The test statistic is less than - 1.796
Hypothesisi test
H0: μ = 46
Ha: μ < 46
This is a lower tailed test
mean = 42
standard deviation = 11.9
sample size n = 12
The level of significance α = 0.05
degree of freedom df = n - 1 = 12 - 1 = 11
Test statistic = (x - mean)/(standard deviation / √n) = (42 - 46)/(11.9 / √12) = - 1.164
Test statistic = - 1.164
Using t- table, we can observe that the p - value is between 0.10 and 0.15
Using excel we find p - value = P(t < - 1.796)
p value = 0.1344
H0: μ < 46, rejection rule is
Reject H0 if test statistic < - 1. 796
Therefore, we reject the hypothesis as the test statistic is less than - 1.796
To learn more about test statistic refer here
https://brainly.com/question/15980493
#SPJ4
First Derivative Test vs Second Derivative Test for Local Extrema
The First Derivative Test for Local Extrema is the name of the procedure when it is used to find the values of the local maximum or minimum function.
The second derivative may be used to determine the local extrema of a function under certain conditions.
A function is said to have a local (relative) extremum at a critical point if the derivative of the function changes sign near that location. At the critical point, the function has a local (relative) maximum if the derivative switches from being positive (growing function) to negative (decreasing function). The function, however, has a local (relative) minimum at the critical point if the derivative switches from negative (decreasing function) to positive (growing function). The First Derivative Test for Local Extrema is the name of the procedure when it is used to find the values of the local maximum or minimum function.
Under certain circumstances, one can utilize the second derivative to identify the local extrema of a function. A function has a local minimum at this point if it has a critical point when f′(x) = 0 and the second derivative is positive. However, if the function contains a critical point at which the second derivative is negative and f′(x) = 0, then f has a local maximum at this location. The Second Derivative Test for Local Extrema is the name of this method.
To know more about derivative tests visit: brainly.com/question/29064109
#SPJ4
Which of the following is a factor of (x+y)³ - (x³+y³) ?
choose the correct answer
x²+xy²+2xy
x²+y²-xy
xy²
3xy
Answer:
3 x y (y + x)
Step-by-step explanation:
Factor the following:
(y + x)^3 - (y^3 + x^3)
Factor the sum of two cubes. y^3 + x^3 = (y + x) (y^2 - x y + x^2):
(y + x)^3 - ((y + x) (y^2 - x y + x^2))
Factor y + x out of (y + x)^3 - (y + x) (y^2 - x y + x^2), resulting in (y + x) ((y + x)^(3 - 1) - (y^2 - x y + x^2)):
(y + x) ((y + x)^(3 - 1) - (y^2 - x y + x^2))
3 - 1 = 2:
(y + x) ((y + x)^2 - (y^2 - x y + x^2))
(y + x) (y + x) = (x) (x) + (x) (y) + (y) (x) + (y) (y) = x^2 + x y + x y + y^2 = y^2 + 2 x y + x^2:
(y + x) ((y^2 + 2 x y + x^2) - (y^2 - x y + x^2))
-(y^2 - x y + x^2) = -y^2 + x y - x^2:
(y + x) (x^2 + 2 x y + y^2 + (-y^2 + x y - x^2))
Grouping like terms, y^2 - y^2 + 2 x y + x y + x^2 - x^2 = (2 x y + x y) + (y^2 - y^2) + (x^2 - x^2):
((2 x y + x y) + (y^2 - y^2) + (x^2 - x^2)) (y + x)
x y 2 + x y = x y×3:
(3 x y + (y^2 - y^2) + (x^2 - x^2)) (y + x)
y^2 - y^2 = 0:
(3 x y + (x^2 - x^2)) (y + x)
x^2 - x^2 = 0:
Answer: 3 x y (y + x)
Can someone explain how to simplify radicals, cube roots, and rational radicals? Also how do I simplify a radical that has exponents?
An expression with a square root is referred to as a radical expression.
