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T.A.=
Answers
Answer: Total area of the given prism is (104 + 16√13) Square inches.
Step-by-step explanation:
By the given diagram,
In the right triangular prism,
The sides of the base ( right triangle ) are 4 inches and 6 inches,
We have to finds : T.A. ( the total area of the prism )
Thus, the total base area of the prism = 2 × ( Area of triangle having base 4 inches and height 6 inches )
= 2× ( 1/2 × 4 × 6 )
= 4 × 6
= 24 square inches,
Let the hypotenuse of the triangles having sides 4 and 6 is x inches, ( shown in the diagram )
Thus, by the given diagram,
[tex]x^2 =4^2+6^2[/tex]
[tex]x^2 = 16 + 36[/tex]
[tex]x^2 = 52[/tex]
[tex]x=2\sqrt{13}[/tex]
Now, the total lateral area of the prism,
= 8×2√13 + 8×4 + 8×6
= 16√13 + 32 + 48
= (16√13 + 80) square inches,
Since, the total area of the given prism (T.A.) = Total base area of the prism(B.A.) + Total lateral area ( L.A.)
= 24 + 16√13 + 80
= (104 + 16√13) Square inches.
Related Questions
Find the equation of the line.
A) y= -3/2 x + 1
B) y= -2/3 x - 1
C) y= 2/3 x + 1
D) y= 3/2 x - 1
Answers
Hope this helps
Answer:
It’s y=2/3x+1 that’s the equation of the line.
Step-by-step explanation:
Solve 6,394 divided by 42 =
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The required quotient is [tex]152[/tex] and remainder is [tex]10[/tex].
Given that [tex]6394[/tex] ÷ [tex]42[/tex].
Long division states that [tex]divident= divisor*quotient+remainder[/tex].
Let [tex]a[/tex] and [tex]b[/tex] be any real number. Consider [tex]a[/tex] ÷ [tex]b[/tex] gives
[tex]a=bq+r[/tex], [tex]q[/tex] is quotient [tex]r[/tex] is remainder and its value is [tex]0\leq r < b[/tex].
[tex]\begin{array}{ccccc}42)&006394(152&\\-&42____________&\\&219& \\&\\-&210&\\&0094\\-&0084\\&0010\end{array}\right][/tex]
Hence, the required quotient is [tex]152[/tex] and remainder is [tex]10[/tex].
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Item 18 A spherical ball with a volume of 972π in.3 is packaged in a box that is in the shape of a cube. The edge length of the box is equal to the diameter of the ball. What is the volume of the box?
Answers
Volume of the given box is 5832 in³
Volume of the cube:
Given a spherical ball with a volume of 972π in.³,
Since the volume of a sphere is (4/3)πr³, we can find that the radius of the sphere is 9 inches.
The edge length of the cube (box) is twice the radius (diameter of the sphere), so the edge length of the cube is equal to 18 inches.
The volume of the cube is then (18³) in³
Volume of the cube = 5832 in³
A person who is 55 feet tall is standing 168168 feet from the base of a tree, and the tree casts a 180180 foot shadow. the person's shadow is 1212 feet in length. what is the height of the tree?
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If 75% of the students in Toby’s grade voted, how many students are in Toby’s grade?
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Answer:
The total number of students in Toby's grade is 200.
Answer:number of students who voted= 75%= 150
75% of total number of students= 150
The total number of students in Toby's grade is 200.
Step-by-step explanation:
What is the positive solution of x2 – 36 = 5x?
Answers
Answer:
The positive solution is x=9
Step-by-step explanation:
Given the equation
[tex]x^2-36=5x[/tex]
we have to find the positive solution of above equation.
[tex]Equation: x^2-5x-36=0[/tex]
By splitting middle-term method
[tex]x^2-5x-36=0[/tex]
[tex]x^2-9x+4x-36=0[/tex]
[tex]x(x-9)+4(x-9)=0[/tex]
[tex](x+4)(x-9)=0[/tex]
[tex]x+4=0, x-9=0[/tex]
The solution is x=-4 and x=9
Hence, the positive solution is x=9
How do you know the sum of a positive and negative integer will be negative?
