A solid oblique pyramid has a regular pentagonal base. the base has an edge length of 2.16 ft and an area of 8 ft2. angle acb measures 30°. a solid oblique pyramid has a regular pentagonal base. the base has an edge length of 2.16 feet and an area of 8 feet squared. point a is the apex and point c is the center of the hexagon. line a b shows the vertical height of the pyramid. triangle a b c is a right triangle with base length of 7 startroot 3 endroot feet. what is the volume of the pyramid, to the nearest cubic foot? 5 ft3 9 ft3 14 ft3 19 ft3
The volume of the Oblique pyramid is 19 \(ft^{2}\)
We know, the volume of a pyramid is \(\frac{1}{2}\) × B × h
where B is the area of the base and h is the height of the pyramid.
Given: The pentagonal base has an edge length of 2.16 ft and an area of 8 \(ft^{2}\) and angle ACB measures 30°.
Consider triangle ACB
tan30° = \(\frac{AB}{CB}\)
\(\frac{1}{\sqrt{3} }\) = \(\frac{AB}{7\sqrt{3} }\)
AB = 0.58 × \(7\sqrt{3}\)
AB = 0.58 × 12.12
AB = 7.03
Now, the volume of the oblique pyramid will be
V = \(\frac{1}{2}\) × 8 × 7.03
V = 18.75
V ≈ 19 \(ft^{2}\)
Refer to the complete question given below.
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Answer:19
Step-by-step explanation:
An object occupies the region between the unit sphere at the origin and a sphere of radius 2 with center at the origin, and has density equal to the distance from the origin. Find the mass.
The mass of the solid is 7π/2 units.
The task is to calculate the mass of the solid.
Step-by-step solution: The solid occupies the region between the unit sphere at the origin and a sphere of radius 2 with the center at the origin. The spherical coordinates in 3D space are (r,θ,φ), where:r = radius, θ = polar angle, φ = azimuthal angle.
The equations of the given sphere are r=1 for the unit sphere and r=2 for the second sphere.
Using spherical coordinates, the solid can be defined as 1≤r≤2, 0≤θ≤2π, 0≤φ≤π.
The density is equal to the distance from the origin, i.e. ρ = r.
The mass of the solid is given by the triple integral ρ dV taken over the solid, where dV is the volume element in spherical coordinates.dV = r²sin φ dφdθdr
The limits for the triple integral are: 0 ≤ θ ≤ 2π, 0 ≤ φ ≤ π, and 1 ≤ r ≤ 2.M = ∭ρ dV = ∭r(r²sin φ) dφdθdr= ∫[0,2π]∫[0,π]∫[1,2] r³sin φ drdφdθ= ∫[0,2π]∫[0,π] -cos φ [r⁴/4]₁ ₂ drdφdθ= ∫[0,2π]∫[0,π] 7/4 cos φ dφdθ= ∫[0,2π] 7sin φ/4 ]₀ π dθ= 14π/4= 7π/2 units.
The mass of the solid is 7π/2 units.
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Jaime makes the following claim.
An angle with a measure of π/3 radians in a circle with a radius of 3 inches is smaller than an angle with a measure of π/3 radians in a circle with a radius of 6 inches. This is because the radian measure is based on the length of the radius of the circle and a radius of 3 inches is smaller than a radius of 6 inches.
1. Review Jaime’s statement and what you know about angles and radians.
a. Explain whether you agree with Jaime’s statement or not.
b. Provide examples to support your whether you agree or disagree.
In the case above, Jaime claim is true.
The explanation to agree with Jaime’s statement or not is that the longer the length of the radius, the longer the length of the arc.What is the claim about?1. Note that radian measure:
= \(\frac{60° }{360°}\) x 2π x 3
= 1/6 x 6π
= π
2. Note that radian measure:
= \(\frac{60° }{360°}\) x 2π x 6
= 1/6 x 2π x 6
=2π
So we can write it as:
π/3 x 180°/π = 60°
Therefore, via the solution above, Jaime claim is true.
3. Note that: Radian measures: the percentage of arc measures x 2π x radius and so one can say that The explanation to agree with Jaime’s statement or not is that the longer the length of the radius, the longer the length of the arc.
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If the slope is -4/3 and the ordered pair is 3,-5 what is the equation?
Answer:
y=-4/3x-4
Step-by-step explanation:
y=mx+y intercept <--- formula i used
Find the value of x.
The value of x is 10.
