Step-by-step explanation:
the problem description is seemingly contradicting itself.
"without replacement" means that you don't put the picked item back into the bag or "pool" of items.
and that means that after Rebecka picked a puppy, Aaron CANNOT pick the same one at all.
but then it says that they both may select the same one. which means it is WITH replacement.
so, what is it now ?
I have to give you both answers, and you will have to clarify with your original question or directly with your teacher what is the true condition.
in any case, a probability is always
desired cases / total possible cases.
WITH replacement (they can both pick the same puppy) :
there are 10 puppies, from which 3 are poodles.
so, total possible cases = 10, desired cases = 3
the probability to pick a poodle at the 1st pick = 3/10.
the picked puppy goes back.
the probability to pick a poodle at the 2nd pick = 3/10.
the probability that both picks are poodles is
3/10 × 3/10 = 9/100 = 0.09
WITHOUT replacement :
the first picked puppy is not returned to the group of 10 puppies, so, it can't be picked again, and the number of available puppies gets less as each puppy is removed. this changes the probabilities.
at the beginning we have 10 puppies, from which 3 are poodles.
the probability to pick a poodle at the 1st pick = 3/10.
the picked puppy does NOT go back.
now we have 9 puppies for Aaron to pick from. and for our desired cases for the second pick we have to combine it with the outcome, that the first pick was a poodle.
that means we have only 2 poodles left in the group of 9 puppies.
the probability to pick a poodle at the 2nd pick = 2/9.
the probability that both picks are poodles is therefore
3/10 × 2/9 = 6/90 = 1/15 = 0.066666666...
can disjunction introduction (either ∨il or ∨ir ) be used to derive any type of formula other than a disjunction?
It is impossible to use a disjunction introduction to derive any other type of formula besides disjunctive formulas.
What is Disjunction Introduction?A rule of inference in propositional logic and virtually every other deduction system is referred to as disjunction introduction.
It is right to state that it is not possible to use a disjunction introduction to derive any other type of formula besides disjunctive formulas.
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Identify the constant of proportionality from the table.
xy
3 6
4 8
7 14
9 18
A car drives at a speed of 90 km/h for 2 hours and 20 minutes
How far does the car drive?
Answer:
210km
Step-by-step explanation:
2hours = 180km
2hours = 120minutes
40mins =180/3
=60km
20mins=60/2
=30km
2h and 20mins =30+180
=210km
Answer:
210kms
Step-by-step explanation:
Speed of the car per hour = 90km/h
or, speed of the car per minute = 90/60kms=1.5km/minute
Now,
car drives for 2hours and 20 minutes
or, (2*60 +20) minutes= 140minutes
Distance of the car drive= minutes travelled* speed per minute
= 140*1.5kms
=210kms
Five sisters bought a present for their mother. They received a 10% discount on the original price of the gift. After the discount was taken, each sister paid $5.40. What was the original price of the gift?
I need an answer soon! Pleasle
Answer:
$30 is the original price.
Step-by-step explanation:
Let x be the original price of the gift. The sisters got a 10% discount, so the price paid by them is 0.90x.
The five sisters each paid $5.40, so the total they paid was:
5*($5.40) = $27.
This is equal to the 0.90x:
0.90x = $27
x = $27/0.90
x = $30
Chocolates
how many solutions exists for the given equation?
3x+13=3(x+6)+1
Answer:
No Solutions.
Step-by-step explanation:
original equation
3x+13 = 3(x+6)+1
distribute 3
3x+13 = 3x+18+1
simplify
3x+13 = 3x+19
since the slope is the same for both equations and the y-intercept is different the two equations are parallel meaning they will never intersect so there are no solutions.
Answer:
No solutions
Step-by-step explanation:
3x + 13 = 3 (x + 6) + 1
3x + 13 = 3x + 18 + 1
3x + 13 = 3x + 19
3x + 13 = 3x + 19 meaning no solution since they aren't equivalent to each other
Here is a list of ages (years) of children in a room:
8
,
8
,
9
,
5
,
10
,
4
,
9
State the median.
Answer:
5
Step-by-step explanation:
median basically means the number which is in the middle so 8,8,9, 5 ,10,4,9
the median is 5 because left and right middle is 5 that's why it is median
On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2). Everything to the left of the line is shaded.
