A plane intersecting a rectangular prism can create different cross-sectional shapes depending on the orientation of the plane. A plane intersects the pyramid parallel to its base. The cross section is a rectangle A plane intersects the pyramid perpendicular to its base and through the top vertex. The cross section is a triangle
A plane intersecting a rectangular prism can create different cross-sectional shapes depending on the orientation of the plane. Let's explore the two scenarios you mentioned:
Plane parallel to the base: When a plane intersects the rectangular prism parallel to its base, the resulting cross section is also a rectangle. The shape of the cross section will have the same dimensions as the base of the rectangular prism.
Plane perpendicular to the base and through the top vertex: In this case, the cross section will be a triangle. The shape of the cross section will be determined by the intersection of the plane with the three sides of the rectangular prism. The base of the triangle will be formed by the side of the rectangular prism, while the other two sides will be formed by the edges connecting the top vertex of the pyramid to the corresponding vertices of the base.
It's important to note that a rectangular prism is different from a pyramid. A rectangular prism has six rectangular faces, while a pyramid has a polygonal base (in this case, a rectangle) and triangular faces converging to a single point called the apex or top vertex.
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the coldest temperature ever recorded on earth was -89.2
The statement that "the coldest temperature ever recorded on earth was - 89. 2 ° " is True.
What was the coldest temperature recorded ?The Soviet Union's Vostok Station in Antarctica recorded the coldest temperature ever observed on Earth, measuring at -89.2°C on July 21, 1983 via satellite and weather station data.
This natural occurrence saw a temperature that presents significant risks to animal and human life due to poor insulation available against such extreme colds. Without suitable warming tools, survival is near impossible.
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Which uppercase letters among W, X, Y, and Z have both
reflective and rotational symmetry?
Answer:
X
Step-by-step explanation:
Reflective symmetry, also known as mirror symmetry, exists when a figure can be reflected across a line and appear the same. Rotational symmetry exists when a figure can be rotated about a point by a certain degree less than 360 and still appear the same.
Among the uppercase letters W, X, Y, and Z:
The letter W has no reflective or rotational symmetry.
The letter X has both reflective and rotational symmetry. It's symmetrical on both the vertical and horizontal axes and has a rotational symmetry of 180 degrees.
The letter Y only has reflective symmetry on the vertical axis, but it does not have rotational symmetry.
The letter Z also has reflective symmetry on the horizontal axis, but it does not have rotational symmetry.
So among these letters, only X has both reflective and rotational symmetry.
Find the surface area of the cylinder. Round your number to the nearest tenth if necessary
3ft 2ft
94.2 square feet is the surface area of the cylinder
The given cylinder has a height of 2 ft and radius of 3 ft
We have to find the surface area of cylinder
Surface area =2πrh+2πr²
Substitute the values of radius and height
=2πr(r+h)
=2×3.14×3(3+2)
=18.84(5)
=18.84×5
Surface area=94.2 square feet
Hence, the surface area of the cylinder is 94.2 square feet
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Evaluate
--(5-1)(5²).
Answer:
100
Step-by-step explanation:
You want the value of --(5-1)(5²).
Minus signsThe even number of leading minus signs cancel each other, so the effect is as if there were no leading minus signs.
--(5 -1)(5²)
= --(4)(25)
= --(100)
= -(-100)
= 100
__
Additional comment
As always, the value of a numeric expression can be found using a calculator.
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A top travels 8 centimeters each time it is spun. if it is spun 7 times what distance does it travel?
If a top travels 8 centimeters each time it is spun and it is spun 7 times, the total distance it travels is 56 centimeters.
How the total distance is determined:The total distance is determined by multiplication of the distance traveled per spin and the number of spins.
Multiplication involves the multiplicand, the multiplier, and the product.
The traveling distance per spun = 8 centimeters
The number of spinning of the top = 7 times
The total distance = 56 centimeters (8 x 7)
Thus, using multiplication, the total distance the top travels after the 7th spin is 56 centimeters.
