Answer:
To solve this problem using cylindrical coordinates, we need to express the integrand and the limits of integration in terms of cylindrical coordinates. In cylindrical coordinates, a point in 3D space is represented by the radius (r), the angle (theta), and the height (z), where:
x = r cos(theta)
y = r sin(theta)
z = z
The volume element in cylindrical coordinates is given by:
dV = r dr dtheta dz
Now we can write the integral as:
∫∫∫W(x^2+y^2)dV = ∫∫∫W(r^2) r dr dtheta dz
The limits of integration are given by:
0 ≤ z ≤ 2 (since the region of integration is between z=0 and z=2)
0 ≤ r ≤ 5 (since the region of integration is within the circle of radius 5 in the xy-plane)
0 ≤ theta ≤ 2π (since the region of integration extends throughout the entire circle in the xy-plane)
Therefore, we can write the integral as:
∫∫∫W(r^2) r dr dtheta dz
= ∫0^2 ∫0^5 ∫0^2 (r^2) r dz dr dtheta
Integrating with respect to z first, we get:
∫0^2 ∫0^5 ∫0^2 (r^2) r dz dr dtheta
= ∫0^2 ∫0^5 [(r^2) r (2-0)] dr dtheta
= 2 ∫0^5 (r^3) dr ∫0^2 dtheta
= 2 (1/4) (5^4) (2)
= 1250
Therefore, the value of the integral is 1250.
Help!!!!!!!!!!!!
Write the new coordinates of A'B'C' after
the reflection described below
A(5, -1), B(3,-4), C(3, 0)
Reflection across the y-axis
A:
B:
C:
Thus, new coordinates of A'B'C' after the reflection across the y-axis are-
A'(-5, -1), B'(-3,-4), C'(-3, 0).
Explain about the reflection across y-axis:The x-coordinate remains constant when a point is reflected across the x-axis, but the y-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the x-axis as (x, -y).
The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the y-axis as (-x, y).
Given coordinates of ABC.
A(5, -1), B(3,-4), C(3, 0)
Reflection across the y-axis : y coordinates remains same while x coordinate multiplied with -1.
(x,y) -- > (-x, y)
A'(-5, -1), B'(-3,-4), C'(-3, 0)
Thus, new coordinates of A'B'C' after the reflection across the y-axis are-
A'(-5, -1), B'(-3,-4), C'(-3, 0).
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Q3: Use the image to determine the direction and angle of rotation.
graph of triangle ABC in quadrant 4 and a second polygon A prime B prime C prime in quadrant 3
90° clockwise rotation
90° counterclockwise rotation
180° clockwise rotation
360° counterclockwise rotation
the direction and angle of rotation between the two polygons is 180° clockwise rotation.
How to solve the question?
Based on the given information, we can determine the direction and angle of rotation between the two polygons.
First, let's look at the initial positions of the polygons. The graph of triangle ABC is located in Quadrant 4, which means that it is in the bottom-right portion of the coordinate plane. On the other hand, the second polygon A'B'C' is located in Quadrant 3, which is in the bottom-left portion of the coordinate plane.
To find the direction and angle of rotation between the two polygons, we need to imagine rotating one polygon onto the other. We can see that the two polygons are mirror images of each other across the y-axis. Therefore, we can infer that there is a horizontal line of symmetry between the two polygons.
If we rotate polygon A'B'C' 180 degrees clockwise around the origin, it will overlap perfectly with triangle ABC. This is because a 180-degree rotation is equivalent to a half-turn or a flip, which is exactly what we need to make the two polygons overlap. Therefore, the answer is 180° clockwise rotation.
In summary, the direction and angle of rotation between the two polygons is 180° clockwise rotation.
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The table shows the length of the songs played by a radio station during a 90-minute period. Alicia is making a histogram of the data. What frequency should she show for the interval 160-169 seconds?
The frequency for the interval 160-169 seconds is 3.
What is mode of the data?The value that appears the most frequently in a data set is its mode. In the data set, it is the number that appears the most frequently. For instance, in the subsequent data set:
2, 3, 4, 4, 5, 5, 5, 6, 7, 8
Since no other value appears more frequently, the mode is 5, which only appears three times. The data set is considered to have several modes if various values occur with the same greatest frequency. There is no mode if no value appears more than once in the data collection.
From the given table we see that the songs that have the time duration between 160 and 169 is:
162, 168, 165
Hence, the frequency for the interval 160-169 seconds is 3.
