Answer:
reflection over the y-axis; dilation with a scale factor of 0.4; translation 8 units left and 8 units upStep-by-step explanation:
ReflectionThe first transformation changes the sign of the x-coordinate. That means a point that was some number of units (3, for example) right of the y-axis will be transformed to a point 3 untis left of the y-axis. It is reflected across the y-axis.
__
DilationThe second transformation multiplies each coordinate value by 0.4. A point that was some number of units (3, for example) away from the origin, will be transformed to a point 3×0.4 = 1.2 units from the origin. It is dilated by a factor of 0.4.
__
TranslationThe third transformation subtracts 8 from the x-coordinate and adds 8 to the y-coordinate. The x-coordinate is a measure of the distance to the right of the y-axis, so subtracting 8 from the x-coordinate means the point is 8 fewer units to the right of the y-axis. It is translated left 8 units.
Similarly, the y-coordinate is a measure of the distance up from the x-axis. Adding 8 to the y-coordinate will move the point 8 more units up from the x-axis. It is translated up 8 units.
A new car is purchased for 15100 dollars. The value of the car depreciates at 12. 25% per year. To the nearest year, how long will it be until the value of the car is 2300 dollars?
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill &\$2300\\ P=\textit{initial amount}\dotfill &\$15100\\ r=rate\to 12.25\%\to \frac{12.25}{100}\dotfill &0.1225\\ t=years \end{cases} \\\\\\ 2300=15100(1 - 0.1225)^{t}\implies \cfrac{2300}{15100}=(1 - 0.1225)^{t}\implies \cfrac{23}{151}=0.8775^t[/tex]
[tex]\log\left( \cfrac{23}{151} \right)=\log(0.8775^t)\implies \log\left( \cfrac{23}{151} \right)=t\log(0.8775) \\\\\\ \cfrac{~~\log\left( \frac{23}{151} \right)~~}{\log(0.8775)}=t\implies 14.4\approx t\qquad \textit{about 14 years and 146 days}[/tex]
1. 4 A box contains 300 discs of different colours. There are 100 pink discs, 100 blue discs and 100 orange discs. The discs of each colour are numbered from 0 to 99. Five discs are selected at random, one at a time, with replacement. Find
(i) the probability that no orange discs are selected. [3]
(ii) the probability that exactly 2 discs with numbers ending in a 6 are selected. [4]
(iii) the probability that exactly 2 orange discs with numbers ending in a 6 are selected. [4]
(iv) the mean and variance of the number of pink discs selected. [8]
1. 5 The mean number of defective batteries in packs of 20 is 1. 6. Use a binomial distribution to calculate the probability that a randomly chosen pack of 20 will have more than 2 defective batteries
The probability that no orange discs are selected is 0.1295 and the probability that exactly 2 discs with numbers ending in a 6 are selected is 0.0721.
How to calculate probability?The probability that no orange discs are selected will be:
= 200C5 / 300C5
= 0.1295
The probability that exactly 2 discs with numbers ending in a 6 are selected will be:
= (30C2 × 270C3) / (300C5)
= 0.0721
The probability that exactly 2 orange discs with numbers ending in a 6 are selected will be:
= (100C2 × 290C3) / (300C5)
= 0.0092
The mean of the number of pink discs selected will be:
= np
= 5 × 1/3
= 5/3
The variance will be:
= 5 × 1/3 × 2/3
= 10/9 = 1.11
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Bryce has $28. He spends $15. Then, his mom gives him $5 more. Which equation shows how Bryce can correctly find his total amount of money?
Answer:
28 - 15 + 5 = 18. Add and subtract will get you ,your answer. Bryce has $18
Step-by-step explanation:
Simple math hope this helped
ANS FASTestttttttttttttttttttttttt
Answer:
x is 75° ........................
6. Owen weighed 3 different bugs. List the bugs
in order from lightest to heaviest.
