As an example, if the centre of dilation were in the centre of a circle with radius 5 and was going through a scale factor 2 dilation, the radius would be 10.
The process of dilation involves growing an object's size without changing its shape. The size of the item may increase or decrease depending on the scale factor. Using dilation math, a square with side 5 units may be made wider to have side 15 units, but the shape of the square remains the same.
Enlargements that generate a bigger picture are called dilations. Reduction describes the dilatation that shrinks the picture. The starting figure is stretched or contracted during a dilatation. The scale factor (or ratio) and the centre of a dilatation are both described. Occasionally, the words "dilate" and words like "magnify," "disptend," "expand," "inflate," and "swell" are used interchangeably. All of these words suggest "expanding in size or volume," but the word "dilate" specifically refers to increased diameter.
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The diagram below shows a logo formed by removing a semicircle with diameter AB and a
rhombus DEFG from an isosceles trapezium ABCE where AE = BC.
Find the area of the logo.
The area of the logo is 136. 14 cm²
Determining the area
First, let's find the area of the semicircle
Area of semicircle = 1/2(πr²)
radius = 8/2 = 4cm
Substitute into the formula
Area of semicircle = [tex]\frac{1}{2} * 3. 142 * 4 * 4[/tex] = 25. 135 cm²
Now, let's find area of trapezium
Area of trapezium = [tex]\frac{a + b}{2} * h[/tex]
Area = [tex]\frac{12 + 10. 2}{2} * 10[/tex]
Area = [tex]11. 1 * 10[/tex]
Area = 111 cm²
Area of logo = Area of trapezium + area of semicircle
Area of logo = 111 + 25. 135
Area of logo = 136. 14 cm²
Thus, the area of the logo is 136. 14 cm²
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In total, 2 baseballs and 3 footballs cost $67. a football is $4 more than 3 times the cost of a baseball. find the cost of a baseball
The cost of the Baseball is $5.
Lets take football cost as "x"
And taking baseball cost as "y"
According to given conditions,
2y + 3x = 67
x= 3y + 4
Lets put the values of x in equation (1):
2y + 3 (3y+4) = 67
=> 2y + 9y + 12 = 67
=> 11y = 55
y = 5
x = 3(5) + 4
x = 19
Hence the cost of the Baseball is $5.
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What is the recursive formula for the geometric sequence with this explicit
formula?
a^n=9(-1/3)^(n-1)
A machine has 28 identical components which function independently. The probability that a component will fail is 0.19 . The machine will stop working if more than three components fail. Find the probability that the machine will be working. Round to the nearest thousandth.
By definition of a binomial random variable, the probability that the machine will be working is 0.82045.
Definition of probabilityFirst of all, you should know that the Probability is the greater or lesser possibility that a certain event will occur.
In other words, the probability establishes a relationship between the number of favorable events and the total number of possible events.
Definition of random variableOn the other hand, a random variable is a function that associates a real number, perfectly defined, to each sample point.
A random variable is discrete if the numbers it gives rise to are integers.
Definition of binomial distributionFinally, a binomial distribution is a discrete probability distribution that describes the number of successes in performing n independent experiments on a random variable.
The expression to calculate the binomial distribution is:
P(X=x)=([tex]n\\ x[/tex]) pˣ qⁿ⁻ˣ
Where:
n = Number of trials/experimentsx = Number of successesp = Probability of successq = Probability of failure (1-p)Remember that:
([tex]n\\ x[/tex])=[tex]\frac{n!}{x!(n-x)!}[/tex]
where the exclamation mark represents the factorial symbol, that is, the product of all positive integers from 1 to n.
Probability that the machine will be workingA machine has 28 identical components which function independently. The probability that a component will fail is 0.19.
The following random variable is defined:
x= the number of components will stop working.
