Using it's concept, it is found that there is a 0.1541 = 15.41% probability that the first three balls are drawn out of the box alternated in colour.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Considering the situation described, the ways that alternate colored balls can be taken with the probabilities given as follows:
R(5/8) - W(3/9) - R(5/11).W(3/8) - R(5/10) - W(5/11).Hence the probability that the first three balls are drawn out of the box alternated in colour is given by:
[tex]p = \frac{5}{8} \times \frac{3}{9} \times \frac{5}{11} + \frac{3}{8} \times \frac{5}{10} \times \frac{5}{11} = 0.0689 + 0.0852 = 0.1541[/tex].
0.1541 = 15.41% probability that the first three balls are drawn out of the box alternated in colour.
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Raya buys a van for £9500 plus VAT at 20%
Raya pays a deposit for the van.
She then pays the rest of the cost in 12 equal payments of £665 each month.
Find the ratio of the deposit Ray pays to the total of the 12 equal payments.
Give your answer in its simplest form.
Step-by-step explanation:
yo thara bhai joginder tu he ek bndr
i need help i don’t know how to solve these!
Its actually pretty simple, all you do is graph both inequalities and wherever both of the shaded areas overlap is where all of the solutions will be. Hope this helps
Graph the function.
For the function whose graph is shown below, which is the correct formula for the function?
Answer:
[tex]\displaystyle{y=-3x-1}[/tex]
Step-by-step explanation:
I have two methods: standard-learning which will explain overall mathematically - basically formula, etc. - while the other one trick-tips method will rely on choices rather mathematical calculations but with explanation on why and how.
Standard-LearningFirst, let’s pick two points that are integers since they are easily to be found via graphs. We see that (-1,2) and (0,-1) is a part of the graph so now we finally have picked two points for our calculations.
When we have finally picked two points, we will be using them for slope calculation. This part is crucial for finding an equation of a line because a line has to contain slope in its equation.
To calculate the slope, we use rise over run formula which is:
[tex]\displaystyle{\dfrac{\Delta y}{\Delta x} = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
Note that [tex]\displaystyle{\Delta}[/tex] is delta - in both mathematic and physics, it means changes in.
So, we will be using those two points that we have picked to substitute in the slope formula. Let’s determine that [tex]\displaystyle{(x_2,y_2)=(-1,2)}[/tex] and [tex]\displaystyle{(x_1,y_1)=(0,-1)}[/tex].
Therefore, our slope will be:
[tex]\displaystyle{m=\dfrac{2-(-1)}{-1-0}}\\\\\displaystyle{m=\dfrac{2+1}{-1}}\\\\\displaystyle{m=-3}[/tex]
Next, find the y-intercept. From the graph, we see that the graph intercepts at (0,-1) which is y-intercept so we will only use y-value. Hence, b = -1.
From the slope-intercept form:
[tex]\displaystyle{y=mx+b}[/tex]
Substitute m (slope) = -3 and b (y-intercept) = -1. Hence, the equation of line is:
[tex]\displaystyle{y=-3x-1}[/tex]
Fast Way (Trick-Tips)Relying on choices and knowledge of graph, notice that there are slopes of 3 and -3.
Keep in mind that if slope is negative, it will decrease down and if slope is positive, it will increase up.
Therefore, cut off all choices with positive slopes which are 1 and 3. We are now left with 2 and 4.
Next, look at the graph and tell its y-intercept. It intercepts y at y = -1 so we take value of -1.
So choice 4 is cut off and now we have choice 2 as the answer.
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Which ordered pair would form a proportional relationship with the point graphed below?
On a coordinate plane, a line goes through points (0, 0), (10, 40) and (negative 10, negative 40).
(40, 10)
(–5, –10)
(5, 20)
(–10, –20)
Answer:
(5,20)
Step-by-step explanation:
divide both sides of (10, 40) by the same number 2 and you will get (5,20). The points should all lie on the same straight line to form a proportional relationship.
