Luc is correct in stating that the line will remain the same with certain dilation centers, such as the origin (0, 0) and the point (3, -4). These centers of dilation will cause a scale factor of 2, but the line will remain the same.
To check if Luc is correct, we can calculate the points of the dilation with scale factor 2.
For the origin (0, 0):
Point A: (x, y) = (0, 3)
Point B: (x, y) = (-4, -3)
Dilated Point A: (x, y) = (0, 6)
Dilated Point B: (x, y) = (-8, -6)
Equation of the dilated line: y = -4x + 6
This shows that the line is dilated with scale factor 2, but is the same line.
For the point (3, -4):
Point A: (x, y) = (3, -1)
Point B: (x, y) = (-1, -7)
Dilated Point A: (x, y) = (6, -2)
Dilated Point B: (x, y) = (-2, -14)
Equation of the dilated line: y = -4x + 3
This shows that the line is dilated with scale factor 2, but is the same line.
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Four siblings have a total of 3/4 pound of candy leftover from Halloween. If they split
it equally, how much will each child have?
Answer:
Each child will have 3/16 pound of Halloween candy.
Step-by-step explanation:
To find out how much candy each sibling gets, we need to divide 3/4 by 4
3/4 divided by 1/4 = 3/16
Therefore, our answer is 3/16.
Adella wants to have $10,000. 00 saved in 5 years. Her local bank offers an account at 4% APR
compounding monthly. How much would she need to deposit to reach her goal?
$8000. 33
$8191. 67
$8189. 67
$8219. 29
The deposit to be made to save $10,000 in 5 years is $8189.67 when compounded monthly.
What is compound interest?Compound interest is interest on a loan or deposit that is calculated on both the principal amount and the interest accumulated in previous periods. It differs from simple interest, which is calculated on the principal only. Compound interest can be more favorable to the lender and more expensive to the borrower. The frequency of compounding (annual, quarterly, monthly, etc.) also affects the total amount of interest earned or paid.
Given that:
A = $10,000
r = 4% = 0.04
t = 5 years
n = 12 (since the compounding is monthly)
P = ?
The compound interest is given as follows:
[tex]A= P(1+\frac{r}{n} )^{nt}[/tex]
Substituting the values in the formula we have:
[tex]10000= P(1+\frac{0.04}{12} )^{(12)(5)}\\\\10000= P(1+0.0033 )^{(60)}\\\\10000= P(1.0033 )^{(60)}\\\\10000= P(1.2185)\\\\P= \frac{10000}{1.2185} \\\\P=8189.67[/tex]
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A diagonal of a polyhedron is a line segment connecting two non-adjacent vertices. How many diagonals does a pentagonal prism have
A pentagonal prism have 35 diagonals.
We know tha in a polygon or polyhedron the formula for finding the number of diagonals is: n(n-3)/2,
where n= the number of sides
We find the number of diagonals of a pentagonal prism.
As we know a pentagonal prism has two pentagonal bases like top and bottom and five rectangular sides.
For a pentagonal prism n = 10
So, using above formula the total number of diagonals would be,
d = [10 × (10 - 3)] / 2
d = (10 × 7) / 2
d = 70/2
d = 35
Therefore, the total number of diagonals would be = 35
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What is g(4) when given the function g(x) = 6x + 32?
Answer:
The value of g(4) of the given function is 56.
It costs $3 to bowl a game and $2 for shoe rental Write an expression for the total cost (in dollars) of g games.
Answer: , P = 2 +3g
Step-by-step explanation:
D t
-60 0
-56 10
-24 90
-20 100
-8 130
0 150
Choose the correct statement.
Select one:
a.
The function is
D(t)=52t−150
b.
The function is
D(t)=25t−150
c.
The function is
D(t)=52t−60
d.
The function is
D(t)=25t−60
Answer: To determine the correct statement, you need to find a pattern in the values of D(t). You can do this by finding the difference between consecutive values of D(t).