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879 dived by 8 with remainder ad fraction
Answer: 109.875
Step-by-step explanation: 879 / 8 = 109.875 because if you divide 8 by 9 you get 1 so after you would divide 79 by 8 = 9.875 so then you put 109 then after but the decimals 109.875.
What’s the answers to this?
The vector representing the radius at the given position is -13i - j - 5k.
The magnitude of the radius vector is 13.96 units.
What is the vector representing the radius?
The vector representing the radius at the given position is calculated as follows;
center of the sphere = (11, 5, 2)
The point of the radius = ( -2, 4, -3 )
The radius vector = ( - 2 - 11) , ( 4 - 5), ( -3 - 2)
r = ( -13, - 1, - 5)
r = -13i - j - 5k
The magnitude of the radius vector is calculated as follows;
| r | = √ x² + y² + z²
where;
x, y, z are the various component of the radius| r | = √[ ( -13²) + ( -1)² + ( -5 )² ]
| r | = √ ( 169 + 1 + 25 )
| r | = √ ( 195 )
| r | = 13.96 units
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Which is true about the solution to the system of inequalities shown? y > 3x + 1 y < 3x – 3 On a coordinate plane, 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 2, negative 5) and (0, 1). Everything to the left of the line is shaded. The second line has a positive slope and goes through (0, negative 3) and (1, 0). Everything to the right of the line is shaded. Only values that satisfy y > 3x + 1 are solutions. Only values that satisfy y < 3x – 3 are solutions. Values that satisfy either y > 3x + 1 or y < 3x – 3 are solutions. There are no solutions.
There are no solutions to the system of inequalities Option (d)
Inequalities are a fundamental concept in mathematics and are commonly used in solving problems that involve ranges of values.
A system of two inequalities is a set of two inequalities that are considered together. In this case, the system of inequalities is
y > 3x + 1
y < 3x - 3
The inequality y > 3x + 1 represents a line on the coordinate plane with a slope of 3 and a y-intercept of 1. The inequality y < 3x - 3 represents another line on the coordinate plane with a slope of 3 and a y-intercept of -3. We can draw these lines on the coordinate plane and shade the regions that satisfy each inequality.
The first line has a positive slope and goes through (negative 2, negative 5) and (0, 1). Everything to the left of the line is shaded. The second line has a positive slope and goes through (0, negative 3) and (1, 0). Everything to the right of the line is shaded.
We can start by analyzing the inequality y > 3x + 1. This inequality represents the region above the line with a slope of 3 and a y-intercept of 1. Therefore, any point that is above this line satisfies this inequality.
Next, we analyze the inequality y < 3x - 3. This inequality represents the region below the line with a slope of 3 and a y-intercept of -3. Therefore, any point that is below this line satisfies this inequality.
To determine which values satisfy both inequalities, we need to find the region that satisfies both inequalities. This region is the intersection of the regions that satisfy each inequality.
When we analyze the regions that satisfy each inequality, we see that there is no region that satisfies both inequalities. Therefore, there are no values that satisfy the system of inequalities shown.
There are no solutions to the system of inequalities y > 3x + 1 and y < 3x - 3 by analyzing the regions that satisfy each inequality on a coordinate plane. The lack of a solution is determined by the fact that there is no region that satisfies both inequalities.
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Complete Question :
Which is true about the solution to the system of inequalities shown?
y > 3x + 1
y < 3x – 3
On a coordinate plane, 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 2, negative 5) and (0, 1). Everything to the left of the line is shaded. The second line has a positive slope and goes through (0, negative 3) and (1, 0). Everything to the right of the line is shaded.
Options:
a)Only values that satisfy y > 3x + 1 are solutions.
b)Only values that satisfy y < 3x – 3 are solutions.
c)Values that satisfy either y > 3x + 1 or y < 3x – 3 are solutions.
d)There are no solutions.
