Answers
Answer:
SA = 48 cm²
Step-by-step explanation:
the surface area (SA) is the sum of the areas of the 5 faces.
1 square and 4 congruent triangles form the pyramid
area of square = 4 × 4 = 16 cm²
area of triangle = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
here b = 4 and h = 4
area = [tex]\frac{1}{2}[/tex] × 4 × 4 = 2 × 4 = 8 cm²
area of 4 triangles = 4 × 8 = 32 cm²
SA = 16 + 32 = 48 cm²
Related Questions
Find the 8th term of the geometric sequence 10, 50, 250,...
Answers
The 8th term of the sequence is 781, 250.
We have geometric sequence 10, 50, 250,...
First term= 10
Common ratio = 50/10 = 5
So, the 8th term of sequence is
= 10 x [tex]r^{8-1[/tex]
= 10 x [tex]r^7[/tex]
= 10 x [tex](5)^7[/tex]
= 10 x 5 x 5 x 5 x 5 x5 x 5 x 5
= 10 x 78125
= 781, 250
Thus, the 8th term of the sequence is 781, 250.
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Let f = (2x^2 − 4x + 1)(x^4 + 1). Find a splitting field and determine the Galois group of f over each of the following fields:
(a) Q √
(b) Q( 2)
(c) Q(i)
(d) Q(ζ), where ζ = e2πi/8 is a primitive eighth root of 1 in C (e) R
Answers
Answer:
To find a splitting field for f, we first factor f completely over Q:
f = (2x^2 − 4x + 1)(x^4 + 1) = 2(x - 1/2)^2(x^4 + 1)
The roots of the quadratic factor are x = 1/2 ± 1/2√2, which are real, and the roots of the quartic factor are x = ±i. Therefore, a splitting field for f is Q(i, √2).
(a) Q(√2): The roots of the quadratic factor are real, so they are already in Q(√2). The roots of the quartic factor are ±i, which are not in Q(√2). Therefore, the Galois group of f over Q(√2) is isomorphic to Z/2Z.
(b) Q(2): The roots of the quadratic factor are not in Q(2). However, both i and √2 are in Q(2), so Q(2) contains a splitting field for f. Therefore, the Galois group of f over Q(2) is trivial, since there is only one automorphism of Q(2) that fixes Q.
(c) Q(i): The roots of the quadratic factor are not in Q(i). However, √2 is in Q(i), so Q(i) contains a splitting field for f. The Galois group of f over Q(i) is isomorphic to Z/2Z × Z/2Z, since there are two complex roots and two real roots, and the complex roots are conjugates of each other.
(d) Q(ζ): The roots of the quadratic factor are not in Q(ζ). However, both i and √2 are in Q(ζ), since ζ^4 = i and ζ^8 = √2. Therefore, Q(ζ) contains a splitting field for f. The Galois group of f over Q(ζ) is isomorphic to Z/2Z × Z/2Z, since there are two complex roots and two real roots, and the complex roots are conjugates of each other.
(e) R: The roots of the quadratic factor are real, so they are already in R. The roots of the quartic factor are ±i, which are not in R. Therefore, the Galois group of f over R is isomorphic to Z/2Z.
the coordinate grid shows 4 locations. Each unit on the grid represents 1 city block. Jeremiah walk twice around the rectangular path connecting the four locations. how many city blocks does Jeremiah walk
Answers
From the graph, Jerimiah walks along 44 city blocks.
Hence the correct option is (D).
It is given that each unit on the grid represents 1 city block.
From the given graph we can see that
Number of city block between Restaurant and Museum = 7
Number of city blocks between Museum and Hotel = 4
Number of city blocks between Hotel and Arena = 7
Number of city blocks between Arena and Restaurant = 4
Total number of city blocks along the rectangular path = (7 + 4 + 7 + 4) = 22 city blocks.
Jerimiah walks twice around the rectangular path.
So Jerimiah walks through = 2*22 = 44 city blocks.
Hence the correct option will be (D).
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The question is incomplete. The complete question will be -
The box and whisker blot below represent some data set. Which is the maximum value of the data?
Answers
The maximum value of the data = 64
We know that in the box and whisker plot with the left end of the whisker represents the minimum value of the data and the right end of the whisker represents the maximum value.
From the attached box and whisker plot, we can observe that between two numbers on the number line there are 5 equal units.