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The complete question is:
ben and david plot the locations of their houses and the park on the grid show below. they r planning to each start at home and travel in a straight line to the park. how many times greater is the distance ben travels to get to the park than the distance david travels?
The distance Ben travels to get to the park is approximately 2.21 times greater than the distance David travels. This is found by using the distance formula to calculate the distances each person travels and then comparing the results.
To solve this problem, we need to find the distance between each person's house and the park using the distance formula
distance = √((x₂ - x₁)² + (y₂ - y₁)²)
For Ben
distance = √((-2 - 4)² + (-2 - 6)²) = √((-6)² + (-8)²) = √(100) = 10
For David
distance = √((-2 - (-7))² + (-2 - (-6))²) = √((5)² + (4)²) = √(41)
So the ratio of Ben's distance to David's distance is
10 / √(41) ≈ 2.21
Therefore, Ben's distance is about 2.21 times greater than David's distance.
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Someone pls help me I’m so confused
The number of triangles that are displayed can be found to be 216 triangles.
How to find the number of triangles ?Each rectangular tile has a decorative pattern of 3 equal-sized squares, and each square is divided into 2 same-sized triangles. Therefore, each tile has 3 squares * 2 triangles per square = 6 triangles.
Marnie uses 36 of these tiles on the wall behind her kitchen stove. To find the total number of triangles displayed, multiply the number of triangles per tile by the total number of tiles:
Total triangles = 6 triangles per tile x 36 tiles = 216 triangles
So, there are 216 triangles displayed on the wall behind Marnie's kitchen stove.
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Is a triangle with sides of 5 meters, 12 meters, and 13 meters a right triangle? Explain/Show your work.
Answer:
Step-by-step explanation:
Find the volume of the cone below if the radius is 12 height is 12
Answer:
Work smartly not hard.
Step-by-step explanation:
AI
A flagpole is 12 feet fall. Its shadow is
11 feet long. How far is it from the top of the flagpole to the end of its shadow?
The distance from the top of the flagpole to the end of its shadow is approximately 10.02 feet.
Explain the term distance
Distance refers to the measurement of the space between two objects or points. It is typically measured in units such as meters, kilometres, miles, or feet. The distance can be calculated using various methods, including using maps, GPS technology, or mathematical formulas.
According to the given information
We can set up the following proportion:
h / 12 = d / 11
We can cross-multiply to get:
h x 11 = 12 x d
Simplifying further:
d = (h x 11) / 12
We need to solve for d, so we need to find the value of h. Using the Pythagorean theorem, we can set up the following equation:
h² + d² = 12²
Substituting d = (h x 11) / 12, we get:
h² + ((h x 11) / 12)² = 12²
Simplifying:
h² + (121h²) / 144 = 144
Multiplying both sides by 144/265:
265h² / 144 = 144
Solving for h:
h² = (144 x 144) / 265
h = √(20736 / 265)
h = √(78.113)
Now we can substitute this value into our earlier equation to find d:
d = (√(78.113) x 11) / 12
d ≈ 10.02 feet
Therefore, the distance from the top of the flagpole to the end of its shadow is approximately 10.02 feet.
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A quadratic function yields negative values between x = 2 and x = 6. Its minimum value is −2. What are the coordinates of the y-intercept? Enter your answer by filling in the boxes.
Answer:
Since the quadratic function has a minimum value at some point between x = 2 and x = 6, its graph is a downward-facing parabola.
Let's assume that the function is of form f(x) = ax^2 + bx + c, where a, b, and c are constants.
Since the minimum value of the function is −2, we know that the vertex of the parabola lies on the line y = -2. Also, we know that the x-coordinate of the vertex is the average of 2 and 6, which is 4.
Therefore, the equation of the parabola can be written as f(x) = a(x-4)^2 - 2.
Since the y-intercept is the value of y when x = 0, we can find it by plugging in x = 0 into the equation of the parabola:
f(0) = a(0-4)^2 - 2
f(0) = 16a - 2
We know that the function yields negative values between x = 2 and x = 6, so the parabola must intersect the y-axis below the x-axis. This means that the y-intercept is negative.
To find the y-intercept, we need to solve the equation 16a - 2 = 0, which gives us a = 1/8.
Therefore, the equation of the parabola is f(x) = (1/8)(x-4)^2 - 2.
Finally, we can find the y-intercept by plugging in x = 0:
f(0) = (1/8)(0-4)^2 - 2
f(0) = 8 - 2
f(0) = 6
So the coordinates of the y-intercept are (0, 6).