We have,
Base= 24
Hypotenuse= x+ 16
Base= x
Using Pythagoras theorem
H² = P² + B²
(x+16)² = x² + 24²
x² + 256 + 32x = x² + 576
x² - x² + 256 - 576 + 32x= 0
-320 + 32x= 0
32x= 320
x= 320/32
x= 10
Thus, the value of x is 10.
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Determine whether each triangle below will form a unique triangle, no triangle or more than one triangle based on the criterion given.
Answer:
A: A unique triangle
B: A unique triangle
C: More than a triangle
A newspaper in Germany reported that the more semesters needed to complete an academic program at the university, the greater the starting salary in the first year of a job. The report was based on a study that used a random sample of 24 people who had recently completed an academic program. Information was collected on the number of semesters each person in the sample needed to complete the program and the starting salary, in thousands of euros, for the first year of a job. The data are shown in the scatterplot below. 70 65 60 55 Starting Salary (1.000 euros) 50 45 35 30 25 5 10 15 20 Number of Semesters (a) Does the scatterplot support the newspaper report about number of semesters and starting salary? Justify your answer. b) The coefficient of determination is 0.335. Interpret this value in the context of this problem. c) Determine the value of the correlation coefficient. Interpret this value in the context of this problem.
a) Yes, It does. The scatterplot support the newspaper report about number of semesters and starting salary.
b) The value is relatively low, indicating that there are other factors that also contribute to starting salary.
c) The correlation coefficient is a value between -1 and 1 that measures the strength and direction of the linear association between two variables.
The Correlation Coefficienta) The scatterplot appears to show a positive association between the number of semesters needed to complete an academic program and the starting salary in the first year of a job. As the number of semesters increases, the starting salary generally increases as well. Therefore, the scatterplot supports the newspaper report.
b) The coefficient of determination, or R-squared value, represents the proportion of the variation in the dependent variable (starting salary) that is explained by the independent variable (number of semesters). A value of 0.335 means that 33.5% of the variation in starting salary is explained by the number of semesters. This value is relatively low, indicating that there are other factors that also contribute to starting salary.
c) The correlation coefficient is a value between -1 and 1 that measures the strength and direction of the linear association between two variables. A value of 1 indicates a perfect positive correlation, a value of -1 indicates a perfect negative correlation, and a value of 0 indicates no correlation. The correlation coefficient for this data is not provided in the problem, so it is not possible to determine it. Without the correlation coefficient, it is not possible to interpret the strength and direction of the association between number of semesters and starting salary.
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To evaluate 8^2/3 find
To evaluate \(8^{\frac{2}{3} }\) first find the square of 8 and then take the cube root.
What are exponents?The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.
Depending on the powers they possess, many rules of exponents are given.
Law of Multiplication: Exponents should be added while keeping the base constant when multiplying like bases.
Exponents should be multiplied while bases are kept constant when bases are raised by a power of two or more.
Division Rule: When dividing like bases, maintain the base constant and deduct the exponent of the denominator from the exponent of the numerator.
The given value can be written as:
\(8^{\frac{2}{3} } = \sqrt[3]{8^{2} }\)
Hence, to evaluate \(8^{\frac{2}{3} }\) first find the square of 8 and then take the cube root.
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Find an example of a 2×3 matrix A and a 3×2 matrix B such that, letting T(x)=Ax and U(x)=Bx, the composition T∘U is a reflection over the line y=x.
The example of 2×3 matrix A and a 3×2 matrix B such that, letting T(x)=Ax and U(x)=Bx is reflection Ab.
Matrices, the plural form of matrix, are the groupings of numbers, variables, symbols, or phrases in a rectangular table with varying rows and columns. These are rectangular arrays with specified operations such as addition, multiplication, and transposition. The elements of the matrix are the numbers or entries in it. The horizontal entries of matrices are referred to as rows, whereas the vertical elements are referred to as columns.
Let,
\(B = \left[\begin{array}{cc}0&1\\1&0&0&0\end{array}\right] , A = \left[\begin{array}{ccc}1&0&0\\0&1&0\\\end{array}\right]\)
Then,
\(AB =\left[\begin{array}{ccc}1&0&0\\0&1&0\\\end{array}\right] \left[\begin{array}{cc}0&1&1&0&0&0\\\end{array}\right] \\\\AB = \left[\begin{array}{cc}0&1&1&0\\\end{array}\right]\)
Therefore, Ab is reflection about y = x .
As U = Bx and T∘U
A matrix is a rectangular array of integers, variables, symbols, or expressions that are defined for subtraction, addition, and multiplication operations. The number of rows and columns in a matrix determines its size (also known as the order of the matrix).
