Explanation:
We can factor out 8 like so
2^40 + 2^39 + 2^36 = 2^3*2^37 + 2^3*2^36 + 2^3*2^33
2^40 + 2^39 + 2^36 = 2^3*(2^37 + 2^36 + 2^33)
2^40 + 2^39 + 2^36 = 8*(2^37 + 2^36 + 2^33)
Showing that 8 is a factor of 2^40 + 2^39 + 2^36
In other words, 2^40 + 2^39 + 2^36 is divisible by 8
Two teaching methods, A and B, are implemented for learning Spanish. There is a 70% chance of successfully learning Spanish if method A is used, and a 85% chance of success if methodB is used. However, method B is substantially more 3. time consuming and is therefore used only 20% of the time (method A is used the other 80% of the time). The following notations are suggested:
A-Method A is used.
B-Method B is used.
L-Spanish was learned successfully Interpret each of the probabilities given in the original problem in probability
a) notation with their respective values (four of these).
b) Draw a Probability Tree representing each of the probabilities mentioned above.
c) What is the likelihood a person does not learn Spanish?
d) A student learned the spanish successfully. What is the probability that they were taught by method B?
Answer:
(a) Shown below.
(b) Shown below.
(c) The probability that a person does not learn Spanish is 0.18.
(d) The probability that method B was used given that a student learned the Spanish successfully is 0.83.
Step-by-step explanation:
(a)
Consider the provided data.
[tex]P(A)=0.20\\P(B)=0.80\\P(L|A)=0.70\\P(L|B)=0.85[/tex]
Then the probability of not learning Spanish using the respective methods are:
[tex]P(L'|A)=1-P(L|A)=1-0.70=0.30\\\\P(L'|B)=1-P(L|B)=1-0.70=0.15[/tex]
(b)
The Probability Tree representing each of the probabilities mentioned above is attached below.
(c)
Compute the probability that a person does not learn Spanish as follows:
[tex]P(L')=P(L'|A)P(A)+P(L'|B)P(B)[/tex]
[tex]=(0.30\times 0.20)+(0.15\times 0.80)\\\\=0.06+0.12\\\\=0.18[/tex]
Thus, the probability that a person does not learn Spanish is 0.18.
(d)
Compute the probability that method B was used given that a student learned the Spanish successfully as follows:
[tex]P(B|L)=\frac{P(L|B)P(B)}{P(L|A)P(A)+P(L|B)P(B)}[/tex]
[tex]=\frac{(0.85\times 0.80)}{(0.70\times 0.20)+(0.85\times 0.80)}\\\\=\frac{0.68}{0.14+0.68}\\\\=0.82927\\\\\approx 0.83[/tex]
Thus, the probability that method B was used given that a student learned the Spanish successfully is 0.83.
What is the prime factorization of 50?
2x25
2x5
2x5²
Answer:
2x5²
Step-by-step explanation:
[tex]25 = 2 \times 5 \times 5 = 2 \times {5}^{2} \\ [/tex]
Answer:
2x5²
Step-by-step explanation:
find the zero of the following function: f(×)=(×-1)/(×-3)
Answer:
[tex]\boxed{\sf \ \ x = 1 \ \ }[/tex]
Step-by-step explanation:
Hello,
First of all we need to take x different from 3 as dividing by 0 is not allowed
then for x real different from 3
[tex]f(x)=0\\\\<=> \dfrac{x-1}{x-3}=0\\\\<=> x-1 = 0\\\\<=> x = 1[/tex]
hope this helps
‼️10 points‼️
1. Match the graph with its equation.
A. y=-3
B. x=-3
C. x=3
D. y=3
Answer:
y=-3
Step-by-step explanation:
This is a horizontal line
Horizontal lines are of the form
y=
The y value is -3
y=-3
━━━━━━━☆☆━━━━━━━
▹ Answer
A. y = -3
▹ Step-by-Step Explanation
Y is represented by a horizontal line and it passes through the point -3 therefore, the answer is y = -3.