Which linear inequality is represented by the graph?
y < 3x + 2
y > 3x + 2
y < One-thirdx + 2
y > One-thirdx + 2
The correct answer is option B which is y > 3x + 2.
What is inequality?Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
The given statement says that On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2)
The plot of the inequality is given in the graph attached with the answer the inequality will be y > 3x +2 which passes through the points (-3,-7 ) and ( 0, 2 ).
Therefore the correct answer is option B which is y > 3x + 2.
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Write the ratio using fraction notation and reduce.
HINT: Be sure to compare like units.
$5 to $35
A. 7
B. 15
C. 5
D. 17
The ratio using fraction notation of $5 to $35 would be 7.
What is a fraction?A fraction represents a part of a number or any number of equal parts.
To convert a ratio into a fraction,
We will simply use the first number as the numerator and the second number as the denominator.
So the fraction = 35/5.
= 7
Since there are no more common factors, the fraction is in its lowest form which is 7.
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help please!!!!!!!!!
describe the effect of the transformation (x,y) to (x,y+4)
A. vertical stretch without reflection
B. horizontal translation of 4 units
C. vertical stretch with reflection
D. Vertical translation of 4 units
Which equation would have real zero(s) corresponding to the x-intercept(s) of the graph below?
Answer:
the first one listed (y = -[tex]2^{x}[/tex] + 4)
Step-by-step explanation:
a 0 at an x-intercept means that when plugging in that number, you get a 0 as a y-value.
So, the easiest method to use is to plug x=2 into each equation listed, because we can see that (2,0) is a point on this graph
if y= -[tex]2^x\\[/tex] + 4
y = -2² + 4
y = -4 + 4
y = 0
This means that this graph has corresponding real zero(s) to the function y= [tex]-2^x[/tex] + 4
(I chose which graph to test by looking to see which option seemed right)
Kelsey has $100 in an account the interest-rate is 11% compounded annually to the nearest cent how much will she have in two years
Answer:
$123.21 (nearest cent)
Step-by-step explanation:
Annual Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+r\right)^{t} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)t = time (in years)Given:
P = $100r = 11% = 0.11t = 2 yearsSubstitute the given values into the formula and solve for A:
[tex]\implies \sf A=100\left(1+0.11\right)^{2}[/tex]
[tex]\implies \sf A=100\left(1.11\right)^{2}[/tex]
[tex]\implies \sf A=123.21[/tex]
Therefore, the value of the account in 2 years will be $123.21 (nearest cent).
Consider the quadratic function y = 1/5 (x – 2)2 + 5.
Which statements are true about the function and its graph? Select TWO options.
A) The vertex of the function is (–2, 5).
B) There are no real roots for the function.
C) The graph of the function opens down.
D) The graph contains the point (2, 5).
E) The graph intersects the x-axis at one unique point.
Answer:
B and D
Step-by-step explanation:
vertex(2,5) so D is correct
there are no real roots for the function B is correct
I want to verify my work answer for the below SSAT question.
Thank you
Cindy throws a rock in the air. The rock's height, y, in feet, with respect to time, x, in seconds can be modeled by the function y=-2x^2+10x+28. When does the rock hit the ground in seconds
My work:
y=-2x^2+10x+28
0= -2(x^2-5x-14) (While knowing that the zero is supposed to be there, I don't understand why 0= -2(x^2-5x-14) )
(x-7)(x+2)
(-7,+2)
I put 2 as the answer, but when checking it was 7?
What part did I do wrong?
Answer:
7
Step-by-step explanation:
You were correct in setting the equation equal to 0 because the problem is asking for when the rock hits the ground and in this problem, you may assume that the ground is y=0, unless the problem says otherwise.
Ok so where you went wrong is that when you factored out and got
(x-7)(x+2), which is correct, you forgot to set these equal to zero (because your actual equation is set to zero). So you should have
x-7 = 0
and
x+2 = 0
and this gives the actual answers +7 and -2. And since time cant be negative its 7 seconds.
This was a silly mistake and happens a lot more often than you think, so I wouldn't worry too much but make sure you practice more, better to lose points on harder questions than easy ones.
