. Standard Deviation of box is 0.3
c. z-test value is 7.70
d. The difference does not appear due to chances of Variation.
Step-by-step explanation:
The standard deviation is :
[tex]\sqrt{0.1 * 0.9}[/tex] = 0.3
The standard deviation of the box is 0.3 approximately.
Z-score is [tex]\frac{x-u}{standard error}[/tex]
Z-score = [tex]\frac{173-100}{9.4868}[/tex]
the value of z-score is 7.70.
The sum of the first 5 terms of an AP is 30 and the sum of the four term from T6 to T9 (inclusive) is 69. Find the AP
Answer: The AP = 1, ⁷/₂, 6, ¹⁷/₂, 11 ..............
Step-by-step explanation:
From the first statement,
S₅ = ⁵/₂(2a + ( n - 1 )d } = 30
5(2a + 4d )d = 60
10a + 20d = 60
reduce to lowest term to easy calculation by dividing through by 10
a + 2d = 6 -----------------------------------1
second statement
sum of the next 4 terms inclusive
T₉ = ⁹/₂(2a + 8d ) = 69
9(2a + 8d ) = 30 + 69
18a + 72d = 99 x 2
18a + 72d = 198
divide through by 18 to reduce to lowest time
a + 4d = 11 ------------------------------------------2
Now solve the two equation simultaneously to find a and d
a + 2d = 6
a + 4d = 11
-2d = -5
d = ⁵/₂.
Now substitute for d to get a
a + 2(⁵/₂) = 6
a + 5 = 6
a = 6 - 5
a = 1.
Therefore the AP = 1 , ⁷/₂ , 6 , ¹⁷/₂ , 11 , ..............
The AP if, The sum of the first 5 terms of an AP is 30 and the sum of the four terms from T6 to T9 is 69, is 1, ⁷/₂, 6, ¹⁷/₂, 11, and so on.
What is sequence?
An ordered collection of objects that allows repetitions is referred to as a sequence. It has members, just like a set does. The length of the sequence is determined by the number of items.
Given:
The sum of the first 5 terms of an AP is 30,
Write the equations as shown below,
S₅ = ⁵/₂(2a + ( n - 1 )d } = 30
5(2a + 4d )d = 60
10a + 20d = 60
reduce to lowest term to easy calculation by dividing through by 10
a + 2d = 6
T₉ = ⁹/₂(2a + 8d ) = 69 (sum of the next 4 terms inclusive)
9(2a + 8d ) = 30 + 69
18a + 72d = 99 x 2
18a + 72d = 198
a + 4d = 11
Solve the equation as shown below,
d = ⁵/₂, and a = 1.
Therefore, the AP = 1, ⁷/₂, 6, ¹⁷/₂, 11, and so on.
To know more about the sequence:
https://brainly.com/question/28615767
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what is the domain of f(x)=(1/4)^x
Answer:
B All real numbers
hope you wil understand
Answer:
[tex]\boxed{\sf B. \ All \ real \ numbers}[/tex]
Step-by-step explanation:
The domain is all possible values for x.
[tex]f(x)=(\frac{1}{4} )^x[/tex]
There are no restrictions on the value of x.
The domain is all real numbers.
let f(x) = 9x - 2 and g(x) = -x + 3. find f(g(x)). a. -9x - 2 b. -9x + 5 c. -9x + 25 d. -9x + 27
Answer:
See below.
Step-by-step explanation:
[tex]f(x)=9x-2 \text{ and } g(x)=-x+3\\f(g(x))=f(-x+3)\\f(-x+3)=9(-x+3)-2\\\text{Distribute and Simplify}\\-9x+27-2\\=-9x+25\\\text{Therefore, f(g(x))=-9x+25}\\\text{The answer is C}[/tex]
answer no explantion pls i need asap
Answer:
Below.
Step-by-step explanation:
Area = 5(x + 3)
= 5x + 15
Perimeter = 2(x + 3) + 2(5)
= 2x + 6 + 10
= 2x + 16.
4. The general population (Population 2) has a mean of 30 and a standard deviation of 5, and the cutoff Z score for significance in a study involving one participant is 1.96. If the raw score obtained by the participant is 45, what decisions should be made about the null and research hypotheses?
