The surface area of the triangular pyramid in the image given is calculated as: C. 323 square inches.
How to Find the Surface Area of a Triangular Pyramid Using its Net?To find the surface area of the triangular pyramid, find the area of each face and the base as shown in the net given and add all together.
Area of the three triangular faces = 3(1/2 * base * height)
= 3(1/2 * 15 * 10)
= 3(75)
= 225 square inches
Area of the triangular base = 1/2 * base * height
= 1/2 * 15 * 13
= 97.5 square inches
The surface area = 225 + 97.5 = 322.5
≈ 323 square inches.
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I need help with at least one of these questions (maybe all ) *geometry tangents in circles*
Using Pythagoras Theorem, we have the solutions as:
3) Length of AB = 32 in
4) x = 24
5) Perimeter of PRQ = 35
How to use Pythagoras Theorem?Pythagoras Theorem is the way in which you can find the missing length of a right angled triangle.
3) Using Pythagoras theorem, we can say that:
Radius = √(16² - 5²)
Radius = √231
Radius = 15.2
Thus, AB will be twice the measurement of 16 as the perpendicular distance to bth chords are the same. Thus:
AB = 16 * 2 = 32 in
4) Using Pythagoras theorem,
x = √((18 + 7)² - 7²)
x = √(625 - 49)
x = 24
5) Using Pythagoras theorem, we can say that:
PC = 8.66
RC = √((14² - 8.66²)
RC = 11
Thus:
Perimeter of PRQ = 14 + 10 + 11 = 35
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Given a reduced echelon matrix in R3 is 1--1 iff the homogeneous system Ax = 0 has only the trivial solution iff there are no free variables.
A. True B. False
A reduced echelon matrix in R3 is 1--1 if and only if the homogeneous system Ax = 0 has only the trivial solution if and only if there are no free variables.
The statement is true.
A reduced echelon matrix in R3 represents a linear system of equations that can be solved using Gaussian elimination.
The reduced echelon form of a matrix is obtained by performing row operations that reduce the matrix to a triangular form, with ones on the main diagonal and zeros below it.
If the homogeneous system Ax = 0 has only the trivial solution, it means that the only solution to the system is the zero vector.
In other words, there are no non-zero vectors that satisfy the system.
This is equivalent to saying that the rank of the matrix is equal to the number of columns, or in other words, there are no free variables in the system.
If the system has no free variables, it means that each variable can be expressed as a unique function of the other variables.
This implies that the system has a unique solution, or in other words, the mapping from the system of equations to the solution vector is one-to-one.
If the system is one-to-one, it means that each solution vector corresponds to a unique system of equations.
This implies that there are no redundant equations or variables, and therefore no free variables.
Hence, the homogeneous system Ax = 0 has only the trivial solution.
The statement is true.
A reduced echelon matrix in R3 is 1--1 if and only if the homogeneous system Ax = 0 has only the trivial solution if and only if there are no free variables.
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The radius of a circle is 9 millimeters. What is the circle's circumference?
Use 3.14 for л.
Answer:
56.55
Step-by-step explanation:
C=2πr=2·π·9≈56.54867
..............................
Answer:
below
Step-by-step explanation:
1.
[tex] \sqrt{80 } = 4 \sqrt5[/tex]
[tex]5 \sqrt{45} = 15 \sqrt{5} [/tex]
[tex]4 \sqrt{5} + 15 \sqrt{5} = 19 \sqrt{5} [/tex]
2.
[tex]2 \sqrt{72} = 12 \sqrt{2} [/tex]
[tex]3 \sqrt{50} = 15 \sqrt{2} [/tex]
[tex]12 \sqrt{2} - 15 \sqrt{2} = - 3 \sqrt{2} [/tex]
if £1=9.60DKK, how much is 55p in DKK. Answer to 2d.p.
Answer:3
Step-by-step explanation:
1+2=3
............................... help
Answer:
Based on the given options, the correct answer is A.
Option A states that the price in the year 2012 is $18,000, which describes a point on a graph or chart that represents a data point for the year 2012 and a value of $18,000. This is a common way to describe a data point on a graph or chart.
Option B is not a logical description of a point and does not provide a clear indication of the relationship between the year and the price.
Option C describes a different price point for the year 2012 than option A.
Option D describes a point in the year 2010, not 2012 as specified in the question stem.
Option E describes a different price point for the year 2010 than option D and does not specify the price in 2012.
Answer:
In the year 2012, the price is 18000
Step-by-step explanation:
The x coordinate is 2012
The y coordinate is 18000
The price is 18000 and the year is 2012.