How to simplify radicals, cube roots, and rational radicals?Radical simplification:
Find the biggest square factor of the radicand while simplifying a radical.When a radical's radicand doesn't have a square number factor, it is said to be in its simplest form.Eg : [tex]\frac{x^{\sqrt{9} } }{x^{\sqrt{4} } } =x^{3-2} = x^{1} = x[/tex]Cube root simplification:
The process here is the polar opposite of cubing a phrase. When calculating a term's cube root, we look for the word that, when multiplied by itself three times, yields the term we are calculating the cube root of.Eg : [tex]\sqrt[3]{27} =\sqrt[3]{3^{3} } = [3^{3}]^{\frac{1}{3}} = 3[/tex]Rational radical simplification :
Find the greatest radicand factor that is a perfect power of the index. Utilizing that factor, rewrite the radicand as the product of two factors.Use the product rule to rewrite the radical as the union of two radicals.Reduce the perfect power to its simplest form. Eg :[tex]\frac{2}{\sqrt{5} -1} \\\\=\frac{2}{\sqrt{5} -1} *\frac{\sqrt{5}+1}{\sqrt{5}+1} \\\\=\frac{2(\sqrt{5} +1) }{4} \\\\=\frac{\sqrt{5} +1 }{2}[/tex]
Exponential radical simplification :
Exponents should be multiplied together when you're simplifying exponential expressions that have been increased to another exponent. Working out each exponent the difficult way will demonstrate that this is true for both positive and negative exponents.Eg :[tex](5^{2} )^{3} \\=(5^{2} ) (5^{2} )(5^{2} )\\=25 *25*25\\=15625[/tex]
To learn more about cube root, refer:
https://brainly.com/question/24486461
#SPJ1
function F is defined by the equation f(x)=x to the power of 2. what is f(2)
The value of f(2) is 4.
What is a function?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
The domain and range of the function are the set of values of f(x) that are produced by the values in the domain of the function, which is the set of values of x. In addition to f(x), alternative shorthand symbols for functions of the independent variable x include g(x) and P(x), especially when the nature of the function is ambiguous or uncertain.
Given function is
f(x) = x²
Putting x = 2 in the given function:
f(2) = 2²
Putting 2² = 4 in the above function:
f(2) = 4
To learn more about equation of a function, click on below link:
https://brainly.com/question/22333482
#SPJ1
find the total interest for a principal of $125,000 at a rate of 7.5% for 5 years paid monthly
Answer:
Calculation Steps:
First, convert R as a percent to r as a decimal
r = R/100
r = 7.5/100
r = 0.075 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 125,000.00(1 + 0.075/12)(12)(5)
A = 125,000.00(1 + 0.00625)(60)
A = $181,661.80
Summary:
The total amount accrued, principal plus interest, with compound interest on a principal of $125,000.00 at a rate of 7.5% per year compounded 12 times per year over 5 years is $181,661.80.
the given set is a basis for a subspace w. use the gram-schmidt process to produce an orthogonal basis for w.
y₁ = [1 -4 0 1] and y₂ = [5 1 -6 -1] is the orthogonal basis for w using Gram-Schmidt process.
Given,
The set;
x₁ = [1 -4 0 1]
x₂ = [7 -7 -6 1]
We have to produce the orthogonal basis for w using the Gram-Schmidt process;
Here,
y₁ = x₁ = [1 -4 0 1]
Now,
Solve for y₂
y₂ = x₂ - [x₂y₁ / y₁y₁] y₁
That is,
y₂ = [7 -7 -6 1] - ( [7 -7 -6 1] [1 -4 0 1] / [1 -4 0 1] [1 -4 0 1] ) × [1 -4 0 1]
y₂ = [7 -7 -6 1] - (7 + 28 - 0 + 1) / (1 + 16 + 0 + 1) × [1 -4 0 1]
y₂ = [7 -7 -6 1] - 36/18 × [1 -4 0 1]
y₂ = [7 -7 -6 1] - 2 × [1 -4 0 1]
y₂ = [7 -7 -6 1] - [2 8 0 2]
y₂ = [5 1 -6 -1]
That is,
The orthogonal basis for w using Gram-Schmidt process is,
y₁ = [1 -4 0 1] and y₂ = [5 1 -6 -1]
Learn more about Gram-Schmidt process here;
https://brainly.com/question/17132977
#SPJ4
Gary's cat weighs 11 pounds. How many ounces does Gary's cat weigh?
Answer:
Gary would weigh 176 ounces.