Answer:
D
Step-by-step explanation:
Mary goes walking everyday she walks 14ft every 4 seconds which is equation models the relationship between the time Mary walks x and the distance she walks y
Answer:
y=3.5x
Step-by-step explanation:
to find the the feet mary walks per second, divide 14 by 4
14/4=3.5 feet/second
the total distance mary walks can be represented by multiplying the number of feet she walks per second by the number of seconds she walks
y= 3.5x
in this model, x is seconds
On the first day of the month, Sandra starts to read a 420-page book. She is determined to read 30
pages each night. The function P (d) = 420-30d specifies the number of pages P remaining
after Sandra does her reading on day d of the month.
Which equation offers a solution giving the day of the month Sandra finishes, and what day of the
month is that?
OP(d)=0; day 21
OP(d)-30; day 21
OP(d) = 420; day 21
OP(d) = 420; day 14
OP(d) = 0; day 14
OP (d)-30; day 14
Answer:
P(d) = 0; 14 days
Step-by-step explanation:
First part of answer: Setting P(d) = 0 would allow us to find the day Sandra finishes since P represents the pages remaining the book will be finished when there are 0 pages left to read.
Second part of answer: We can solve the equation P(d) = 0 = 420 - 30d to see how it would take 14 days to finish the book and have 0 pages left to read:
Step 1: Subtract 420 from both sides:
(0 = 420 - 30d) - 420
-420 = -30d
Step 2: Divide both sides by -3 to solve for d:
(-420 = -30d) / -30
14 = d
65 POINTS!!!!!! PLEASE ANSWER QUICK
The probabilities are: 1a) P(A) = 12, 1b)P(B) = 1.055 + 1,160 = 1,161.055 . 1c) P(A and B) = P(AB) = 1.055
How to find the probabilitiesP(A) = 12
P(B) = 1.055 + 1,160 = 1,161.055
P(A and B) = P(AB) = 1.055
To determine if the events A and B are independent, we need to check if P(A and B) = P(A) * P(B).
P(A) * P(B) = 12 * 1,161.055 = 13,932.66
Since P(AB) = 1.055 is not equal to P(A) * P(B) = 13,932.66, the events A and B are not independent.
P(A | B) = P(AB) / P(B) = 1.055 / 1,161.055 ≈ 0.0009098
To convert this probability to a percentage, we multiply by 100:
Percentage chance = P(A | B) * 100 ≈ 0.0009098 * 100 ≈ 0.091%
Therefore, the company should report a percentage chance of approximately 0.091% to the person as an estimate of their risk of developing the disease based on the study.
The reasoning behind this estimation is that among those who have the genetic variation (B), the probability of having the disease (A) is approximately 0.0009098, which corresponds to 0.091% when expressed as a percentage.
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The figure below can be used to prove the Pythagorean Theorem. Use the drop-down menus to complete the proof. b Click the arrows to choose an answer from each menu. The expression Choose.. represents the area of the figure as the sum of the area of the shaded triangles and the area of the white square.
The expression 2ab + [tex]c^2[/tex] represents the area of the figure as the sum of the area of the shaded triangles and the area of the white square.
The equivalent expression [tex]a^2 +b^2+2ab[/tex] use the length of the figure to represent the area.
[tex]2ab +c^2=a^2+b^2+2ab[/tex]
Subtracting 2ab from both sides
[tex]c^2=a^2+b^2[/tex]
Figure of a square with some shaded triangles.
Area of the triangle formula is 1/2 times base times height
base =a and height =a
Area of one triangle = 1/2ab
There are 4 shaded triangles
Area of 4 shaded triangles = 4 x 1/2ab
Area of the square = side times side
Now we find the area of outer square. side length is a+b
Area of outside square = (a + b)(a + b) = [tex](a+b)^2[/tex] = [tex]a^2 +b^2+2ab[/tex]
Using the length of the figure to represent the area.
Thus, now set both the areas equal to each other.
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Your question seems incomplete, the probable complete question is
Please help. Any unnecessary answers will be reported.