The difference between -60 and 0 is 60.
The difference between 0 and 10 is 10.
The difference between 10 and 90 is 80.
The difference between 90 and 100 is 10.
The difference between 100 and 130 is 30.
The difference between 130 and 150 is 20.
The pattern that emerges is that the difference between consecutive values of D(t) is always 25. This means that the correct statement is "The function is D(t)=25t−60". The correct answer is therefore d.
Step-by-step explanation:
Ali found out the number of rooms in each of 40 houses in a town. He used the information to complete the frequency table. Number of Rooms Frequency 4 4 5. 7 6 10 7 12 8 5 9 2 Calculate the mean number of rooms.
The mean number of rooms = 6
We know that the formula for the mean.
mean = sum of all observations / total number of observations
First we find thr total number of rooms, from given frequency table.
Number of Rooms Frequency Total number of rooms
4 4 16
5 7 35
6 10 60
7 12 84
8 5 40
9 2 18
So, the total number of rooms of 40 houses in a town would be,
16 + 35 + 60 + 84 + 40 + 18 = 253
And the total number of houses = 40
Using above formula of mean, the mean number of rooms would be,
x = 253/40
x = 6.325
Therefore, on an average there are 6 rooms in each house.
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There are 20 gloves in a drawer: 5 pairs of black gloves, 3 pairs of brown,
and 2 pairs of gray. You select the gloves in the dark and can check them
only after a selection has been made. What is the smallest number of gloves
you need to select to guarantee getting the following?
(a) At least one matching pair
(b) At least one matching pair of each color
The number of gloves selected for each cases is 11 and 19 gloves respectively.
How is selection done?
In mathematics, most of the times selection is done using permutation and combination.
Putting things or numbers in order is known as a permutation.
Combinations are a means to choose items or numbers from a collection of items or groups of items without regard to their order.
Given,
Total black gloves = 5 left hand+ 5 right hand
Total brown gloves = 3 left hand + 3 right hand
Total gray gloves = 2 left hand + 2 right hand
Now to find the least number of gloves for the given conditions, we start with the worst condition.
a) To get at least one matching pair, we first consider no matching pair, which is (5 +3+2) gloves of only left only or right only hand of each colour.
Now to make one pair, we need to select only one glove of the opposite hand of any colour.
Therefore to get atleast one matching pair, smallest number of gloves to be selected = 5 + 3 + 2 + 1 = 11 gloves
b) In this case also we start with worst case.
For no matching pair of each colour we have to take 10 black gloves, 6 brown gloves and 2 gray gloves of any one hand.
Therefore to get matching pair of each colour, we have to take one more gray glove.
Therefore to get atleast one matching pair of each colour, smallest number of gloves to be selected = 10 + 6 + 2 + 1 = 19 gloves.
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Eric went for a drive in his new car. He drove for 182.4 miles at a speed for 57 miles per hour. For how many hours did he drive?
Answer:
3.2 hours
Step-by-step explanation:
182.4÷57=3.2
time divided by speed equals time
x^2=Σ(o-e)^2/e
17. A candidate for mayor is discussing the crime rate in the city. She asks the police department to provide some statistics on how many people out of a group of 500
people were victims of four specific crimes. She expects that she can verify this information by doing her own survey. She then asks a group of 500 people to identify
whether they were victims of the same crimes. Her results are the observed quantities, and the police data are the expected quantities. The following is a table of the
results.
Category: observed/ expected
Robbery
24/18
Assault
15/21
Discrimination
79/56
Theft
124/138
Calculate the chi-square value for her survey. Remember, to calculate the chi-square value, use the formula shown.