Answers
[tex]8+(-3)=+5[/tex]
If what you're asking is, under what condition will the sum of a positive and negative be negative, then it's when the absolute value of the negative number is greater than the positive number. For example:
positive number: 8
negative number: -10
[tex]8+(-10)=-2[/tex]
This sum is negative. Note that [tex]\mid{-10}\mid\ \textgreater \ 8[/tex].
The data shows the number of grams of fat found in 9 different health bars.12, 14, 16, 16.5, 11, 18, 18, 14, 20 What is the IQR (interquartile range) for the data?
9
5
16
18
Answers
The interquartile range (IQR) for the given health bar fat content data set is 5 grams, calculated by subtracting the first quartile (13) from the third quartile (18).
To calculate the interquartile range (IQR) of the given health bar data set, first, we must organize the numbers in ascending order: 11, 12, 14, 14, 16, 16.5, 18, 18, 20. The IQR is the difference between the third quartile (Q3) and the first quartile (Q1).
Find the median (the middle value) of the dataset, which will also serve as the second quartile (Q2). The median of the dataset here is 16.
To find Q1, calculate the median of the lower half of the data (not including the median of the dataset if your dataset has an odd number of values). So the lower half of the data is 11, 12, 14, 14, and the median of this is 13.
To find Q3, calculate the median of the upper half of the data. The upper half following our median is 16.5, 18, 18, 20, with a median value of 18.
The IQR is Q3 - Q1, which is 18 - 13 = 5.
Thus, the IQR for the health bars' fat content data is 5 grams.
20 POINTS!
Verify the identity.
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[tex]R_s=\left(\dfrac{1}{\sin x}-1\right):\dfrac{\cos x}{\sin x}=\left(\dfrac{1}{\sin x}-\dfrac{\sin x}{\sin x}\right)\cdot\dfrac{\sin x}{\cos x}\\\\=\dfrac{1-\sin x}{\sin x}\cdot\dfrac{\sin x}{\cos x}=\dfrac{1-\sin x}{\cos x}\cdot\dfrac{1+\sin x}{1+\sin x}=\dfrac{1-\sin^2x}{\cos x(1+\sin x)}\\\\=\dfrac{\cos^2x}{\cos x(1+\sin x)}=\dfrac{\cos x}{1+\sin x} \\\\L_s=R_s[/tex]
[tex]Used:\\\csc x=\dfrac{1}{\sin x}\\\\\cot x=\dfrac{\cos x}{\sin x}\\\\\sin^2x+\cos^2x=1\to\cos^2x=1-\sin^2x\\\\(a-b)(a+b)=a^2-b^2[/tex]
An artist is creating a large conical sculpture for a park. The cone has a height of 16 m of and a diameter of 25 m. Find the volume the sculpture to the nearest hundredth.
A. 833.33 m3
B. 7,850 m3
C. 2,616.67 m3
D. 209.33 m3
Answers
The volume of the conical sculpture is calculated using the formula for the volume of a cone, 1/3πr²h. Substituting the given values, the volume is found to be approximately 2,616.67 m³.
Explanation:The subject of this question is focused on calculating the volume of a cone. To find the volume of a cone, we apply the formula 1/3πr²h, where r is the radius and h is the height. Given in the question, the height (h) of the cone is 16 m and the diameter is 25 m. The radius is half of the diameter so it is 25/2 = 12.5 m. Substituting these values into the formula gives us:
Volume = 1/3πr²h
= 1/3 * π *(12.5 m)² * 16 m
≈ 2,616.67 m³
So, the volume of the sculpture to the nearest hundredth is approximately 2,616.67 m³. Thus, Option C is the correct answer.