You are in a competition that involves building card towers. The quickest person to reach 100 stories wins the competition. After reaching 5 stories of cards as shown in the picture below, you needed to use 40 cards.
How many cards will be necessary to build , in a similar way, a tower with 100 stories? Make sure you include work.
The 10,100 cards will be necessary to build a 100-story card tower.
To build a 100-story card tower, we can use the triangular number formula to calculate the total number of cards needed. The formula is:
Triangular number = (n * (n + 1)) / 2
In this case, n represents the number of stories in the tower (100). Plug in the value for n:
Triangular number = (100 * (100 + 1)) / 2
Triangular number = (100 * 101) / 2
Triangular number = 10,100 / 2
Triangular number = 5,050
Additionally, each story requires two cards, so we multiply the triangular number by 2 to get the total number of cards:
Total cards = 5,050 * 2
Total cards = 10,100
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here is my algebra 13 homework, can someone please help me quick!
The decreasing interval of function is (-∞ , 0) .
The decreasing interval in the function is said to be when the value of the derivative f' (x) ≤ 0 .
Decreasing interval is when f(x) is decreasing as x is increasing.
Here the graph is of a parabola the equation of a upper parabola is
f(x) = x²
Now doing derivation of the parabola equation, we get
f'(x) = 2x
As for decreasing interval we will put
f'(x) ≤ 0
Putting the value of f'(x) in the equation
2x ≤ 0
x ≤ 0
Decreasing interval (-∞ , 0)
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I need the steps for this one
Answer:
[tex]-61[/tex]
Step-by-step explanation:
[tex]\mathrm{We\ have\ f(}x)=-3x^2-2x+4\\\mathrm{Put}\ x=-5,\\\mathrm{f}(-5)=-3(-5)^2-2(-5)+4=-3(25)+10+4=-75+10+4=-61[/tex]
Can a triangle be formed with side lengths 4,8,11? Explain
No because 11-8<4
Yes because 11-4<8
No because 4+8>11
Yes because 4+8>11
Directions: For A and B, use the given rules to write the first five terms in each
sequence. Then, use the terms to create ordered pairs for each numerical pattern.
A. Rule 1: Add 3 starting from 13.
Rule 2: 25-2x, where x is equal to 5, 6, 7, 8, 9.
Sequence 2
Sequence 1
B. Rule 1: Multiply by 3, then add 2, starting from 1.
Rule 2: Multiply by 2, then add 3, starting from 6.
Sequence 1
Sequence 2
Ordered Pair
Ordered Pair
OFFERING 50 POINTS
In solving the sequence using the provided rules, we have:
A) Sequence 1: 13, 16, 19, 22, 25.
Sequence 2: 15, 13, 11, 9, 7.
Ordered Pair: (13, 15), (16, 13), (19, 11), (22, 9), (25, 7)
B) Sequence 1: 1, 5, 17, 53, 159.
Sequence 2: 6, 15, 33, 69, 141.
Ordered Pair: (1, 6), (5, 15), (17, 33), (53, 69), (159, 141).
How to solve the sequence?Using the given rules, we can solve the sequence as follows:
A. Rule 1: Add 3 starting from 13
The first five terms in Sequence 1 would be:
13, 13 +3 = 16, 16 +3 = 19, 19 + 3 = 22, 22 + 3 = 25.
13, 16, 19, 22, 25
Using Rule 2: 25-2x, where x is equal to 5, 6, 7, 8, 9
The first five terms in Sequence 2 would be:
25 - 2(5) = 25 - 10 = 15
25 - 2(6) = 25 - 12 = 13
25 - 2(7) = 25 - 14 = 11
25 - 2(8) = 25 - 16 = 9
25 - 2(9) = 25 - 18 = 7
The ordered pairs for each numerical pattern would be:
(13, 15), (16, 13), (19, 11), (22, 9), (25, 7)
B. Rule 1: Multiply by 3, then add 2, starting from 1
The first five terms in Sequence 1:
1, (1 * 3) + 2 = 5, (5 * 3) + 2 = 17, (17 * 3) + 2 = 53, (53 * 3) + 2 = 159
Using Rule 2: Multiply by 2, then add 3, starting from 6
The first five terms in Sequence 2:
6, (6 * 2) + 3 = 15, (15 * 2) + 3 = 33, (33 * 2) + 3 = 69, (69 * 2) + 3 = 141
The ordered pairs for each numerical pattern would be:
(1, 6), (5, 15), (17, 33), (53, 69), (159, 141)
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What are the first two steps in solving the radical equation below?