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Twice a number added to another number is 15. The sum of the two numbers is 11. Find the numbers. Write the numbers from least to greatest
Answer:
(6,8)
I know because I did it coool
Kasey has taken down 6 shirts and 3 pair of pants on her vacation.What is the number of different shirt and pants combinations that she can choose to wear?
if values is an array of int containing 5, 10, 15, 20, 25, 30, 35, 40, the following recursive method returns if it is invoked as mystery (2)
The recursive method "mystery" returns the sum of the values in an array that are divisible by the integer passed as an argument. When called with 2 as the argument, the method returns 70.
The "mystery" method is a recursive function that takes two parameters: an array of integers and an integer n. The function returns the sum of all elements in the array that are divisible by n. When the "mystery" method is called with an array containing 5, 10, 15, 20, 25, 30, 35, and 40, and n=2, the method first checks if the array is empty. If the array is empty, the function returns 0. If the array is not empty, the method checks if the first element in the array is divisible by n=2. If it is divisible, the function adds the element to the sum of the remaining elements in the array that are divisible by n. If it is not divisible, the function adds the sum of the remaining elements in the array that are divisible by n to the result.
In this case, the first element of the array is 5, which is not divisible by 2, so the function calculates the sum of the remaining elements in the array that are divisible by 2. This sum is equal to 10 + 20 + 30 = 60. Therefore, the function returns 60 as the result.
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1000
900
800
Q3.A landscaping company offers their services as following:
$240 for a full landscape plan, plus $30 per hour to do the work
Display this data on the grid below. Label carefully both the axes.Identify the variables and explain why
you think this is a linear relation. What is the initial value for the relation and the rate of change.
Time (hours)
Cost ($)
6
2
4
8
10
12
14
0
The independent variable is time (hours), and the dependent variable is cost ($). The given relation is linear because it has a constant rate of change. The initial value for this relation is $240 and the rate of change is $30 per hour.
The table for the given relation is
Time (hours) Cost ($)
0 240
2 300
4 360
6 420
8 480
10 540
12 600
14 660
In this relation, the independent variable is time (hours), and the dependent variable is cost ($). The time is the input to the relation, and the cost is the output that is dependent on the input.
We can see that this relation is linear because it has a constant rate of change. The cost increases by $30 for each hour of work, which means that the slope of the line is constant.
The initial value for this relation is $240, which represents the cost of the full landscape plan. The rate of change is $30 per hour, which represents the additional cost for each hour of work. Therefore, the equation for this linear relation is
Cost = 30 x Time + 240
where "Cost" is the cost in dollars, "Time" is the time in hours, 30 is the rate of change, and 240 is the initial value.
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Use the drawing tool(s) to form the correct answer on the provided number line.
Consider the given functions.
Function 1
f(x) = -5x + 11 + 10
Function 2
g(x)
-2
Represent the interval where both functions are decreasing on the number line provided.
30
20
10-
-10-
-20-
-30-
2
6
x
On its entire domain, f(x) is declining.
We just need to think about function 1's behaviour because function 2 is a constant function and is neither increasing nor decreasing.
Finding the location of its negative derivative will help us understand where f(x) = -5x + 21 is declining. For all values of x, the derivative of f(x) equals -5, which is negative. As a result, f(x) is getting smaller across the board.
Hence, the range where both functions are decreasing can be represented as the complete domain of function 1: (-, ). On a number line, the following can be used to represent this interval:
-30 -20 -10 0 10 20 30
—-|——|——| ——|——-| ——-|—— |—-
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Answer:
see photos
Step-by-step explanation:
Plato/Edmentum
If the cost of 7m is Rs. 1470, find the cost of 5m cloth
By using unitary method, we found that the cost of 5m cloth is Rs. 1050.
According to the unitary method, the cost of 1 meter of cloth is equal to the total cost of 7 meters of cloth divided by 7. That is,
Cost of 1m cloth = Total cost of 7m cloth/7
We know that the total cost of 7m cloth is Rs. 1470. Therefore,
Cost of 1m cloth = 1470/7
Cost of 1m cloth = Rs. 210
This means that the cost of 1 meter of cloth is Rs. 210. Now, we need to find the cost of 5m cloth. To do that, we can use the unitary method again.
Cost of 5m cloth = Cost of 1m cloth x 5
Cost of 5m cloth = Rs. 210 x 5
Cost of 5m cloth = Rs. 1050
Therefore, the cost of 5m cloth is Rs. 1050.