Good luck with your exam !
Answer:
7 seconds
Step-by-step explanation:
Given function:
[tex]y=-2x^2+10x+28[/tex]
where:
y = height above the ground (in feet)x = time (in seconds)To find the time when the rock hits the ground, set the equation to zero and solve for x.
First, simplify by factoring out the common term -2:
[tex]\implies -2(x^2-5x-14)=0[/tex]
Divide both sides by -2:
[tex]\implies x^2-5x-14=0[/tex]
To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to ac and sum to b.
[tex]\implies ac=1 \cdot -14=-14[/tex]
[tex]\implies b=-5[/tex]
Therefore, the two numbers that multiply to -14 and sum to -5 are: -7 and 2
Rewrite b as the sum of these two numbers:
[tex]\implies x^2-7x+2x-14=0[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies x(x-7)+2(x-7)=0[/tex]
Factor out the common term (x - 7):
[tex]\implies (x+2)(x-7)=0[/tex]
Therefore:
[tex]\implies x+2=0 \implies x=-2[/tex]
[tex]\implies x-7=0 \implies x=7[/tex]
As time cannot be negative, the rock hits the ground in 7 seconds.
does someone mind helping me with this problem? Thank you!
Answer:
-20
2(xy-7)=-20 with x=-1 y=3
Step-by-step explanation:
2(xy-7)=?
When variables are connected such as xy, this means to multiply.
x=-1
y=3
Multiply the x and the y together.
-1*3=-3. Plug that into the equation.
2(-3-7)=?
Subtract the inside the parenthesis.
2(-10)=?
Multiply. Remember when multiplying a positive and a negative the answer will always be a negative.
2(-10)=-20
This means that 2(xy-7)=-20 with the x=-1 and y=3.
Hope this helps!
If not, I am sorry.
Determine the length
The length of KI is 10 cms.
What is Length?The skill of measuring the lengths of objects and understanding the units of length is very crucial as it helps us to interact with our environment in a more organized manner.
Here, ΔRJS ≈ Δ IJK
then JR / JI = SR/KI
1/2 =5 /ki
kI = 5 X 2
kI = 10 units.
Thus, The length of KI is 10 cms.
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PLEASE HELP!
Find the degree measure of each numbered angle.
Answer:
1=76°
2=76°
3=36°
Step-by-step explanation:
To find 1, add the other angles in the triangle and subtract by 180.
85+19=104
180-104=76.
1 is equal to 2 so 2=76
To find 3, add 76 and 68, then subtract by 180.
76+68=144
180+144=36
3=36
Hope this helps!
If not, I am sorry.
Answer:
m∠1 = 76°
m∠2 = 76°
m∠3 = 36°
Step-by-step explanation:
The interior angles in a triangle sum to 180°
⇒ m∠1 + 85° + 19° = 180°
⇒ m∠1 + 104° = 180°
⇒ m∠1 + 104° - 104° = 180° - 104°
⇒ m∠1 = 76°
Vertical Angle Theorem
When two straight lines intersect, they form two pairs of angles. The vertically opposite (non-adjacent) angles are congruent.
⇒ m∠2 = m∠1
⇒ m∠2 = 76°
The interior angles in a triangle sum to 180°
⇒ m∠2 + m∠3 + 68° = 180°
⇒ 76° + m∠3 + 68° = 180°
⇒ m∠3 + 144° = 180°
⇒ m∠3 + 144° - 144°= 180° - 144°
⇒ m∠3 = 36°
DRAW AND WRITE SHORT NOTES ON THE FOLLOWING Properties of the various types 1 Triangle: (Equilateral, Isoceles, Right - angled, Scalene
2. Quadrilaterals. (square, rectangle, Rhombus, parallelograph trapezium, kite
ASAP PLEASE FIRST AND CORRECT WILL GRT BRAINLIEST ANSWER
Answer:
Triangles:
- Equilateral: Has three equal sides
- Isosceles: Has two equal sides
- Right angled: One angle of a right angle triangle measures 90 degrees
- Scalene: All sides are different lengths
Quadrilaterals:
- Square: Has four right angles and four equal sides
- Rectangle: Has four right angles and opposite sides are equal
- Rhombus: A parallelogram with four equal sides
- Parallelogram: Opposite sides are equal and parallel
- Trapezium: At least one set of sides are parallel
- Kite: Two pairs of adjacent sides are the same length
In the diagram, a circle centered at the origin, a right triangle, and the Pythagorean theorem are used to derive the equation of a circle, x2 + y2 = r2.