√x+1-4 = 8
A. Square both sides and then subtract 1 from both sides.
B. Add 4 to both sides and then subtract 1 from both sides.
C. Square both sides and then add 4 to both sides.
D. Add 4 to both sides and then square both sides.
SUBMIT
The first two steps in solving the radical equation, √x+1-4 = 8 is D. Add 4 to both sides and then square both sides.
How do we solve the radical equation?We can solve the radical equation by adding 4 to both sides and then squaring both sides.
Given equation: √x+1 - 4 = 8.
The First step: add 4 to both sides of the equation:
√x+1 - 4 + 4 = 8 + 4
Simplifying the equation:
√x+1 = 12
The Second step: square both sides of the equation to eliminate the square root:
(√x+1)² = 12²
Squaring both sides gives:
x + 1 = 144
Finally, subtract 1 from both sides to isolate x:
x + 1 - 1 = 144 - 1
x = 143
So, adding 4 to both sides and then squaring both sides are the first two steps in solving the equation.
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What is the definition of postulate? A. an assumption, presumed to be true, that is used as the basis for a logical argument B. a statement that has been shown to be false by logical argument C. a statement that has been shown to be true by logical argument D. a statement, known to be false, that is used as the basis for a logical argument
Postulate is an assumption, presumed to be true, that is used as the basis for a logical argument.
We have,
A postulate is a statement or proposition that is accepted as true without proof.
It is an assumption or starting point in a logical argument that is considered to be self-evident or evident based on previous experience or observation.
In mathematics,
Postulates are used to define the basic concepts and axioms that form the foundation of a particular system of thought.
They are often used as the starting point for deriving other mathematical concepts and theorems.
Postulates are also known as axioms or assumptions.
Thus,
Postulate is an assumption, presumed to be true, that is used as the basis for a logical argument.
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If your heart beats 48 times in 40 seconds, which proportion could be used to make the best estimate for the number of beats in 60 seconds? A. 48/40 = 60/x B. 40/60 = 48/x C. 48/40 = 60/x D. 48/60 = 40/x
Given statement solution :- The correct proportion to make the best estimate for the number of beats in 60 seconds is:
A. 48/40 = 60/x
To make the best estimate for the number of beats in 60 seconds, we need to find the proportion that relates the beats per second in the given scenario to the desired duration of 60 seconds.
Let's set up the proportion using the given information:
Heart beats per second (beats/sec) = 48 beats / 40 seconds
We want to find the number of beats in 60 seconds (x beats / 60 seconds).
The correct proportion would be:
48 beats / 40 seconds = x beats / 60 seconds
Therefore, the correct proportion to make the best estimate for the number of beats in 60 seconds is:
A. 48/40 = 60/x
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find the volume of each figure. round to the nearest tenth as needed. please show the work, will mark the brainliest.
Answer:
4. 4155.3cm³
5. 783m³
6. 1962.44821094mm³
#4 Explanation:
First, you would separate the 2 shapes it consists of, a cylinder and a cone.
For the cone, you would use the equation (1/3)πr²h. Fill in the appropriate variables with the numbers from the formula. Pi, π, is a number itself so you leave it as it is.
r = radius = 8cm
h = height = 14cm
(1/3)(π)(8)²(14)
Put this equation into a calculator, it's important to include the parentheses or it might give you the incorrect answer, this is so that it separates the different values while multiplying. After inputting it, it should give you:
v = 938.289005872cm³
Then, you would have to find the volume of the cylinder, using the equation; πr²h.