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For the complex number z = (5sqrt(3))/4 - 5/4 * i what is the polar form
Answer: 3
Step-by-step explanation:
The required polar form of the equation is \(Z = 5/2cos30 - 5/2sin30i.\)
For the complex number z = (5sqrt(3))/4 - 5/4 * i the polar form is to be determined.
The number that constitutes real and imaginary numbers are called complex numbers. The standard form of complex number = a + bi
\(z = 5\sqrt{3}/4 - 5/4i\)
the polar form complex numbner can be given as
\(z = rcos\theta +rsin\theta i\) - - - - - -(1)
where r = \(\sqrt{a^2+b^2}\)
and \(\theta=tan^-\frac{b}{a}\)
Since a = 5√3/4 and b = -5/4
\(r = \sqrt{(5\sqrt{3}/4)^2+(5/4)^2}\)
r = 10/4
r = 5/2
Now,
\(\theta=tan^-\frac{b}{a}\)
\(\theta=tan^-\frac{-5/4}{5\sqrt{3}/4 }\\\theta=tan^-\frac{1}{\sqrt{3} }\\\theta=tan^-(-tan30)\\\theta=-30\)
Now the polar form is given by substituting the values of r and \(\theta\) in equation 1
Here,
\(z = 5/2cos30 +5/2sin(-30)i\\z = 5/2cos30-5/2sin30 i\)
Thus, the required polar form of the equation is \(Z = 5/2cos30 - 5/2sin30i.\)
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NEED HELLPPPPP !!!!
Answer:
x = 14
Step-by-step explanation:
Triagle GIA and Triangle GNT are congruent.
Enter the value of x below.
x+6=9
Answer:
x = 3
Step-by-step explanation:
x + 6 = 9
Subtract 6 from both sides :
x = 9 - 6
x = 3
Hope this helped and have a good day
Answer:
x = 3
Step-by-step explanation:
x + 6 = 9 Subtract from both sides of the equation
x + 6 - 6 += 9 - 6
x = 3
Check:
x + 6 = 9
3 + 6 = 9
9 = 9 Checks
Write these ratios in their simplest form
a.2 litres:600ml
b. 8h:1 day
c. 3km:250m
Answer: a. 1ml : 2ml b. 1h : 3h c. 12m : 1m
Step-by-step explanation:
a. 2 litres = 200ml
200ml : 600ml = 1ml : 3ml
b. 1 day = 24 hours
8h : 24h = 1h : 3h
c. 3 km = 3000m
3000m : 250m = 12m : 1m
71 ×10 ^ 3 Scientific Notation
Answer:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 1010. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
7.1×1047.1×104
The required regular notation of 71 ×10³ Scientific Notation is71,000.
Given that,
Scientific notation is given of 71 ×10³ regular notation of the number is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
here,
Scientific notation = 71 ×10³
Regular notation = 71 ×10³
71 ×10³ = 71 * 10 * 10 * 10
71 ×10³ = 71000
Thus, the required regular notation of 71 ×10³ Scientific Notation is71,000.
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un automovil viaja de una ciudad a otra que esta a 163km y tarda 2 horas y media. ¿cual es su velocidad
The velocity of the car traveling from one city to another that is 163 km away and takes 2 and a half hours to reach can be calculated as 65.2 km/hour. This is determined by dividing the distance traveled by the time taken, or 163 km / 2.5 hours.
What is velocity?Velocity is a measure of an object's displacement over time. It specifies both the object's speed and direction of movement, and is expressed in units of distance per unit of time, such as meters per second or kilometers per hour.
What is distance?Distance is the measure of how far apart two points or objects are. It is typically measured in units such as kilometers, miles, meters, or feet.
According to the given information:
To find the velocity of the car, we need to use the formula:
Velocity = Distance / Time
In this case, the distance traveled by the car is 163km and the time taken to travel that distance is 2.5 hours.
Substituting the values into the formula, we get:
Velocity = 163 km / 2.5 hours
Simplifying, we get:
Velocity = 65.2 km/h
Therefore, the velocity of the car is 65.2 km/h.
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The cost of a taxi fare is $5 plus $1.50 per kilometre travelled. a) Derive a formula for calculating the cost, $P, of travelling n km. b) Use your formula to calculate the cost of travelling 25 km. please help me
Answer:
Step-by-step explanation:
Formula
P = 5 + 1.50n
P is the total Cost
n is the number of Km travelled.
Solution
Substitute n = 25 into the formula
P = 5 + 1.5 * 25
P = 5 + 37.5
P = 42.50
Answer
42.50 dollars for 25 km.