Answer: 5,20
Step-by-step explanation:
find the new prices after the given percentage increases.
a] £35 increased by 10%
b} £105.99 increased by 12%
Answer:
a] 38.5$
b] 118.71$
Step-by-step explanation:
A)35$ was increased by 10%
So:
10% of 35$
10/100 x 35 ($)
3.5$
So 35$ was increased by 3.5$ and the new price is 38.5$
B)105.99$ was increased by 12%
So:
12% of 105.99$
12/100 x 105.99$
=12.7188$
Let's round it to the nearest hundredths:
12.72$
So 105.99$ was increased by 12.72$ and the new price is 118.71$
HOPE IT HELPS :D
Tip: "of" means multiplication in Maths.
How many complex roots does the equation 0=3x5−x4−5x2+1 have?
The given polynomial equation 3x⁵ − x⁴ − 5x² + 1 = 0 has two complex roots.
What is a polynomial?A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.
The given polynomial equation below is:
0 = 3x⁵ − x⁴ − 5x² + 1
3x⁵ − x⁴ − 5x² + 1 = 0
The given polynomial equation is a polynomial of degree 5.
The simplest method is to solve it graphically using a graphing program.
Clearly, the polynomial equation is a degree 5 equation, hence it has a maximum of 5 roots.
We may now locate the roots of the equation using the graph.
Since there are 3 real roots, the remaining are two complexes, so there are 2 complex roots
Hence, the given polynomial equation 3x⁵ − x⁴ − 5x² + 1 = 0 has two complex roots.
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What is 9 squared?
Why?
Why do we call this "Squared"?
What is 5 cubed?
Why?
Why do we call this "Cubed"?
Answer:
The squared root of 9 is 3
Why - Half of 9 is 3
Why do we called this squared - It is the positive solution of the equation x2 = 9. The number 9 is a perfect square.
5 Cubed is equal to 125
Why - The number 125 on prime factorization gives 5 × 5 × 5. On combining the prime factors in groups of 3 gives 5
Why do we call this cubed = The cube of a number is that number times itself times itself. 5 cubed, denoted 53, is equal to 5×5×5, or 125.
15. 3x-5=3
16. 3(x-2) = 4(x + 3)
17. +3=
18. 2==
19. 4-2-3
X+2
20.-2-3-3
21. 쭉 = 큭
22. 2x-5-1=3-x
3. 2x + ==3(x-1)
4. 10x-1=x+4
5. k=8k-2
6. -x + 2 = 3x-27
4
7. 1-6x = -x +
B.
9. 2-(x + 1) = 2 + 5x
D. 2(1-x) = 10 - (x + 2)
. 9x - (4x - 5) = 3x - 11
x-9=3(x + 1)
-xx-2)-4=x+6▸
+ 2x
6(5-4x) = -4(5x + 11)
Answer:
tgnjfgznjE XVNJ
Step-by-step explanation:
rtjtejWEJAREfnndzjt
Answer:
15. 2.66
16. - 18
17. Impossible
18. Impossible
19. - 1
20. - 8
21.
On a coordinate plane, a line goes through (negative 2, negative 4) and (2, 2). a point is at (negative 3, 1). what is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (−3, 1)? y – 1=negative three-halves(x 3) y – 1=negative two-thirds(x 3) y – 1= two-thirds(x 3) y – 1= three-halves(x 3)
The equation, in point-slope form, of the line that is parallel to the given line and passes through the point is y - 1 = 3/2(x+3)
Equation of a lineA line is the distance between two points. The equation of a line in point-slope form is expressed as:
y - y0 = m(x-x0)
Given the coordinates (-2, -4) and (2, 2) on the line, the slope is expressed as:
Slope = 2-(-4)/2-(-2)
Slope = (6)/4
Slope = 3/2
Find the equation of the line
y -(1) = 3/2(x-(-3))
y - 1 = 3/2(x+3)
Hence the equation, in point-slope form, of the line that is parallel to the given line and passes through the point is y - 1 = 3/2(x+3)
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Answer:
d
Step-by-step explanation:
If p() = x2 - 1 and q(x) - 5(x-1), which expression is equivalent to (p - q)(x)?