The radius would be the same as the cone, and the height is as the problem states, 16cm.
Solve the problem after inputting the values:
π(8)²(16)= 3216.99087728cm³
Then, add the values to get the total volume.
938.289005872cm³ + 3216.99087728cm³ =
4155.27988315cm³
Round to nearest tenth: 4155.3cm³
#5 Explanation:
Again, you would separate the shapes into 2 separate ones.
The top one is a triangular prism and uses the equation (1/2)bh.
b = base = 9m
h = 12m
(1/2)(9)(12) = 54m³
The bottom shape is a rectangular prism, where we use the equation L×W×H.
Length = 9m
Width = 9m
Height = 9m
Substitute the numbers into the equation.
9×9×9 = 729m³
Add both of them together to get the total volume:
54m³ + 729m³ = 783m³
#6 Equation:
In this figure, we are looking for the outer shape, so we will have to subtract the smaller cone.
First, we find the total volume, and we will use the same equation, (1/3)πr²h.
radius = half of diameter = 20/2 = 10mm
h = 20mm
(1/3)π(10)²(20) = 2094.39510239mm³
Second, we find the volume of the smaller cone, using the same equation, (1/3)πr²h.
In order to find the diameter, we will have to subtract the 7 mm that are on either side of the cone, so 20 - 14 = 6, then divide it by 2 so we can get the necessary radius. 6/2 = 3
r = 3mm
h = 14mm
Substitute values into equation and use calculator to solve.
(1/3)π(3)²(14) = 131.946891451mm³
Subtract the value of the smaller cone from total volume in order to get the volume for this figure.
2094.39510239mm³ - 131.946891451mm³ =
1962.44821094mm³
Question 8
Match each compound to its correct type.
8.1
CO
hydroxide
8.2
CO₂
carbonate
8.3
SO₂
8.4
CaCO
8.5
NaOH
oxide
trioxide
dioxide
8.1 CO: oxide
8.2 CO₂: dioxide
8.3 SO₂: dioxide
8.4 CaCO:
8.5 NaOH:
8.1 CO: oxide
CO represents carbon monoxide, which is composed of one carbon atom (C) and one oxygen atom (O). It is classified as an oxide because it consists of oxygen combined with another element.
8.2 CO₂: dioxide
CO₂ represents carbon dioxide, which consists of one carbon atom (C) and two oxygen atoms (O). It is classified as a dioxide because it contains two oxygen atoms per molecule.
8.3 SO₂: dioxide
SO₂ represents sulfur dioxide, composed of one sulfur atom (S) and two oxygen atoms (O). It is also classified as a dioxide because it contains two oxygen atoms per molecule.
8.4 CaCO: This formula is incomplete or incorrect. It seems to be missing a subscript or superscript to indicate the number of atoms or ions involved. Please provide the correct formula, and I'll be happy to match it with its type.
8.5 NaOH: hydroxide
NaOH represents sodium hydroxide, which consists of one sodium ion (Na⁺) and one hydroxide ion (OH⁻). It is classified as a hydroxide because it contains the hydroxide ion, which is composed of one oxygen atom and one hydrogen atom.
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The diagram shows a right-angled triangle.
24 cm
18 cm
_Not to scale
Calculate the value oft. Give your answer correct to 1 decimal place.
Answer:
can i have a photo, please?
Step-by-step explanation:
Pls can someone help me?
I’m pretty sure the value of a->60
b-> 110
c->80
What do i write for the reasons of them tho? Pls help! thanks
The values of the angles a, b and c are 60°, 110° and 80° respectively.
Given is a figure we need to find the measure of the angles given,
a, b, c.