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How to solve this problem
Answers
Solve for y
Cos(A) = adjacent / hypotenuse
Cos(A) = y / 8
y = 8 * cos(A)
y = 8 * cos(73)
y = 8 * 0.2924
y = 2.339
Step Two
Solve for x
Sin(A) = opposite / hypotenuse
Sin(73) = x / 8
x = 8 * sin(73)
x = 8 * 0.9563
x = 7.550
Check
x^2 + y^2 =? 8^2
2.339^2 + 7.55^2 =? 8^2
5.471 + 58.53 =? 64
64.000921 = 64 which is close enough.
Kelly wants to know if the number of words on a page in her geometry book is generally more than the number of words on a page in her science book. She takes a random sample of 25 pages in each book, then calculates the mean, median, and mean absolute deviation for the 25 samples of each book.
Kelly claims that because the mean number of words on each page in the science book is greater than the mean number of words on each page in the geometry book, the science book has more words per page. Based on the data, is this a valid inference?
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Answer:
No, because there is a lot of variability in the science book data
Step-by-step explanation:
A system of equations that has an infinite number of solutions is called a(n) ______ system of equations.
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A system of equations with an infinite number of solutions is known as a consistent and dependent system. These systems occur when equations are essentially the same, leading to all solutions satisfying all the equations, often represented by overlapping graphs in the case of linear equations.
Explanation:A system of equations that has an infinite number of solutions is called a consistent and dependent system of equations. When a system is consistent and dependent, it means that the equations describe the same line or geometric shape, leading to an infinite number of points that satisfy all equations in the system simultaneously. This scenario often arises when the equations in the system are multiple forms of the same equation, or when they can be algebraically manipulated to become the same equation.
In practical terms, if you were to graph the equations in a consistent and dependent system, you would see that they overlap completely. For instance, if two linear equations represent the same line, any point on that line is a solution to both equations, hence the infinite solutions. A key aspect of understanding such systems is realizing that they do not lead to a single unique solution but rather a set of solutions that satisfy all conditions outlined by the equations in the system.
A system of equations with an infinite number of solutions is referred to as a consistent and dependent system, indicating the equations describe the same line.
A system of equations that has an infinite number of solutions is called a consistent and dependent system of equations. This type of system occurs when the equations involved describe the same geometric line, meaning every point on the line is a solution to the system, hence an infinite number of solutions. Such systems often arise in various mathematical contexts, including linear algebra and differential equations, where they indicate a fundamental underlying symmetry or redundancy in the system's constraints.This occurs when the equations are dependent, leading to multiple possible solutions that satisfy all the equations simultaneously.
What is the value of c when the expression 21.2x + c is equivalent to 5.3(4x − 2.6)?
Answers
To find our answer we need to work out the parenthesis. This is for instance possible using rainbow technique.
[tex]5.3(4x - 2.6) = \\ 5.3 \times 4x - 5.3 \times 2.6 = \\ 21.2x - 13.78[/tex]
Therefore the value of c = - 13.78.
~ Hope this helps you!
Comparing with 21.2x + c:-
the value of c = -13.78 Answer
You fly a hot air balloon 1.5 miles above the ground. What is the measure of BD⌢, the portion of Earth that you can see? Round your answer to the nearest tenth. (Earth's radius is approximately 4000 miles.)
Answers
Answer:
3.1
Step-by-step explanation:
If you are doing this for big ideas, the answer ended up being 3.1
I'm sorry if you wanted the work, I found the answer from something else that didn't show the work but this was the correct answer...
To find the measure of BD⌓, the visible portion of Earth's surface from a hot air balloon 1.5 miles above the ground, convert the height to kilometers and use the formula D = 112.88 km × √h to get the distance to the horizon, which is about 175.4 km. Then, calculate the semicircular distance visible by using C/2 = (π × D) / 2, which results in approximately 276.1 km for the measure of BD⌓.
Explanation:To calculate the measure of BD⌓, the portion of Earth's surface that is visible from a hot air balloon 1.5 miles above the ground, you can use the formula for the distance to the horizon, given as D = 112.88 km × √h, where h is the height above the Earth's surface. In this case, we must convert the height of 1.5 miles to kilometers before applying the formula, as the formula uses kilometers.
The conversion from miles to kilometers is 1 mile = 1.60934 kilometers, so 1.5 miles is approximately 2.414 km.
