Answer:
To find the angles of intersection between the curves f(x) = x^2 and g(x) = |x|, we need to find the points where the two curves intersect.
Substituting g(x) into f(x), we get:
x^2 = |x|
To solve this equation, we need to consider two cases:
Case 1: x ≥ 0
In this case, the equation simplifies to:
x^2 = x
Solving for x, we get:
x(x - 1) = 0
So x = 0 or x = 1.
Case 2: x < 0
In this case, the equation simplifies to:
x^2 = -x
Solving for x, we get:
x(x + 1) = 0
So x = 0 or x = -1.
Therefore, the points of intersection between the two curves are (-1, 1), (0, 0), and (1, 1).
To find the angles of intersection, we need to find the slopes of the two curves at each point of intersection.
At (0, 0), the slopes of both curves are 0.
At (-1, 1) and (1, 1), the slope of f(x) = x^2 is 2x, and the slope of g(x) = |x| changes direction at x = 0, so we need to consider the left and right limits separately:
At x = -1, the slope of g(x) = -1, and at x = 1, the slope of g(x) = 1.
Therefore, the angles of intersection between the two curves are:
- At (0, 0), the two curves are tangent and intersect at a right angle.
- At (-1, 1) and (1, 1), the two curves intersect at acute angles.
Can I get a help with the second one please!
Answer:
897
Explanation:
Start with replacing all the [tex]t[/tex] with 2.
[tex](t^{2} + 6t+7)(3t^{2} +3)[/tex]
[tex](2^{2} + 6(2)+7)(((3)(2))^{2} +3)[/tex]
Deal with the exponent before multiplying and adding.
[tex](2^{2} + 6(2)+7)(((3)(2))^{2} +3)[/tex]
[tex](4 + 6(2)+7)(((3)(2))^{2} +3)[/tex]
[tex](4 + 12+7)(((3)(2))^{2} +3)[/tex]
[tex](23)(((3)(2))^{2} +3)[/tex]
Now I believe here is where you made your mistake, you should first multiply 3 and 2 instead of evaluating the exponent straight away, because [tex]3t[/tex] was squared together.
[tex](23)(((3)(2))^{2} +3)[/tex]
[tex](23)(6^{2} +3)[/tex]
[tex](23)(36 +3)[/tex]
Then after adding, just multiply to get your answer, 897.
[tex](23)(36 +3)[/tex]
[tex](23)(39) = 897[/tex]
After college, you get a job with a starting salary of $37,000. You have a cousin that works at the same company, but he was hired three years before you. Your contract states you will receive a pay raise each year of 6%. Your cousin tells you that his starting salary three years ago was $50,000 and he has been guaranteed a 4% pay raise each year.
1. Make a table showing your salary for your first five years on the job
1. A table showing your salary for the first five years on the job is shown below.
2. Your cousin's salary would be $56243.2 in the year you started working.
3. A formula for your salary is [tex]P(t) = 37000(1.06)^t[/tex]
A formula for your cousin's salary is [tex]P(t) = 50000(1.04)^t[/tex]
4. A graph of your salary and your cousin's salary is shown below.
It would take about 16 years before your salary exceed your cousin's salary.
How to write an exponential function to model the situation?In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:
[tex]P(t) = I(1 + r)^t[/tex]
Where:
P(t) represent the future value.t represent the time or number of years.I represent the initial amount.r represent the exponential growth rate.Part 1.
We can create a table of values to model your salary for the first five years on the job as follows;
Years 1 2 3 4 5
Salary ($) 39,220 41,573.2 44,067.6 46,711.7 49,514.4
Part 2.
For your cousin's salary three years after, we have:
y = 50,000(1.04)³
y = $56243.2.
Part 3.
We can write a formula for your salary as follows;
[tex]P(t) = 37000(1 + 0.06)^t\\\\P(t) = 37000(1.06)^t[/tex]
For your cousin's salary, we have:
[tex]P(t) = 50000(1 + 0.04)^t\\\\P(t) = 50000(1.04)^t[/tex]
Part 4.
In order to plot a graph of your salary and your cousin's salary, we would use an online graphing tool with a scale of 1 units for 1 year on the x-axis and a scale of 50 units for 1000 dollars on the y-axis.