So, the value of each unit length = 4 unit
Here, the left end of the whisker has value 8 and the right end of the whisker has value 64
This means that the meaximum value = 64
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The sun of the 2 digits of a certain number is 5. If 9 is added to the original number, the new number will have the original digits reversed. Find the number
Answers
Answer:
23
Step-by-step explanation:
Assume the digits are
1, 4 or 2,3
The number can be 14, 41, 23, 32
Test each one:
14 + 9 = 23 does not work
41 + 9 = 50 does not work
23 + 9 = 32 works
32 + 9 = 41 does not work
A carnival game has 160 rubber ducks floating in a pool. The person playing the game takes out one duck and looks at it.
If there’s a red mark on the bottom of the duck, the person wins a small prize.
If there’s a blue mark on the bottom of the duck, the person wins a large prize.
Many ducks do not have a mark.
After 50 people have played the game, only 3 of them have won a small prize, and none of them have won a large prize.
Estimate the number of the 160 ducks that you think have blue marks.
Answers
The estimated number of the 160 ducks that have blue marks would be 5 ducks.
How to estimate the number ?Assuming none of the 50 people have received a considerable reward, it is probable that winning a small prize bears higher odds than claiming a more substantial one. Estimating, the probability of achieving a large prize may be considered half as likely to succeed as obtaining a smaller sum:
P ( large prize ) :
= 0.5 x P(small prize)
= 0.5 x 0.06 = 0.03
Number of ducks with blue marks (large prize):
= ( total number of ducks ) x P( large prize )
= 160 x 0.03
= 4.8
= 5 ducks
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Please help me geometry too hard
Answers
The value of distance between two points on graph is,
⇒ d = √32 units
We have to given that;
The coordinates of two points are,
⇒ (9, - 4) and (5, -8)
We know that;
The distance between two points (x₁ , y₁) and (x₂, y₂) is,
⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²
Hence, The value of distance between two points on graph is,
⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²
⇒ d = √ (5 - 9)² + (- 8 - (-4))²
⇒ d = √ 16 + 16
⇒ d = √32
Thus, The value of distance between two points on graph is,
⇒ d = √32 units
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Find the 12th term of the geometric sequence 7,−21,63,
Answers
The 12th term of the geometric sequence is -1,240,029
How to find the 12th term of the sequence?The general formula for the nth therm is:
A(n) = A(1)*(r)^(n - 1)
Where A(1) is the first term, in this case 7.
r is the common ratio, to get it, take the quotient between two consecutive terms:
-21/7 = -3
Then the formula is:
A(n) = 7*(-3)^(n - 1)
The 12th term will be:
A(12) = 7*(-3)^(12 - 1) = -1,240,029
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Consider the following triangle.
A right triangle. The side opposite to theta is 5 meters and the side adjacent is 6 meters.
Determine the measure of the angle represented by Theta using the inverse tangent function.
a.
50.2º
b.
56.4º
c.
39.8º
d.
33.6º
Answers
Answer:
Step-by-step explanation:
tan theta=5/6
theta=tan-1(5/6)
=39.8º
Which best demonstrates the way consumers and producers influence each other in the free-market system? O assembly line Circular-flow model downward spiral O flow chart
Answers
Answer:
The best choice is:
Circular-flow model
The circular-flow model demonstrates how consumer demand and production supply influence each other in a market economy. Some key points:
• Consumers demand goods and services by spending money (aggregate demand). This drives production.
• Producers supply goods and services to meet demand (aggregate supply). But supply depends on and influences demand.
• There is a continuous flow and feedback loop between consumers, producers, and the money/resources flowing between them.
The circular-flow model highlights this interconnectedness and interdependence. It shows how consumer spending drives production, which in turn enables more consumer spending, and so on. Changes in demand, supply, spending or consumption ripple through the economy.
The other choices do not accurately represent this relationship:
• Assembly line - Focuses on supply-side production process, not the demand-supply feedback loop.
• Downward spiral - Implies a negative, self-defeating cycle rather than the mutually supporting feedback in the circular-flow model.
• Flow chart - Too generic. A flow chart could represent any process, not specifically the demand-supply relationship.
So in summary, the circular-flow model is the best choice as it demonstrates the way consumer demand and producer supply interact with and influence each other in a free market system. The circular flow of money, resources, supply and demand relies on this interconnection.
Does this help explain the circular-flow model and why it is the best choice? Let me know if you have any other questions!
Step-by-step explanation:
What is the probability that either event will occur?
12
A
4
B
24
P(A or B) = P(A) + P(B)
P(A or B) = [?]
Enter as a decimal rounded to the nearest hundredth.
Answers
From the given information, the probability that either event will occur is 0.7.