Answer:
[tex]\text{If p(x) = x2 - 1 and q(x) = 5(x - 1), the expression which is equivalent to}[/tex] [tex]\text{ (p - q)(x) is (x2 - 1) - 5(x - 1).}[/tex]
Step-by-step explanation:
Given:
p(x) = 2x2 - 1q(x) = 3(x - 1)To find:
(p - q)(x)We know:
(p - q)(x) = p(x) - q(x)Substitute
(2x^2 - 1) - 3(x - 1)[tex]\text{Therefore, the expression equivalent to (p - q)(x) is (2x2 - 1) - 3(x - 1).}[/tex]
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
Answer:
2.3p – 10.1 = 6.49p – 4 [tex]\huge \checkmark[/tex]
230p – 1010 = 650p – 400 – p [tex]\huge \checkmark[/tex]
Step-by-step explanation:
……………………………………………
2.3p – 10.1 = 6.5p – 4 – 0.01p
⇔ 2.3p – 10.1 = (6.5p – 0.01p) – 4
⇔ 2.3p – 10.1 = (6.5 – 0.01)p – 4
⇔ 2.3p – 10.1 = (6.49)p – 4
⇔ 2.3p – 10.1 = 6.49p – 4
_______________________
_______________________
2.3p – 10.1 = 6.5p – 4 – 0.01p
⇔ 100 × (2.3p – 10.1) = 100 × (6.5p – 4 – 0.01p) multiply both sides by 100
⇔ 100 × (2.3p – 10.1) = 100 × (6.5p – 4 – 0.01p)
⇔ 230p – 1010 = 650p – 400 – p
……………………………………………………
Jose paid $1.12 for a dozen eggs at his local grocery store. Determine the cost of 18 eggs.
Answer:
$1.68
Step-by-step explanation:
1 dozen is 12.
18 is the same as 12 + 6
6 eggs is half of 12 eggs.
Since 12 eggs cost $1.12, then 6 eggs cost half of $1.12, or $1.12/2 = $0.56.
18 = 12 + 6, so
the price of 18 eggs = the price of 12 eggs + the price of 6 eggs.
price of 18 eggs = $1.12 + $0.56 = $1.68
Expand & simplify
3(t+5)+5(t−6)
Answer:
8t - 15
Explanation:
⇒ 3(t+5)+5(t−6)
distribute inside parenthesis
⇒ 3(t) + 3(5) + 5(t) + 5(-6)
multiply the variables
⇒ 3t + 15 + 5t - 30
collect like terms
⇒ 3t + 5t + 15 - 30
add/ subtract like terms
⇒ 8t - 15
Solution: 8t-15
Detailed explanation:
First the problem asks us to expand
[tex]\tt 3(t+5)=3\cdot t +3\cdot5=3t+15[/tex]
Similarly
[tex]\tt 5(t-6)=5\cdot t -5\cdot 6=5t-30[/tex]
Therefore
[tex]\tt 3t+15+5t-30[/tex]
Upon combining like terms
[tex]\tt 8t+15-30[/tex]
Upon doing this further
[tex]\tt 8t-15[/tex]
In AABC, what is the value of x?
Answer:
x = 6.5
Step-by-step explanation:
* since it's a triangle ALL the angles inside should give you 180° * Equate everything to 180°
8x + 10x - 10°+ 10x + 8° = 180°( sum of angles on a triangle)
28x - 2° = 180° * group like terms*
28x = 182°
x = 6.5
If 1=3 2=3 3=5 4=4 5=4 then 6=?
The value of the 6 is 3.
If you write 1 in word then you will write one and if you count the letter it will give you 3
Similarly, if you write the numbers 2,3,4,5 in word and count the number you will get 3,5,4,4 respectively.