In the year 2012, the price is 18000.
Find the exact value: tan 13pi/12
(Use the fact that 13pi/12 = 3pi/4 + pi/3
Thanks in advance!
Answer: the exact value of tan(13π/12) is √3 + 2.
Step-by-step explanation: The trigonometric equation demonstrating the equality between the tangent of 13π/12 and the tangent of 3π/4 added to π/3 may be expressed in the formal and technical tone often employed in academic writing as follows: tan(13π/12) = tan(3π/4 + π/3).
Through utilization of the identity, tan(a+b) = (tan(a) + tan(b)) / (1 - tan(a)*tan(b)), the given expression may be rendered more concise.
The trigonometric expression tan(13π/12) can be represented as (tan(3π/4) + tan(π/3)) divided by (1 - tan(3π/4) multiplied by tan(π/3)).
It is established that:
it can be observed that the value of the trigonometric function of tan(3π/4) is -1.
The mathematical expression "tan(π/3) = √3" signifies that the trigonometric tangent function of the angle π/3 is equivalent to the square root of three.
Upon substitution of the aforementioned values, the resulting output is obtained.
The trigonometric function of tan(13π/12) can be expressed as a quotient between two real numbers. Specifically, it can be represented in the form (-1 + √3) / (1 + (-1) * √3).
By utilizing the conjugate of the denominator and performing the operation of multiplication on both the numerator and denominator, the resulting expression is obtained:
The trigonometric function of tangent evaluated at 13π/12 is expressed as the product of two fractions. The numerator of the first fraction is comprised of the difference of the values -1 and the positive square root of 3, while the denominator is the sum of the value 1 and the product of -1 and the square root of 3. The numerator of the second fraction is the sum of the values 1 and the positive square root of 3, while the denominator is the sum of the same values.
The trigonometric identity expressed as tan(13π/12) has been rendered in symbolic form, wherein the numerator is the summation of -1, √3, √3, and -3. The denominator is the product of (1 + √3) and (1 - √3).
The mathematical expression tan(13π/12) can be represented as (-2√3 - 4) / (-2).
The mathematical expression tan(13π/12) is equivalent to the value of √3 + 2.
Probability basics!!
I really need help on how to do this please
Answers must be fraction or original decimal
The probability that the student picked at random from the graduating class will be a male would be = 0.51
The probability that the student picked at random from the graduating class will be receiving an education degree = 0.3.
How to calculate the probability of the given variables?To calculate the probability of the given variables, the formula given below is used.
Probability = Possible outcome/sample space.
For question 1.)
Possible outcome = 4057
sample space = 7909
probability = 4057/7909 = 0.51
For question 2.)
Possible outcome = 2700
sample space =7909
probability = 2700/7909= 0.3
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A coin tossed what is the theoretical probability of the coin landing on heads
Answer: 50%
Step-by-step explanation: each side has a 1 in 2 chance of landing on it
Which of the following options have the same value as 72%, percent of 50?
Malia drinks 2 pints of milk each day. How many days does it take her to drink 1 gallon of milk?
HELP ME AND I'LL GIVE YOU 100 POINTS!!! ANSWER IT HONESTLY PLS!!!
Find the area, in square inches, of the composite figure.
12 in.
2 in.
3 in.
3 in.
25 in.
looks somewhat like what my problem looks like but with the numbers I listed
0.305 in word form??
help me please
Answer:
three hundred five thousanths
Step-by-step explanation:
The length of ribbons found at a seamstress are listed.
5, 8, 10, 12, 12, 19
What is the appropriate measure of variability for the data shown, and what is its value?
The range is the best measure of variability and equals 14.
The IQR is the best measure of variability and equals 4.
The mean is the best measure of variability and equals 11.
The median is the best measure of variability and equals 11.
The most appropriate measure of variability which can be used for the data given is IQR and the measure is 4.
Given data set is,
5, 8, 10, 12, 12, 19
Mean and median are the measures of central tendency and not variability.
So they are not appropriate.
Remaining options are Range and IQR.
Range is the difference of the maximum value and the minimum value.
Here, range = 19 - 5 = 14
But range will be affected by the outliers and is not an appropriate measure of variability.
Remaining is IQR, which is the measure of the spread of middle 50% of the data.
IQR = Third quartile - First quartile.
Third quartile = 12 and the first quartile = 8
IQR = 12 - 8 = 4
Hence the appropriate measure is IQR.