A. 12.68
B. 8.56
C. 8.15
D. 14.58
On solving the provided question we cans ay that - the value of the following exponent is
what are exponents?Exponentiation, often known as "b raised to the nth power," is a mathematical operation denoted by the symbol bn that involves two numbers: a base number, b, and an exponent, or power, n. Exponents show how many times a number has been multiplied by itself. As an illustration, 2-3 (written as 23) denotes: 2 x 2 x 2 = 8. 23 is not equivalent to 2 + 3 = 6. Recall that an integer raised to the power of one equals itself. A approach to express huge numbers as powers is through the use of exponents. Exponent, then, is the quantity that indicates how many times a number has been multiplied by itself. As an illustration, 6 is multiplied by 4 to provide 6 x 6 x 6 x 6. It may be expressed as 64. 4 is where
here,
= [tex]10^2 X 10^-3[/tex] X 32
= 100 X 1/1000 X 32
=1/10 X 32
=3.2
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A fifth grader takes a standardized achievement test (mean = 125, standard deviation = 15) and
scores a 148. What percent of children made higher than a 148?
the child's percentile rank is 93 th percentile. It means he performed better than [tex]$93 \%$[/tex]of the total number of students.
What is Percentile rank?When compared to other students in the same grade and topic, for instance, a student's percentile rank shows how well they performed. The percentile rank of a student indicates whether their score was on par with or higher than that of the norm group's percentage of pupils. In statistics, the percent of scores in a frequency distribution that are lower than a specific score is known as the percentile rank of that score. A percentile rank returns a numerical value, which really indicates the proportion of people who fall inside that range. Since it is a percentile, its range is always between 1 and 99, with 50 serving as its mean or average rank. Only normalized values or data are ever usable in this fashion.- Mean, $\boldsymbol{\mu}=125$.- Population standard deviation, $\sigma=15$.- Marks obtained by child $(X)=148$Need to find the percentile rank for child's score.
Let[tex]$\mathrm{X}$[/tex]denote marks obtained by the child in the achievement test.
The [tex]$\mathrm{Z}$[/tex]value is given as,
[tex]$$Z=\frac{X-\mu}{\sigma}$$[/tex]
Using equation (1), the required percentile rank for child's score is expressed as,
[tex]& Z=\frac{148-125}{15} \\[/tex]
[tex]& Z=1.533[/tex]
The probability value corresponding to the Z=1.533, obtained from the Z table is 0.93736.
Thus, the percentile is 0.93736.
Therefore, the child's percentile rank is 93 th percentile. It means he performed better than [tex]$93 \%$[/tex]of the total number of students.
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A 5 m 60 cm high vertical pole cat a hadow 3 m 20 cm long. Find at the ame time
(i) the length of the hadow cat by another pole 10 m 50 cm high,
On solving the provided question we can say that equation formed is x/y = k, x = ky => y₂ = (10.5 × 3.2) / 5.6 => y₂ = 6
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
x/y = k, x = ky
where k is a constant.
Thus, x₁ / y₁ = x₂ / y₂
5.6 / 3.2 = 10.5 / y₂
5.6 × y₂ = 10.5 × 3.2
y₂ = (10.5 × 3.2) / 5.6
y₂ = 6
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Melody has two different posters to put up in her bedroom. Poster A has an area of 450 square inches. Poster B has an area of 326 square inches. How much area of Melody's bedroom wall will the two posters cover, in square inches?
The two posters will cover 776 square inches of Melody's bedroom wall.
To find this, you add the area of the two posters together. Poster A has an area of 450 square inches, and poster B has an area of 326 square inches. By adding these two values together, we get 450 + 326 = 776 square inches. This is the total area that the two posters will cover on Melody's bedroom wall. It is important to note that this is assuming that the posters do not overlap each other and that they are placed next to each other, covering an equal area of the wall.
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y^2=1/5(x-4), (24,2)
P is the centroid of ΔXYZ. If XU = 48, what is PU?
The value of the PU in the given triangle is 19.
What is centroid?The center of the thing is represented by its centroid. The centroid of a triangle is the location where the triangle's three medians intersect. It can alternatively be described as the location where the three medians come together. A line connecting a side's midpoint and the triangle's opposite vertex is called the median.