Bug
Fly
Spider
Bee
Weight
2.5 x 10-4 ounces
7.1 x 10-5 ounces
4 x 10-3 ounces
A. Spider, Fly, Bee
B. Fly, Bee, Spider
C. Spider, Bee, Fly
D. Fly, Spider, Bee
Find the volume of the prism.
Answer: The formula for the volume of a prism is obtained by taking the product of the base area and height of the prism. The volume of a prism is given as V = B × H where, "V" is the volume of the prism, "B" is the base area of the prism, and "H" is the height of the prism.
Which is an equation of the line containing the points (4, 6) and (6, 10) in standard form?
A. −2x+y=−2
B. 2x−y=−2
C. −2x−y=−22
D. −2x+y=−8
please show step by step
Answer:
A. −2x+y=−2
Step-by-step explanation:
If a sequence is 0,1,1,2,3,5 what is the 11th number in the sequence?
Answer:
55
Step-by-step explanation:
This is the Fibonacci sequence! Filling out the rest of the numbers, 55 is the 11th number in this sequence.
What's the slope and y-intercept of the equation 3x + 4y = 8? A) m = –3∕4; b = 2 B) m = –4; b = 3 C) m = 3∕4; b = –2 D) m = –3; b = –4
Answer:
A) m = –3∕4; b = 2Step-by-step explanation:
The slope-intercept form is
y = mx + b, where m- slope, b- y-interceptConvert the given equation into slope-intercept form
3x + 4y = 84y = - 3x + 8y = - 3/4x + 2The slope is:
m = - 3/4The y-intercept is:
b = 2Correct choice is A
First isolate y
3x+4y=84y=-3x+8y=-3/4x+8/4y=-3/4x+2Compare to slope intercept form y=mx+b
Slope=m=-3/4y intercept=b=23x+2x+6v-9g+hd+2v-1g
Answer:
5x+8x-10g+hd
Step-by-step explanation:
please mark me as brainlest
Hey there!
3x + 2x + 6v - 9g + hd + 2v - 1g
= 3x + 2x + 6v - 9g + 1hd + 2v - 1g
COMBINE the LIKE TERMS
= (3x + 2x) + (6v + 2v) - (9g - 1g) + (1hd)
= 3x + 2x + 6v + 2v - 9g - 1g + 1hd
= 5x + 7v - 10g + 1hd
= 5x + 7v - 10g + hd
= hd - 10g + 8v + 5x
Therefore, your answer is:
hd - 10g + 8v + 5x
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
A tank in the shape of a hemisphere has a radius of 7 feet. if the liquid that fills the tank has a density of 93 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
The total weight of the liquid that filled the hemispheric tank to the nearest full pounds is 66775 pounds.
What is the volume of an hemisphere?An hemisphere is half of a sphere. Therefore,
volume = 2 / 3 πr³
where,
r = radiusTherefore,
r = 7 feet
volume = 2 / 3 × 3.14 × 7³
volume = 2 / 3 × 3.14 × 343
volume = 2154.04 / 3
volume = 718.013333333
volume = 718.013
Therefore,
density = mass / volume
93 = mass / 718.013
mass = 718.013 × 93
mass = 66775.24
mass ≈ 66775 pounds
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James has 16 balloons . 1/4 of his ballons are red. How many red ballons does he have
Answer:
James has 4 red balloons
Step-by-step explanation:
16 × 1/4 = 4
You could also say 16 ÷ 4 = 4
Hope that helps!
Here, angles A is 23 degrees. What can we say about other angles B and C…. Help please
Answer:
Both are 157 degrees
Step-by-step explanation:
A and B form a linear pair, meaning together they should create 180 degrees. 180 - 23 = 157. Since B and C are vertical angles, they must both be the same. A vertical angle is when two angles are on opposite sides.