100 Points! Algebra question, photo attached. Only looking for an answer to B. Please show as much work as possible. Thank you!
Answer:f/g=29
Step-by-step explanation:
Answer: (f/g)=29
Hope this helps
4 divide by 3/5 as a fration
Answer:
6 and 2/3
Step-by-step explanation:
4 divided by 3/5 is the same as 4 divided by 0.6
4 divided by 0.6 equals 6.6 repeating...
or
6 and 2/3
In a spring, the tension (Tnewtons) is directly proportional to its extension ( x cm). When the tension is 150 newtons, the extension is 6 cm. (a) Find a formula for T' in terms of x. T = AD
The formula for tension (T) in terms of extension (x) is T = 25x.
The given statement is T = kx, where T is the tension, x is the extension, and k is the proportionality constant.
To solve this problem, we need to find the value of k. We can do that by substituting the given values of T and x into the equation:
T = kx
150 = k×6
k = 25
Therefore, the formula for tension (T) in terms of extension (x) is T = 25x.
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-7 4/5 divided by X = -5 1/5
The value of the variable is 3/2
What is a fraction?A fraction cam simply be described as an expression that is being used to represent the part of a whole number, a whole variable or element.
There are different types of fractions. They are listed as;
Improper fractionsProper fractionsComplex fractionsSimple fractionsMixed fractionsFrom the information given, we have that;
-7 4/5 divided by X = -5 1/5
convert to improper fractions, we have;
-39/5/x = -26/5
Now, cross multiply the values, we have;
-39/5 = -26x/5
cross multiply
-130x = -195
Divide both sides
x = -195/-130
x = 39/26 = 3/2
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if k(x) = 3x, then f'(x)=? A. x³Ln3 B. 3xLn3 C. 3x/Lnx D. 3/3xLn3
The correct option is B .solution of given problem with the help of integrating the given function is 3xLn3
what is integration and function ?The area under a curve in a given range can be calculated mathematically via integration. To locate the region between the curve and the x-axis, it is necessary to find a function's antiderivative and evaluate it twice.
A function is a rule that gives each input value a distinct output value. It can be compared to a machine that processes inputs into outputs in accordance with a predetermined rule or formula.
According to given informationTo find f'(x), we need to take the derivative of f(x), where f(x) is the antiderivative of k(x).
Since k(x) = 3x, we can find f(x) by integrating 3x with respect to x:
f(x) = ∫ 3x dx = 3/2 x² + C
where C is a constant of integration.
Now we can find f'(x) by taking the derivative of f(x):
f'(x) = d/dx (3/2 x² + C) = 3x
Therefore, the answer is (B) 3xLn3. Option (A) is incorrect because there is no natural logarithm term in the derivative of f(x). Option (C) is incorrect because the derivative of 3x is 3, not 3/Ln(x). Option (D) is incorrect because there is no x in the denominator of the natural logarithm term.
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determina el volumen cuyo diametro es de 8 y su altura de 15 cm
Answer:
3016 centímetros cúbicos.
Step-by-step explanation:
El radio del cilindro es de 8 cm y la altura es de 15 cm. Sustituya 8 por r y 15 por h en la fórmula . Simplifique. Por lo tanto, el volumen del cilindro es de alrededor de 3016 centímetros cúbicos.
Is a triangle with sides of 5 meters, 12 meters, and 13 meters a right triangle? Explain/Show your work.
Answer:
yes it is if you bisect 5m on a 12m line
HURRY DUE TONIGHT
Jenny mixed 4 kg of mixed nuts containing 16% peanuts with 12 kg of mixed nuts containing 40% peanuts. What percent of the new mixture if peanuts?
A. 34%
B. 13%
The new mixture contains 34% peanuts.
The correct option is A
We have,
Jenny mixed 4 kg of mixed nuts containing 16% peanuts with 12 kg of mixed nuts containing 40% peanuts.
First, Total weight = 4 kg + 12 kg = 16 kg
Now, Total weight in kilograms is = (4 kg) (0.16) + (12 kg) (0.40)
= 0.64 kg + 4.80 kg
= 5.44 kg.
Now, the Percent of peanuts
= (Total amount of peanuts / Total weight) x 100%
= (5.44 kg / 16 kg) x 100
= 34%
Thus, the new mixture contains 34% peanuts.