Given,
'p' is the centroid of triangle XYZ and XU is 57.
Since p is the centroid the 'U', 'V', and 'W' are the mid pint of side'YZ', 'XZ', and 'XY'
from the centroid Theorem, we can write;
XP = 2/3 * XU
plug the values 'XU' in the above equation:
XP = 2/3 *57
XP = 2*19
XP = 38
from figure:
XP + PU = XU
PU = XU - XP
Plug 'XU' and 'XP'
PU = 57 -38
PU = 19
therefore, the PU of the given triangle is 19 units.
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Complete question:
Albert has 225 strawberry plants that he wants to plant in a square formation in evenly spaced rows. How many strawberry plants should he plant in each row?
Answer:
15
Step-by-step explanation:
to determine the number of plants per row, take the square root of 225
sqrt(225) = 15
There should be 15 plants per row
Answer:
Step-by-step explanation:
Since the formation of the strawberry plants should represent a square, it implies that the dimensions of the formation (i.e length and breadth) must be equal.
To achieve this, we have to calculate its square root as the formula for the area of any square is given as (side)^2.
Now, [tex]\sqrt{225}[/tex] = 15
implies that each as well as each column will contain 15 strawberry plants
What is undecidable problem give two examples?
An undecidable problem is one for which it has been demonstrated that it is impossible to develop an algorithm that always leads to the correct yes-or-no answer. Two examples are:
The Whitehead problem The halting problemWhat the halting problem?The halting problem is the problem of determining whether a computer programme will finish running or continue to run indefinitely based on a description of the programme and an input. Alan Turing demonstrated in 1936 that a general algorithm for solving the halting problem for all possible program-input pairs does not exist.
A "pathological" programme g, when called with some input, can pass its own source and input to f and then specifically do the opposite of what f predicts g will do. This case cannot be handled by any f. A key part of the proof is a mathematical definition of a computer and programme, known as a Turing machine; the halting problem is intractable over Turing machines.
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A line starts at (negative 2, 0), goes to (5, question mark), and then goes down to (6, 0).
What would the height need to be for this curve to be a density curve?
One-fourth
One-half
StartFraction 1 Over 8 EndFraction
StartFraction 1 Over 16 EndFraction
answer is one fourth
What the height would need for this curve to be a density curve is; One-half
How to interpret Density Curves?The criteria for a curve to be a density curve is as follows;
1. The curve must always be non-negative. This tells us that the y-value of the curve must be greater than or equal to 0 at every given point.
2. The area under the curve must always be equal to 1.
Now, we are told that the curve starts at (-2, 0) and then goes to (5, question mark), and then goes down to (6, 0),.
This means that the area under the curve will be a trapezoid that has a height of question mark and then bases of length 3 (from -2 to 5) and length 1 (from 5 to 6).
The area of this trapezoid will be equal to the sum of the bases times the height divided by 2, or:
Area = ((3 + 1) × question mark)/2
Since the area under the curve must be equal to 1, we can set up the equation:
1 = ((3 + 1) × question mark) / 2
Solving for question mark, we will:
The question mark = 2/4
The question mark = 1/2
Therefore, we can conclude that the height of the curve is 1/2
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In ΔNOP,
m
∠
N
=
(
9
x
+
8
)
∘
m∠N=(9x+8)
∘
,
m
∠
O
=
(
4
x
+
13
)
∘
m∠O=(4x+13)
∘
, and
m
∠
P
=
(
2
x
−
6
)
∘
m∠P=(2x−6)
∘
. Find
m
∠
N
.
m∠N
Answer: 15
Step-by-step explanation: In ΔNOP,
m
∠
N
=
(
9
x
+
8
)
∘
m∠N=(9x+8)
∘
,
m
∠
O
=
(
4
x
+
13
)
∘
m∠O=(4x+13)
∘
, and
m
∠
P
=
(
2
x
−
6
)
∘
m∠P=(2x−6)
∘
. Find
m
∠
N
.
m∠N
A pendulum of length 1m and period 2.01s is placed at the top of Mount Everest
having an altitude of 8849m. Calculate the value of ‘g’ at that point.