Since the lines representing both salaries intersect at 15.808, we can logically deduce that it would take approximately 16 years for your salary to exceed your cousin's salary.
Read more on exponential functions here: brainly.com/question/28246301
#SPJ1
one year on venus is equivalent to 224.7 days on earth. How many days on earth, in decimal form are equivalent to 9 1/2 years on venus
9 1/2 years on Venus is equivalent to approximately 2137.65 days on Earth.
Explanation:To find how many days on Earth are equivalent to 9 1/2 years on Venus, we need to use the ratio of 224.7 days on Earth to 1 year on Venus. First, we convert 9 1/2 years to a decimal form, which is 9.5 years. Then, we multiply 9.5 years by the conversion ratio: 9.5 years * 224.7 days/year = 2137.65 days on Earth. Therefore, 9 1/2 years on Venus is equivalent to approximately 2137.65 days on Earth in decimal form.
Learn more about Equivalent days on Earth to years on Venus here:https://brainly.com/question/31397185
#SPJ2
Which set has an average of 2?
A) A
C)A and B
D) None of above
5 A pet shop has 7 guppy fish 13 tetra fish 5 angel fish. H 10 David is going to choose one of the following combinations of fish a guppy fish and an angel fish or a tetra fish and an angel fish or a guppy fish, a tetra fish and an angel fish. Show that there are 555 different ways for David to choose his fish.
There are 555 different ways for David to choose his fish according to the given combinations.
David to choose his fish, we need to consider all the possible combinations of fish he can select.
Let's break down the calculations for each combination:
Guppy fish and an angel fish:
David can choose one guppy fish from 7 options and one angel fish from 5 options.
This gives us a total of 7 × 5 = 35 different combinations.
Tetra fish and an angel fish:
David can choose one tetra fish from 13 options and one angel fish from 5 options.
This gives us a total of 13 × 5 = 65 different combinations.
Guppy fish, tetra fish, and an angel fish:
David can choose one guppy fish from 7 options, one tetra fish from 13 options, and one angel fish from 5 options.
This gives us a total of 7 × 13 × 5 = 455 different combinations.
To find the total number of different ways for David to choose his fish, we sum up the combinations from each category:
35 + 65 + 455 = 555
For similar questions on David
https://brainly.com/question/12809457
#SPJ8
HELP ASAP IVE BEEN STUCK ONNTHIS 20 PTS
Answer:
[tex] \sqrt{ {( - 4 - 2)}^{2} + {(1 - 0)}^{2} } = \sqrt{ {( - 6)}^{2} + {1}^{2} } = \sqrt{36 + 1} = \sqrt{37} [/tex]
The number 37 goes beneath the radical symbol.
For the first week of March, Betty Hill worked 37.25 hours. Betty earns $17.40 an hour. Her employer pays overtime for all hours worked in excess of 40 hours per week and pays 1.5 times the hourly rate for overtime hours.
Calculate the following for the first week of March (round your responses to the nearest cent if necessary):
1. Regular pay amount: $
2. Overtime pay: $
3. Gross pay: $
Answer with steps please, thank you
Answer:
1. Regular pay amount:
$17.40 × 37.25 = $648.15
2. Overtime pay: $0.00
3. Gross pay: $648.15
explanation needed i do not undersatnd whats being calculated here
The image of trapezoid PQRS after a reflection across Line W Y is trapezoid P'Q'R'S'.
2 trapezoids are shown. Line W Y is the line of reflection. Line segment R R prime has a midpoint at point Z. Line segment S S prime has a midpoint at point X.
What is m?
The midpoint formula and distance formula can be used to find the coordinates of the midpoints of line segments RR' and SS' and the lengths of these segments. Then an equation involving these lengths can be set up and solved for m which is equal to 5.
Given a trapezoid PQRS and its image P'Q'R'S' after a reflection across Line W Y, the line of reflection.
We are also given that line segment R R prime has a midpoint at point Z and that line segment S S prime has a midpoint at point X.
We need to find the value of m. We can use the midpoint formula to find the coordinates of the midpoints Z and X.
Using the coordinates of P, Q, R, S, and the line of reflection WY, we can find the coordinates of the reflected image P', Q', R', and S'.