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For each equation, decide whether the line it represents is parallel to p, perpendicular to p, or
neither of these.
y=-3x + 10 is _____
y − 5 = − 1/3(x + 2) is _____
y = 1/3x is ______
-3x + y = 1 is _____
y=-3x + 10 is neither of these.
y − 5 = − 1/3(x + 2) is perpendicular to p
y = 1/3x is neither of these.
-3x + y = 1 is parallel to p
What are parallel lines?
Parallel lines are coplanar infinite straight lines in geometry that never intersect. In the same three-dimensional space, parallel planes are any planes that never cross. Curves with a fixed minimum distance between them and no contact or intersection are said to be parallel.
The line p passes through the points (2,2) and (-1,1).
The slope of the line is m = (-1-2) /(1-2)= 3.
Now compare the y=-3x + 10 with y = mx +c:
m₁ = -3, c=10
The slope of the line y=-3x + 10 is -3.
The product m and m₁ is 3 ×(-3) = -9
y=-3x + 10 is neither of these.
Rewrite the equation y − 5 = − 1/3(x + 2)
y = (− 1/3)x - (2/3) + 5
Now compare they = (− 1/3)x - (2/3) + 5 with y = mx +c:
m₂ = − 1/3, c=10
The product m and m₂ is 3 ×( − 1/3) = -1
Thus y − 5 = − 1/3(x + 2) is perpendicular to p.
Now compare the y=1/3x with y = mx +c:
m₃ = 1/3, c=0
The slope of the line y=1/3x + 10 is 1/3.
m₃≠m and mm₃ ≠ -1 , thus y=1/3x is neither of these.
Rewrite the equation -3x + y = 1
y= 3x +1
Now compare the y= 3x +1 with y = mx +c:
m₄ =3, c=1
Since m₄ = m. thus -3x + y = 1 is parallel to p.
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Surface area of rectangular pyramid 2(½ ×w×h)+2(½×l×h)+(l×w)
The first term represents area of the two triangular faces having base of pyramid, second term represents area of two triangular faces having length of the rectangle, third term represents area of rectangular base.
A rectangular pyramid is a solid figure with a rectangular base and four triangular faces that meet at a single point, known as the apex. To find the surface area of a rectangular pyramid, we need to calculate the area of each face and add them together.
The formula for the surface area of a rectangular pyramid is:
Surface area = 2(1/2 x base x height) + 2(1/2 x length x height) + (length x base)
The first term, 2(1/2 x base x height), represents the area of the two triangular faces that share the base of the pyramid. The second term, 2(1/2 x length x height), represents the area of the two triangular faces that share the length of the rectangle. The third term, (length x base), represents the area of the rectangular base.
By multiplying each term by its appropriate values and adding them together, we can find the total surface area of the rectangular pyramid.
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Complete question is:
Surface area = 2(1/2 x base x height) + 2(1/2 x length x height) + (length x base). Explain what each term represents?
3-1 The roof area of a fable roof is made up of two rectangles. (True or False)
Given statement "The roof area of a gable roof is made up of two rectangles"
The given statement is True.
Because, A gable roof consists of two sloping roof surfaces that meet at the top, forming a triangle shape on both ends of the building.
Each of these sloping surfaces can be represented as a rectangle, and the combined area of these two rectangles represents the total roof area.
Area is a measure of the amount of space inside a two-dimensional (2D) or three-dimensional (3D) shape.
It is typically measured in square units, such as square meters, square feet, or square inches.
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retail price $24.50; discount rate 15%
If y=5/3+4 what’s Y and what slope would that make?
Answer: 5/3
Step-by-step explanation:
y = mx +b
m is equal to the slope
b is the y intercept
therefore, m or 5/3 is the slope.
Can you pls help? This is geometry
The equation of the circle with a center at the origin and a diameter of 8 is x² + y² = 16
Define circleA circle is a two-dimensional shape that is defined as a set of points that are equidistant from a fixed point called the center. The radius of a circle is the separation between its centre and any other point on the circle. Another way to think of a circle is as the collection of all points (locus) at a certain radius from the centre.
If the center of the circle is at the origin, then the equation of the circle can be written in the form of:
x² + y² = r²
where r denotes the circle's radius.
Since the diameter of the circle is 8, the radius is half of that, or 4. Consequently, the circle's equation is as follows:
x² + y² = 4²
x² + y² = 16
So the equation of the circle with a center at the origin and a diameter of 8 is x² + y² = 16.