Help? Luis has saved $15. He doubles the amount he saves each week. Does this represent an exponential function? Choose the correct word in each drop-down menu.
This___ represent an exponential function, because his savings increase by a constant___
1st blank (does not, does)
2nd blank (ratio, difference)
Answer:
1). Does Not
2). Ratio
Step-by-step explanation:
According to the Question,
Given that, Luis has saved $15. He doubles the amount he saves each week.
This DOES NOT represent an exponential function, because his savings increase by a constant RATIO.Identify all number sets to which the square root of 25 belongs to.
Answer:
SOLUTION: Explain why the square root of 25 belongs to 4 subsets of the real numbers , but the square root of 5 only belongs to 1 . tell which subsets each belong to and why .
Step-by-step explanation:
The square root of 25 is 5, which
1. A rational number, since 5 is the ratio of the two integers 5 and 1.
2. An integer since 5 is an element of {...,-3,-2,-1,0,1,2,3,.}
3. A whole number, since 5 is an element of {0,1,2,3.}
4. A counting number, since 5 is an element of {1,2,3,}
The square root of 5 is only
1. An irrational number, since it is not the ratio of any two integers.
[It can only be approximated by
this nonrepeating infinite decimal, it goes on forever:
2.2360679774997896964091736687312762354406183596115257...]
help quick plz must get this correct I will make u a brainllest
Answer:
CPCTC
Step-by-step explanation:
You already proved that triangle BAD is congruent to CAD, this means that all of the corresponding angles and sides with be congruent (CPCTC). That means BD is congruent to CD. Hope this helps!
HELP ME PLEASE I DON’T UNDERSTAND give answers and working please
Calculate the circumference and area of a circle.
To find the circumference, you double the radius and multiply by pi. To find the area, you square the radius and multiply by pi.
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
93° (to the nearest degree)
Step-by-step explanation:
sum of the interior angles of a triangle = 180°
Find angle C first, then subtract angle C and angle B from 180° to find angle A.
Use the sine rule \(\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}\) to find angle C:
Therefore,
\(\frac{sinB}{b}=\frac{sinC}{c}\)
\(\frac{sin38}{9}=\frac{sinC}{11}\)
angle C = 48.80523914...°
Angle A = 180 - 38 - 48.80523914...°
= 93.19476086..°
= 93° (to the nearest degree)
A rectangular prism has a length of 3 1/2 inches, a width of 5 inches, and a height of 1 1/2 inches. What is the volume of the prism? Enter your answer in the box as a simplified mixed number or a decimal. Can anyone please help me
Answer:
26.25 or 26 1/4
Step-by-step explanation:
Formula for rectangular prism:
\(V=lwh\)
Substitute in our known values:
V=3.5(5)(1.5)
solve
V=26.25
The volume is 26.25 (decimal form) or 26 1/4.
Hope this helps! :)
Answer: 26.25 in³
Step-by-step explanation:
Given volume formula for a rectangular prism:
V = LWH
First, I am going to turn the \(\frac{1}{2}\)s into 0.5 to make it easier to multiply using a calculator. 3 and one-half becomes 3.5 and 1 and a half becomes 1.5.
Substitute known values and solve by multiplying.
V = LWH
V = (3.5 in)(5 in)(1.5 in)
V = 26.25 in³
If x - 12 squareroot of x + 36 = 0, what is the value of x? a. 6 b. 6^2 c. 6^3 d. 6^4
The solution to the equation x - 12√x + 36 = 0 is the value of x is 6². Thus, the option (b) is correct.
To solve the equation x - 12√x + 36 = 0, we can use substitution to simplify the equation.
Let's substitute a variable to represent √x:
Let √x = y
Now, we can rewrite the equation as:
y² - 12y + 36 = 0
This is a quadratic equation that can be factored as:
(y - 6)(y - 6) = 0
(y - 6)² = 0
Now, we can solve for y:
y - 6 = 0
y = 6
Since y represents √x, we can substitute back:
√x = 6
To find the value of x, we square both sides:
(√x)² = 6²
x = 6²
Therefore, the value of x is 6².
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The complete question is as follows:
If x - 12 √(x + 36) = 0, what is the value of x?
a. 6
b. 6²
c. 6³
d. 6⁴
I need help with my math!!!
Answer:
A
Step-by-step explanation:
Answer:
I’m not sure if I’m right but here I go.
Step-by-step explanation:
Each line goes from zero and down, look at the ponies where they are and find the coordinates.