Answers
The lateral area and surface area of the cuboid are 72 square feet and 142 square feet, respectively. The lateral area and surface area of the prism are 42 square cm and 62 square cm, respectively.
To find the lateral area and surface area of the given cuboid and prism, we need to use the formulas for each.
For the cuboid:
1. Lateral Area: The lateral area of a cuboid can be found by adding the areas of its four side faces. Since the cuboid has a length of 7 feet, a breadth of 5 feet, and a height of 3 feet, we can calculate the lateral area as follows:
- Side 1: length * height = 7 feet * 3 feet = 21 square feet
- Side 2: breadth * height = 5 feet * 3 feet = 15 square feet
- Side 3: length * height = 7 feet * 3 feet = 21 square feet
- Side 4: breadth * height = 5 feet * 3 feet = 15 square feet
The total lateral area is the sum of these four areas: 21 + 15 + 21 + 15 = 72 square feet.
2. Surface Area: The surface area of a cuboid is found by adding the areas of all six faces. In addition to the lateral area, we need to include the areas of the top and bottom faces. Using the dimensions of the cuboid, we can calculate the surface area as follows:
- Top face: length * breadth = 7 feet * 5 feet = 35 square feet
- Bottom face: length * breadth = 7 feet * 5 feet = 35 square feet
The total surface area is the sum of these six areas: 72 (lateral area) + 35 (top face) + 35 (bottom face) = 142 square feet.
Now, for the prism:
1. Lateral Area: To find the lateral area of the prism, we need to find the perimeter of the base and multiply it by the height of the prism. Since the prism has a base with a length of 5 cm and a breadth of 2 cm, the perimeter is: 2 * (length + breadth) = 2 * (5 cm + 2 cm) = 2 * 7 cm = 14 cm.
The lateral area is obtained by multiplying the perimeter by the height: 14 cm * 3 cm = 42 square cm.
2. Surface Area: The surface area of the prism is the sum of the lateral area and twice the area of the base. Since the base is a rectangle with a length of 5 cm and a breadth of 2 cm, its area is: length * breadth = 5 cm * 2 cm = 10 square cm.
The surface area is then calculated as: 42 (lateral area) + 2 * 10 (area of the base) = 42 + 20 = 62 square cm.
Related Questions
The price of an apple is one third that of an orange. Robert paid $10.80 for 5 oranges and 12 apples.
(a) How many apples could he buy for $10.80?
(b) How much does one apple cost?
Answers
Answer:
a: 27 apples
b: $0.40 apples
Step-by-step explanation:
a: another way of saying that the price of an apple one-third that of an orange is that you can get 3 apples for the price of 1 orange. If he bought 5 oranges, he could have gotten 15 apples, so 27 apples total.
b: $10.80/27 = $0.40 per apple
Find the area of the shaded polygons:
Answers
I think the last one is maybe ten, maybe
Answer:
Step-by-step explanation:
no
Lines AB and AC tangent to circle k(O) at B and C respectively. Find BC, if m∠OAB=30°, and AB=5 cm.
Answers
Answer:
5 cm
Step-by-step explanation:
ΔABC is equilateral, so BC = AB = 5 cm.
____
AO is the perpendicular bisector of BC and the angle bisector of angle A, so ∠OAC = ∠OAB = 30°. Then vertex angle BAC of isosceles triangle ABC is 60°, which means all angles in the triangle are 60° and the triangle is equilateral.
The length of BC is 5cm
Given that line AB is tangent to circle K at point B, and line AC is tangent to circle K at point C, we know that the radius of the circle at the point of tangency is perpendicular to the tangent line. Therefore, OB is perpendicular to AB, and OC is perpendicular to AC. This forms two right triangles,[tex]$\triangle OAB$ and $\triangle OAC$.[/tex]
Let's denote OB as the side opposite the 30° angle and OA as the hypotenuse. Then we have:
[tex]OB = $\frac{1}{2}$AB = $\frac{1}{2} \times 5$ cm = 2.5 cm[/tex]
OA = AB = 5 cm (since AB is the hypotenuse of the right triangle)
Now, since the circle is the same, OA is also the radius of the circle, and thus OB = OC = 2.5 cm.