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
The length of a square is 2x cm. The breadth and length of a rectangle are x cm and (2x + 1) cm
respectively. If both have the same perimeter. find the value of x.
Answer:
I hope it will help you.......
PLEASE HELP ME!!! ASAP!!!
Answer:
a, Side DE and side AB have to be equal to keep the order of AAS.
b, AC and DF have to be equal for the same reason.
Kini earns 9 dollars an hour at her job and her allowance is 8 dollars per week. Duke earns 7.50 dollars an hour and his allowance is 16 dollars per week. How many hours do kini and duke need to work in order to save the same amount of money in one week.
Answer:
Step-by-step explanation:
y = 9x + 8
y = 7.5x + 16
1.5x = 8
x = 5.3 hours
Answer:
5.3hrs or 5hrs 18mins
Step-by-step explanation:
First, we have to put the information given to us about the money they earn into an expression
Let x represent the number of hours Kini and Duke work and y represent the total amount of money they earn in a week.
y(kini) = 9x + 8
y(duke) = 7.5x + 16
Now we subtract the x values and the constant values
9x - 7.5x = 1.5x
16 - 8 = 8
Make these into an equation
1.5x = 8
Divide both sides by 1.5 so x(the number of hours the both work) can stand alone.
[tex]\frac{1.5x}{1.5} =\frac{8}{1.5}[/tex]
x = 5.3hrs or 5hrs and 18 mins
Which of the following statements is true for the figures shown?
Answer:
Option D is the correct answer.
Step-by-step explanation:
A-p-e-x :)
Use the formula v = u + at to find the velocity when
• the initial velocity is 3 m/s
• the acceleration is 1.5 m/s^2
• the time is 7 seconds
Answer:
13.5 m/s
Step-by-step explanation:
plug the acceleration and time back in the equation and you get the answer. hope this helps!
Answer:
Answer : 13.5
Step-by-step explanation:
v = u + at
v = 3 + 1.5 ( 7 )
v = 3 + 10.5
v = 13.5
What is the slope of the line that contains the points (-1, 2) and (3, 3)?
O A. 4
O B. 4
ОС.
4
OD.
4
Answer:
the answer shoudl be OB 4
Where do the graphs go ?
Answer:
1 goes into not pro
2 goes to not pro
3 goes into pro
and 4 goes into not pro
Step-by-step explanation:
proportional is a straight line
non proportional is not a line
Consider triangle QRS. The legs each have a length of 10 units. Triangle Q R S is shown. Angle Q S R is 90 degrees. The length of Q X is 10 and the length of S R is 10. What is the length of the hypotenuse of the triangle?
Answer:
10 square root 2
Step-by-step explanation:
Answer: D). 10 StartRoot 2 EndRoot units
Step-by-step explanation:
Consider the following quadratic equation. -4x^2+bx-11=0 Determine a possible value of b so that the quadratic has two complex solutions.
Answer:
Step-by-step explanation:
hello,
for [tex]ax^2+bx+c=0[/tex]
[tex]\Delta = b^2-4ac[/tex]
so here
[tex]\Delta = b^2-4*(-4)*(-11)=b^2-176[/tex]
to have two complex solutions we need [tex]\Delta < 0\\[/tex]
so [tex]b^2<176[/tex]
[tex]<=> b < \sqrt{176}=13.266...[/tex]
for instance we can take b = 0
hope this helps
Answer:
The correct answer is 12.
Step-by-step explanation:
i got it correct on my test, thanks to comment on the question above.
Which of the following is an equivalent form of the
compound inequality -22 > -5x - 72 -3? (1 point)
Select one:
O a. -5x - 75 -22 and -5x - 72-3
O b. -5x - 7> -22 and -5x - 72-3
O c. -5x > -22 and -7 -3
O d. -5x - 7 < -22 and -5x - 75 -3
Step-by-step explanation:
_22greater than minus 2 x minus minus 72 minus 3
72 minus 22 minus 3greathan than 2x
49greatern than 2 x
Is triangleLMN cong triangleOQP? If so, name the postulate that applies.