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In a survey 7 out of 8 people preferred cooking to washing dishes what percentage of the people surveyed preferred cooking
The percentage of the people that preferred cooking who where surveyed would be = 87.2%
How to calculate the percentage of people who preferred cooking?The total number of people surveyed = 8
The total number of people that preferred cooking = 7
The percentage of people that preferred cooking;
= 7/8×100/1
= 700/8
= 87.2%
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Fred's science class is going to the Ancient Dig adventure park. His teacher got the school group package, which costs $308. The package covers the entrance fee for the group, a private dig site, and an activity guide. Fred's teacher upgraded the package to include a fossil tool kit for each of the 22 students, bringing the total to $440. Which equation can you use to find k, the cost of each tool kit?
Answer: (440-308) ÷ 22 = The cost of each tool kit is 6 dollars
Step-by-step explanation:
The original price of the field trip was $308 after the price fof each tool kit was added the price was $440.
The total costs of all the tool kits was 132
440-308=132
the total cost of the tool kits divided by the number of kids will get the price of each tool kit
132÷22 =
K=
Juliet tell her in Israel our volunteer firefighters on Saturday to volunteer fire department hell is annual coin drop fundraiser at street light after one hour Keller had collected $42.50 more than Julia. Israel had collected $15 less than Keller. The three firefighters collected $125.95 in total. How much did each person collect?
Part A: Choose all equations that represents this problem. J= the amount Julia collected, K= the amount Keller collected, I = the amount Israel collected.
Options:
A: 125.95=J+(42.5+J)+(J+15)
B: 125.95=K+42.5+K-15
C: 125.95=I+(1+15)+(I-27.5)
D: 125.95=K+(K-42.5)+(K-15)
Part B: Keller collected 42.50 more than Julia, and Israel had collected 15 less than Keller. The three firefighters collected $125.95 in total. How much did each person collect?
Options:
$125.95
$61.15
$46.15
$42.50
$64.80
$18.65
$15.00
Part A: A
Part B: Julia collected 18.65, Keller collected 61.15, and Israel collected 45.15
If f(x)=x^2+10sinx, show that there is a number c such that f(c)=1000.
Answer:
Step-by-step explanation:
Name:
Date:
2.
5.
Directions: Solve for x
This is a 2-page document
Directions identify the similar triangles in the diagram, then sketch them so the coresponding
sides and angles have the same orientation
1.
52
48
Per
20
9.24 and 32
طلال سلال
kl ma jkk
Jkm-kim
Unit 7: Right Triangles & Trigonometry
Homework 3: Similar Right Triangles
& Geometric Mean
X=4.8
6.
22.4
13.2
26
Directions: Find the geometric mean of each pair of numbers.
7.16 and 27
8. 5 and 36
10.8 and 48
The geometric means of the pairs of numbers are approximately:
14.85 for 7.16 and 27
13.42 for 5 and 36
22.94 for 10.8 and 48.
How to calculate the meanIt should be noted that to find the geometric mean of two numbers, we multiply them together and then take the square root of the result. So, for each pair of numbers, we can follow these steps:
Multiply the two numbers together.
Take the square root of the product.
Using this formula, we get:
7.16 and 27:
Geometric mean = √(7.16 × 27) ≈ 14.85
5 and 36:
Geometric mean = √(5 × 36) = √180 ≈ 13.42
10.8 and 48:
Geometric mean = √(10.8 × 48) ≈ 22.94
Therefore, the geometric means of the pairs of numbers are approximately:
14.85 for 7.16 and 27
13.42 for 5 and 36
22.94 for 10.8 and 48.
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PLEASE HELP MEE‼️‼️
Tell me which each 3 boxes should I pick for each one of them PLEASE READ them I beg (proportional relationships)
number one take the second
Find the value of x.
Applying the intersecting secants theorem, the value of x is calculated as: x = 5.
What is the Intersecting Secants Theorem?According to the intersecting secants theorem, if two secant lines intersect outside of a circle, then the product of the length of one secant segment and its external segment is equal to the product of the length of the other secant segment and its external segment.
Using the theorem, the equation below is created to find the value of x:
4(4 + 5) = (x - 2)(x - 2 + x + 4)
4(9) = (x - 2)(2x + 2)
36 = 2x² - 2x - 4
2x² - 2x - 4 - 36 = 0
2x² - 2x - 40 = 0
Factorize:
(x + 4)(x - 5) = 0
x = -4 or x = 5
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Use the expression below to complete the following tasks.
(3a2 - 5ab + b2) - (-3a2 + 2b2 + 8ab)
What is the additive inverse of the polynomial being subtracted?After you rewrite subtraction as addition of the additive inverse, how can the like terms be grouped?