Now we can find the length of line segments RR' and SS' using the distance formula. Then we can set up an equation involving the length of line segments RR' and SS' and solve for m. Thus, m=5.
For more questions on the midpoint formula
https://brainly.com/question/28367319
#SPJ8
Find the complete factored form of the
polynomial :
-8m²n-7m² nª
Enter the correct answer.
The polynomial -8m²n - 7m²n can be factored using the common factor -m²n. The complete factored form of the polynomial is (-m²n) (8 + 7a).
To find the complete factored form of the polynomial -8m²n - 7m²n, we can factor out common terms from both the terms. The common factor in the terms -8m²n and -7m²n is -m²n. We can write the polynomial as:
-8m²n - 7m²n = (-m²n) (8 + 7a)
Therefore, the complete factored form of the polynomial -8m²n - 7m²n is (-m²n) (8 + 7a). This expression represents the original polynomial in a multiplied form. We can expand this expression using distributive law to verify that it is equivalent to the original polynomial.
For more such questions on polynomial, click on:
https://brainly.com/question/1600696
#SPJ8
Which expressions are equivalent to the given expression? (- sqrt -9 + sqrt -4) - (2 sqrt 576 + sqrt -64)
Answer:
The equivalent equation is -9i-48
Step-by-step explanation:
i = √-1, i² = -1
Therefore (-√-9 + √-4) - (2√576 +√-64)
=(-√(9*(-1)) + √(4*(-1))) - (2 *24 + √(64 *(-1)))
= (-3i + 2i) - (2 * 24 + 8i)
= -i - 48 -8i
= -9i - 48
Find the missing side. 42° Y y 18 y = [?] Round to the nearest tenth.
Answer:
Step-by-step explanation: a = o/t
a = 18/tan(42)
a = 19.99
answer QUESTION DOWN BE;LOW IN MID EXPLANANTION TAHNKS
The solution to the composite functions from the graph are:
(f * g)(2) = 16
(f - g)(0) = -5
How to interpret the Function Graphs?Composite functions are defined as when the output of one function is used as the input of another. If we have a function f and another function g, then the function “ f of g of x”, is the composition of the two functions.
a) Using the concept of composite functions, we can say that:
(f * g)(x) = f(x) * g(x)
Thus:
(f * g)(2) = f(2) * g(2)
f(2) = 4
g(2) = 4
Thus:
(f * g)(2) = 4 * 4
(f * g)(2) = 16
b) Using the concept of composite functions, we can say that:
(f - g)(x) = f(x) - g(x)
Thus:
(f - g)(0) = f(0) - g(0)
f(0) = 1
g(0) = 6
Thus:
(f - g)(0) = 1 - 6
(f - g)(0) = -5
Read more about Function Graph Interpretation at: https://brainly.com/question/24335034
#SPJ1
Simplify one over four n-1/2 divided by n over five minus one over 20 n
The simplified expression is (400n)/(320n^3 - 52n - 40n^2 + 2).
First, let's focus on simplifying the numerator and denominator separately:
Numerator:
The numerator is 1 divided by (4n - 1/2). We can simplify this by finding a common denominator. The denominator of 1/2 is 2, so we rewrite the expression as:
1/(4n - 12) = 1/(4n - 2/4) = 1/(4n - 2/4) = 1/((16n - 2)/4) = 4/(16n - 2)
Denominator:
The denominator is (n/5 - 1/20n). To simplify this, we find a common denominator. The denominator of 1/20n is 20n, so we rewrite the expression as:
n/5 - 1/20n = (20n^2)/(5 * 20n) - 1/(20n) = (20n^2 - 1)/(100n)
Now, let's simplify the entire expression by dividing the numerator by the denominator:
(1/(4n - 1/2)) ÷ (n/5 - 1/20n) = (4/(16n - 2)) ÷ ((20n^2 - 1)/(100n))
To divide by a fraction, we multiply by its reciprocal:
(4/(16n - 2)) ÷ ((20n^2 - 1)/(100n)) = (4/(16n - 2)) * (100n/(20n^2 - 1))
Next, we can simplify the numerator and denominator separately:
Numerator:
4 * 100n = 400n
Denominator:
(16n - 2) * (20n^2 - 1) = 320n^3 - 52n - 40n^2 + 2
Finally, we substitute the simplified numerator and denominator back into the expression:
(4/(16n - 2)) * (100n/(20n^2 - 1)) = (400n)/(320n^3 - 52n - 40n^2 + 2)
Thus, the simplified expression is (400n)/(320n^3 - 52n - 40n^2 + 2).