From the given Venn diagram,
Number of A = 4
Number of B = 24
Number of others = 12
Total number = A + B + others = 4 + 24 + 12 = 40
Probability of event A occurring = number of A / Total number = 4/40 = 1/10 = 0.1
Probability of event B occuring = number of B / Total number = 24/40 = 3/5 = 0.6
Now, the probability of either event will occur = P(A or B) = P(A) + P(B)
P(A or B) = 0.1 +0.6 = 0.7
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Rectangle WXYZ is dilated by a factor of 3 to make rectangle W'X'Y'Z. What is the perimeter of rectangle W'X'Y'Z?
Answers
The perimeter of rectangle W'X'Y'Z is 16 units
Perimeter of rectangle:he rectangle has four sides. There are two lengths and two widths in a rectangle. Therefore, the perimeter of the rectangle is twice the sum of two adjacent sides that are length and width. The formula is given by:
Perimeter of rectangle = 2(l + b)
We have :
Rectangle WXYZ will be the dilated by a scale factor of 1/2 creating rectangle W'X'Y'Z'
So, By the image:
The analysis will be the:
Rectangle of WXYZ = 2 × 4
and, The rectangle of W'X'Y'Z' = 2 × WXYZ
= 16
W'X' = 4
W'Z' = 4
Hence, The perimeter of rectangle is = 4 + 4 + 4 + 4 = 16
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The given question is incomplete, So i take the similar question :
Rectangle WXYZ will be the dilated by a scale factor of 1/2 creating rectangle W'X'Y'Z'. What is the perimeter of rectangle W'X'Y'Z?
And also to see the attachment.
I NEED HELP WITH TTHIS PROBLEM IN STATISTICS
Answers
Answer:
Step-by-step explanation:
the median would be 9.
(X-3)/4+(x-1)/5-(x-2)/3=1
Answers
i Got u Bro! Answer:X=8x/15+77/15
:D
Reasoning What is the height of the square pyramid? Use pencil and paper. Once you know which length represents the hypotenuse, does it matter which length you substitute for a and which length you substitute for b? Explain.
Answers
The height of the pyramid is 30.14 in
We have,
Using the Pythagorean theorem,
Hypotenuse = 32.6 in
Base = 24.8/2 = 12.4 in
Height = x
Now,
32.6² = 12.4² + x²
x² = 1062.76 - 153.76
x² = 909
x = 30.15
Thus,'
The height of the pyramid is 30.14 in
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Needing help finding this answer!
Answers
Answer:
78.947%
Step-by-step explanation:
It says A OR B, so:
5/19 + 6/19 + 4/19
11/19 + 4/19
15/19 = approx. 0.78947 = 78.947%
Find the measure of angle A.
60x
O 60°
O 30°
O 23°
O 37°
30x
A
Answers
Answer:
Step-by-step explanation:
sum of angles in a triangle=180º
90+60x+30x=180
90+90x=180
90(1+x)=180
1+x=2
x=1
angle A=30º
7 -6 2
If A = 6
6 -5 -7
2
-8
8
and B =
CERE
-8 -7 5
-1
-9
5
9 -4
7, find A + B.
Answers
Answer:
To find A + B, we need to add the corresponding entries of A and B. That is,
A + B = [a_ij + b_ij],
where a_ij and b_ij are the entries of A and B, respectively, in the ith row and jth column.
Using this formula, we get:
A + B = 7 + (-8) -6 + (-7) 2 + 5
6 + (-1) 6 + (-9) -5 + 4
-5 + 9 -7 + 5 8 + (-4)
= -1 -7 7
5 1
4
Therefore, A + B is the matrix:
-1 -7 7
5 1
4
Identify the area of a regular hexagon with side length 14in. rounded to the nearest tenth.
Answers
The area of a regular hexagon with side length 14 inches is 509.22 square inches.
Given that, a regular hexagon with side length 14 inches.
We know that, area of a regular hexagon can be calculated using A=3√3/2 a².
Here, area of a regular hexagon = 3√3/2 ×14²
= 3√3 ×98
= 509.22 square inches
Therefore, the area of a regular hexagon with side length 14 inches is 509.22 square inches.
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Given that a/b=3/4 and b/c=5/6 find a:b:c Give you answer in its simplest form
Answers
Answer:
LCM of 4 and 5 is 20.
a/b = 3/4 = 15/20
b/c = 5/6 = 20/24
a:b:c = 15:20:24
Find the indicated confidence interval. Assume the standard error comes from a bootstrap distribution that is approximately normally distributed.
Answers
The 95% confidence interval is (22.8876, 49.1124)..