Answer:
The null hypothesis is rejected and research hypotheses is supported
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 30[/tex]
The standard deviation is [tex]\sigma = 5[/tex]
The sample size is n = 1
The cutoff Z score for significance is [tex]Z_{\alpha } = 1.96[/tex]
The mean score is [tex]\= x = 45[/tex]
Generally the test hypothesis is mathematically represented as
[tex]t = \frac{\= x - \mu }{ \frac{ \sigma }{\sqrt{n} } }[/tex]
=> [tex]t = \frac{45 - 30 }{ \frac{ 5}{\sqrt{1} } }[/tex]
=> [tex]t = 3[/tex]
From the obtained value we can see that [tex]t > Z_{\alpha }[/tex]
Hence the null hypothesis is rejected and research hypotheses is supported
What are the zeros of , where
? help please need some help someone help please
[tex]{ \boxed{\boxed{\begin{array}{cc} \maltese \bf \: given \\ \\ \rm \: f(x) = ( {x}^{2} + 16)( {x}^{2} - 9) \\ \\ \bf \: for \: zeroes \\ \\ \pink{ \boxed{\boxed{\begin{array}{c | c} \bf \: {x}^{2} + 16 = 0 & \bf \: {x}^{2} - 9 = 0 \\ \\ = > {x}^{2} = - 16& {x}^{2} = 9 \\ \\ = > x = \pm \sqrt{ - 16} &x = \pm \: \sqrt{9} \\ \\ = > x = \pm \sqrt{ {i}^{2} {4}^{2} } &x = \pm \: \sqrt{ {3}^{2} } \\ \\ = > x = \pm \: 4i&x = \pm3 \end{array}}}} \\ \\ \rm \: x = \pm3 \: and \pm \: 4i\end{array}}}}[/tex]
Option A is the correct answer
What is the perimeter of the triangle?
If the average yield of cucumber acre is 800 kg, with a variance 1600 kg, and that the amount of the cucumber follows the normal distribution. 1- What percentage of a cucumber give the crop amount between 778 and 834 kg? 2- What the probability of cucumber give the crop exceed 900 kg ?
Answer:
a
The percentage is
[tex]P(x_1 < X < x_2 ) = 51.1 \%[/tex]
b
The probability is [tex]P(Z > 2.5 ) = 0.0062097[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 800[/tex]
The variance is [tex]var(x) = 1600 \ kg[/tex]
The range consider is [tex]x_1 = 778 \ kg \ x_2 = 834 \ kg[/tex]
The value consider in second question is [tex]x = 900 \ kg[/tex]
Generally the standard deviation is mathematically represented as
[tex]\sigma = \sqrt{var (x)}[/tex]
substituting value
[tex]\sigma = \sqrt{1600}[/tex]
[tex]\sigma = 40[/tex]
The percentage of a cucumber give the crop amount between 778 and 834 kg is mathematically represented as
[tex]P(x_1 < X < x_2 ) = P( \frac{x_1 - \mu }{\sigma} < \frac{X - \mu }{ \sigma } < \frac{x_2 - \mu }{\sigma } )[/tex]
Generally [tex]\frac{X - \mu }{ \sigma } = Z (standardized \ value \ of \ X)[/tex]
So
[tex]P(x_1 < X < x_2 ) = P( \frac{778 - 800 }{40} < Z< \frac{834 - 800 }{40 } )[/tex]
[tex]P(x_1 < X < x_2 ) = P(z_2 < 0.85) - P(z_1 < -0.55)[/tex]
From the z-table the value for [tex]P(z_1 < 0.85) = 0.80234[/tex]
and [tex]P(z_1 < -0.55) = 0.29116[/tex]
So
[tex]P(x_1 < X < x_2 ) = 0.80234 - 0.29116[/tex]
[tex]P(x_1 < X < x_2 ) = 0.51118[/tex]
The percentage is
[tex]P(x_1 < X < x_2 ) = 51.1 \%[/tex]
The probability of cucumber give the crop exceed 900 kg is mathematically represented as
[tex]P(X > x ) = P(\frac{X - \mu }{\sigma } > \frac{x - \mu }{\sigma } )[/tex]
substituting values
[tex]P(X > x ) = P( \frac{X - \mu }{\sigma } >\frac{900 - 800 }{40 } )[/tex]
