Answer:
y = -⁸/₉(x + 1)² +5Step-by-step explanation:
y = a(x - h)² + k - vertex form of quadratic function with vertex (h, k)
y = a(x - (-1))² + 5 - vertex form of quadratic function with vertex (-1, 5)
y = a(x +1)² + 5
graph goes through (2, -3) so if x=2 then y =-3
-3 = a(2+1)² + 5
-3 -5 = a×3² + 5 - 5
-8 = 9a
a = -⁸/₉
So the equation of the function:
y = -⁸/₉(x + 1)² + 5
12. If a family is chosen at random from the set of all families with exactly three children, find the probability
that: (2Marks)
a) the family has three boys if it is known that one child is a boy.
b) the family has three boys if it is known that the first child is a boy.
Answer:
(a) 0.25
(b) 0.125
Step-by-step explanation:
The probability of the child being a boy or a girl is 50%.
That is, P (B) = 0.50 = P (G).
It is provided that the family selected has three children.
(a)
Compute the probability that the family has three boys if it is known that one child is a boy as follows:
[tex]P(3B|1B)=\frac{P(3B\cap 1B)}{P(1B)}[/tex]
[tex]=\frac{P(3B)}{P(1B)}\\\\=\frac{(0.50)^{3}}{0.50}\\\\=0.25[/tex]
Thus, the probability that the family has three boys if it is known that one child is a boy is 0.25.
(b)
Compute the probability that the family has three boys if it is known that the first child is a boy as follows:
The gender of the children are independent of each other.
So, if the first child is a boy then the probability of having three boys is:
P (3 boys | 1st boy) = P (1st boy) × P (2nd boy) × P (3rd boy)
= (0.50)³
= 0.125
Thus, the probability that the family has three boys if it is known that the first child is a boy is 0.125.
Eric walks 7 km East in 2 hours and then 2.5 km West in 1 hour.
___ km/hr is the average speed and ___ km/hr is the average velocity for the whole journey that Eric takes.
Answer:
Average speed = 3.17 km/h and Average velocity = 1.5 km/h
Step-by-step explanation:
It is given that,
Eric walks 7 km East in 2 hours and then 2.5 km West in 1 hour.
Average speed = distance/time
Distance = 7km + 2.5 km = 9.5 km
Time = 2 h + 1 h = 3 h
Average speed,
[tex]s=\dfrac{9.5\ km}{3\ h}\\\\s=3.17\ km/h[/tex]
Average velocity = displacement/time
Displacement = 7 km +(-2.5 km) = 4.5 km
Average velocity,
[tex]v=\dfrac{4.5\ km}{3\ h}\\\\v=1.5\ km/h[/tex]
So, 3.17 km/h is the average speed and 1.5 km/h is the average velocity for the whole journey that Eric takes.
A fruit basket has 6 apples.
It has twice as many oranges as apples and twice as many
apples as bananas. How many more oranges than bananas
are there? Write the equation & answer
Answer: There are 9 more oranges than bananas because there are 6 apples, 12 oranges, and 3 bananas. (12-3=9)
According to the diagram, which statement is NOT true?
Real Numbers
Irrational Numbers
Rational Numbers
Integers
Whole Numbers
Counting
Numbers
А
All counting numbers are also rational numbers.
All whole numbers are integers.
B
C All rational numbers are real numbers.
D
AB rational numbers are integers
Answer:
all rational numbers are intergers
Step-by-step explanation:
a and b are positive integers and a+b=2009!
what is the amount of ordered pairs of (a, b)?
Answer:
[tex]2000 \: and \: 9.[/tex]
[tex]it \: could \: be \: the \: sum \: of \: any \: two \: \\ positive \: integers \: so \: they \: are : \\ 2000 \: and \: 9[/tex]
Let's consider a much smaller value and work our way up to the factorial 2009!
Start with a+b = 2. The value 2 is the smallest right hand side possible since a > 0 and b > 0, so a = b = 1 is the smallest a,b possible.
The only solution to a+b = 2 is a = b = 1 as mentioned.
----------
Now move onto a+b = 3. We have two solutions:
a = 1, b = 2
a = 2, b = 1
-----------
Now move onto a+b = 4. We have three solutions
a = 1, b = 3
a = 2, b = 2
a = 3, b = 1
Note how 'a' counts up while b counts down. I have 'a' starting at the smallest value, and b is set to add with 'a', getting to the right hand side.
So 'a' counts up to 3, while b counts down from 3.
We cannot reach 4 since 0 is not allowed for a or b.
-------------
The conjecture is that a+b = k has k-1 positive integer solutions. A simple proof of this is to list out all solutions like so
a = 1, b = k-1
a = 2, b = k-2
a = 3, b = k-3
....
a = k-3, b = 3
a = k-2, b = 2
a = k-1, b = 1
Where k > 2
Going from 1 to k-1 is exactly k-1 items. It's similar to how {1,2,3,..,m} has m different integers in it. Replace m with k-1 and you have the same idea.