So,
70° + 50° + a = 180° [making linear pair angles]
120° + a = 180°
a = 60°
50° + a = b [corresponding angles between parallel lines]
b = 50° + 60°
b = 110°
a + 40° + ∠HFE = 180° [angle sum property of a triangle]
60° + 40° + ∠HFE = 180°
∠HFE = 80°
∠HFE = c [alternate angles between parallel lines]
c = 80°
Hence the values of the angles a, b and c are 60°, 110° and 80° respectively.
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The number 1.3 is both a(n) __________ and a(n) __________ number.
The number 1.3 is both a rational and an irrational number.
What is the number 1.3?The number 1.3 is a rational number because it can be expressed as the quotient of two integers, namely 13/10.
The number 1.3 an irrational number because it cannot be expressed as the ratio of two integers, without repeating or terminating decimals, and its decimal representation goes on forever without repeating.
So we can conclude that the number 1.3 is both rational and irrational number.
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It is given that f(x) =1/x³, for x > 0. Show that f is a decreasing function.
The function f(x) = 1/x³ is indeed a decreasing function for x > 0.
To show that the function f(x) = 1/x³ is a decreasing function, we need to demonstrate that the derivative of f(x) is negative for all x > 0.
Let's calculate the derivative of f(x) with respect to x:
f'(x) = d/dx (1/x³)
Using the power rule for differentiation, we can rewrite the expression as:
[tex]f'(x) = (-3) / x^{(3+1)[/tex]
Simplifying further, we have:
f'(x) = -3 / x⁴
Now, to show that f(x) is decreasing, we need to prove that f'(x) < 0 for all x > 0.
Substituting x = 1 in f'(x), we get:
f'(1) = -3 / 1⁴ = -3
Since -3 is negative, we can conclude that f'(x) < 0 for all x > 0.
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A cone with a height of 50 meters has a volume of 5,400π meters cubed. What is the radius of the cone?
The radius of the cone with the given volume which is is terms of π would be = 18m
How to calculate the radius of a cone?To determine the radius of the cone, the formula that should be used in the formula for the volume of cone which would be given below;
Volume of cone =1/3πr²h
where;
radius = ?
volume = 5,400π
height = 50m
That is;
5,400π = 1/3×π×r²×50
make r² the subject of formula;
r² = 5400π×3/50π
= 108×3
= 324
r = √324
= 18
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Directions: Complete the table below.
Scientific Notation
5.397 x 10^2
Convert it to Standard Notation
The standard notation for the given scientific notation[tex]5.397 * 10^2[/tex] is 539.7
How to convert to standard notationTo convert the given scientific notation [tex]5.397 * 10^2[/tex]to standard notation, you simply need to multiply the coefficient (5.397) by the power of [tex]10 (10^2).[/tex]
The power of 10 indicates how many places the decimal point should be moved to the right. In this case, [tex]10^2[/tex] means moving the decimal point two places to the right.
Multiplying the coefficient 5.397 by
[tex]10^2[/tex]
gives us:
[tex]5.397 \times 10^2 = 5.397 \times \ 100 = 539.7[/tex]
Therefore, the standard notation for the given scientific notation 5.397 x [tex]10^2[/tex] is 539.7.
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Question One
Consider the following information that relates to a certain
economy
C= 40 +0.35
I = 70- 2r
G=400
T= 15+0.2Y
X=240
M=45+0.4Y
r = 0.5
Required:
i). Compute the autonomous investment, government
expenditure, export, and tax multipliers
ii). Find the equilibrium income
i) Compute the autonomous investment, government the MPM is 0.4.
AI = 1 / (1 - 0.35) = 1 / 0.65 ≈ 1.538 (approximately)
GM = 1 / (1 - 0.35) = 1 / 0.65 ≈ 1.538 (approximately)
XM = 1 / (1 - 0.4) = 1 / 0.6 ≈ 1.667 (approximately)
TM = -0.35 / (1 - 0.35) ≈ -0.538 (approximately)
ii) The equilibrium income is approximately 709.52.
To compute the autonomous investment (A), government expenditure (G), export (X), and tax (T) multipliers, we need to use the following formulas:
Autonomous Investment Multiplier (AI):
AI = 1 / (1 - MPC)
where MPC is the marginal propensity to consume.