Answer: A pendulum of length 1m and period 2.01s is placed at the top of Mount Everest having an altitude of 8849m. Calculate the value of 'g' at that point.
The period of this pendulum can be solved using the formula shown in the picture below. T is the period in seconds; L is the length in meters and g is the acceleration due to gravity which is equal to 9.81 m/s²near the equator.
T = 2 × π × (square root of 1.00 m / 9.81 m/s²)
T = 2 * 3.1416 * (square root of 0.101936799)
T = 6.2832 * 0.319275428
T = 2.00 seconds
The period of this pendulum correct to 3 significant figures is 2.00 seconds.
The frequency of this pendulum is solved by the formula f = 1/T
f = 1/2.00 seconds
f = 0.500 hertz
Answer: 9.76 m/s^2
Step-by-step explanation:
Find the coefficient of the $x^2$ term in the expansion of the product$$(2x^2 3x 4)(5x^2 6x 7).$$
The coefficient of [tex]x^{2}[/tex] in [tex](2x^{2}-3x-4)-(5x^{2}+6x-7)[/tex] is -3.
A coefficient is a multiplicative factor in a polynomial, series, or expression in mathematics. It is typically a number, although it can also be any expression (including variables such as a, b and c). They may also be referred to as parameters if the coefficients are variables in and of themselves. The coefficient in an expression that is not related to any variables is called the constant coefficient (also known as constant term or free coefficient).
Given equation,
[tex](2x^{2}-3x-4)-(5x^{2}+6x-7)[/tex]
= [tex]2x^{2}-3x-4-5x^{2}-6x+7[/tex]
= [tex]-3x^{2}-9x+3[/tex]
Hence, coefficient of [tex]x^{2}[/tex] is -3.
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5. Use the properties of logarithms to expand log₂
constant multiple of variables. (Assume all variables are positive.)
as a sum, difference, and/or
Answer:
1/2log₂(a-1) -log₂(9)
Step-by-step explanation:
You want the expanded form of log₂(√(a-1)/9).
Rules of logarithmsThe relevant rules of logarithms are ...
log(a^b) = b·log(a)
log(a/b) = log(a) -log(b)
The rules are applicable for any base.
Application[tex]\log_2{\dfrac{\sqrt{a-1}}{9}}=\log_2{(\sqrt{a-1})}-\log_2{(9)}=\boxed{\dfrac{1}{2}\log_2{(a-1)}-\log_2{(9)}}[/tex]
PLS HELP ASAP 50 POINTS!!!
Identify or mark the missing side or angle that would make triangle ABC congruent to triangle PDF by AAS
The angles that would make triangle ABC congruent to triangle PDF by AAS are ∠ ACB and ∠ PFD i.e. ∠ ACB = ∠ PFD.
What is triangle?Three straight lines coming together create a triangle. There are three sides and three corners on every triangle (angles). A triangle's vertex is the intersection of two of its sides. Any one of a triangle's three sides can serve as its base, however typically the bottom side is used.
Given:
The triangle ABC and PDF are concurrent by AAS,
The AAS concurrency required two angles and one side to be equal,
Here,
AB = PD,
∠ ABC = ∠ PDF
Now one more angle is required to be equal,
∠ ACB = ∠ PFD
Thus, the missing angle is ∠ ACB and ∠ PFD.
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........... I donr know what I'm doing-
Intercept = 1
Equation - y = -(2/5)x + 1
How do you find the third side of a right triangle with two sides?
The Third side of the right triangle with two sides can be found by Pythagoras Theorem that means by adding the square of other two sides .