Therefore [tex], $\triangle OBC$[/tex] is an equilateral triangle because all angles are 60° and the sides opposite these angles are equal. Hence, BC = OB = OC = 2.5 cm.
Thus, BC = OB + OC' = 2.5 cm + 2.5 cm = 5 cm.
But this is not the final answer. We have to consider that the length of the chord BC is equal to the diameter of the circle because the tangents from a common external point to a circle are equal in length. Therefore, the diameter of the circle is twice the length of the radius OB (or OC').
Diameter = 2 * OB = 2 * 2.5 cm = 5 cm
BC = 5cm
in a right circular cylinder of height 2 meters, if the volume is increasing at 10 m^3/min how fast is the radius of the cylinder increasing when the radius is 4in?
Answers
Given dimensions:
Height of the cylinder = 2 m
Volume is increasing at a rate of = 10 m³/min
Radius = 4 inches
Converting radius in meters.
1 inch = 0.0254 meters
4 inches = [tex]4\times0.0254=0.1016[/tex] meters
[tex]\frac{dv}{dt}=10[/tex]
we have to find, [tex]\frac{dr}{dt}=?[/tex]
Volume of the cylinder is given by [tex]\pi r^{2} h[/tex]
= [tex]\pi r^{2} *2 = 2\pi r^{2}[/tex]
Now differentiating with respect to 't'
[tex]\frac{dv}{dt} = \frac{d}{dt} (2\pi r^{2})[/tex]
[tex]\frac{dv}{dt} = 2\pi (2r)(\frac{dr}{dt})[/tex]
[tex]10=2\pi (2*0.1016)\frac{dr}{dt}[/tex]
[tex]10=2*3.14(0.2032)\frac{dr}{dt}[/tex]
[tex]\frac{dr}{dt}=\frac{10}{1.276}[/tex]
= 7.83 meter per minute.
The sum of two numbers is 69. The larger number is three less than twice the smaller number. Find the numbers.
Answers
Answer:
x = 45, y = 24.
Step-by-step explanation:
If the 2 numbers are x and y:
x + y = 69...........(1)
x = 2y - 3
x - 2y = -3...........(2)
Subtract: (1) - (2):
x - x + y - (-2y) = 69 - (-3)
y + 2y = 72
3y = 72
y = 24.
From equation 1:-
x + 24 = 69
x = 45.
The numbers are x = 24 and y = 45 respectively.
What is algebraic expression?An algebraic expression in mathematics is a combination of terms both constant and variable. For example, we can write the expressions as -
2x + 3y + 5
2z + y
x + 3y
Given is that the sum of two numbers is 69. The larger number is three less than twice the smaller number.
Assume that the numbers are {x} and {y}. So, we can write the equations as -
x + y = 69
y = 2x - 3
Rewriting equation {1}, we get -
x + y = 69
x + 2x - 3 = 69
3x = 72
x = 24
and
y = 2 x 24 - 3
y = 45
Therefore, the numbers are x = 24 and y = 45 respectively.
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Which ratio correctly compares 2 feet to 48 inches, when the lengths are written using the same units?
Note: 12 inches = 1 foot
A. 2 : 1
B. 24 : 1
C. 1 : 24
D.1 : 2
Answers
Answer: OPTION D
Step-by-step explanation:
To solve this problem you must apply the proccedure shown below:
- Convert from 48 inches to foot. You know that 12 inches=1 foot. Then you have:
[tex](48inches)(\frac{1foot}{12inches})=4feet[/tex]
- Therefore, keeping on mind that 48 inches is 4 feet, and you must find the ratio that correctly compares 2 feet to 48 inches, you can write:
[tex]ratio=\frac{2feet}{4feet}[/tex]
- Reduce the fraction, then:
[tex]ratio=\frac{1}{2}[/tex]
- You can rewrite it as following:
[tex]ratio=1:2[/tex]
Answer:
D
Step-by-step explanation:
Consider the equation log5(x + 5) = x2.
What are the approximate solutions of the equation? Check all that apply.
Answers
Answer:
x ≈ -0.93, x ≈ 1.06
Step-by-step explanation:
A graphing calculator can show you the approximate solutions. (It is also capable of refining those solutions to full calculator precision, if you need.)