This confirms there are k-1 solutions listed above.
The last step is to simply replace k with 2009! and we have 2009! - 1 different ordered pair solutions
Since the factorial 2009! is so massive, it's best to not expand this out using a calculator. Many calculators would produce "overflow", or similar, if you tried to compute the factorial 2009!
Accrotime is a manufacturer of quartz crystal watches. Accrotime researchers have shown that the watches have an average life of 26 months before certain electronic components deteriorate, causing the watch to become unreliable. The standard deviation of watch lifetimes is 4 months, and the distribution of lifetimes is normal. A button hyperlink to the SALT program that reads: Use SALT. (a) If Accrotime guarantees a full refund on any defective watch for 2 years after purchase, what percentage of total production will the company expect to replace? (Round your answer to two decimal places.) Incorrect: Your answer is incorrect. % (b) If Accrotime does not want to make refunds on more than 6% of the watches it makes, how long should the guarantee period be (to the nearest month)? months
Answer:
a
[tex]P(X < 24 )= 21.186\% [/tex]
b
[tex]x = 19.78 \ months[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 26 \ months[/tex]
The standard deviation is [tex]\sigma = 4 \ months[/tex]
Generally 2 year is equal to 24 months
Generally the percentage of total production will the company expect to replace is mathematically represented as
[tex]P(X < 24 )= P(\frac{X - \mu }{ \sigma} < \frac{24 - 26}{4} )[/tex]
Generally [tex]\frac{X - \mu}{\sigma } =Z (The \ standardized \ value \ of \ X )[/tex]
[tex]P(X < 24 )= P(Z < -0.8 )[/tex]
Generally from the z-table
[tex]P(Z < -0.8) = 0.21186[/tex]
So
[tex]P(X < 24 )= 0.21186[/tex]
Converting to percentage
[tex]P(X < 24 )= 0.21186 * 100[/tex]
=> [tex]P(X < 24 )= 21.186\% [/tex]
Generally the duration that should be the guarantee period if Accrotime does not want to make refunds on more than 6% is mathematically evaluated as
[tex]P(X < x) = P(\frac{X - \mu }{\sigma} < \frac{x - 26}{4} )= 0.06[/tex]
=> [tex]P(X < x) = P(Z < \frac{x - 26}{4} )= 0.06[/tex]
From the normal distribution table the z-score for 0.06 at the lower tail is
[tex]z = -1.555[/tex]
So
[tex]\frac{x - 26}{4} = -1.555[/tex]
=> [tex]x = 19.78 \ months[/tex]
Four different towns in the same state grew in size due to a revitalization effort. The population of town A grew from 22,000 to 24,500 in 4 years. The population of town B grew from 31,200 to 34,770 in 6 years. The population of town C grew from 18,000 to 22,000 in 5 years. The population of town D grew from 32,000 to 34,100 in 3 years. Which town had the greatest average change in population over the corresponding time period?(1 point)
Answer:
Town C.
Step-by-step explanation:
Average change of population with time for town A = [tex] \frac{24,500 - 22,000}{4} = \frac{2,500}{4} = 625 [/tex]
Average change of population with time for town B = [tex] \frac{34,770 - 31,200}{6} = \frac{3,570}{6} = 595 [/tex]
Average change of population with time for town C = [tex] \frac{22,000 - 18,000}{5} = \frac{4,000}{5} = 800 [/tex]
Average change of population with time for town D = [tex] \frac{34,100 - 32,000}{3} = \frac{2,100}{3} = 700 [/tex]
Town C had the greatest average change in population over time (800/yr).
Answer:
its c
Step-by-step explanation:
whats the product of (3-2i) and (7+6i)?
Answer: the product is = 33+4i
Step-by-step explanation:
21+4i-12i^2
21+4i-12(-1) i^2=-1
21+4i+12
your answer would be 33+4i .
8x-13+4+1=90 helppppppp
Answer:
x = 49/4
Step-by-step explanation:
Sarah is planning to download music and has purchased a monthly package for $12.00 plus $0.60 for each song that she downloads. If Sarah’s bill this month totaled $39.00 how many songs did she download?
Answer:
Sarah downloaded 65 songs.
Write the two-column proof from start to finish.
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Please HELP!!!!!!!!!!!!!!!!
Answer:
sum = (180)(20) = 3600
Step-by-step explanation:
First...
(n-2)180˚ = Sum Of Interior Angles or SOIA
So...
(22-2)180 = SOIA
Then...
20*180 = SOIA
Finally...