What is Pythagoras Theorem ?
The Pythagoras Theorem states that the , in a Right Triangle, the square of the hypotenuse side (longest side) is equal to the sum of squares of the other two sides“.
The sides of this triangle are named as Perpendicular, Base and Hypotenuse. where , the hypotenuse is longest side of the triangle , because , it is opposite to the angle 90°.
Therefore , the third side (longest side) of a right triangle with two sides can be found by adding the square of the other two sides .
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Expand 2/3(t - 2) pleaseee helppppp asap
Answer:
[tex]\frac{2t-4}{3}[/tex]
Step-by-step explanation:
[tex]\frac{2}{3}[/tex][tex](t-2)\\[/tex]
=> [tex](\frac{2}{3} * t ) + (\frac{2}{3} * -2)[/tex]
=> [tex]\frac{2t}{3} + (-\frac{4}{3})[/tex]
=> [tex]\frac{2t-4}{3}[/tex]
Hope you understood!!
Manish and Ravi are reading the same series of books. As of today, Manish has read a total of 544 pages. If he reads at the same pace, after 8 days he will read a total of 928 pages.
The total number of pages that Ravi has read is modeled by the equation y=51x+594, where x is the number of days after today, and y is the total number of pages read.
Who will finish the series first? Why?
Select the response that correctly answers both questions.
Responses
Ravi will finish first, because he has already read more than Manish as of today, and he reads more than Manish each day.
Ravi will finish first, because he has already read more than Manish as of today, and he reads more than Manish each day.
Ravi will finish first, because even though Manish has read more as of today, Ravi reads faster overall.
Ravi will finish first, because even though Manish has read more as of today, Ravi reads faster overall.
Manish, because even though Ravi has read more as of today, Manish reads faster overall.
Manish, because even though Ravi has read more as of today, Manish reads faster overall.
Manish will finish first because he has already read more than Ravi as of today, and he reads more than Ravi each day.
The person that will finish the series first is;
Ravi will finish first, because even though Manish has read more as of today, Ravi reads faster overall.
How to interpret Linear Equation Problems?The general equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Total pages manish has read as at today = 544 pages
He reads at the same pace and after 8 days he has read 928 pages. Thus, the equation that represents the number of pages that Manish has read is; 928 = 8m + 544
922 - 544 = 8m
m = 378/8
m = 47.25
Thus, his rate is 47.25 pages per day
The equation for Ravi is y = 51x + 594
This shows a rate of 51 pages per day
Thus, Ravi will finish first
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What is the solution to 3 4?
The solution of the fraction 3/4 is 0.75
The term fraction is defined as represent the parts of a whole or collection of objects
Here we have given the fraction 3/4.
Now, we have to do the following steps in order to find the decimal equivalent for the fraction.
First of all we just need to divide the numerator by the denominator.
Then we get the fraction is 3/4 which means we need to divide: 3 ÷ 4.
The division process is illustrated on the following image.
Then the decimal equivalent to the fraction written as 3/4 is expressed as 0.75 in the decimal form.
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the scale on a map is 1:5000000
two towns are 7cm apart on the map
work out the actual distance between the towns
Answer:
Step-by-step explanation:
scale,= 1 : 5000000
it means 1 cm depicts 5000000cm
or 50000m else 50km
the distance between two towns in map = 7cm
so the distance between two towns = 7 *50
= 350km
How do you find the third angle of a triangle if two angles are given?
To find the third angle of a triangle if you know the measures of the other two angles, you can use the fact that the sum of the measures of the angles in any triangle is always 180 degrees.
For example, let's say you know that angle A measures x degrees and angle B measures y degrees. To find the measure of angle C (the third angle), you can use the following equation:
x + y + C = 180°
To solve for C, you can subtract x and y from both sides of the equation:
C = 180 - x - y
So, the measure of angle C is equal to 180 degrees minus the measure of angle A and angle B.
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