_____
Comment on the graphical solution
I prefer to have the calculator show me the zeros of a function, where the zeros correspond to solutions of the original equation. For the purpose, it is sufficient to define the function as the difference between the sides of the original equation.
__
The definition of g(x) in the attachment corresponds to the iterator of Newton's Iteration method for finding zeros of a function. When the input and output values of that iteration function match, the value of x is a zero of the function f(x).
what type of function can approach zero as x decreases without end?
A. linear. B. quadratic
C. exponential. D. Constant
Answers
Answer: c. Exponential
What is defaulting?Getting a low credit score
Opening too many credit accounts
Building a credit history
Failing to pay debt
Answers
Answer:
Failing to pay debt
Step-by-step explanation:
Final answer:
Defaulting on a debt, failing to pay debt, and building a credit history are crucial aspects of managing one's financial health.
Explanation:
Defaulting on a debt occurs when a borrower fails to repay the loan according to the terms agreed upon with the lender. This can lead to serious consequences such as damage to one's credit score and possible legal actions taken by the lender.
One of the contributing factors to defaulting is failing to pay debt on time. This affects a person's credit history and the lender's trust in the borrower's ability to repay borrowed money.
It is important to build a credit history by responsibly managing credit accounts, paying bills on time, and avoiding opening too many accounts rapidly to maintain a good credit score and prevent defaulting.
A phone company wants to know if its customers are satisfied with their service. 100 people are surveyed. The results show that 40 people are satisfied. There are 1,200 people the company services. About how many people are satisfied with their service?
Answers
100:40
=2.5
1200 : 2.5
=480
About 480 people out of the 1,200 customers are likely satisfied with their service.
To determine how many of the company's customers are likely satisfied with their service based on the survey results, we can use the concept of proportions. This involves simple multiplication and understanding ratios in percentages.
Find the proportion of satisfied customers in the survey:
Number of satisfied customers in the survey: 40
Total number of people surveyed: 100
Proportion of satisfied customers = (Number of satisfied customers) / (Total number of people surveyed)
Proportion of satisfied customers = 40 / 100 = 0.4 or 40%
Apply this proportion to the entire customer base:
Total number of the company's customers: 1,200
Estimate of satisfied customers = Proportion of satisfied customers × Total customers
Estimate of satisfied customers = 0.4 × 1,200 = 480
What is the explicit formula for this sequence? -5,-3,-1,1,3
Answers
Answer:
b
Step-by-step explanation:
100%
The explicit formula for the sequence -5, -3, -1, 1, 3 is a_n = -5 + (n - 1)2.
What is an arithmetic sequence?Each term of an arithmetic sequence can be found using the formula:
a_n = a + (n-1)d
Where a is the first term,n is the position of the term,a_n is the nth term of the sequence,d is the common difference of the sequence.We can find the explicit formula for this sequence as follows:
The given sequence is 5, -3, -1, 1, 3.
From this, we can see that the value of:
a = -5
d = -3 - (-5) = -3 + 5 = 2
∴ The explicit formula can be written as:
a_n = -5 + (n - 1)2
Therefore we have found the explicit formula for the sequence -5, -3, -1, 1, 3 as a_n = -5 + (n - 1)2.
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this is a dilation I need to know if it is an reduction or enlargement and explain also the scale factor and explain please help me
Answers
Answer:
a) reductionb) 1/2Step-by-step explanation:
a) The image A'B'C'D' is smaller than the original ABCD, so the dilation is a reduction. The image is reduced in size from the original.
__
b) Each image point is 1/2 the distance of the original point from the origin. Count the grid squares to see this, or compare coordinates:
A'(-1, 2) = 1/2·A(-2, 4)
Thus the scale factor is 1/2.
select the rigid transformation
Answers
Answer:
(x, y) ⇒ (-x, y)
Step-by-step explanation:
Any transformation that multiplies a variable by something other than ±1 is not a rigid transformation — it involves some sort of dilation. Constants can be added or subtracted to effect translation, but none of the transformations shown here do any translation.
The first transformation is a reflection across the y-axis, hence the rigid transformation you're looking for.
_____
Comment on rotations
A rotation about the origin can be written in the form ...