Step-by-step explanation:
One pound is sixteen ounces so just multiply sixteen and 11. ( 16 * 11 = 176 )
I hope this helped you! Have an amazing day :)
Answer: 176 ounces
Step-by-step explanation:
To convert pounds to ounces, multiply the initial value by 16. Since we have the weight of Gary's cat as 11 pounds, their weight in ounces should be 11 * 16 = 176 ounces.
Use rounding to estimate 162.6+4.4. Round 162.6 to the nearest ten.
162.6
+ 4.4
Separate decimals
162 + 4 = 166
0.6 + 0.4 = 1
166 + 1 = 167
162.6
Nearest ten is 160
Hope this helps
a farmer wishes to enclose a rectangular area of 80,000 square feet and divide it into three pens with fencing parallel to one of the sides of the rectangle. what is the minimum amount of fence that he can use?
The minimum amount of fence that he can use is 1600 ft.
Given ;
Area of rectangular = 80,000 sq. ft
i.e. xy = 80,000
Total fencing needed ,
x + y + x + y + 2y = 2x + 4y
To minimize 2x + 4y, constrained to xy = 80,000
i.e. xy = 80,000
⇒ y = 80,000/x
⇒ so, s = 2x + 4 (80,000/x) to be minimized
⇒ To minimum value at ds/dx = 0
i.e. s = 2x + 4 (80,000/x)
= 2x + (3,20,00/x)
⇒ Now, ds/dx = 0 = 2 + (3,20,000) - [tex]\frac{1}{x^{2} }[/tex]
⇒ [tex]\frac{320000}{x^{2} } = 2[/tex]
⇒ [tex]x^{2} = 160000[/tex]
⇒ x = 400
∴ x = 400 ft
y = 80,000/400 = 200
∴ y = 200 ft
Total frencing is
⇒ 2x + 4y = 2 × 400 + 4 × 200
= 800 + 800
= 1600 ft
∴ The minimum amount of fence that he can use is 1600 ft.
Learn more about rectangle area here ;
https://brainly.com/question/25292087
#SPJ4
you are to enclose a rectangular garden with 180 yards of fencing. what dimensions (width and length) for the garden will maximize the area? what is the area with these dimensions?
Dimensions of the rectangular garden are 45 yards each and area with the calculated dimensions are 2025 square yards.
As given in the question,
Perimeter of the rectangular garden is equal to 180 yards
Let 'x' be the length and 'y' be the width of the rectangular garden
2 ( x + y ) = 180
⇒ x + y = 90
⇒ y = 90 -x
Area of the rectangular garden 'A' = xy
⇒ A = x ( 90 - x)
⇒ A = 90x - x²
To maximize the area dA/dx = 0
dA/dx = 90 - 2x
⇒ 90 - 2x = 0
⇒ 2x = 90
⇒ x = 45 yards
⇒ y = 45 yards
Area of the rectangular garden = 45 × 45
= 2025 square yards
Therefore, the dimensions of the garden are 45 yards each and area of the rectangular garden is equal to 2025 square yards.
Learn more about area here
brainly.com/question/27683633
#SPJ4
10. Why are median and IQR better statistics than mean and standard deviation for describing
skewed probability distributions?
Median and IQR are better statistics than mean and standard deviation for describing skewed probability distributions because it's based on values that come from the middle half of the distribution, it's unlikely to be influenced by outliers.
Why is the IQR and median better?Because it is unaffected by outliers, the IQR is frequently regarded as a more accurate measure of spread than the range. The variance and standard deviation are indicators of how widely the data are dispersed from the mean. Each observed data value's proximity to the mean is summarized.
The best indicator of variability in data sets with outliers or skewed distributions is the interquartile range. It's unlikely to be impacted by outliers because it's based on values that come from the middle half of the distribution.
Learn more about interquartile range on
https://brainly.com/question/4102829
#SPJ1
find the dimensions of the rectangular corral split into 2 pens of the same size producing the greatest possible enclosed area given 300 feet of fencing.
The dimensions of the rectangular corral:
length = 75 ft and width = 5 ft
Let m be the length of the rectangular corral and n be the width of the rectangular corral.
The perimeter of the rectangular corral,
P = 2m + 2n
The rectangular corral split into 2 pens of the same size.
So, P = 2m + 3n
The 2 pens producing the greatest possible enclosed area given 300 feet of fencing.