[tex]P(X > x ) = P(Z >2.5 )[/tex]
From the z-table the value for [tex]P(Z > 2.5 ) = 0.0062097[/tex]
Determine whether or not F is a conservative vector field. If it is, find a function f such that F = ∇f. (If the vector field is not conservative, enter DNE.) F(x, y) = (3x2 − 2y2)i + (4xy + 4)j
In order for F to be conservative, there must be a scalar function f such that the gradient of f is equal to F. This means
[tex]\dfrac{\partial f}{\partial x}=3x^2-2y^2[/tex]
[tex]\dfrac{\partial f}{\partial y}=4xy+4[/tex]
Integrate both sides of the first equation with respect to x :
[tex]f(x,y)=x^3-2xy^2+g(y)[/tex]
Differentiate both sides with respect to y :
[tex]\dfrac{\partial f}{\partial y}=-4xy+\dfrac{\mathrm dg}{\mathrm dy}=4xy+4\implies\dfrac{\mathrm dg}{\mathrm dy}=8xy+4[/tex]
But we assume g is a function of y, which means its derivative can't possibly contain x, so there is no scalar function f whose gradient is F. Therefore F is not conservative.
In this problem, since the condition of equal derivatives does not apply, the vector field is not conservative.
A vector field can be described as:
[tex]F = <P,Q>[/tex]
It is conservative if:
[tex]\frac{\partial P}{\partial y} = \frac{\partial Q}{\partial x}[/tex]
In this problem, the field is:
[tex]F = <3x^2 - 2y^2, 4xy + 4>[/tex]
Then:
[tex]P(x,y) = 3x^2 - 2y^2[/tex]
[tex]\frac{\partial P}{\partial y} = -4y[/tex]
[tex]Q(x,y) = 4xy + 4[/tex]
[tex]\frac{\partial Q}{\partial x} = 4y[/tex]
Since [tex]\frac{\partial P}{\partial y} \neq \frac{\partial Q}{\partial x}[/tex], the field is not conservative.
A similar problem is given at https://brainly.com/question/15236009
The size of a television is the length of the diagonal of its screen in inches. The aspect ratio of the screens of older televisions is 4:3, while the aspect ratio of newer wide-screen televisions is 16:9. Find the width and height of an older 35-inch television whose screen has an aspect ratio of 4:3.
Answer:
The Width = 28 inches
The Height = 21 inches
Step-by-step explanation:
We are told in the question that:
The width and height of an older 35-inch television whose screen has an aspect ratio of 4:3
Using Pythagoras Theorem
Width² + Height² = Diagonal²
Since we known that the size of a television is the length of the diagonal of its screen in inches.
Hence, for this new TV
Width² + Height² = 35²
We are given ratio: 4:3 as aspect ratio
Width = 4x
Height = 3x
(4x)² +(3x)² = 35²
= 16x² + 9x² = 35²
25x² = 1225
x² = 1225/25
x² = 49
x = √49
x = 7
Hence, for the 35 inch tv set
The Width = 4x
= 4 × 7
= 28 inches.
The Height = 3x
= 3 × 7
= 21 inches
Let E and F be two events of an experiment with sample space S. Suppose P(E) = 0.6, P(F) = 0.3, and P(E ∩ F) = 0.1. Compute the values below.
(a) P(E ∪ F) =
(b) P(Ec) =
(c) P(Fc ) =
(d) P(Ec ∩ F) =
Answer:
(a) P(E∪F)= 0.8
(b) P(Ec)= 0.4
(c) P(Fc)= 0.7
(d) P(Ec∩F)= 0.8
Step-by-step explanation:
(a) It is called a union of two events A and B, and A ∪ B (read as "A union B") is designated to the event formed by all the elements of A and all of B. The event A∪B occurs when they do A or B or both.