(x, y) ⇒ (ax -by, bx +ay)
where a^2 +b^2 = 1 and b/a = tan(angle of rotation)
This rigid transformation is an exception to the statement above about multiplication by something other than ±1.
Natalie and 5 of her friends are going bowling.It costs $3 to play one game and $2 for each person to rent a pair of bowling shoes. If they spent a total of $21,how many games did they play?
Answers
To find out how many games Natalie and her friends played, we subtracted the total shoe rental cost for 6 people from the $21 spent and divided the remainder by the cost per game, which gave us a result of 3 games played.
Explanation:The question asks us to solve a real-world math problem where Natalie and her friends go bowling and spend a total of $21. The cost to play one game is $3 and shoe rental is $2 per person.
To determine the number of games they played, we need to calculate the cost of shoe rental for all people and then figure out how much of the $21 was left for the games.
First, we calculate the shoe rental for 6 people (Natalie and her 5 friends):
Shoe rental per person = $2Total shoe rental cost = 6 people × $2/person = $12Next, we subtract the shoe rental cost from the total amount spent to find the amount spent on games:
Total amount spent on games = $21 - $12 = $9Finally, we divide the amount spent on games by the cost per game to find the number of games played:
Cost per game = $3Number of games played = $9 / $3/game = 3 gamesNatalie and her friends played 3 games of bowling.
what is the sum of measurements of the interior angles of a 12-gon?
Answers
Answer:
1800
Step-by-step explanation:
Given in the question a polygon of 12 sides
Formula to calculate sum of interior angles of 12-gon is
(n – 2)180where n is the number of sides
which in this case = 12
plug values in the formula above
(12 - 2)180
12*180 - 180(2)
2160 - 360
1800
Sum of measurements of the interior angles of a 12sided polygon is 1800
Answer:
=1800°
Step-by-step explanation:
A 12 sided figure is called a do-decagon or a 12-gon. The general formula for calculating the sum of all interior angles of a regular polygon is=180(n-2)
n represents the number of sides of the polygon.
Therefore, the sum of all angles= 180(12-2)
=1800°
what is the volume?
Answers
Answer:
1282.82ft³
Step-by-step explanation:
To find the volume of the entire shape, we first need to find the volume of the cone and the cylinder separately.
Let's begin by getting the volume of the cylinder.
The formula to find the volume of a cylinder is:
[tex]V=\pi r^{2}h[/tex]
r = 7 ft
h = 6 ft
Let's plug in our values into the formula.
[tex]V=\pi (7)^{2}6[/tex]
[tex]V=\pi (49)6[/tex]
[tex]V=\pi (294)[/tex]
[tex]V=923.63[/tex]ft³
Now that we have the volume of our cylinder we need to find the volume of the cone.
The volume of the cone can be found by using the formula:
[tex]V=\dfrac{1}{3}\pi r^{2}h[/tex]
Our variables for the cone are:
r = 7 ft
h = 7 ft
[tex]V=\dfrac{1}{3}\pi (7)^{2}(7)[/tex]
[tex]V=\dfrac{1}{3}\pi (49)(7)[/tex]
[tex]V=\dfrac{1}{3}\pi (343)[/tex]
[tex]V=\dfrac{1}{3}1077.57[/tex]
[tex]V=359.19[/tex]ft³
Now that we found both of the volumes of the two shapes, we can then simply get the sum of both volumes to get the total volume of the shape.
Total Volume = 923.63ft³ + 359.19ft³
Total Volume = 1282.82ft³
in this right triangle the length of the hypotenuse, BC, is
Answers
Answer:
√13 units
Step-by-step explanation:
Find points B and C on the figure and locate the line between those points. The number next to the line is its length. Read the length from the diagram.
In a right triangle, the hypotenuse is the side across from the 90 degree angle. Without more information, we can't determine the length of the hypotenuse (BC), but if the lengths of the other two sides or the measurements of the other angles are known, the Pythagorean theorem or trigonometry can be used. It is expressed as BC^2 = AB^2 + AC^2.
Explanation:In a right triangle, the hypotenuse is the side that is opposite to the 90 degrees angle. In your right triangle, as you mentioned the sides as BC, I assume you have a triangle ABC where B and C are the two base angles and A is the right angle (90 degrees).