300 = 2m + 3n
n = (300 - 2m)/3
Area of the rectangular corral,
A = m * n
A(n) = m * (300 - 2m)/3
A(m) = (300/3)*m - (2/3)*m
Taking derivatives on both sides of the equation:
A'(m) = 100 - (4/3)*m
for A'(m) = 0,
100 - (4/3)*m = 0
m = 100 * (3/4)
m = 75
So, n = (300 - 2(75))/3
n = 50
Therefore, the length of the rectangular corral = 75 ft and width = 5 ft
Learn more about perimeter of rectangle here:
https://brainly.com/question/29595517
#SPJ4
How should a common data source like social media comments be categorized? 1 structured data 2 unstructured data 3 temporary data 4 dirty data
Common data sources like social media comments are categorized as unstructured data. (Option 2)
Unstructured data refers to information that does not have a pre-defined data model or is not organized in a pre-defined manner. Unstructured data is a dataset that is not stored in a specific structured format and is generally text-heavy, but may contain data such as dates, numbers, and facts. Unstructured data does have an internal structure, but it is not predefined through data models. It might be human generated, or machine generated in a textual or a non-textual format. Examples of unstructured data are social media comments, blog posts, videos, and documents.
Learn more about Unstructured data:
https://brainly.com/question/28851700
#SPJ4
How many meters tall is the tree?
Nate heard stories about the massive Sierra redwoods in California and looked forward to seeing one of these trees for himself. On his first actual encounter with one of the trees, Nate wants to know just how tall the tree is. He places a mirror on the ground and experiments several times until he determines the correct distance from the base of the tree as well as the correct angle of incidence that allows him to see the top of the tree.
Answer:
95 meters
Step-by-step explanation:
Given the dimensions of the triangles shown in the figure, you want the height of the tree.
Similar trianglesThe ratio of the height of the triangle to the base is the same for both triangles shown. That means ...
1.9/0.75 = x/(38.25 -0.75)
where x represents the height of the tree.
Multiplying by (38.25 -0.75), we have ...
[tex]x=\dfrac{(38.25-0.75)\cdot1.9}{0.75}=1.9\left(\dfrac{38.25}{0.75}-1\right)=95[/tex]
The height of the tree is 95 meters.
the cdc estimated that 12% of women who have recently given birth suffer from ppd. however, this research only reflected self-reported cases. therefore, one group dedicated to helping women and their families with ppd believes that the true percentage of women who suffer from ppd is much higher. the group conducts a simple random sample of 139 women who had given birth in the last year and discovers that 25 of them report having ppd. based on this evidence, can the group claim that the true percentage of women who have ppd is greater than 12%? use a 0.05 level of significance. step 2 of 3 : compute the value of the test statistic. round your answer to two decimal places.
The actual percentage of female people with ppd is more than 12%.
What is ppd ?Many women experience postpartum depression (commonly known as PPD), which is a medical disorder. After giving delivery, there are intense emotions of sadness, anxiety (concern), and exhaustion that persist for a long time. You may find it challenging to care for both you and your infant as a result of these feelings. PPD can occur at any point following childbirth. Within 1 to 3 weeks of giving birth, it frequently begins. To get better, it need treatment.
What does true percentage mean in statistics?And that's basically what TS% is. A measure of scoring efficiency based on the number of points scored over the number of possessions in which they attempted to score. The actual TS% formula multiplies the denominator by 2 to put the number into a percentage scale, but it's the same result on a different scale
to learn more about percentage of women having ppd visit:
https://brainly.com/question/28168955
#SPJ4
a company wants to hire a software engineer, an administrative assistant, and a sales representative. there are 4 possible candidates for the position of software engineer, 4 for the position of administrative assistant, and 6 for the position of sales representative. how many ways are there to choose the three people who will be hired?
The number of ways in which we can select a software engineer, an administrative assistant, and a sales representative is 48.
Since we are only choosing one option from each category, the number of alternatives for each category is equal to the number of combinations for each category .
Using the equation for each pair and then adding them up,
C (n,r) = n! / (r! (n - r)! )
we get the required number of combinations as 48.
Factorial
There are n! techniques of arranging n unique things into an ordered sequence, permutations where n = r.