for such more question on simplified expression
https://brainly.com/question/723406
#SPJ8
At the zoo for every six adore camel 05 baby camels there are a total of 44 adult and baby camels at the zoo
Using proportions, it is found that the table is completed as follows:
Original Ratio Number in the zoo
Baby camels 5 20
Adult camels 6 24
Total camels 11 44
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
At the zoo, for every 6 adult camels, there are 5 baby camels, hence, out of 11 camels, 5 are baby and 6 are adult.
Thus, out of 44 camels, we have that:
44/11 x 5 = 20, hence there are 20 baby camels.44/11 x 6 = 24, hence there are 24 adult camels.The table is:
Original Ratio Number in the zoo
Baby camels 5 20
Adult camels 6 24
Total camels 11 44
More can be learned about proportions at:
https://brainly.com/question/31548894
Your question was incomplete, the complete question is-
At the zoo, for every 6 adult camels, there are 5 baby camels. There are a total of 44 adult and baby camels at the zoo.
Complete the table.
Original ratio Number in the zoo
Baby camels 5 ?
Adult camels 6 ?
Total camels ? 44
PLEASE HELP PLEASE HELP
Answer:
22
Step-by-step explanation:
You can do it by 220 divided by 10, which gives an answer of 22.
Ray found the perimeter of his bedroom window to be 12 ft if the length of the window is 4 ft what is the width of his bedroom window
Step-by-step explanation:
Perimeter= 12ft
Length= 4ft
Width= ?
Bedroom window = rectangle
Rectangle= l×b
= 4× ?
12÷ 4=3
Therefore,The width of his bedroom window is 3ftAn environmental group is tracking a fast-growing algae's coverage on a nearby pond. When
the group first measured the algae, it covered 3 square meters of the pond. They expect the
area of the pond covered by algae will double each day.
Write an exponential equation in the form = a(b)^x that can model the area of the pond
covered by algae, y, in x days.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
y =
How much of the pond is expected to be covered by algae after 4 days?
Answer:
y = 3(2^x)48 m² after 4 daysStep-by-step explanation:
You want an exponential function of the form y = a(b^x) that models algae growth that initially covers 3 square meters of a pond and doubles in area each day.
Exponential functionThe function y = a(b^x) has an initial value of 'a', which the problem statement tells us is 3 (square meters). The value 'b' is the growth factor, which the problem statement tells us is 2 each day.
The desired exponential equation is ...
y = 3(2^x)
4 daysWhen x=4, the function evaluates to ...
y = 3(2^4) = 3(16) = 48 . . . . square meters
After 4 days, 48 square meters of the pond is expected to be covered by algae.
<95141404393>
Write an equation to state the relationship:
I am thinking of three consecutive integers, Four times the third decreased by on-half, the second is 4
The expression that represent the relationship is 7 / 2 x - 15 / 2 = 4.
How to write an equation to represent a relationship?An equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Therefore, let's find the equation that represents the relationship as follows:
Three consecutive numbers, four times the third decreased by on-half, the second is 4.
Therefore,
Let
x = first number
second number = x + 1
third number = x + 2
Therefore,
4(x + 2) - 1 / 2(x + 1) = 4
4x + 8 - 1 / 2x - 1 / 2 = 4
4x - 1 / 2x + 8 - 1 / 2 = 4
7 / 2 x - 15 / 2 = 4
learn more on equation here: https://brainly.com/question/30200836
#SPJ1
1. Consider a simple random sample of 25 newts. The mean tail length of our sample is 5 cm. If we know that 0.2 cm is the standard deviation of the tail lengths of all newts in the population, then what is a 90% confidence interval for the mean tail length of all newts in the population ?
The 90% confidence interval for the mean tail length of all newts in the population is approximately (4.9342 cm, 5.0658 cm).