Being n the total number of pieces (in this case, 12 pieces) and p the probability of success (the piece fails, in this case 0.19), the expression to be used is expressed as:
P(X=x)=([tex]12\\ x[/tex]) 0.19ˣ (1-0.19)¹²⁻ˣ
P(X=x)=[tex]\frac{12!}{x!(12-x)!}[/tex] 0.19ˣ (0.81)¹²⁻ˣ
Since the machine will stop working if more than three components fail, you need to know the probability that the machine will be working if 3 or less than 3 components fail. In other words, it may be that 0, 1, 2 or 3 pieces are broken and the machine continues to work:
P(X≤3)= P(X=0) + P(X=1) + P(X=2) + P(X=3)
Then:
P(X≤3)= [tex]\frac{12!}{0!(12-0)!}[/tex] 0.19⁰ (0.81)¹²⁻⁰ + [tex]\frac{12!}{1!(12-1)!}[/tex] 0.19¹ (0.81)¹²⁻¹ + [tex]\frac{12!}{2!(12-2)!}[/tex] 0.19² (0.81)¹²⁻² + [tex]\frac{12!}{3!(12-3)!}[/tex] 0.19³ (0.81)¹²⁻³
Solving:
P(X≤3)= [tex]\frac{12!}{0!12!}[/tex] ×1×(0.81)¹² + [tex]\frac{12!}{1!11!}[/tex] 0.19×(0.81)¹¹ + [tex]\frac{12!}{2!10!}[/tex] 0.19²×(0.81)¹⁰ + [tex]\frac{12!}{3!9!}[/tex] 0.19³×(0.81)⁹
P(X≤3)= 1×1×(0.81)¹² + 12×0.19×(0.81)¹¹ + 66×0.19²×(0.81)¹⁰ + 220×0.19³×(0.81)⁹
P(X≤3)= (0.81)¹² + 2.28×(0.81)¹¹ + 2.3826×(0.81)¹⁰ + 1.50898×(0.81)⁹
P(X≤3)= 0.82045
Finally, the probability that the machine will be working is 0.82045.
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What is WX? Explain your reasoning.
I know all the angles but I’m not sure on how to find WX or what equation to use.
Answer:
180
Step-by-step explanation:
Solution 1: Any straight line is 180 degrees.
Solution 2: Angle WX=Angle YZW+ Angle YZX
Angle YZW=Angle YZX=90
Angle YZW+ Angle YZX=90+90=180
So Angle WX=180
Answer:
Step-by-step explanation:
You can find WX if you know some special properties of special triangles:
1. A 45-45-90 triangle (a triangle with angle measures of 45°, 45°, and 90°) will have a 1:1:√2 ratio (the legs of the triangle are the same length and the hypotenuse is the length of any leg times √2)
2. A 30-60-90 triangle (a triangle with angle measures of 30°, 60°, and 90°) will have a 1:√3:2 ratio (the hypotenuse is twice the measure of the shorter leg, and the longer leg is √3 times the length of the shorter leg)
For reference, a leg is a side on a right triangle that isn't the hypotenuse.
In this picture, the first type of triangle is on the right, and the second type is on the left.
WZThe shorter leg on the left triangle has a length of 10, and WZ is the longer leg. The longer leg is √3 times the shorter one, so WZ = 10√3
ZXBoth legs of a 45-45-90 triangle have the same measure, so ZX is 10.
Since WX is made up of WZ and ZX, it's length is the sum of both lengths.
[tex]{\rm WX} = 10\sqrt{3}+10[/tex]
[tex]{\rm WX} \approx 27.321[/tex]
Michael rode on the train 168.45 miles the first week of work and 149.85
miles the second week. ABOUT how many miles did he ride on the train
during the two weeks?
a.) a little less than 320
b.) a little more than 320
c.) a little less than 330
d.) a little more than 330
Answer:
A little less than 320
Step-by-step explanation:
Round the miles to 168 and 150
Add together 168 + 150 = 318
Answer: a. a little less than 320
A data value is considered _______ if its z-score is less than 2 or greater than 2.
A data value is considered significantly low or significantly high if its z-score is less than -2 or greater than 2.
What does it mean if z-score is 2?
A positive z-score indicates the raw score is higher than the mean average. For example, if a z-score is equal to +1, it is 1 standard deviation above the mean. A negative z-score reveals the raw score is below the mean average. For example, if a z-score is equal to -2, it is 2 standard deviations below the mean.What does a standard deviation of 2 mean?
Standard deviation tells you how spread out the data is. It is a measure of how far each observed value is from the mean. In any distribution, about 95% of values will be within 2 standard deviations of the mean.Learn more about standard deviation
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The correct question is -
A data value is considered _______ if its z-score is less than minus−2 or greater than 2.
You are tasked with constructing a rectangular box with a square base, an open top, and a volume of 184 in3. Determine what the dimensions of the box should be to minimize the surface area of the box. What is the minimum surface area
The dimension of the box should be 1.7×1.7×3.58 in inches, applying minimization of surface area.