To find the 95% confidence interval for the difference in means between two populations, we can use the formula:
CI = (x1 - x2) ± z*(SE)
where x1 and x2 are the sample means of the two populations, SE is the standard error, z is the critical value from the standard normal distribution corresponding to the level of confidence.
Substituting the given values into the formula, we have:
CI = (264 - 228) ± 1.96*(6.69)
Simplifying this expression, we have:
CI = 36 ± 13.1124
Therefore, the 95% confidence interval for the difference in means between the two populations is (22.8876, 49.1124).
This means that we are 95% confident that the true population difference in means falls between 22.8876 and 49.1124. We can interpret this interval as a range of plausible values for the population difference in means, based on the sample data.
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Gunther Jr. High School has a student to teacher ratio of 25 to 2. Which of the following rational numbers is an equivalent representation of this ratio?
Answers
Answer:
Step-by-step explanation:
To find an equivalent ratio with smaller numbers, we can divide both 25 and 2 by their greatest common factor, which is 1:25 ÷ 1 = 25
2 ÷ 1 = 2Therefore, the ratio can be written as:25 : 2To write this ratio as a rational number, we can divide 25 by 2:25 ÷ 2 = 12.5So an equivalent representation of the ratio 25 : 2 is the rational number 12.5.
Write the quadratic equation in standard form:
-12x + x² + 14 = -5x
Answers
I Got u Bro Answer: x2-7x+14=0
Answer:
Step-by-step explanation:
X^2-7x+14=0
What are the angles of rotation for a regular
pentagon? (Select all that apply)
al. 60
672
(C) 90
d) 144
(l/180
1216
g) 360
Please show work or give an explanation please
Answers
The angles of rotation for a regular pentagon are:
b) 72°d) 144°f) 216°g) 360°Pentagon angle of rotation explainedA Regular Pentagon has five equal sides and five equal angles.
Since the sum of the interior angles of a polygon with n sides is given as:
(n-2) x 180°, then we have:
(5-2) x 180 = 540°.
Note that n = sides of pentagon which is 5
Since all angles in a regular pentagon are equal, each angle measures (540/5) = 108°.
The angles of rotation for a regular polygon are given by the formula 360/n, where n is the number of sides.
Therefore, the angles of rotation for a regular pentagon is:
360/5 = 72°,
Any other angles will be in the multiple of 72. Therefore we have:
2 x 72 = 144°, 3 x 72 = 216°,4 x 72 = 288°5 x 72 = 360°Note that a full rotation is 360°.
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Find that the radius of curvature of ^2y=x^3-a^3
at the point where the
curves cut the X-axis.
Answers
The radius of curvature of the curve [tex]a^{2y[/tex]=x³-a³ at the point where the curve intersects the x-axis is 27[tex]a^{\frac{3}{2}[/tex].
To find the radius of curvature of the curve [tex]a^{2y[/tex]=x³-a³ at the point where the curve intersects the x-axis, we need to first find the equation of the curve and then determine the value of y and its derivative at that point.
When the curve intersects the x-axis, y=0. Therefore, we have:
a⁰ = x³ - a³
x³ = a³
x = a
Next, we need to find the derivative of y with respect to x:
dy/dx = -2x/(3a²√(x³-a³))
At the point where x=a and y=0, we have:
dy/dx = -2a/(3a²√(a³-a³)) = 0
Therefore, the radius of curvature is given by:
R = (1/|d²y/dx²|) = (1/|d/dx(dy/dx)|)
To find d/dx(dy/dx), we need to differentiate the expression for dy/dx with respect to x:
d/dx(dy/dx) = -2/(3a²(x³-a³[tex])^{\frac{3}{2}[/tex]) + 4x²/(9a⁴(x³-a³[tex])^{\frac{1}{2}[/tex])
At x=a, we have:
d/dx(dy/dx) = -2/(3a²(a³-a³[tex])^{\frac{3}{2}[/tex]) + 4a²/(9a⁴(a³-a³[tex])^{\frac{1}{2}[/tex]) = -2/27a³
Therefore, the radius of curvature is:
R = (1/|-2/27a³|) = 27[tex]a^{\frac{3}{2}[/tex]
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Find the value of x in the figure below 53° ,24° and x°
Answers
Answer:46
Step-by-step explanation:
traingle ABD = 53 + 24 + 47 + x = 180
134+x=180
x=180-134
x=46
Noah tried to prove that
cos
(
�
)
=
sin
(
�
)
cos(θ)=sin(θ)cosine, left parenthesis, theta, right parenthesis, equals, sine, left parenthesis, theta, right parenthesis using the following diagram. His proof is not correct.