Inserting h = 2.414 km into the formula, we get:
D = 112.88 km × √2.414
D = 112.88 km × 1.5535 (approx)
D ≈ 175.4 km (rounded to the nearest tenth)
This is the straight-line distance to the horizon. To find the measure of the arc BD, which is the portion of the Earth's surface visible, we can treat this distance as the radius of a circle and calculate the circumference. However, since we are only looking at the visible part, which is a semicircle, we use half of the circumference C = π × D.
The measure of BD⌓ is therefore approximately:
C/2 = (π × 175.4 km) / 2
C/2 ≈ 276.1 km
Thus, the measure of BD⌓ to the nearest tenth is 276.1 km.
How do I simplify this expression
Answers
= 4x(x + 5) - 3(x + 5)
= 4x^2 + 20x - 3x - 15
= 4x^2 + 17x - 15 Answer
Please help me out here.
Answers
When you multiply two exponents with the same base together, you can add the indexes together. For example, if you had y * y², you could make it y³, by adding the indexes of 2 and 1.
In this scenario, you can look at the last choice, where it has [tex] x^{9} [/tex] * x. You add the indexes of 9 and 1, to get [tex] \sqrt[3]{ x^{10} } [/tex]
That's equivalent to the equation given, so your answer would be the last choice.
Using a straightedge, or using technology, sketch an obtuse, scalene triangle. Make sure to include your sketch in your answer.
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You roll a number cube and flip a coin. find the probability of rolling an even number and flipping heads. write your answer as a fraction in simplest form.
Answers
Hope this helped!
Final answer:
To calculate the combined probability of rolling an even number on a number cube and flipping heads on a coin, you multiply the separate probabilities of each event, which are 1/2 and 1/2 respectively, resulting in a combined probability of 1/4.
Explanation:
The probability of rolling an even number on a number cube (which is a standard six-sided die) is 3 out of 6 since there are three even numbers (2, 4, 6) and six possible outcomes overall. This simplifies to 1/2. The probability of flipping heads on a coin is 1/2 since there are two possible outcomes, heads or tails, and both are equally likely if the coin is fair.
To find the combined probability of two independent events (rolling an even number and flipping heads), you multiply the probabilities of each event together. So, the probability of rolling an even number and flipping heads is 1/2 (for the number cube) times 1/2 (for the coin), which equals 1/4 or 25%.
In the simplest form, the fraction is written as 1/4.
Which of the following have the same value as the fraction below?
8/5 A.
Check all that apply.
A. 2.20
B. 220%
C. 1.60
D. 160%
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The problem is in the first picture and the questions are in the second one. I have no idea how to do any of this.
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You are given that CB = 271 feet. You are also given that <CAB = 30 degrees.
So you can use Sin(<CAB) = opposite / hypotenuse or
hypotenuse = opposite / sin(<CAB)
hypotenuse = 271 / 0.5
hypotenuse (AB) = 542 feet.
Problem B
CD = 772 feet Given in table
<ACD = 74o Given on drawing.
We need to find AC which is not given
Cos 30 = adjacent / hypotenuse.
adjacent = hypotenuse * Cos(30)
adjacent = AB * Cos(30)
Adjacent = 542 * cos(30)
Adjacent = AC = 469.4 feet
Now we need to start again
AC = 469.4
<ACD = 74
CD = 772
AD = ???
AD^2 = AC^2 + CD^2 - 2 * AC * CD * Cos(74)
AD^2 = 595984 + 220336.4 - 399538
AD^2 = 416782.1
AD = sqrt(416782.1)
AD = 645.59
Problem 3
I'll set it up for you. And give you the answer I get, but I'm going to leave it to you mostly. It just follows what I've done above.
DC = 645.59
CE = 561
DE = 543
DC^2 = CE^2 + DE^2 - 2* CE * DE * Cos(E)
645.59^2 = 561^2 + 543^2 - 2*561*543 * Cos(E)
Cos(E) = -0.3164
E = cos-1(0.3164)
E = 108.45 degrees.