On a coordinate plane, circle Q is centered at the origin with radius r. Triangle P Q S is shown. Point Q is at (0, 0) and points P is at (x, y). The length of Q P is r, the length of P S is y, and the length of Q S is x. Angle P S Q is a right angle.
If the center of the circle were moved from the origin to the point (h, k) and point P at (x, y) remains on the edge of the circle, which could represent the equation of the new circle?
(h + x)2 + (k + y)2 = r2
(x – h)2 + (y – k)2 = r2
(k + x)2 + (h + y)2 = r2
(x – k)2 + (y – h)2 = r2 7-foot radius.
Based on the information provided, the equation of this new circle is equal to: B. (x - h)² + (y - k)² = r²
The equation of a circle.Mathematically, the equation of a circle can be derived by using Pythagorean theorem;
x² + y² = r²
Where:
h and k represents the coordinates at the center.r is the radius of a circle.After translating h units along the x-axis and k units along y-axis on a coordinate plane, the equation of this new circle is given by:
(x - h)² + (y - k)² = r²
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Answer: B) (x – h)2 + (y – k)2 = r2
Step-by-step explanation:
If you vertically stretch the exponential function f(x)=2^x by a factor of 3 what is the equation of the new function
The new equation will become f(x) = 3([tex]2^{x}[/tex]).
The given information is the stretch factor which is 3 and the equation f(x)=[tex]2^{x}[/tex].
When there is a vertical strecth factor, you need to multiply the equation by the stretch factor.
By stretching the function, the value of y has to be multiplied by 3, will now be equal to 3f(x)
The new equation will become f(x) = 3([tex]2^{x}[/tex]).
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please be quick im being timed
Answer:
this one
Step-by-step explanation:
What is the value of y? 17.5ft 12.5ft 11.6ft 16.5ft
Answer:
y = 16.5 ft
Step-by-step explanation:
• in the right triangle BCD :
cos(∠BCD) = 8/14
________
• In the right triangle ABC :
cos(∠BCA) = 14/(8+y)
________
Since ∠BCD and ∠BCA are the same one
then
cos(∠BCD) = cos(∠BCA)
Therefore
[tex]\frac{8}{14} =\frac{14}{y+8}[/tex]
[tex]\Longleftrightarrow 8(y+8)=14^2[/tex]
[tex]\Longleftrightarrow 8y+64=196[/tex]
[tex]\Longleftrightarrow 8y=196-64[/tex]
[tex]\Longleftrightarrow 8y=132[/tex]
[tex]\Longleftrightarrow y=\frac{132}{8}[/tex]
[tex]\Longleftrightarrow y=16.5[/tex]
Find the value of x. Round the length to the nearest tenth.
Answer:
5.1 yd
Step-by-step explanation:
tan(25°) = x/11
x = 11tan(25°)=5.1 yd
whats 27 x 300 / 34 x 6
Answer:
Use Calculator:
Approximately. 1429.411
Step-by-step explanation:
Hope it Helps!!!
Please explain the bottom two the ones with the explanation box
First we must solve the bottom situations.
___________________________________________ (2A and 2B)
First expression (2A): 2v+8.3+2v-6.1
⇒ Collect like terms
(2v + 2v) + (8.3 - 6.1)
⇒ Simplify
4b + 2.2
Second expression (2B): 3v+14.4-v
⇒ Collect like terms
(3v - v) + 14.4
⇒ Simplify
2v + 14.4
They are not equivalent because when simplified they both have different coefficients and constants each of different values.
_____________________________________________ (4A and 4B)
First expression (4A): 10 + 3 (1/3x + 2)
⇒ Simplify 1/3x to x/3.
10 + 3(x/3 + 2)
⇒ Expand by distributing terms.
10 + x + 6
⇒ Collect like terms.
x + (10 + 6)
⇒ Simplify.
x + 16
Second expression: x + 16
This expression can not be simplified any further. This is because it is a simplified version of another expression.