Answer:
Step-by-step explanation:
Linear pair: Two angles form linear pair if they are adjacent angles and their non common arms are opposite rays.
a +b = 180 {Linear pair}
23 + b = 180
b = 180 - 23
b = 157°
c = b {Vertically opposite angles are congruent}
c = 157°
Mandy bought a rectangular shelf that is 1 2/3 feet long and 5/8 feet wide. What is the area of the shelf? Enter your answer as a mixed number in simplest form by filling in the boxes. $$ ft²
The area of a rectangular shelf with length of 1 2 / 3 ft and width of 5 / 8 ft is [tex]1\frac{1}{24}[/tex] ft
How to find area of a rectangle?
A rectangle is a quadrilateral. It has 2 opposite sides equal to each other.
Therefore,
area of rectangle = lw
where
l = lengthw = widthTherefore,
length = 1 2 / 3 = 5 / 3 ft
width = 5 / 8 ft
area = 5 / 3 × 5 / 8
area = 25 / 24 ft
area = [tex]1\frac{1}{24}[/tex] ft
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*will give free brainliest* You estimated that you would need 252 more points to move up a level on your favorite video game. But after earning just 240more points, you leveled up! What was your percent error?
Answer:
5%
Step-by-step explanation:
(240 - 252/240)×100
oml please don’t say anything that doesn’t help,
do any of you know what 1 3/4 + 1/6 + ____= 7 1/2 is and can you tell me how you got it
Answer:
first convert mixed fraction to improper fraction then solve by taking LCM
hope the above process helps
Answer:
5 7/12
Step-by-step explanation:
1/6 can be converted to 2/12
1 3/4 can be converted to 1 9/12
Add them together, you'll get 1 11/12
7 1/2 is equal to 7 6/12
7 6/12 - 1 11/12 = 5 7/12
5 /12 is your answer
7k^2=21,952
Volume of cylinders, cones, and spheres
What is the answer please
Answer:56Step-by-step explanation:7k²=21952
k²=21952/7
k²=3136
k=√3136
k=56
PLS MARK ME AS BRAINLIEST
A path is made of red tiles and blue tiles.
1/5 of the tiles are red.
a) Write down the ratio of red tiles to blue tiles in its simplest form.
Answer:
The ratio of red tiles to blue tiles is 1 to 4.
Step-by-step explanation:
Since 1/5 of the tiles are red, 4/5 of the tiles are blue, giving the ratio of red tiles to blue tiles as 1 to 4.
Martin has a pencil case which contains 4 blue pens and 3 green pens. Martin picks a pen at random from the pencil case. He notes its colour, and then replaces it. He does this two more times. Work out the probability that when Martin takes three pens, exactly two are the same colour. (3 marks)
Answer: How do you not understand this?
I understand it perfectly.
Step-by-step explanation:
The probability that when Martin takes three pens, exactly two are the same color is 26.53%.
Probability
Given:
Blue pens=4
Green pens=3
Hence:
Probability=4³+3³÷(4+3)³
Probability=64+27/343
Probability=91/343
Probability=0.2653×100
Probability=25.53%
Therefore the probability that when Martin takes three pens, exactly two are the same color is 26.53%.
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Need help with solving for X
Answer:
[tex]\huge\boxed{\sf x = 10}[/tex]
Step-by-step explanation:
Since the two angles are complementary angles, the measures of these angles add up to 90 degrees.
5x + 25 + x + 5 = 90
5x + x + 25 + 5 = 90
6x + 30 = 90
Subtract 30 to both sides
6x = 90 - 30
6x = 60
Divide 6 to both sides
x = 60 / 6
x = 10
[tex]\rule[225]{225}{2}[/tex]
50 students each did a mathematics test. the mean score for these 50 students was 8.4. there were 30 boys. the mean score for these bots were 8.25. workout the mean score for the girls.
[(30 x 8,25) + (20 x n)] / 50 = 8,4
247,5 + 20 x n = 420
n = (420 - 247,5) : 20
n = 8,625
Reporting bots and absurd answers. will give brainliest when possible
Which is the equation of a hyperbola with directrices at y = ±2 and foci at (0, 6) and (0, −6)?
x squared over 12 minus y squared over 24 equals 1
x squared over 12 minus y squared over 48 equals 1
y squared over 12 minus x squared over 24 equals 1
y squared over 48 minus x squared over 12 equals 1
Answer:
The answer is y squared over 12 minus x squared over 24 equals 1
Step-by-step explanation:
which is the largest living thing?