Combination
The number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter and replacements are not allowed.
Permutation
The number of ways to choose a sample of r elements from a set of n distinct objects when order does matter and replacements are not allowed. When n = r this reduces to n! , a simple factorial of n.
To learn more about combinations
https://brainly.com/question/20211959
#SPJ4
Work out
(
8.8
×
10
−
2
)
+
(
3.4
×
10
−
4
)
Give your answer in standard form
Answer:
9.14
Step-by-step explanation:
To add these numbers, we first need to rewrite them in standard form, which means expressing them as a number between 1 and 10, multiplied by a power of 10.
The first number, (8.8 × 10^-2), is already in standard form.
The second number, (3.4 × 10^-4), is not in standard form. To rewrite it in standard form, we divide 3.4 by 10 twice:
(3.4 × 10^-4) = (0.34 × 10^-2) = (3.4 × 10^-3)
Now that both numbers are in standard form, we can add them:
(8.8 × 10^-2) + (3.4 × 10^-3) = 8.8 + 0.34 = 9.14
The final answer is 9.14.
Answer:
9.14
(8.8 × 10 − 2) + (3.4 × 10 − 4) = 9.14
6-x³ + x when x = -2
Answer:
12 I thinkStep-by-step explanation:
6-(-2^3)+-2
A recipe for one batch of cookies calls for 3 cups of sugar and 2 tablespoons of salt.
How many batches can you make with 12 cups of sugar and 8 tablespoons of salt?
Which one would it be?
Solving the given equation we get value of x as -3/2 i.e option (a) is correct option.
What are exponents and its properties?
A number's exponent indicates how many times the number has been multiplied by itself. Example: Since 2 is multiplied by itself 4 times, 2×2×2×2 can be expressed as [tex]2^{4}[/tex]. Here, 4 is referred to as the "exponent" or "power," while 2 is referred to as the "base."
Generally speaking, [tex]x^{n}[/tex] denotes that x has been multiplied by itself n times.
Raise a power to a power
[tex](x^{a}) ^{b}=x^{ab}[/tex]
This is called the power of a power property
Negative exponents are the reciprocals of the positive exponents.
[tex]x^{-a}=\frac{1}{x^a}[/tex]
The same properties of exponents apply for both positive and negative exponents.
[tex](1/25)^x = 125\\ 25^{-x} = 125\\(5^2)^{-x} = 5^3\\5^{-2x} = 5^3\\\implies -2x = 3\\\implies x = -3/2[/tex]
i.e.
Option (a) is correct.
To know more about exponent properties, follow link:
https://brainly.com/question/3187898
#SPJ1
(1 point) standard automobile license plates in a country display 2 numbers, followed by 3 letters, followed by 2 numbers. how many different standard plates are possible in this system? (assume repetition of letters and numbers is allowed.) your answer is :
Therefore ,there are 158,184,000 ways to create a license plate in this system.
What is combination ?A selection from a group of separate items is called a combination in mathematics, and the order in which the elements are chosen is irrelevant (unlike permutations). An apple and a pear, an apple and an orange, or a pear and an orange are three combinations of two fruits that can be chosen from a set of three fruits, such as an apple, an orange, and a pear. Formally speaking, a set S's k-combination is a subset of S's k unique components. Two combinations are therefore equal if and only if they have the same elements in both combinations.
According to the counting principle, the total number of ways to obtain a license plate is calculated by multiplying the number of times each of these events might occur together.
The first number (the digits 1 through 9) can be obtained in nine different ways.
There are 26 methods to obtain the first letter. There are 26 ways to obtain the following letter (repetition is acceptable).
There are 26 methods to get the third letter, 10 ways to get the next number (zero is acceptable), and 10 ways to get the following number with repetitions.
How many ways are there to get the next number? 10 ways\s.
Thus ,total options for obtaining a license plate:
9 x 26 x 26 x 26 x 10 x 10=158184000
Therefore ,there are 158,184,000 ways to create a license plate in this system.
To know more about combination , visit
https://brainly.com/question/27058178
#SPJ4
A vacant lot is assessed at $36,000. What property tax must be paid on the lot if the tax rate is 2.4 cents per $1? PLEASE SHOW WORK
Answer:
The property tax that must be paid on the lot is $864.