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URGENT - Will also give brainliest to simple answer
The area of the sector in terms of pi is: 75π cm²
The Length of arc = 15π cm
What is the Area of a Sector and Length of an Arc of a Circle?Area of a sector = ∅/360 * πr²
Length of arc = ∅/360 * 2πr, where r is the radius and ∅ is the reference angle.
Given the following:
Reference angle (∅) = 270°
Radius of circle (r) = 10 cm
Area of the sector = 270/360 * π * 10²
Area of the sector = 75π cm²
Length of arc = 15π cm
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A ran a 20-mile race that she completed in 2.5 hours.
If A ran at a constant speed for the entire race,what was her speed in miles per hour?
SHOW YOUR WORK
Answer:
The answer for speed is 8 miles/hr
Step-by-step explanation:
speed =distance/time
s=20/2.6
s=8miles/hr
You have $910 in your checking account. You have paid $185 in bill's online, which were immediately deducted from your checking account. The following day you withdrew $30 for lunch, bought pants for $43, and purchased a gift card for $15 using your debit card. After, you returned the pants for a full refund. How much is in your checking account?
Answer:
Therefore, the answer to how much is in the checking account is $677.
Step-by-step explanation:
The amount in the checking account after all the transactions would be $677.
Here's the breakdown of the transactions:
Starting balance: $910
Bill payment: -$185
Withdrawal for lunch: -$30
Purchase of pants: -$43
Purchase of gift card: -$15
Refund for pants: +$43
Total = $910 - $185 - $30 - $43 - $15 + $43 = $677
Determine the value for c and the covariance and correlation for the joint probability mass function fXY(x,y) = c(x + y) for x = 1, 2, 3 and y = 1, 2, 3
The first step is to determine the value for c. We know that the joint probability mass function must sum to 1 over all possible values of X and Y. So, we can write:
∑∑ [tex]f_{xy}[/tex](x,y) = 1
Substituting the given function [tex]f_{xy}[/tex](x,y) = c(x + y) for each combination of x and y, we have:
c(1+1) + c(1+2) + c(1+3) + c(2+1) + c(2+2) + c(2+3) + c(3+1) + c(3+2) + c(3+3) = 1
Simplifying this equation, we get:
12c = 1
Therefore, the value of c is 1/12
Now, we can use this value to calculate the covariance between X and Y. The covariance measures the degree to which two random variables vary together. It is defined as
cov(X,Y) = E[XY] - E[X]E[Y]
where E[XY] is the expected value of the product of X and Y, and E[X] and E[Y] are the expected values of X and Y, respectively.
To calculate E[XY], we use the joint probability mass function:
E[XY] = ∑∑ xy [tex]f_{xy}[/tex](x,y)
Substituting the given function [tex]f_{xy}[/tex](x,y) = c(x + y) for each combination of x and y, we have,
E[XY] = c(1+1) + 2c(1+2+2+3) + 3c(1+3+3+2)
Simplifying this equation, we get,
E[XY] = 28/12
To calculate E[X] and E[Y], we use the marginal probability mass functions:
fx(x) = ∑y [tex]f_{xy}[/tex](x,y)
fy(y) = ∑x [tex]f_{xy}[/tex](x,y)
Substituting the given function [tex]f_{xy}[/tex](x,y) = c(x + y) for each combination of x and y, we have:
fx₁ = 2c
fx₂ = 4c
fx₃ = 6c
fy₁ = 2c
fy₂ = 4c
fy₃= 6c
Using these marginal probability mass functions, we can calculate E[X] and E[Y]:
E[X] = ∑x x fx(x) = 2c + 8c + 18c = 28/12
E[Y] = ∑y y fy(y) = 2c + 8c + 18c = 28/12
Therefore, the covariance between X and Y is:
cov(X,Y) = E[XY] - E[X]E[Y] = 28/12 - (28/12)(28/12) = -4/144
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Find the volume of the cone. Use 3. 14 for π. Round to the nearest tenth.
A. 18,324. 8 cm3
B. 1,271. 7 cm3
C. 1,527. 1 cm3
D. 4,581. 2 cm3
The volume of the cone is1527.1 cm³
And the correct answer is an option (c)
We know that he formula for the volume of the cone is:
V = 1/3(π × r² × h)
Here, the diameter of the base of the cone is 15 cm
so, the radius of the cone would be,
r = 15/2 cm
r = 7.5 cm
And the slant heihgt of the cone is l = 27 cm
Using Pythagoras theorem the height h of the cone would be,
h = √(l² - r²)
h = √(27² - 7.5²)
h = √(672.75)
h = 25.94 cm
Using above formula, the volume of the cone would be,
V = 1/3(π × r² × h)
V = 1/3(π × (7.5)² × 25.94)
V = 1527.99 cm³
V = 1527.1 cm³
Therefore, the correct answer is an option (c)
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Find the complete question below.
a first-grade teacher is reviewing expanded form with her students and is using the number 74 as an example. she explains to students that since the value of the 7 is actually 70, the expanded form of 74 is 70 4. she notices that several students seem confused. what step could she take to improve students' understanding of expanded form?