3600 = SOIA
Please helpppp pleaseee
Answer:
-5x⁹ y⁵
Step-by-step explanation:
x⁵y² ((-5x⁴)(y³)) = -5x⁹ y⁵
Answer: x5y2(5x4y3) =5x9y5
Step-by-step explanation:
plss explain 30 points
Answer:
The height increases as the ferris wheel goes up.
Step-by-step explanation:
Answer:
The ferris wheel goes up and that is the height and when the ferris wheel goes down that is the time so the line goes up and down just like the graph shown
Step-by-step explanation:
a cookie recipe calls for 1 2/3 cups of sugar. If you plan on changing the recipe to make 2 1/2 times as much, how many cups of sugar will you need?
Answer:
4 1/6
Step-by-step explanation:
2 1/2 times 1 2/3 change those numbers into an improper fraction which are 5/2 for 2 1/2 and 5/3 for 1 2/3 multiply 5/2 and 5/3 you get 25/6 change the 25/6 into a mixed number and you get 4 1/6
Hank draws a line with a zero slope through the points
(–2, 4) and (3, b). Which value of b could represent Hank’s second point?
–3
–1
4
9
Answer:
It's 4
Step-by-step explanation:
Answer:
The answer is C which is 4
Step-by-step explanation:
I just took the test and got it right
Hopefully this helps you
pls mark brainlest
x - 17 = 32 * linear equations
Answer: x=49
x-17=32
Subtract 17 from both sides.
x=32+17
x=49
About 12 weeks ago, there were 21 mold spores found in a garden. After a few weeks of observation, it is determined that the number of mold spores in the garden is tripling every 6 weeks. The number of mold spores, M, at any given time in the garden is equal to the product of the initial amount of spores, I, and 3 to the power of n, where n is the number of times the amount of mold spores has tripled. How many mold spores are in the garden today?
Answer:
189 spores
Step-by-step explanation:
The number of mold spores triple every 6 weeks. So in 12 weeks, it has tripled twice.
Given that:
M = I x [tex]3^{n}[/tex]
where M is the number of mold spore, I is the initial amount of spores, and n is the number of times the amount of mold spores has tripled.
Since, I = 21 and n = 2, we have;
M = 21 x [tex]3^{2}[/tex]
= 21 x 9
= 189
There would be 189 spores in the garden today.
I WILL GIVE 30 POINTS PLEASE Sinorice put $7.200 in a savings account that pays 3.295 interest compounded annually.
After 3 years, he deposited another $5.000 in the account. What is the value of the account
after 8 years?
A $14 98240
B $15.116.25
C $15.596.30
D $16.073.60
how do i put 5x^2+6+3xy^5-2x in standard form
Answer:
it's 3xy^5 + 5x^2 -2x +6
Follow the steps and finish the solution.
7 (x minus 3) = 28
Distributive property: 7 x minus 21 = 28. Addition property of equality: 7 x = 49. Division property of equality: x = blank.
What is the value of x?
7
9
42
56
Answer:
X=7
Hope this helps, and have a Great Day. You got this!!!
Step-by-step explanation:
help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
neither
Step-by-step explanation:
Answer:
(c)
Step-by-step explanation:
If these are
Parallel, slope of both the lines is same.
Perpendicular, if they are -ve reciprocal of each other.
In y = mx + c, slope is m.
Compare,
Slope of y=4x+1, is 4.
of 8y-16=2x is 2/8 = 1/4, which is reciprocal of 4,but not -ve.
So it is neither ll nor perpendicular.
WILL MARK BRAINLIST!!!!
DBA Study Guide –
2.01 ESSENTIAL QUESTIONS
• What are the Transformations and how do they move?
• How can you tell the difference between the preimage and the transformed image by looking at the figures on a graph?
•
• 2.03 ESSENTIAL QUESTIONS
• What are the names of the Theorems that we use to prove triangles congruent?
• What does it mean for two shapes to be congruent?
2.04 ESSENTIAL QUESTIONS
How do you prove each of the following theorems using either a two-column, paragraph, or flow chart proof:
• Isosceles Triangle Theorem
2.06 ESSENTIAL QUESTIONS
• What are the characteristics of squares, rhombi, kites, and trapezoids?
Answer: These are some of the questions not all of them
There are four types of transformations: reflection, rotation, translation and enlargement. Translation (also known as Slide) moves a shape by sliding it up, down, sideways or diagonally, without turning it or making it bigger or smaller. Reflection (also known as Flip) in a line produces a mirror image in which corresponding points on the original shape and the mirror image are always the same distance from the mirror line. Rotation (also known as Turn) turns a shape through a clockwise or anti-clockwise angle about a fixed point known as the Centre of Rotation. All lines in the shape rotate through the same angle. Rotation, (just like reflection) changes the orientation and position of the shape, but everything else stays the same. Enlargement (also known as Dilation) is a transformation. However, it is different from reflection, rotation and translation because it changes the size of an object. Transformations which leave the dimensions of the object and its image unchanged are called isometric transformations. Examples of isometrics are reflection, rotation and translation. Transformations which do alter the dimension of the object when they act on them are called non-isometric transformation Examples are the enlargement. The image of a transformation is the shape after the transformation. The preimage of a transformation is the shape before the transformation. If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent. SAS: If any two angles and the included side are the same in both triangles, then the triangles are congruent. n geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
i need help ASAPPPP A spinner has 3 equal sections, one that is red, one yellow, and one blue. The spinner is spun 20 times and the results are recorded in the table.