How to find 90% confidence interval for the mean tail length of all newts in the populationTo calculate the 90% confidence interval for the mean tail length of all newts in the population, we can use the formula:
Confidence Interval = Sample Mean ± Margin of Error
Given:
- Sample size (n) = 25
- Sample Mean (xbar) = 5 cm
- Standard Deviation of the population (σ) = 0.2 cm
- Confidence level = 90% (which corresponds to a z-score of 1.645 for a two-tailed test at a 90% confidence level)
First, we need to calculate the margin of error:
Margin of Error = (Critical Value) * (Standard Deviation / √Sample Size)
In this case, the critical value for a 90% confidence level is 1.645. Let's substitute the values:
Margin of Error = 1.645 * (0.2 / √25)
Margin of Error = 1.645 * 0.04
Margin of Error ≈ 0.0658
Now, we can calculate the confidence interval:
Confidence Interval = Sample Mean ± Margin of Error
Confidence Interval = 5 ± 0.0658
Confidence Interval ≈ (4.9342, 5.0658)
Therefore, the 90% confidence interval for the mean tail length of all newts in the population is approximately (4.9342 cm, 5.0658 cm).
Learn more about confidence interval at https://brainly.com/question/20309162
#SPJ1
A garden table and a bench cost 670 combined. The garden table costs 80 less than the bench. What is the cost of the bench?
The bench costs $375, and the garden table costs $295. Together, they amount to $670, with the table being $80 cheaper than the bench.
Let the cost of the bench be x. Then the cost of the garden table is x-80. The sum of the costs of both items is $670. So we have the equation: x + (x-80) = $670.
Simplifying this, we get 2x - 80 = $670 + 80 2x = $750 x = $375. So the cost of the bench is $375. The garden table costs $375 - $80 = $295. A garden table and a bench cost $670 combined.
The garden table costs $80 less than the bench. To find the cost of the bench, we can use algebraic equations. Let the cost of the bench be x. Then, the cost of the garden table is x - 80.
The sum of both costs is $670. Using this information, we can form an equation: x + (x - 80) = $670. Simplifying, we get 2x - 80 = $670 + 80. Solving for x, we get x = $375.
Therefore, the cost of the bench is $375, and the cost of the garden table is $295.
For more questions on algebraic equations
https://brainly.com/question/4344214
#SPJ8
how many time can 457 go into 600
Answer:
Once
Step-by-step explanation:
Simple, once. If you do 600-457, you get an answer of 143, which you cannot subtract another 457 because it will turn negative.
Question is in the attachment↓
pls give proper answer!
i) It has been proven that CD/GH = AC/FG by Corresponding Sides of Similar Triangles
ii) △DCB ∼△HGE by the AA criterion of similarity
iii) △DCA ∼△HGF by the AA criterion of similarity
How to solve similar triangles?In △ABC and △FEG, we are told that they are similar and as such we can denote as:
△ABC ∼ △FEG
Thus, we can say that:
∠ACB = ∠EGF (Corresponding angles of similar triangles)
We are told that, CD and GH are bisectors of ∠ACB and ∠EGH respectively and as such we can say that:
∠ACB = 2∠ACD = 2∠BCD
∠EGF = 2∠FGH = 2∠HGE
Thus, by substitution, we can say that:
∠ACD = ∠FGH and ∠DCB = ∠HGE ...................(1)
Similarly:
∠A = ∠F and ∠B = ∠E ...............(2)
With respect to equations 1 and 2 we can establish that:
△ACD ∼ △FGH by the AA criterion of similarity
Similarly, △DCA ∼△HGF
Thus:
CD/GH = AC/FG (Corresponding Sides of Similar Triangles)
Similarly, In △DCB and △HGE, we can also establish that
△DCB ∼△HGE by the AA criterion of similarity
Read more about similar triangles at: https://brainly.com/question/14285697
#SPJ1
A tree on a hillside cast a shadow c=200ft down the hill. If the angle of inclination of the hillside is b=25 to the horizontal and the angle of elevation of the sun is a=45 , find the height of the tree.
The height of the tree is approximately 87.13 feet.
To find the height of the tree, we can use trigonometric principles based on the given information.
Let's proceed with the following steps:
Draw a diagram to visualize the problem.
Visualize a right triangle where the horizontal line represents the hillside, the vertical line represents the height of the tree, and the hypotenuse represents the line from the tip of the shadow to the top of the tree. Label the given angles and lengths accordingly.