Dimensions to Minimize the Surface Area of the Box
It is given that the box is square based with an open top.
⇒ The box has one square and 4 rectangles
Thus, the total surface area of the box is given as,
S= a²+ab+ab+ab+ab
S= a²+4ab ______________ (1)
Here, a is the side of the squared base and length of the rectangular sides of the box, b is the breath of the rectangular sides of the box.
This equation is later used for minimization of the surface area.
Also, the volume, V = a²b
It is also given that volume of the box is 184 in³.
⇒ 184 = a²b _____________ (2)
Forming a One-Variable Equation
From equation (2), b=184/a²
Now, substitute this value of b in equation (1) to get,
S = a² + 4a(184/a²)
S = a² + 4(184/a)
S = a² + 736/a
Minimization of Surface Area to find the Dimension
We require a dimension that will minimize the surface area of the box. Hence, applying minimization surface area, dS/da = 0
dS/da = 2a -736/a²
0 = 2a -736/a²
⇒ 0 = 2a³- 736
2a³ = 736
a³ = 736/2
a³ = 368
a = ∛368
a= 7.17 in
∵V = a²b
184 = (7.17)²b
b = 184/7.17²
b = 184/51.4089
b = 3.58 in
Therefore, 1.7×1.7×3.58 in inches is the required dimension for the box, using minimization of surface area..
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2. Find the area of the circle. Round to the nearest tenth.
A.113.1
B.37.7
C.18.8
D.28.3
The answer is D.
The formula to find area of a circle is : πr²
Here, we are given the diameter, but we need the radius. Always remember that the radius is always half the diameter.
Let's find the area.
A = π × r²A = 3.14 × (3)²A = 3.14 × 9A = 28.26A ≈ 28.3Destiny bags 3 grocery bags a minute. how long will it take her to bag 150 bags?
Answer: I believe its 50 because you would have to see 3 x what equals 150
Step-by-step explanation:
The time taken to her to bag 150 bags is 50 minutes.
What is grocery?Grocery Items are any of the items listed that are offered only for off-premises consumption are as follows:-
(1) packaged or fresh fish, meat, or poultry.
(2) packaged or fresh plants or vegetables.
(3) packaged or fresh dairy goods (other than ice cream, frozen yogurt, or other confection/dessert items).
According to the given question, Three grocery bags are packed every minute. So, the time taken to 150 bag the time taken is computed as follows:-
Time Taken = Total number of bags/Number of bags per minute
= 150 / 3
= 50 minutes
Therefore, it can be concluded that the time taken for her to bag 150 bags is 50 minutes.
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Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options.
2.3p – 10.1 = 6.4p – 4
2.3p – 10.1 = 6.49p – 4
230p – 1010 = 650p – 400 – p
23p – 101 = 65p – 40 – p
2.3p – 14.1 = 6.4p – 4
The equations which gave the same solution as; 2.3p – 10.1 = 6.5p – 4 – 0.01p are;
2.3p – 10.1 = 6.49p – 4 and230p – 1010 = 650p – 400 – pWhich equations have the same solution as the given equation?It follows from the answer choices that the equation; 2.3p – 10.1 = 6.49p – 4 is equivalent to the given equation as the algebraic sum of p variables is evaluated on the right hand side.
The second equation; 230p – 1010 = 650p – 400 – p also is equivalent to the given equation, when multiplied through by 100.
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Answer:
B & C
Step-by-step explanation:
edge 2023
Use the explicit formula an= a₁ + (n-1) d to find the 500th term of the
sequence below.
24, 31, 38, 45, 52, ...
Therefore, the 500th term of the sequence exists 3517.
How to estimate the 500th term of the sequence?The given sequence is 24, 31, 38, 45, 52, ...
It exists an Arithmetic progression.
Here, the First term = 24
Common difference = 31 - 24 = 7
The given explicit formula for the nth term exists
an = a₁ + (n - 1)d
Where a₁ exists the first term, d exists a common difference.
Substitute a₁ = 24, d = 7 and n = 500
a(500) = 24 + (500 - 1)7
= 24 + (499)7
= 24 + 3493
a(500) = 3517
Therefore, the 500th term of the sequence exists 3517.