What is the value of x in the equation x + 10 = 13?
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A basket contains the following pieces of fruit: 3 apples, 2 oranges, 2 bananas, 2 pears, and 5 peaches. Jack picks a fruit at random and does not replace it. Then Bethany picks a fruit at random. What is the probability that Jack gets a peach and Bethany gets an orange?
Answers
You have to find the probabilities of them happening separately
To do this you do the amount of favorable outcomes over the total amount of outcomes
3 + 2 + 2 + 2 + 5 = 14 total fruit
The chance of Jack getting a peach is 5 / 14
The chance of Bethany getting an orange is 2 / 13 because Jack did not put the fruit back in so their is one less to choose from
You multiply the two probabilities to find the probability of them happening in a row
5/14 * 2/13 = 5/91
The answer is 5/91
Hope this helps!
simplify by 2
10/182 ÷ 2/2
5/91
5 over 91
find the solution of this system of equations
-6x-2y=8
7x-2y=-5
Answers
Select the property that allows the statement 10 = y to be written y = 10.
Commutative - addition
Distributive
Associative - multiplication
Symmetric
Commutative - multiplication
Associative - addition
Identity - addition
Answers
This is the symmetric property
Hope this helps!
The property that allows the statement 10 = y to be written y = 10 is:
Symmetric
Step-by-step explanation:We know that for any set A. if a and b are two elements of the set A.
Then if a is related to b by some relation then by the symmetric property b must be related to a by the same property.
Here 10 is related to y by the equality relation.
i.e. 10=y
Hence, by the symmetric property we have that y must be related to 10 by the same equality relation.
i.e. y=10
The difference of a number and 8 is the same as 34 less the number. find the number.
Answers
34 less the number is 34-n.
n-8=34-n
2n=34+8
2n=42
n=21
The question is a simple algebra problem. By setting up and solving the equation 'x - 8 = 34 - x', we find that the number is 21.
Explanation:The subject of this question is algebra, and involves setting up and solving an equation. Let's denote the unknown number as 'x'. Following the question, we can set up the equation as 'x - 8 = 34 - x'.
To solve the equation, let's add 'x' to both sides to get 2x - 8 = 34. Then, add 8 to both sides to get 2x = 42. Finally, divide each side by 2, so that 'x = 21'.
So, the number that satisfies the equation is 21.
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a glass jar contains 1 red, 3 green, 2 blue, and 4 yellow marbles. if a single marble is chosen at random from the jar, what is the probability that it is red
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[tex] \frac{1}{10} [/tex]
suppose you deposit 1,000 ina savings account that pays interest at an annual rate of 5%. if no money is added or withdrawn from the account answer the following questions. How much money will be in the account after 3 years? How much will be in the account after 18 years? How many years will it take for the account to contain 1,500? How many years will it take for the account to contain 2,000?
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Time req'd for amount to reach $1500 from $1000:
1500=1000(1+0.05)^t, or 1.5=1.05^t
ln 1.5
ln 1.5 = t ln 1.05, so that t = ------------ = 8.31 years, or 8 yr 3 3/4 months
ln 1.05
Graph the six terms of a finite series where a1 = −3 and r = 1.5.
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For the given series:
[tex]a_{1}=-3 \\ r=1.5 [/tex]
Each term of the geometric series is obtained by multiplying the previous term by common ratio.
So the next terms will be:
-4.5, -6.75, -10.125, -15.1875, -22.78125
The general formula for the G.P would be:
[tex] a_{n}=-3(1.5)^{n-1} [/tex]
On plotting the series, the result will be like this:
Answer:
the answer is C
Step-by-step explanation:
What is the slope of a line that is parallel to the line y = x + 2?
Answers
y = x + 2
⇒ slope = 1
⇒Slope of the parallel line = 1
Answer: 1
Answer:
I’m going to assume you didn’t put the 3/4x in your equation, if you had, the answer would’ve been 3/4.
Step-by-step explanation:
REMEMBER
If the equation is parallel, it will have the same slope as the other equation parallel to it.