Which function has the given properties below? the domain is the set of all real numbers. one x-intercept is (startfraction pi over 2 endfraction, 0 endfraction). the maximum value is 3. the y-intercept is (0, –3). y = –3sin(x) y = –3cos(x) y = 3sin(x) y = 3cos(x)
The required function with maximum value 3 and x and y-intercepts π/2 and 3 respectively is y=-3cos(x)
What is a function?
A function is a rule that relates two variables.
Let us check the x-intercept, y-intercept, and maximum value for each function.
1)y =-3Sin(x)
for x-intercept put y=0
0 = -3Sin(x)
Sin(x) =0
x=0
for y-intercept put x=0
y=-3Sin0
y=0
The maximum value of the given function =the lower limit of the range of -3Sin(x) i.e. 3
Similarly, for y = -3cos(x)
x-intercept =π/2
y-intercept = 3
Maximum value of function = lower limit of the range of 3cos(x) i.e. 3
Therefore, the required function with maximum value 3 and x and y-intercepts π/2 and 3 respectively is y=-3cos(x)
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Answer:
B. y = –3cos(x)
Step-by-step explanation:
Im extremely sure, have a great day
What is the volume of the following rectangular prism?
1 1/3 units
4 1/2units?
Answer:
6 units
Step-by-step explanation:
4 1/2 x 1 1/3= 6
100pts Help rounding!
Answer:
5
Step-by-step explanation:
5 158/559
= 5 + 158/559
= 5 + 0.28264758
= 5.28264758
= 5 (rounded to nearest whole number)
Answer:
5
Explanation:
[tex]\rightarrow \sf 5\dfrac{158}{559}[/tex]
[tex]\rightarrow \sf 5.282647585[/tex]
The whole number is the quotient in any fraction.
Help me please boghngghjgy
Answer:
224
Step-by-step explanation:
7×8×4= 224 that is the answer
Find the side labeled x.
help please
Answer:
x=7.51
Step-by-step explanation:
Tangent would be the easiest option here in this problem so to do this set up the proportion
[tex] \frac{ \tan(30) }{1} = \frac{x}{13}[/tex]
Cross multiply to get x=tan30(13)
Multiply tan30 by 13 to get the answer to x which is
x=7.51 rounded to the nearest hundredth
let a and b be the roots of the equation x^2 - 3x - 1 = 0. Find a^3 + b^3
hint: a^3 + b^3 = (a+b)(a^2-ab+b^2)
URGENT PLEASE
Answer:
Correct option is A)
Given,a,b are distance roots of x
3
+3x
2
−1=0
⇒a
3
+3a
2
−1=0 and b
3
+3b
2
−1=0
let the third root be c
then c
3
+3c
2
−1=0
product of roots =
a
−d
=
1
−(−1)
=1
⇒
abc=1
c=
ab
1
but c is root of x
3
+3x
2
−1=0
⇒c
3
+3x
2
−1=0
⇒
(ab)
3
1
+
(ab)
2
3
−1=0
⇒
1+3ab−(ab)
3
=0
.....(1)
in equation (1)
(ab)
3
−3(ab)−1=0
⇒ab is root of
x
3
−3x−1=0
∴(ab) is root of
x
3
−3x−1=0
How can you find percents
Answer:
To find the percentage of a number when it is in decimal form, you just need to multiply the decimal number by 100. For example, to convert 0.5 to a percentage, 0.5 x 100 = 50%. The second case involves a fraction. If the given number is in fractional form, first convert it to a decimal value and multiply by 100.
Step-by-step explanation:
. For example, to convert 0.5 to a percentage, 0.5 x 100 = 50%
hope this will help