Without additional information such as the lengths of the other two sides (AB, AC), or the measurements of angles B or C, it is impossible to determine the length of the hypotenuse (BC). However, if you do have this information, you can use the Pythagorean theorem or trigonometric ratios to find the length. Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (BC) is equal to the sum of the squares of the lengths of the other two sides. It is expressed as BC^2 = AB^2 + AC^2.
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Ms. Wilson’s taxable income is 36,201. She is filling as single, and she has already paid $5344 in federal tax’s. What will she receive or pay after she figures her taxes for the year?
A. She will receive a refund of $258.
B. She will pay $258.
C. She will receive a refund of $245.
D. She will pay $245.
Answers
Answer: it should be will receive a refund of $278
Step-by-step explanation:
That’s just what was on my test though
Hope that helps somebody
The amount Ms. Wilson will receive after she figures out her tax for the year is; $999.88
Tax rate and Tax bracketThe tax bracket Ms. Wilson falls into demands that she pays 12% of her taxable income in tax.
Hence, the tax she's supposed to pay is;
Tax = (12/100)× 36,201Tax per annum = $4,344.12.Hence, she will receive after she figures her taxes for the year is; $5344 - $4,344.12 = $999.88
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Can someone explain 2.2
Answers
Answer:
C. 2
Step-by-step explanation:
Point B is 6-(-4) = 10 units up from point A. A point (F) that partitions that distance in the ratio 3:2 will be 3/(3+2) = 3/5 of the distance from A to B. That is, it will be ...
3/5 · 10 units = 6 units
above A. The y-coordinate of F will be 6 units added to the y-coordinate of point A, -4 +6 = 2.
The 5th picture with the question I need help with.
Answers
Answer:
Step-by-step explanation:
27
Please help
problem 4 I took picture of
problem 13
the perimeter of a rectangle is 336 inches. the ratio of the length to the width is 9:5. Find the length of the rectangle.
problem 16
a blueprint for a house states that 2 inches on the blueprint represent 8 feet. If the width of a window is 2.5 inches on the blueprint, what is the actual windows with?
Answers
Answer:
Since 2 inches represent 8 feet then 2.5 would represent x feet so
2/8 = 2.5/x
By doing cross multiplication :
2 x = 20 --> x = 10 feet
Step-by-step explanation:
Which statement about the rates of changes of Functions A and B as shown is true?
Answers
Answer: function b has a greater rate of change
A suspension cable is attached to a bridge at both ends 70 feet above the bridge deck. The suspension cable reaches its lowest point at a horizontal distance of 140 feet.
Which graph represents the situation?
Answers
Answer:
graph D
Step-by-step explanation:
You want to choose the graph with a y-intercept of 70 and an x-intercept of 140. Graph D matches that.
___
Comment on graph D
The horizontal scale is a bit weird in that the numbers don't correspond to hash marks on the horizontal axis. The hash mark between the numbers 120 and 160 will correspond to a distance of 140 ft. That is where the graph touches the horizontal axis, so that is one indication it is the graph you want.
what is the multiplicative inverse of 2/5
Answers
Answer:
5/2
Step-by-step explanation:
The multiplicative inverse is what me need to multiply by to get 1
2/5 * what = 1
Multiply by the reciprocal
5/2 *2/5 * what = 1 *5/2
what = 5/2
The multiplicative inverse is 5/2
5/2 is the multiplicative inverse
A parallelogram has sides of length 30 centimeters and 18 centimeters. One of its angles measures 58 degrees. Which is the best estimate for the area of the parallelogram?
F 274.8 CM squared
G 286.2 CM squared
H 457.9 CM squared
J 540.0 CM squared
Answers
Answer:
option H
457.9 CM squared
Step-by-step explanation:
Given that,
base of parallelogram = 30 cm
side of parallelogram = 18 cm
one of the angle of parallelogram = 58°
Formula to calculate area of parallelogram is
area = base x heightTo calculate height we will use trigonometry identity
sinФ = opposite / hypotenusesin(58) = height / 18
height = 15.27
Area = 30 x 15.27
= 457.9 cm²
so the area of parallelogram is 457.9 cm²
Hi there!