Step-by-step explanation:
The assessment value of the lot is $36,000, and the tax rate is 2.4 cents per $1, or 0.024. So the total amount of tax due is calculated as follows:
$36,000 * 0.024 = $<<36000*0.024=864>>864
How do I put this answer as a point?
5x - 4y = 11
x = 3
Answer:
(3,1)
Step-by-step explanation:
hii ! for this question, x = 3, which is your first point. for the second part, you're going to need to plug x into the 5x.
5(3)-4y=11
15-4y=11
subtract 15 from each side
-4y=-4
y=1
(3,1) is gonna be your answer !
Help PLEAZE with all theses
Answer:
Look at the sides and angles.
Step-by-step explanation:
See which sides are equal pr seem so. Use logic.
what's the answer 7x + 7=7(x+_)
the answer is 1
Step-by-step explanation:
Let f(x)represent a function.
f(x-3.5) means f(x) is translated 3.5 units left. 3f(x) implies f(x) is vertically stretched by a factor of 3.5.
How to match the descriptions with the transformations?A function is a relationship between inputs where each input is related to exactly one output. Also, translation means movement on a straight line
In the cartesian plane or graph, movement in the x-axis is either to the left (negative) or right (positive).
Thus, f(x-3.5) implies f(x) is translated 3.5 units left (i.e. -3.5)
For 3.5f(x), when you multiply f(x) by 3.5, you stretch it by 3.5. Thus, f(x) is vertically stretched by a factor of 3.5
Learn more about function on:
brainly.com/question/26103899
#SPJ1
there are 5 friends and the total is 25.87 how much would all of them will pay
Answer:
£5.174
Step-by-step explanation:
Because you do 25.87 divided by 5
Which of the following differential equation is exact?
A. (y2+ x)dx+ (y3 + x)dy = 0
B. (x + y) (dx - dy) = dx + dy
C. 2xydx + (x + y2) dy = 0
D. None of the above
Answer:
B
Step-by-step explanation:
Solve (x + y(x)) (-(dy(x))/(dx) + 1) = (dy(x))/(dx) + 1:
Let v(x) = x + y(x), which gives (dv(x))/(dx) = (dy(x))/(dx) + 1:
(-(dv(x))/(dx) + 2) v(x) = (dv(x))/(dx)
Simplify:
-((dv(x))/(dx) - 2) v(x) = (dv(x))/(dx)
Solve for (dv(x))/(dx):
(dv(x))/(dx) = (2 v(x))/(v(x) + 1)
Divide both sides by v(x)/(v(x) + 1):
((dv(x))/(dx) (v(x) + 1))/v(x) = 2
Integrate both sides with respect to x:
integral((dv(x))/(dx) (v(x) + 1))/v(x) dx = integral2dx
Evaluate the integrals:
log(v(x)) + v(x) = 2 x + c_1, where c_1 is an arbitrary constant.
Solve for v(x):
v(x) = W(e^(2 x + c_1))
Simplify the arbitrary constants:
v(x) = W(c_1 e^(2 x))
Substitute back for y(x) = -x + v(x):
Answer: y(x) = -x + W(c_1 e^(2 x))
PLEASE I NEED HELP MY CLASS IS DUE TOMORROW!!! WILL GIVE 30 POINTS!!! ASAP PLEASE!
Answer:
217
Step-by-step explanation:
Answer:
Step-by-step explanation:
A carpenter used 29 ft of molding in three pieces to trim a garage door. If the
long piece was 1 ft longer than twice the length of each shorter piece, then
how long was each piece?
Answer:
Let's call the length of the long piece x, and the length of each shorter piece y. We can set up the following equation to represent the problem:
x + 2y = 29
Since the long piece is 1 ft longer than twice the length of each shorter piece, we can write this equation as:
x = 2y + 1
Substituting this expression for x in the first equation, we get:
2y + 1 + 2y = 29
Combining like terms on both sides, we get:
4y + 1 = 29
Subtracting 1 from both sides, we get:
4y = 28
Dividing both sides by 4, we get:
y = 7
Substituting this value for y in the expression for x, we get:
x = 2(7) + 1 = 14 + 1 = 15
Thus, the length of the long piece is 15 ft, and the length of each shorter piece is 7 ft.