With additive inverse and by grouping like terms the simplified form of the expression is 6a²-13ab-b².
The given expression is 3a²-5ab+b²-(-3a²+2b²+8ab).
Here,
3a²-5ab+b²+3a²-2b²-8ab
Group like terms, that is
(3a²+3a²)+(-5ab-8ab)+(b²-2b²)
= 6a²-13ab-b²
Therefore, with additive inverse and by grouping like terms the simplified form of the expression is 6a²-13ab-b².
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Determine how many integer solutions there are to
x₁ + x₂ + x3 + x₁ = 20, if
0≤x₁ < 3, 0≤ x₂ < 4, 0≤x3 <5, 0≤x4 < 6
Based on the information given, there are a total of 118 solutions.
How many possible solutions are there?This is a problem of solving a Diophantine equation subject to some conditions. Let's introduce a new variable y4 = 20 - (x1 + x2 + x3 + x4). Then the problem can be restated as finding the number of solutions to:
x1 + x2 + x3 + y4 = 20
Subject to the following conditions:
0 ≤ x1 < 3
0 ≤ x2 < 4
0 ≤ x3 < 5
0 ≤ y4 < 6
We can solve this problem using the technique of generating functions. The generating function for each variable is:
(1 + x + x^2) for x1
(1 + x + x^2 + x^3) for x2
(1 + x + x^2 + x^3 + x^4) for x3
(1 + x + x^2 + x^3 + x^4 + x^5) for y4
The generating function for the equation is the product of the generating functions for each variable:
(1 + x + x^2)^3 (1 + x + x^2 + x^3 + x^4 + x^5)
We need to find the coefficient of x^20 in this generating function. We can use a computer algebra system or a spreadsheet program to expand the product and extract the coefficient. The result is: 1118
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Answer: This problem involves finding the number of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints. We can use the stars and bars method to solve this problem.
Suppose we have 20 stars representing the sum x₁ + x₂ + x3 + x₁. To separate these stars into four groups corresponding to x₁, x₂, x₃, and x₄, we need to place three bars. For example, if we have 20 stars and 3 bars arranged as follows:
**|**||
then the corresponding values of x₁, x₂, x₃, and x₄ are 2, 4, 6, and 8, respectively. Notice that the position of the bars determines the values of x₁, x₂, x₃, and x₄.
In general, the number of ways to place k identical objects (stars) into n distinct groups (corresponding to x₁, x₂, ..., xₙ-₁) using n-1 separators (bars) is given by the binomial coefficient (k+n-1) choose (n-1), which is denoted by C(k+n-1, n-1).
Thus, the number of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints is:
C(20+4-1, 4-1) = C(23, 3) = 1771
However, this count includes solutions that violate the upper bounds on x₁, x₂, x₃, and x₄. To eliminate these solutions, we need to use the principle of inclusion-exclusion.
Let Aᵢ be the set of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints, where xᵢ ≥ mᵢ for some integer mᵢ. Then, we want to find the cardinality of the set:
A = A₀ ∩ A₁ ∩ A₂ ∩ A₃
where A₀ is the set of all non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20, and Aᵢ is the set of solutions that violate the upper bound on xᵢ.
To find the cardinality of A₀, we use the formula above and obtain:
C(20+4-1, 4-1) = 1771
To find the cardinality of Aᵢ, we subtract the number of solutions that violate the upper bound on xᵢ from the total count. For example, to find the cardinality of A₁, we subtract the number of solutions where x₂ ≥ 4 from the total count. To count the number of solutions where x₂ ≥ 4, we fix x₂ = 4 and then count the number of solutions to the equation x₁ + 4 + x₃ + x₄ = 20 subject to the constraints 0 ≤ x₁ < 3, 0 ≤ x₃ < 5, and 0 ≤ x₄ < 6. This count is given by:
C(20-4+3-1, 3-1) = C(18, 2) = 153
Similarly, we can find the cardinalities of A₂ and A₃ by fixing x₃ = 5 and x₄ = 6, respectively. Using the principle of inclusion-exclusion, we obtain:
|A| = |A₀| - |A
Step-by-step explanation:
Luis's cedar chest measures 4 ft long 2 ft wide and 2 1/4 ft high. What is the volume of the chest? PLEASE USE THE FORMULA IN THE STEP BY STEP EXPLANATION! I REALLY NEED HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Please help !!
i only need help with the second problem which is:
5. For 0≤x≤ 6, express g(x) in terms of x. Do not include +C in your final answer.
Your help is very appreciated !!