The first-grade teacher could take several steps to improve her students' understanding of expanded form. she could use manipulatives to help students visualize the concept of place value.
For example, she could use base-ten blocks or colored chips to represent the value of each digit in a number. This would help students see that the value of the 7 in 74 is actually 7 tens or 70.
Second, she could provide more examples and practice problems that gradually increase in difficulty. This would help students build their understanding of expanded form and allow them to apply the concept to a variety of numbers.
Third, she could use real-world examples that students can relate to, such as money or counting objects in a classroom. This would make the concept of expanded form more meaningful and engaging for students.
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given the vertex at (-4, 5) and a-value of 5, write the vertex form of the quadratic equation.
The vertex form of a quadratic equation is y = a(x-h)^2 + k, where (h,k) is the vertex.
To write the vertex form of a quadratic equation given the vertex (-4, 5) and a-value of 5, you can use the vertex form equation:
y = a(x - h)² + k
where (h, k) is the vertex and a is the a-value.
In this case, h = -4, k = 5, and a = 5. Substitute these values into the equation:
y = 5(x - (-4))² + 5
Simplify the equation:
y = 5(x + 4)² + 5
So, the vertex form of the quadratic equation is:
y = 5(x + 4)² + 5
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The vertex form of the quadratic equation is: y = 5[tex](x + 4 )^2[/tex] + 5
A quadratic equation's vertex form is provided by:
y = a[tex](x - h)^2[/tex] + k
where "a" is the coefficient of the parabola and "(h, k)" is its vertex [tex]x^2.[/tex]
Given that the vertex is (-4, 5) and a-value is 5, we can substitute the values into the vertex form equation:
h = -4
k = 5
a = 5
When we enter these numbers into the equation, we obtain:
y = 5(x -[tex](-4) ^2[/tex] + 5
Simplifying the equation, we get:
y = 5[tex](x + 4)^2[/tex] + 5
So, the vertex form of the quadratic equation is:
y = 5[tex](x + 4 )^2[/tex] + 5
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Evaluate the expression when a = 3 and x = -7 .
-a + 9x
The theoretical probability of an albino Galapagos tortoise being born is 0.001%. If 500,000 Galapagos tortoises hatch, how many would you expect to be albino?
So, we would expect about 5 albino Galapagos tortoises to be born out of 500,000 Galapagos tortoises hatched, assuming that the theoretical probability holds true in practice.
What is probability?Probability is a branch of mathematics that deals with the measurement and analysis of random events. It is the study of how likely an event is to occur, expressed as a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event. Probability is used in many areas of mathematics, science, and engineering, such as statistics, physics, finance, and computer science. It is a fundamental concept for understanding and predicting the behavior of random events and systems.
Here,
To find the expected number of albino Galapagos tortoises, we can use the formula:
Expected value = Probability of event * Total number of trials
In this case, the probability of an albino Galapagos tortoise being born is 0.001 or 0.001/100 = 0.00001 (as a decimal). The total number of trials is 500,000, since that is the number of Galapagos tortoises that hatched.
Therefore, the expected number of albino Galapagos tortoises is:
Expected value = 0.00001 * 500,000
= 5
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gif a stock with a beta of 1.3 is expected to return 18% when treasury bills yield 7%, what is the expected return on the market portfolio? enter your answer as a percent rounded to two decimal places?
The expected return on the market portfolio is 15.46.
How to get expected return on the market portfolio?To calculate the expected return on the market portfolio, we can use the Capital Asset Pricing Model (CAPM) formula, which is: Expected Return = Risk-free rate + Beta * (Market return - Risk-free rate)
In this case, the risk-free rate is given as 7% (treasury bills yield), and the beta of the stock is 1.3. We are also given the expected return on the stock as 18%.
Substituting these values into the CAPM formula, we get:
18% = 7% + 1.3 * (Market return - 7%)
Simplifying the equation, we get:
Market return - 7% = (18% - 7%) / 1.3
Market return - 7% = 8.46%
Market return = 7% + 8.46%
Market return = 15.46%
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