If the events are not mutually exclusive, the union of A and B is the sum of the probabilities of the events together, from which the probability of the intersection of the events will be subtracted:
P(A∪B) = P(A) + P(B) - P(A∩B)
In this case:
P(E∪F)= P(E) + P(F) - P(E∩F)
Being P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.1
P(E∪F)= 0.6 + 0.3 - 0.1
P(E∪F)= 0.8
(b) The complement of an event A is defined as the set that contains all the elements of the sample space that do not belong to A. The Complementary Rule establishes that the sum of the probabilities of an event and its complement must be equal to 1. So, if P (A) is the probability that an event A occurs, then the probability that A does NOT occur is P (Ac) = 1- P (A)
In this case: P(Ec)= 1 - P(E)
Then: P(Ec)= 1 - 0.6
P(Ec)= 0.4
(c) In this case: P(Fc)= 1 - P(F)
Then: P(Fc)= 1 - 0.3
P(Fc)= 0.7
(d) The intersection of two events A and B, designated as A ∩ B (read as "A intersection B") is the event formed by the elements that belong simultaneously to A and B. The event A ∩ B occurs when A and B do at once.
As mentioned, the complementary rule states that the sum of the probabilities of an event and its complement must equal 1. Then:
P(Ec intersection F) + P(E intersection F) = P(F)
P(Ec intersection F) + 0.1 = 0.3
P(Ec intersection F)= 0.2
Being:
P(Ec∪F)= P(Ec) + P(F) - P(Ec∩F)
you get:
P(Ec∩F)= P(Ec) + P(F) - P(Ec∪F)
So:
P(Ec∩F)= 0.4 + 0.3 - 0.2
P(Ec∩F)= 0.8
Can someone help me by solving this?
Answer:
30000 times 2.28 equals 68 400
Step-by-step explanation:
Find 0.01 more than 9.154
Answer:
Hey!
Your answer is 9.164!!
Step-by-step explanation:
Adding 0.01 means just adding 1 to THE DIGIT IN THE HUNDRETH PLACE...2 SPACES RIGHT OF DECIMAL POINT!
5+1=6
SUB IN:
9.164
The lines shown below are perpendicular. If the green line has a slope of 2/5
, what is the slope of the red line?
A.
B.
C.
-
D.
-
Answer:
C. [tex] -\frac{5}{2}} [/tex]
Step-by-step explanation:
If two lines on a graph are perpendicular to each other, their slope is said to be negative reciprocals of each other. This means the slope of one, is the negative reciprocal of the other.
This can be represented as [tex] m_1 = \frac{-1}{m_2} [/tex]
Where, [tex] m_1, m_2 [/tex] are slopes of 2 lines (i.e. the red and green lines given in the question) that are perpendicular to one another.
Thus, the slope of the red line would be:
[tex] m_1 = \frac{-1}{\frac{2}{5}} [/tex]
[tex] m_1 = -1*\frac{5}{2}} [/tex]
[tex] m_1 = -\frac{5}{2}} [/tex]
The slope of the red line = [tex] -\frac{5}{2}} [/tex]
Solve the following formula for a.
Answer:
B is correct .trust me
Step-by-step explanation:
Customers receive rewards pints based on the purchase type:
Please solve this question by using the strategy Elimination Method or Solve By Substitution. This is the math equation: 1/2x+y=15 and -x-1/3y=-6
2nd Question: 5/6x+1/3y=0 and 1/2x-2/3y=3
First pair of equations :
[tex]\dfrac{1}{2}x+y=15\ ..(i)\\\\-x-\dfrac{1}{3}y=-6\ ..(ii)[/tex]
Multiply 2 to equation (i), we get
[tex]x+2y=30\ ..(iii)[/tex]
By Elimination Method, Add (i) and (ii) (term with x eliminate), we get
[tex]2y-\dfrac{1}{3}y=30-6\\\\\Rightarrow\ \dfrac{5}{3}y=24\\\\\Rightarrow\ y=\dfrac{24\times3}{5}=14.4[/tex]
put y= 14.4 in (iii), we get
[tex]x+2(14.4)=30\Rightarrow\ x=30-28.8=1.2[/tex]
hence, x=1.2 and y =14.4
Second pair of equations :
[tex]\dfrac{5}{6}x+\dfrac13y=0\ ..(i)\\\\ \dfrac12x-\dfrac{2}{3}y=3\ ..(ii)[/tex]
Multiply 2 to equation (i), we get
[tex]\dfrac{5}{3}x+\dfrac{2}{3}y=0\ ..(iii)[/tex]
Elimination Method, Add (i) and (ii) (term with y eliminate) , we get
[tex]\dfrac53x+\dfrac12x=3\Rightarrow\ \dfrac{10+3}{6}x=3\\\\\Rightarrow\ \dfrac{13}{6}x=3\\\\\Rightarrow\ x=\dfrac{18}{13}[/tex]
put [tex]x=\dfrac{18}{13}[/tex] in (i), we get
[tex]\dfrac{5}{6}(\dfrac{18}{13})+\dfrac{1}{3}y=0\\\\\Rightarrow\ \dfrac{15}{13}+\dfrac{1}{3}y=0\\\\\Rightarrow\ \dfrac{1}{3}y=-\dfrac{15}{13}\\\\\Rightarrow\ y=-\dfrac{45}{13}[/tex]
hence, [tex]x=\dfrac{18}{13}[/tex] and [tex]y=\dfrac{-45}{13}[/tex] .