From the calculation, g increases on the interval [-3, 6) and for 0 ≤ x ≤ 6, g(x) = 6 - 1/2(x-2)^2.
What is the interval that g increases?To determine where g is increasing, we need to find where its derivative, g'(x), is positive. We can find g'(x) by differentiating g(x) with respect to x:
g'(x) = f(x)
Since f(x) is a piecewise-defined function, we need to consider each interval separately.
For -3 ≤ x < 0, f(x) = 3, so g'(x) = 3, which is positive.For 0 ≤ x ≤ 6, f(x) = -x + 3, which is a decreasing function, so g'(x) is also decreasing. However, since f(x) is always non-negative on this interval, g'(x) is non-negative as well.For 6 < x ≤ 9, f(x) = -3, so g'(x) = -3, which is negative.Therefore, g is increasing on the interval [-3, 6).
To justify this, note that g'(x) = 0 at x = 0 and x = 6, where g has local maxima. This means that g is increasing on the intervals (-3, 0) and (0, 6) and decreasing on (6, 9]. Since g is continuous, it cannot have any jumps, so it must be increasing or decreasing on each of these intervals. Since g(-3) = 0 and g(6) = 9, we know that g is increasing on the interval [-3, 6).
We can evaluate g(x) on the interval [0, 6] by integrating f(x) with respect to t from -2 to x:
g(x) = ∫_{-2}^{x} f(t) dt
On the interval [-3, 0), f(t) = 3, so we have:
g(x) = ∫_{-2}^{0} 3 dt + ∫_{0}^{x} (-t + 3) dt
Simplifying the integrals, we get:
g(x) = 6 - 1/2(x-2)^2, for 0 ≤ x ≤ 6
(Note that we can drop the "+C" since it's being evaluated at the limits of integration.)
Therefore, for 0 ≤ x ≤ 6, g(x) = 6 - 1/2(x-2)^2.
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On the SAT exam a total of 25 minutes is allotted for students to answer 20 math questions without the use of a calculator. A guidance counselor would like to know if the students in his school are prepared to complete this portion of the exam in the timeframe allotted. To investigate, the counselor selects a random sample of 35 students and administers this portion of the test. The students are instructed to turn in their test as soon as they have completed the questions. The mean amount of time taken by the students is 23.5 minutes with a standard deviation of 4.8 minutes. The counselor would like to know if the data provide convincing evidence that the true mean amount of time needed for all students of this school to complete this portion of the test is less than 25 minutes and therefore tests the hypotheses H0: μ = 25 versus Ha: μ < 25, where μ = the true mean amount of time needed by students at this school to complete this portion of the exam. The conditions for inference are met. What are the appropriate test statistic and P-value?
The P-value is between 0.025 and 0.05. and t = -1.85
On the SAT exam a total of 25 minutes is allotted for students to answer 20 math questions without the use of a calculator.
Therefore tests the hypotheses:
[tex]H_0[/tex] : μ = 25 versus Ha: μ < 25,
where μ = the true mean amount of time needed by students at this school to complete this portion of the exam.
The alternative hypothesis is:
[tex]H_1:\mu < 25[/tex]
The test statistic is given by:
[tex]t=\frac{x-\mu}{\frac{s}{\sqrt{n} } }[/tex]
The parameters are:
'x' is the sample mean. [tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.the values of the parameters are:
x = 23.5 , [tex]\mu=25[/tex] , s = 4.8, n = 35
Plug all the values in above formula of t- statistic is:
[tex]t = \frac{23.5-25}{\frac{4.8}{\sqrt{35} } }[/tex]
t = -1.85
Using a t-distribution , with a left-tailed test, as we are testing if the mean is less than a value and 35 - 1 = 34 df, the p-value is of 0.0365.
t = –1.85; the P-value is between 0.025 and 0.05.
Learn more about t-distribution at:
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Find the length of the third side. If necessary, write in simplest radical form.
3√3 and 6
Answer: 3
Step-by-step explanation:
You would need to use the Pythagorean theorem to solve this equation. 6 is the hypotenuse and 3[tex]\sqrt{3}[/tex] is the longer leg.
a^2+b^2=c^2
c= hypotenuse
6^2=3[tex]\sqrt{3}[/tex]^2 + a^2
36=27+a^2
36-27=9
[tex]\sqrt{9}[/tex] = 3