Answer:
A. The triangles are congruent by SAS.
Step-by-step explanation:
Two sides of one triangle are congruent to two sides of the other triangle. The included angles of the two triangles are congruent.
The triangles are congruent by SAS.
For the equation y=2x2-16x+30 Identify the vertex and convert into vertex form. Create an inverse function.
Answer:
Vertex: (4, -2)
Vertex form: [tex]y = 2(x-4)^2 - 2[/tex]
Inverse function: [tex]y = (16 \pm\sqrt{16+8x})/4[/tex]
Step-by-step explanation:
The x-coordinate of the vertex can be calculated using the formula:
[tex]x_{vertex} = -b/2a[/tex]
Where a and b are coefficients of the quadratic equation in the form:
[tex]y = ax^2 + bx + c[/tex]
So, using a = 2 and b = -16, we have:
[tex]x_{vertex} = 16/4 = 4[/tex]
To find the y-coordinate of the vertex, we calculate y using the x-coordinate of the vertex:
[tex]y=2*4^2-16*4+30[/tex]
[tex]y = -2[/tex]
So the vertex is (4, -2)
The vertex form is given by:
[tex]y = a(x-h)^2 + k[/tex]
Where h is the x-coordinate of the vertex and k is the y-coordinate of the vertex. Therefore, we have that:
[tex]y = 2(x-4)^2 - 2[/tex]
To create an inverse function, we switch x by y and vice-versa:
[tex]x=2y^2-16y+30[/tex]
[tex]2y^2-16y+30 - x = 0[/tex]
Then, using Bhaskara's formula, we have:
[tex]\Delta = b^2 -4ac = (-16)^2 - 4*2*(30-x) = 16 + 8x[/tex]
[tex]y = (-b \pm\sqrt{\Delta})/2a[/tex]
[tex]y = (16 \pm\sqrt{16+8x})/4[/tex]
It's important to say that this inverse function is not really a function, because one value of x gives two values of y.
two factors of -48 have a difference of 19. the factor with a greater absolute value is positive. what is the sum of the factors? -19, -13 13 or 16
Answer:
-19
Step-by-step explanation:
-19 is the absolute value of 19
hope this helps
Answer:
sum = +13
Step-by-step explanation:
The possible factors of 48 are
{1,2,3,4,6,8,12,16,24,48}
Of these, the pair 3,16 gives a sum of 19 and a product of 48.
We are given that 16 (greater absolute value) is positive, so 3 is negative.
The sum of the two is therefore 16-3 = 13
What's the solution set of –5 < 2x – 1 < 3?
–2 < x < 2
Infinitely many solutions
–3 < x < –2
No solution
Answer:
The answer is - 2 < x < 2
Step-by-step explanation:
–5 < 2x – 1 < 3
Add 1 to both sides to eliminate - 1
That's
- 5 + 1 < 2x - 1 + 1 < 3+ 1
- 4 < 2x < 4
Divide both sides by 2
That's
- 4/2 < 2x/2 < 4/2
The final answer is
- 2 < x < 2Hope this helps you
A history instructor has given the same pretest and the same final examination each semester. He is interested in determining if there is a relationship between the scores of the two tests. He computes the linear correlation coefficient and notes that it is 1.15. What does this correlation coefficient value tell the instructor?
Answer:
The history instructor has made a computational error.
Step-by-step explanation:
We have that the data represents the linear correlation coefficient and notes it is 1.15
The linear correlation coefficient value which is 1.15 does tell the instructor that the history instructor has made a computational error due to the linear correlation coefficient value falls in the range -1 to +1.