Can I get some help with this calculus homework. #6a and 8b. Don't forget to show your work! Thank you!
Answers
Answer:
6a. -8
8b. 1/125
Step-by-step explanation:
If you know powers of 2 and the squares and cubes of small integers, you can work these in your head. There is no "work" to show. Of course, a calculator can evaluate these easily. (see attached)
___
6a. (-128)^(3/7) = ((-2)^7)^(3/7) = (-2)^3 = -8
___
8b. (27^(2/3) +8^(4/3))^(-3/2) = ((3^3)^(2/3) +(2^3)^(4/3))^(-3/2)
= (3^2 +2^4)^(-3/2) = (9+16)^(-3/2) = 25^(-3/2)
= (5^2)^(-3/2) = 5^(-3) = 1/5^3
= 1/125
tomas and emilio are twins. they want to invite their friends to celebarte their shared birthday at the movie theater. they have a budget of $200 to plan their party. the party room at the theater costs $45.99 to rent and include a free cake. movie tickets cost $12.50 each and a small bag of popcorn cost $ 4.50. Tomas write an equation to represent the cost of their party. emilio writes an inequality. both use p to represent the number of people who can attend. wtrite tomas possible equation and emilio possible inequality.
Answers
Answer:
1) 17p + 45.99 = 200
2) 200 > 45.99 + 17p
Step-by-step explanation:
Total Budget = $200
Cost of Party Room = $45.99
Cost of movie ticket for one person = $12.50
Cost of one small bag of popcorn = $4.50
Part 1: Possible Equation by Tomas
The possible equation that can be set up will have the total budget equal to total expenses.
So,
200 = Total Cost of party
200 = Cost of Party Room + Cost of Movie Tickets + Cost of popcorns
If p people attend the party, the cost of movie tickets will be $12.50p and cost of popcorns will be $4.50p, assuming that each person get a small popcorn bag.
So, now the equation will be:
200 = 45.99 + 12.50p + 4.50p
200 = 45.99 + 17p
or
17p + 45.99 = 200
This is a possible equation that Tomas might have used to represent the cost of the party.
Part 2: Possible Inequality by Emilio
Emilio might want to keep the cost below $200 of the entire party. So the possible inequality will be of the form:
200 > Total Cost of party
200 > Cost of Party Room + Cost of Movie Tickets + Cost of popcorns
200 > 45.99 + 12.50p + 4.50p
200 > 45.99 + 17p
This is a possible inequality that Emilio might have used to represent the cost of the party.
In the equation y=(x-2)^2, the minimum value occurs when x is....
And explenation.
Answers
Answer:
x = 2
Step-by-step explanation:
The minimum occurs where the value being squared is zero. x-2 = 0 when x=2.
Which of the following ordered pairs represents a solution to the linear inequality y>2x-3
Answers
Answer:
D. (2, 5)
Step-by-step explanation:
On a graph, (2, 5) is the only point in the solution space.
___
You can evaluate the inequality for each of the points to see which works.
A. 4 > 2·4 -3 . . . . false
B. 12 > 2·9 -3 . . . . false
C. 2 > 2·3 -3 . . . . false
D. 5 > 2·2 -3 . . . . TRUE
what is the sum of the geometric series sigma 15,x=0, 2(1/3)x
Answers
Answer:
[tex]\sum_{x=0}^{15}2(\frac{1}{3})^x=3.0[/tex]
Step-by-step explanation:
We want to evaluate:
[tex]\sum_{x=0}^{15}2(\frac{1}{3})^x[/tex]
When x=0, we obtain the first term of the geometric series as
[tex]a_0=2(\frac{1}{3})^0[/tex]
The common ratio of this geometric series is [tex]r=\frac{1}{3}[/tex]
The sum of the first n-terms of a geometric series is
[tex]S_n=\frac{a(1-r^n)}{1-r}[/tex]
From x=0 to x=15, we have 16 terms.
The sum of the first 16 terms of the geometric series is
[tex]S_{16}=\frac{a(1-(\frac{1}{3})^{16})}{1-\frac{1}{3}}=2.99999993031[/tex]
[tex]\sum_{x=0}^{15}2(\frac{1}{3})^x=3.0[/tex] to the nearest tenth.