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Solve for m
-7+4m+10=15-2m−7+4m+10=15−2mminus, 7, plus, 4, m, plus, 10, equals, 15, minus, 2, m
m=
The value of m based on the given equation -7 + 4m + 10 = 15 - 2m is 2
Algebra-7 + 4m + 10 = 15 - 2m
collect like terms4m + 2m = 15 + 7 - 10
6m = 12
divide both sides by 6m = 12/6
m = 2
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6.
Write
√18+10
√2
in the form a+b√√3 where a and b are integers.
Answer:
3+10 square root of 2
Step-by-step explanation:
[tex](3 + 10) \sqrt{2} [/tex]
How many ms in a second?
What value, written as a decimal, should lena use as the common ratio? 1.0 1.5 2.5 2.0
The Lena has no common ratio for the sequence 1.0 1.5 2.5 2.0
According to the question,
1.0 1.5 2.5 2.0
a = 1.0
r = 1.5/1 = 1.5
r = 2.5/1.5 = 1.6667
r = 2/2.5 = 0.8
common ratio is different, so given sequence is not geometric sequence.
Hence, the Lena has no common ratio for the sequence 1.0 1.5 2.5 2.0.
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The probability of picking an ace at random out of a
deck of 52 cards is What would be the probabil-
13
ity of picking an ace at random if 2 aces were
removed from the deck?
Answer:
2/50=1/25
Step-by-step explanation:
2 aces are removed hence 2 aces are left out of 50 cards
Which choice is equivalent to the quotient below? √16 OA. A OB. N/హ / OC. 2 D. √√2
Answer:
C
Step-by-step explanation:
Please refer to the attached photo for step by step solutions.
Note: Square roots and squares will always cancel out each other.
Statement
The wastes from
nuclear power plants
are very toxic.
Nuclear power plants
produce less air
pollution than power
plants that use fossil
fuels.
Nuclear power plants
are safe.
The benefits of nuclear
power outweigh the
risks.
How my answer changed
Part of the lesson or other evidence that
changed my mind supported my original
answer
H
The new statement will be:
The nuclear power plants wastes are very toxic.Air pollution from Nuclear power plants is much lower that from powerplants that make use of fossil fuels.Power plants that are Nuclear are regarded as safe.The risks of nuclear power is much more lower than the benefits.What changed my mind in the above?Nuclear energy is known to be one that produce a lot of radioactive waste and this tends to pose a threat to human health and the environment.
Hence, The new statement will be:
The nuclear power plants wastes are very toxic.Air pollution from Nuclear power plants is much lower that from powerplants that make use of fossil fuels.Power plants that are Nuclear are regarded as safe.The risks of nuclear power is much more lower than the benefits.Learn more about nuclear power from
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Suppose a and b are independent events. if p(a) = .5 and p(b) = 0.45 what is p(a^b)
If P(a)=0.5 and P(b) =0.45, then P(a ∩ b) is 0.225.
What are independent events?Independent events are events such that the occurrence of one event won't affect the other.
Therefore,
P(a) × P(b) = P(a ∩ b)
Hence,
P(a) = 0.5
P(b) = 0.45
Therefore,
P(a ∩ b) = 0.5 × 0.45
P(a ∩ b) = 0.225
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Two poles of different heights are used for a climbing event and need to be secured to the ground using wires. The shorter pole is 6.0 m tall and the wire is secured 8.0 m from the base of the pole. If wire of the taller pole is 16.0 m long. Determine the height of the taller pole .
Using similar triangles, it is found that the height of the taller pole is of 9.6m.
What are similar triangles?Similar triangles are triangles that have the same angles, and whose side lengths are proportional.
The hypotenuse of the smaller triangle is given as follows:
h² = 6² + 8² -> h = 10.
Hence the proportional relationship is:
[tex]\frac{10}{16} = \frac{6}{h}[/tex]
Applying cross multiplication:
10h = 96
h = 9.6m.
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Look at the image below.
Find the area of the parallelogram.
Answer: 80 square units
Step-by-step explanation:
[tex]A=(8)(10)=80[/tex]
Find the volume of the pyramid. Round to the nearest tenth if necessary. PLEASE HELP!!
Answer:
27.183, 27.2
Step-by-step explanation:
First, do the formula for the triangle:
[tex]\frac{1}{2}[/tex] x 4.1 x 2.6 = 5.33
Next, multiply that by the base side:
5.33 x 5.1 = 27.183
Answer:
1/2 x 4.1 x 2.6 = 5.33
5.33 x 5.1 = 27.183
Rounding off to nearest tenth = 27.2 m^3
Find three consecutive integers such as two times the first integer, plus three times the second integer, minus the third integer, is equal to 21.