What are the counting letters?counting Letters provides a perfect way to introduce number words to beginning readers, as well as discuss the concepts of letters and words.
So, if you write 6 in words you will write six and on counting the letter you will get 3.
Hence, 6 = 3 ans.
Therefore the value of the 6 is 3.
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The first step in determining the solution to the system of equations, y = -x2 - 4x - 3 and y = 2x + 5, algebraically is to set the two equations equal as -x2 - 4x -3 = 2x + 5. What is the next step?
Answer:
See below
Step-by-step explanation:
Next step is to gather 'like' terms
-x2 - 4x -3 = 2x + 5.
x^2 + (4x + 2x) + (3+5) = 0 then simplify
x^2 + 6x + 8 = 0 then factor
(x+4)(x+2) = 0
so either of these terms = 0
x+4 = 0 means x = -4
x+ 2 = 0 means x = - 2
Answer:
d
Step-by-step explanation:
Combine like terms onto one side of the equation.
The Law of Sines states that sin A/b = sin B/c = sin C/a
True
False
Step-by-step explanation:
hope you can understand
In 20 years charlie will be three times as old as he is now.how old is charlie is he now
Answer:
10 years old
Step-by-step explanation:
let his age be x , then in 20 years
x + 20 = 3x ( subtract x from both sides )
20 = 2x ( divide both sides by 2 )
10 = x
Charlie is 10 years old
Question 1 of 10
Solve 10x+16 ≥ 6x+ 20.
O A. x29
OB. x≤ 1
OC. x2 1
OD. x≤ 9
What is the solution to the following equation?
3(x-4)-5-x-3
A. x = 12
B. x=3
C. x=8
D. x = 7
Answer:
D. x = 7
Step-by-step explanation:
NOTE : there should be an equal sign somewhere in the given expression.
suppose the equation is the following:
3(x-4)-5 = x-3
………………………………………………………
3(x - 4) - 5 = x - 3
⇔ 3x - 12 - 5 = x - 3
⇔ 3x - 17 = x - 3
⇔ 3x - 17 + 17= x - 3 + 17
⇔ 3x = x + 14
⇔ 2x = 14
⇔ x = 14/2
⇔ x = 7
2x + 5y = 17 6x - 5y = -9
Answer:
Step-by-step explanation:
Choose the correct simplification of the expression (2x7y)2(y5)3.
The correct simplification of the expression is 4x¹⁴y¹⁷
Given,
The expression is (2x⁷ y)² (y⁵)³
To distribute the exponent, apply the power rule (ab)ⁿ = aⁿbⁿ
Implement the product rule to (2x⁷y)².
Here, we have a = 2x⁷ , b = y and n = 2
=(2x⁷)² y²(y⁵)³
= 2²(x⁷)² y²(y⁵)³
= 4(x⁷)² y²(y⁵)³
Now exponents should be multiplied while using the product rule.
The product rule is (aˣ)ⁿ = aˣⁿ
We apply this to (x⁷)² and (y⁵)³
So the expression becomes,
=4x⁷·² y² (y⁵·³)
= 4x¹⁴ y² y¹⁵
∵ In exponents we have a rule that if bases are same then powers are added i.e, aˣ aⁿ = aˣ⁺ⁿ
∴ 4x¹⁴ y¹⁵ ⁺ ²
= 4x¹⁴ y¹⁷
Hence we get the answer as 4x¹⁴ y¹⁷
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please help i dont know how to do this
En una tienda comercial anuncia descuentos sucecivos del 30% y 20% en todos los electrodomésticos, ¿Que descuento único equivale?