find the measure of x
Answer:
[tex]B)\ x=43[/tex]
Step-by-step explanation:
One is given a circle with many secants within the circle. Please note that a secant refers to any line in a circle that intersects the circle at two points. A diameter is the largest secant in the circle, it passes through the circle's midpoint. One property of a diameter is, if a triangle inscribed in a circle has a side that is a diameter of a circle, then the triangle is a right triangle. One can apply this to the given triangle by stating the following:
[tex]x+47+90=180[/tex]
Simplify,
[tex]x+47+90=180[/tex]
[tex]x+137=180[/tex]
Inverse operations,
[tex]x+137=180[/tex]
[tex]x=43[/tex]
You spend $7.00 at the store. The sales tax is 6%. How much is your total bill?
Please explain how you got the answer if you can.
Answer:
7.42
Step-by-step explanation:
First determine the amount of tax
7 * 6%
7 *.06
.42
Add this to the original bill
7 + .42
7.42
The total cost is 7.42
A manufacturer claims that the calling range (in feet) of its 900-MHz cordless telephone is greater than that of its leading competitor. A sample of 19 phones from the manufacturer had a mean range of 1160 feet with a standard deviation of 32 feet. A sample of 11 similar phones from its competitor had a mean range of 1130 feet with a standard deviation of 30 feet.
Required:
Do the results support the manufacturer's claim?
Complete question is;
A manufacturer claims that the calling range (in feet) of its 900-MHz cordless telephone is greater than that of its leading competitor. A sample of 19 phones from the manufacturer had a mean range of 1160 feet with a standard deviation of 32 feet. A sample of 11 similar phones from its competitor had a mean range of 1130 feet with a standard deviation of 30 feet. Required:
Do the results support the manufacturer's claim?
Let μ1 be the true mean range of the manufacturer's cordless telephone and μ2 be the true mean range of the competitor's cordless telephone. Use a significance level of α = 0.01 for the test. Assume that the population variances are equal and that the two populations are normally distributed
Answer:
We will fail to reject the null hypothesis as there is no sufficient evidence to support the manufacturers claim.
Step-by-step explanation:
For the first sample, we have;
Mean; x'1 = 1160 ft
standard deviation; σ1 = 32 feet
Sample size; n1 = 19
For the second sample, we have;
Mean; x'2 = 1130 ft
Standard deviation; σ2 = 30 ft
Sample size; n2 = 11
The hypotheses are;
Null Hypothesis; H0; μ1 = μ2
Alternative hypothesis; Ha; μ1 > μ2
The test statistic formula for this is;
z = (x'1 - x'2)/√[(σ1)²/n1) + (σ2)²/n2)]
Plugging in the relevant values, we have;
z = (1160 - 1130)/√[(32)²/19) + (30)²/11)]
z = 2.58
From the z-table attached, we have a p-value = 0.99506
This p-value is more than the significance value of 0.01,thus,we will fail to reject the null hypothesis as there is no sufficient evidence to support the manufacturers claim.
A student wrote the following equation and solution. Explain the error and correctly solve the equation: √p = 9/16 p = 3/4
Answer:
see below
Step-by-step explanation:
√p = 9/16
We need to square each side, not take the square root
(√p)^2 =( 9/16)^2
p = 81/256