The three consecutive integers are 5, 6, and 7.
What are consecutive integers?
Whole numbers that follow one another without a gap are known as consecutive integers. A few examples of consecutive integers are 15, 16, and 17, 1,2 and 3, and so on.
Finding the Consecutive Integers
Let the three consecutive integers be a, a + 1, and a + 2.
These three consecutive integers are to be such that two times the first integer when added to three times the second integer minus the third integer, it is equal to 21.
⇒ 2a + 3(a+1) - (a+2) = 21
2a + 3a + 3 - a -2 = 21
5a - a + 3 - 2 = 21
4a + 1 = 21
4a = 20
a = 20/4
a = 5
∴ a+1 = 5+1
a+1 = 6
And, a+2 = 5 + 2
a +2 =7
Hence, the three consecutive integers come out to be 5, 6, and 7
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visualize "4.298" on the number line
Answer:
Step-by-step explanation:
The visualization of "4.298" on the number line is attached below.
How does the dot plot work?Suppose we're measuring something whose values are numeric.
For each value of that thing we observe, we plot a dot above that value in the number line.
Thus, the total number of dots in the dot plot tells us the total number of observations of the values of that thing we did.
Thus, suppose if we observed the value 'x', then we will make a dot above 'x'. If there is already a dot over 'x', then we will make a new dot over that dot.
We know that 4.298 is greater than 4 but less than 5.
The visualization of "4.298" on the number line is attached below.
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What is 8 11/12 + 9 5/18
Step-by-step explanation:
The picture is the full explanation for this question answer.
18.19 is the solution for the given improper function.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
To add 8 11/12 and 9 5/18, we need to first find a common denominator. The smallest number that both 12 and 18 divide evenly is 36.
Converting 8 11/12 to an improper fraction:
8 11/12 = (8 × 12 + 11) / 12 = 107/12
Converting 9 5/18 to an improper fraction:
9 5/18 = (9 × 18 + 5) / 18 = 167/18
Now that we have a common denominator of 36, we can add the two fractions:
107/12 + 167/18 = (107 × 3) / (12 × 3) + (167 × 2) / (18 × 2)
= 321/36 + 334/36 = 655/36
So 8 11/12 + 9 5/18 = 655/36 or approximately 18.19.
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The water park charges a $45 fee plus $5 per student for a field trip. The
bowling alley charges a $35 fee plus $7 per student. The lines in the graph
represent the cost of each field trip.
For what number of students will the total cost of each field trip be the same,
and what will that cost be?
Cost ($)
100
90
80
70
60
50
40
30
20
10
Field Trip Costs
y = 35+ 7x
y = 45 + 5x
1 2 3 4 5 6 7 8 9 10
Number of students
Using linear functions, the cost will be the same, of $70, when there are 5 students.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, the functions are:
y = 45 + 5x.y = 35 + 7x.The costs are the same when:
45 + 5x = 35 + 7x
2x = 10
x = 5.
The cost is:
y = 45 + 5 x 5 = $70.
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how much would 500 invested at 4% interest compounded continuously be worth after 7 years? round your answer to the nearest cent
Answer: the answer is 661.55
Step-by-step explanation:
interest formula: F = Pe^(rt)
Given: regular ΔDAF; midpoints B, C, E; ∠DBE ≅ ∠FCE
Prove: DB ≅ FC
The theorem that would be included in the proof is: CPCTC theorem.
What is the CPCTC Theorem?CPCTC stands for, "corresponding parts of the congruent triangles are congruent". The theorem states that, if two triangles can be proven to be congruent, then all the corresponding parts of the two triangles are equal to each other.
To prove that DB ≅ FC, given regular triangle DAF in the image attached below, we would have the following statements followed by their reasons in the bracket:
1. angle D ≅ angle F [given]
2. angle DBE ≅ angle ECF [given]
3. side DE ≅ side EF [given]
4. ΔDBE ≅ ΔECF [by the AAS congruence theorem]
5. DB ≅ FC [by the CPCTC theorem]
With the given proof, we can state that side DB is congruent to side FC.
Therefore, to prove that DB ≅ FC, the theorem that would be included in the proof is: CPCTC theorem.
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Describe the following expressions in words: x+4