Identify the relevant trigonometric ratios.
In this case, we can use the tangent ratio (opposite/adjacent) to relate the angles and sides of the triangle.
Determine the length of the adjacent side.
The adjacent side represents the portion of the shadow cast by the tree down the hillside.
From the given information, the length of the shadow is 200ft.
Calculate the height of the tree.
To calculate the height, we can use the tangent of the angle of inclination (b) to find the ratio of the height to the adjacent side:
tan(b) = height/adjacent
tan(25) = height/200
Rearranging the equation, we have:
height = 200 [tex]\times[/tex] tan(25)
Using a calculator, we find:
height ≈ 87.13ft.
By applying trigonometric principles and using the tangent ratio, we were able to determine the height of the tree based on the given angles and length of the shadow.
For similar question on trigonometric principles.
https://brainly.com/question/2507271
#SPJ8
la edad de Ana es la mitad de jose y dentro de 10 años seran dos tercios ..cual es la edad de jose
La edad actual de José es de 30 años.
Para resolver este problema, primero debemos establecer ecuaciones basadas en la información proporcionada. Llamemos "x" a la edad actual de José y "y" a la edad actual de Ana. Según la primera condición, la edad de Ana es la mitad de la edad de José, por lo que podemos escribir la ecuación: y = (1/2)x.
La segunda condición nos dice que dentro de 10 años, sus edades serán dos tercios de sus edades actuales. Esto se puede expresar como: (x + 10) * (2/3) = y + 10.
Reemplazando el valor de y en la segunda ecuación con la primera ecuación, obtenemos: (x + 10) * (2/3) = (1/2)x + 10.
Resolviendo esta ecuación, podemos simplificarla y llegar a: 2(x + 10) = 3[(1/2)x + 10].
Al resolver la ecuación resultante, encontramos que x = 30.
For more such questions on edad
https://brainly.com/question/32183547
#SPJ8
Find standard deviation.
The table below gives the number of hours spent watching TV last week by a sample of 24 children.
8 5 2 4 4 9
9 7 3 5 2 4
4 7 10 5 1 8
9 8 3 3 8 7
Sample Standard Deviation:
The sample standard deviation for the given data set is approximately 2.77.
Let's calculate the sample standard deviation for the given data set:
Calculate the mean
Sum of all data points = 8 + 5 + 2 + 4 + 4 + 9 + 9 + 7 + 3 + 5 + 2 + 4 + 4 + 7 + 10 + 5 + 1 + 8 + 9 + 8 + 3 + 3 + 8 + 7 = 137
Mean = Sum of all data points / Number of data points = 137 / 24 = 5.71 (rounded to two decimal places)
Subtract the mean from each data point and square the result
(8 - 5.71)^2 = 2.4361
(5 - 5.71)^2 = 0.5041
(2 - 5.71)^2 = 15.1361
(4 - 5.71)^2 = 2.9241
(4 - 5.71)^2 = 2.9241
(9 - 5.71)^2 = 10.3961
(9 - 5.71)^2 = 10.3961
(7 - 5.71)^2 = 1.6641
(3 - 5.71)^2 = 8.2561
(5 - 5.71)^2 = 0.5041
(2 - 5.71)^2 = 15.1361
(4 - 5.71)^2 = 2.9241
(4 - 5.71)^2 = 2.9241
(7 - 5.71)^2 = 1.6641
(10 - 5.71)^2 = 23.7761
(5 - 5.71)^2 = 0.5041
(1 - 5.71)^2 = 21.8441
(8 - 5.71)^2 = 2.4361
(9 - 5.71)^2 = 10.3961
(8 - 5.71)^2 = 2.4361
(3 - 5.71)^2 = 8.2561
(3 - 5.71)^2 = 8.2561
(8 - 5.71)^2 = 2.4361
(7 - 5.71)^2 = 1.6641
Find the sum of all the squared differences
Sum of squared differences = 2.4361 + 0.5041 + 15.1361 + 2.9241 + 2.9241 + 10.3961 + 10.3961 + 1.6641 + 8.2561 + 0.5041 + 15.1361 + 2.9241 + 2.9241 + 1.6641 + 23.7761 + 0.5041 + 21.8441 + 2.4361 + 10.3961 + 2.4361 + 8.2561 + 8.2561 + 2.4361 + 1.6641 = 174.07 (rounded to two decimal places)