Government Expenditure Multiplier (GM):
GM = 1 / (1 - MPC)
Export Multiplier (XM):
XM = 1 / (1 - MPM)
where MPX is the marginal propensity to import.
Tax Multiplier (TM):
TM = -MPC / (1 - MPC)
Now let's calculate these multipliers using the given information:
i). Compute the multipliers:
MPC = change in consumption / change in income
Here, we can see that the consumption function is given by C = 40 + 0.35Y.
So, the MPC is 0.35.
MPM = change in imports / change in income
Here, we can see that the import function is given by M = 45 + 0.4Y.
So, the MPM is 0.4.
AI = 1 / (1 - 0.35) = 1 / 0.65 ≈ 1.538 (approximately)
GM = 1 / (1 - 0.35) = 1 / 0.65 ≈ 1.538 (approximately)
XM = 1 / (1 - 0.4) = 1 / 0.6 ≈ 1.667 (approximately)
TM = -0.35 / (1 - 0.35) ≈ -0.538 (approximately)
ii). Find the equilibrium income:
To find the equilibrium income, we set aggregate demand (Y) equal to aggregate supply (Y) and solve for Y.
Aggregate demand (Y):
Y = C + I + G + (X - M)
Substituting the given values, we have:
Y = (40 + 0.35Y) + (70 - 2r) + 400 + (240 - (45 + 0.4Y))
Simplifying the equation:
Y = 40 + 0.35Y + 70 - 2(0.5) + 400 + 240 - 45 - 0.4Y
Combining like terms:
Y = 745 - 0.05Y
Bringing Y terms to one side:
1.05Y = 745
Dividing both sides by 1.05:
Y = 745 / 1.05 ≈ 709.52 (approximately)
Therefore, the equilibrium income is approximately 709.52.
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Hi can someone who is great at math please help me with these math questions. I'm struggling with them!!
1) The value of x = 12°
2) For any real value of n, y = n and x = (3/2)n
And the measure of angle B is 68°
3) The measure of angle A is 26° and the measure of angle B is 154°
4) The coordinates of vertex D(4, 0)
1)
We know that a linear pair of angles always add up to 180°
168° + x° = 180°
x = 180° - 168°
x = 12°
2)
Here, in parallelogram ABCD, the measure of angle A = 112°
We know that the opposite angles of a parallelogram are equal.
So, m∠C = 112°
Let measure of angle B and D is p degrees.
∠A + ∠B + ∠C + ∠D = 360°
2p + 2(112) = 360°
p = (360 - 224)/2
p = 68°
so, the measure of angle B is 68°
The opposite sides of a parallelogram are equal.
So, side AD = side BC
(2x + 4) = (3y + 4)
2x = 3y
x = (3/2)y
For any real value of n,
y = n
then x = (3/2)n
3)
Consider parallelogram ABCD.
Let us assume that one of the interior angle measures x and then other interior angle be y.
x is 50 degrees more than 4 times the measure of y
x = 4y + 50
We know that the sum of two interior angles (non-opposite) is 180°
⇒ x + y = 180°
⇒ 4y + 50 + y = 180°
⇒ 5y = 130°
⇒ y = 26°
And the value of x would be,
x = 4(26) + 50
x = 154°
So, the measure of angle A is 26° and the measure of angle B is 154°
4)
Let the fourth vertex be D(a,b)
Since ABCD is a parallelogram, the diagonals bisect each other.
coordinates of midpoint of AC = coordinates of midpoint of BD
By midpoint formula,
((1 + 6)/2, (2 + 4)/2) = ((3 + a)/2 , (6 + b)/2)
comparing x and y coordinates,
(3 + a)/2 = (1 + 6)/2
3 + a = 7
a = 4
(6 + b)/2 = (2 + 4)/2
6 + b = 6
b = 0
So, the coordinates of vertex D(4, 0)
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