A right triangle A B C. Angle B A C is a right angle. Angle A C B is theta.
A right triangle A B C. Angle B A C is a right angle. Angle A C B is theta.
Statement Reason
1
�
∠
�
=
�
m∠B=θm, angle, B, equals, theta The acute angles in a right triangle are congruent.
2
sin
(
�
)
=
�
�
�
�
sin(θ)=
BC
AB
sine, left parenthesis, theta, right parenthesis, equals, start fraction, A, B, divided by, B, C, end fraction Definition of sine.
3
cos
(
�
∠
�
)
=
�
�
�
�
cos(m∠B)=
BC
AB
cosine, left parenthesis, m, angle, B, right parenthesis, equals, start fraction, A, B, divided by, B, C, end fraction Definition of cosine.
4
cos
(
�
)
=
�
�
�
�
cos(θ)=
BC
AB
cosine, left parenthesis, theta, right parenthesis, equals, start fraction, A, B, divided by, B, C, end fraction Substitution.
5
cos
(
�
)
=
sin
(
�
)
cos(θ)=sin(θ)cosine, left parenthesis, theta, right parenthesis, equals, sine, left parenthesis, theta, right parenthesis Substitution
Answers
The possible first mistake Noah made in the evaluation of the sine and cosine of the acute angles of a right triangle is that the acute angles are complementary and are not always congruent. The correct option is the option (A).
(A) Angles ∠B and ∠C are complementary, not congruent
What are complementary angles?Complementary angles are angles that when added together are equivalent to 90°
The possible two column table Noah used to attempt to prove that cos(θ) = sin(θ) obtained in a similar proof on the website can be presented as follows;
Statement [tex]{}[/tex] Reason
1 m∠B = θ [tex]{}[/tex] The acute angles in a right triangle are congruent
2 sin(θ) = AB/BC [tex]{}[/tex] Definition of sine
3 cos(m∠B) = AB/BC [tex]{}[/tex] Definition of cosine
4 cos(θ) = AB/BC [tex]{}[/tex] Substitution
5 cos(θ) = sin(θ) [tex]{}[/tex] Substitution
Part of the question is; What is the first mistake in Noah's statement used to prove that cos(θ) = sin(θ)
The first mistake is the statement and reason that angle m∠B = θ because all acute angles are congruent.
The acute angles in the right triangle are ∠B and ∠C
The sum of the acute angles in a right triangle is; ∠B + ∠C = 90°
Therefore the acute angles in a right triangle are always complementary, and not always congruent.
The correct option is therefore the option (A)
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What is the sum?
X
3
2
+
x+3 x+3 " x+3
0
+
5
X+5
x+3
X+5
3x+27
Ex
x+3
Answers
Answer: 2, 2, 135, 9, 5, 35, 15, 10, 15, 15
Step-by-step explanation:
Mr. James is teaching his students about the volume of rectangular prisms. He has various rectangular prisms with a height of 6 inches. The table shows the relationship between the base of the prism and its volume. Which equation can be used to find B, the area of the base with a volume of V?
Answers
The proportional relationship used to find B, the area of the base with a volume of V, is given as follows:
B = V/6.
What is a proportional relationship?A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.
The equation that defines the proportional relationship is given as follows:
y = kx.
In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.
From the table given in the image at the end of the answer, we have that the base area is a sixth of the volume, hence the equation is:
B = V/6.
Missing InformationThe table is given by the image presented at the end of the answer.
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why does area and perimeter change in different ways
Answers
Answer:
Step-by-step explanation:
Area and perimeter are both measurements used to describe geometric shapes, but they are fundamentally different concepts and therefore change in different ways.The perimeter of a shape is the distance around the outside of the shape. It is a measure of the total length of the boundaries or sides of the shape. Perimeter depends on the length of each side of the shape, and if one or more sides change in length, the perimeter will change accordingly. For example, if you take a square and double the length of one of its sides, the perimeter will double as well.On the other hand, the area of a shape is the measure of the surface enclosed by the shape. It is a measure of the amount of space inside the shape. The area depends on the length and width of the shape, and if one or both of these dimensions change, the area will change accordingly. For example, if you take a square and double the length of one of its sides, the area will increase by a factor of four.In summary, the perimeter of a shape depends on the length of its sides, while the area of a shape depends on its length and width. Therefore, changes to the length of a side will affect the perimeter, but not necessarily the area, while changes to the length or width will affect the area, but not necessarily the perimeter.