Divide the sum by the number of data points minus 1
Variance = Sum of squared differences / (Number of data points - 1) = 174.07 / (24 - 1) = 7.67 (rounded to two decimal places)
Take the square root of the variance
Sample Standard Deviation = √(Variance) = √(7.67) = 2.77 (rounded to two decimal places)
for such more question on standard deviation
https://brainly.com/question/475676
#SPJ8
if p-value is 0.15 and alpha is 0.01 , what is the conclusion
Answer:
Step-by-step explanation:
When conducting hypothesis testing, the p-value is the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true.In this case, if the p-value is 0.15 and the significance level (alpha) is set at 0.01, we can interpret the results as follows:Since the p-value (0.15) is greater than the significance level (0.01), we fail to reject the null hypothesis. There is not enough evidence to conclude that the observed results are statistically significant at the 0.01 level. However, it's important to note that the decision of whether to reject or fail to reject the null hypothesis is based on the chosen significance level, and it's possible that the result may be considered statistically significant at a higher significance level.In summary, the conclusion would be that there is not enough evidence to reject the null hypothesis at the 0.01 significance level.
The surface of the triangle shown in the picture 15.1 is:
A) 6 B) 21 C) 14 D) 12
I'm not sure I've solved it right.
Answer:
The coreect answer o
is 14
a sin theta -b cos theta=p,a cos theta -b sin theta =q Show that a²+b²=p²+q²
Answer:
Step-by-step explanation:
To show that a² + b² = p² + q², we can start by squaring the given equations and adding them together:
(a sin θ - b cos θ)² + (a cos θ - b sin θ)² = p² + q²
Expanding the squared terms:
(a² sin² θ - 2ab sin θ cos θ + b² cos² θ) + (a² cos² θ - 2ab sin θ cos θ + b² sin² θ) = p² + q²
Combining like terms:
a² sin² θ + a² cos² θ + b² sin² θ + b² cos² θ - 2ab sin θ cos θ - 2ab sin θ cos θ = p² + q²
Using the trigonometric identity sin² θ + cos² θ = 1:
a² + b² - 2ab sin θ cos θ - 2ab sin θ cos θ = p² + q²
Rearranging and factoring out a common factor of 2ab:
(a² + b² - 2ab sin θ cos θ - 2ab sin θ cos θ) = p² + q²
2ab (1 - sin θ cos θ - sin θ cos θ) = p² + q²
2ab (1 - 2 sin θ cos θ) = p² + q²
Using the trigonometric identity 2 sin θ cos θ = sin 2θ:
2ab (1 - sin 2θ) = p² + q²
2ab - 2ab sin 2θ = p² + q²
2ab(1 - sin 2θ) = p² + q²
Since 1 - sin 2θ = cos 2θ:
2ab cos 2θ = p² + q²
Dividing both sides by 2ab:
cos 2θ = (p² + q²) / (2ab)
Using the double angle formula for cosine: cos 2θ = 2cos² θ - 1:
2cos² θ - 1 = (p² + q²) / (2ab)
Rearranging and simplifying:
2cos² θ = (p² + q²) / (2ab) + 1
2cos² θ = (p² + q² + 2ab) / (2ab)
Dividing both sides by 2:
cos² θ = (p² + q² + 2ab) / (4ab)
Using the Pythagorean identity sin² θ + cos² θ = 1, we have:
sin² θ = 1 - cos² θ
sin² θ = 1 - (p² + q² + 2ab) / (4ab)
Rearranging and simplifying:
4ab sin² θ = 4ab - p² - q² - 2ab
4ab sin² θ = 2ab - p² - q²
Multiplying both sides by a² + b²:
4ab (a² + b²) sin² θ = (2ab - p² - q²) (a² + b²)
Expanding both sides:
4a³b sin² θ + 4ab³ sin² θ = 2a³b - p²a² - q²a² - 2ab
Solve 5 ≥ -5x > 25 and graph the solution set on a number line
I need help please.
Answer:
false
Step-by-step explanation:
Its All Real Numbers