Color Frequency
Red 7
Yellow 9
Blue 4
Based on these results, what is the experimental probability that the next time the spinner is spun it lands on yellow?
a.0.35
b.0.45
c.0.920
d.0.2
Answer:
B
Step-by-step explanation:
Hope this helps :)
If so mark brainliest
Solve for y.
24=8/3y
Simplify your answer as much as possible.
I can't tell necessarily what the question is but I'd it is 24= 8÷3y then y is 1/9
if the question is 24=8/3(y) then the answer is y=9
Answer:
24 = [tex]\frac{8}{3}[/tex] y
[tex]\frac{8}{3}[/tex] = 2.6 repeating
24 ÷ 2.6 repeating = 9
Step-by-step explanation:
Please help me with this problem and explain
Answer: 29
It is very simple, just substitute.
x = 9, y = 10
Replace the x and y in the expression to that.
You get: 9 + 10 + 10. Just add and you will get 29.
Answer:
9+10+10=29
Step-by-step explanation:
We know that x=9, so where ever we see x we know it is 9. We also know that y=10, so where ever we see y we know it is 10. So then we just replace the variables with our numbers then just add them. That is I got 9+10+10=29
Hope this helps!
solve this equation
6x+13=9x-8
Step-by-step explanation:
Hey there!
Given;
6x + 13 = 9x - 8
Shift "6x" to right side and "-8" to left side and simplify it to get answer.
13+8 = 9x-6x
21 = 3x
x= 21/3
Therefore, x= 7.
Hope it helps...
Coach Right is looking at his students' running times in order to place students into running groups. He is working on forming a group that matches Jim's pace of 4 miles in 38 minutes. Which of these student times would fit into a group that runs at the exact same rate as Jim?
Complete question :
Coach Right is looking at his students' running times in order to place students into running groups. He is working on forming a group that matches Jim's pace of 4 miles in 38 minutes. Which of these student times would fit into a group that runs at the exact same rate as Jim? Prax ran 6 miles in 57 minutes. Jose ran 5 miles in 45.5 minutes. Sandy ran 7 miles in 66.5 minutes. Zynep ran 3 miles in 27 minutes
Answer:
Prax and sandy
Step-by-step explanation:
Given that:
Jim's pace = 4 miles in 38 minutes
Jim's rate = Distance covered / time.
Rate = 4 / 38 = 0.1052631 miles /min
Prax ran 6 miles in 57 minutes:
Prax rate : 6miles / 57 mins = 0.1052631
Jose ran 5 miles in 45.5 minutes:
Jose's rate = 5 miles / 45.5 = 0.1098901 miles /
minute
Sandy ran 7 miles in 66.5 minutes:
Sandy's rate = 7 / 66.5 = 0.1052631 miles / minutes
Zynep ran 3 miles in 27 minutes:
Zynep's rate : 3 / 27 = 0.1111111 miles / minutes
A woman standing on a large rock at the edge of a lake is getting ready to swing from a rope that is tied to a branch that hangs over the water. The length of the rope the woman is holding is 7.3 m long. The woman hopes to land in the water at a point that is 13.7 m away from where she stands on the large rock. The angle between the point where the rope is tied and her landing spot in the water is 89°. What is the distance between the the point where the rope is tied and the point where she wants to land to the nearest tenth of a metre.
Answer:
6.4 m
Step-by-step explanation:
The image attached is a representation of the question. to the river hence the distance between the place where she landed and the rock where she was standing must be horizontal. We are now required to find the shortest vertical distance between the point where the rope was tied and the place where she wants to land.
Note that the woman used the rope to move down in
Applying the cosine rule;
[tex]c^{2} = a^{2} + b^{2} -2ab Cos C[/tex]
[tex]c^{2} = 13.7^{2} + 7.3^{2} - 2(13.7 *7.3) Cos 89o[/tex]
[tex]c^{2} = 6.4 m[/tex]
A cubic function is stretched by a factor of 0.4, opening downward and
shifted 10 units down and 5 units left.
Answer:
the answer is in the link
Step-by-step explanation:
https
bxaha zshkkkvxxxkvvvvwuqgceuuuegieg DONT KNO