These expressions are equivalent because expression 4B is the simplified version of expression 4A.
______________________________________
Level: 7th Grade
Unit: Distributing and Combing Like Terms
What is the standard form of 0.00849
Answer:
8.49 × 10⁻³
Explanation:
Standard form of a number: A. × 10ᵇ
(where 'A' is the number, b is the exponent over 10)
For the number "0.00849", move the decimal point 3 places right so the exponent of 10 is -3.
Standard form: 8.49 × 10⁻³
Other examples of standard/scientific forms are: standard forms
i) 0.043, move the decimal point 2 places right = 4.3 × 10⁻²
ii) 4030, move the decimal point 3 places left = 4.03 × 10³
Answer:
when a number is given in that manner you have to take that decimal between two whole numbers.
and that is the main reason why I took that decimal from 0.0 to 8.49 and since it went towards the right my answer is going to be 8.49 *10 raised to negative 3.
The hollow sphere, in which the circus motorcyclist performs his stunts, has a diameter of 7 m. Find the area available to the motorcyclist for riding.
[tex]\huge\color{red} {\boxed{\tt{A}}} \color{blue} {\boxed{\tt{N}}} \color{hotpink}{\boxed{\tt{S}}} \color{blueviolet}{\boxed{\tt{W}}} \color{fuchsia}{\boxed{\tt{E}}}\color{lavender}{\boxed{\tt{R}}}[/tex]
[tex] \red{ \star} \pmb{Diameter \: of \: the \: sphere = 7 m}[/tex]
[tex] \red{ \star} \pmb{Radius =\frac{7}{2} = 3.5 m}[/tex]
[tex] \pink{\underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}[/tex]
[tex] \sf{Area \: available \: to \: motorcyclist \: for \: riding = Area \: of \: sphere}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{= 4πr^2}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{= 4*\frac{22}{7}*3.5*3.5}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{= 154}[/tex]
The area available to the motorcyclist for riding is 154 m²
Diameter of the sphere = 7m
[tex]{Radius =\frac{7}{2} = 3.5 m}[/tex]
Area available to motorcyclist for riding = Area of sphere
[tex]{= 4πr^2} \\ \\ {= 4*\frac{22}{7}*3.5*3.5} \\ \\ {= 154}.[/tex]
The area available to the motorcyclist for riding is 154 m²
Which equation justifies why 93 - ?
=
(0³) 1_9(²+³)_9
93
(³)
93
³_9(²+³)=9
(0³) -
93
93
=9=9
_g(¹-³)_9
=9
=9
The equation that justifies [tex]9^{1/3}=\sqrt[3]{9}[/tex] is [tex](9^{1/3}) ^{3} = 9^{3/3} = 9[/tex]
How to find equation that justifies another?The expression given is [tex]9^{1/3}=\sqrt[3]{9}[/tex].
The equation that justifies [tex]9^{1/3}=\sqrt[3]{9}[/tex] is as follows:
Therefore, using indices law,
[tex]a^{x/y} =\sqrt[y]{a^{x} }[/tex]
Hence,
[tex]9^{1/3}=\sqrt[3]{9}[/tex]
Therefore, the equation that shows it is correct is as follows;
[tex](9^{1/3}) ^{3} = 9^{3/3} = 9[/tex]
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x(y − 3) + n(3 − y)
5/8 divided by 15/32
Answer: [tex]\frac{4}{3}[/tex] or about 1.333
Step-by-step explanation:
We will use the "keep, change, flip" method to solve. Keep the first number the same, change the division to multiplication, and flip the second number so we have the reciprocal.
[tex]\displaystyle \frac{\frac{5}{8} }{\frac{15}{32} } \,\,\,\,\text{ becomes } \,\,\,\,\frac{5}{8} *\frac{32}{15} =\frac{5*32}{8*15} =\frac{160}{120} =\frac{4}{3}[/tex]
Answer: 4/3
Step-by-step explanation:
find the reciprocal of the divisor
15/32
32/15
Now multiply it with the dividend
5/8
15/32
=5/8
32/15
=5/32
8/15
=160/120
after reducing the fraction the answer is 4/3
in mix form 1 1/3