Answer:
0
Step-by-step explanation:
(x - 4)/(x + 6) - (x - 6)/(x + 4)
Answer:
[tex]\frac{20}{(x+4)(x+6)}[/tex]
Step-by-step explanation:
assuming you require the expression simplified
[tex]\frac{x-4}{x+6}[/tex] - [tex]\frac{x-6}{x+4}[/tex]
multiply the numerator/denominator of the first fraction by (x + 4)
multiply the numerator/denominator of the second fraction by (x + 6)
= [tex]\frac{(x-4)(x+4)}{(x+4)(x+6)}[/tex] - [tex]\frac{(x-6)(x+6)}{(x+4)(x+6)}[/tex] ← expand and simplify numerators leaving the common denominator
= [tex]\frac{x^2-16-(x^2-36)}{(x+4)(x+6)}[/tex]
= [tex]\frac{x^2-16-x^2+36}{(x+4)(x+6)}[/tex]
= [tex]\frac{20}{(x+4)(x+6)}[/tex]
which statement is true about fiction
Answer:
The function is even because of symmetry over x axis
Yaqub, Angus and Iris share 18 slices of pizza in the ratio
1:3:2.
How many slices of pizza does Iris have?
Answer:
6 Slices
Step-by-step explanation:
Total units = 1 + 3 + 2 = 6 Units
6 Units = 18 Slices of Pizza
Iris shared 2 units.
1 Unit = 18/6 = 3 Slices of Pizza
2 Units = 2 * 3 = 6 Slices of Pizza
A farmer has only goats and hens in his farm,on a particular day,he sold 12 animals (goats and hens) and the total number of their legs was 32. how many goats and how many hens did he sell that day?
The number of goats sold is 4 and hens sold is 8.
What is an Equation ?An equation is a mathematical statement which equates two algebraic expression with an equal sign.
Let the total number of goats sold be g
Let the total number of hens sold is h
g + h = 12
The total no. of legs of a goats sold will be 4g
and the total number of legs of a hens sold will be 2h
and it is given that
4g +2h = 32
The system of equation formed is
g + h = 12
4g +2h = 32
Multiplying equation (1) by 2 and then (1) - (2)
-2g = -8
g = 4
Therefore the number of goats sold is 4 and hens sold is 8.
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Use the fraction model to multiply: three multiplied by five sevenths. Leave your answer as an improper fraction. (1 point)
three fraction models, each model is partitioned into seven equal parts, with five parts shaded in each model
eight sevenths
eight tenths
fifteen twenty ones
fifteen sevenths
The product of three and five-sevenths is given by (D) Fifteen sevenths.
In fraction multiplication, we multiply the corresponding position like we multiply numerator with numerator and denominator with another denominator.
The denominator for a whole number is always 1.
Here given the numbers are three and five-sevenths, that is [tex]3,\frac{5}{7}[/tex].
So here since 3 is a whole number then the denominator of it is 1.
We can write 3 as [tex]\frac{3}{1}[/tex].
So product [tex]=\frac{5}{7}\times\frac{3}{1}=\frac{5\times3}{7\times1}=\frac{15}{7}[/tex]
Using the fraction model we get,
Here we can see that there are three bars with seven divisions in which fives are shaded.
So in multiplication with three we have to take the shaded region as the numerator and have to all the shaded and total bar for once.
here a total number of divisions in one bar is 7, so the denominator of the product is 7.
A total number of shaded divisions is 15, so the numerator of the product is 15.
So the product is [tex]\frac{15}{7}[/tex], that is fifteen sevenths.
Hence the correct option is (D) Fifteen sevenths.
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Choose any set of Pythagorean triplets of your choice and illustrate them using graph sheet.
Example given below:
The required Pythagorean triplets are hypotenuse, perpendicular and base is 13, 12 and 5 respectively.
In a right angled triangle, its side, such as hypotenuse, perpendicular and base is Pythagorean triplets.
We have
Hypohypotenuse = 13
perpendicular = 12
base = 5
Which satisfies the condition of the Pythagorean theorem.
[tex]a^2+b^2=c^2\\12^2+5^2=c^2\\169=c^2[/tex]
and c = 13
Thus, the required value of Pythagorean triplets satisfies the Pythagorean theorem.
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