Therefore, the history instructor has made a computational error.
please help !! what’s the answer? i don’t understand !!
Answer:
992
Step-by-step explanation:
You must convert the meter the kilometer by miltiplying by 1000
and when you do it you must multiply 0.992 by 1000 since it is a fraction .
or you can work it this way :
0.992⇒1m x(the new rate) ⇒1000m x= 0.992*1000= 992How do you do this? Please help!
Answer: 7/36
Step-by-step explanation:
As you can see, 7 of the 36 squares are multiples of 5. Also, pls brainliest, this took forever.
Based on a recent poll, there is a 50-50 chance that randomly selected adut has pierced ears, Express the indicated degree of likelihood as a proabability value between 0 and 1.
Answer:
1/2 or 0.5
Step-by-step explanation:
Saying that there is a 50-50 chance of an event happening is equivalent to saying there is a 1 in 2 chance. Therefore, expressing that degree of likelihood as a value between 0 and 1:
[tex]\frac{1}{2}=0.50[/tex]
There is a 1/2 or 0.5 chance that a randomly selected adult has pierced ears.
Answer:
1/2 or 0.5
Step-by-step explanation:
50-50 chance between 0-1 means half of 0-1 which is 1/2 or 0.5
1/2 or 0.5!
find the value of k if (x-3) is a factor of P(x)=2x3-5x2+3x+k
Answer:
k = -18
Step-by-step explanation:
If x-3 is a factor, what this means is that if we substitute;
x = 3 into the equation, we should get 0
This is from the factor theorem
Thus ;
P(3) = 0 = 2(3)^3 -5(3)^2 + 3(3) + k
0 = 54 - 45 + 9 + k
k + 18 = 0
k = -18
Factor completely x3 + 6x2 + 8x + 48. A (x − 6)(x2 − 8) B (x − 6)(x2 + 8) C (x + 6)(x2 − 8) D (x + 6)(x2 + 8)
Answer:
(x+6)(x^2+8)
D
Step-by-step explanation:
x^3 + 6x^2 + 8x + 48=
x2(x+6)+8(x+6)= take x+6 common factor
(x+6)(x^2+8)
given the polynomial function below find F(2)
F(x) = 5x^3 -2x^2 + 3
Answer:
35
Step-by-step explanation:
f(x)=5x^3-2x^2+3
f(2)=5x2^3-2x2^2+3
=5x8-2x4+3
=40-8+3
=40-5
=35
Answer:
35
Step-by-step explanation:
F(x) = 5x^3 -2x^2 + 3
Let x=2
F(2) = 5(2)^3 -2(2)^2 + 3
= 5*8 -2(4) +3
= 40 -8+3
= 32+3
= 35
A train travels 600 km in one hour .what is the trains Velocity in meters /seconds?
Answer:
166.6666 metres/second
Step-by-step explanation:
1 km/hr = 5m/18s
600*5/18
Find the midpoint of the line segment with end coordinates of: ( − 1 , − 6 ) and ( 4 , 5 ) Give coordinates as decimals where appropriate.
Answer:
(1.5 , -0.5)
Step-by-step explanation:
formula:
x_midpoint=(x1+x2)/2
y_midpoint=(y1+y2)/2
y coordinate: (-1 +4)/2
x coordinate: (-6+5)/2
Describe how the graph of the parent function
y=
is transformed when graphing y = 8x - 3
The graph is translated 3 units
Answer:
Down
Stretched by a factor of 2
Step-by-step explanation:
The transformed function is translated to the right along the x-axis and stretched by a scale factor of 2.
What is transformation?A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.
Given is a function, y = [tex]\sqrt[3]{x}[/tex] being transformed into y = [tex]\sqrt[3]{8x} -3[/tex]
We see, that, in the function, 3 is being subtracted from x, we mean the translation is right along the x-axis
And, ∛x is converted into 2∛x, that shows a stretched in the graph,
Hence, The transformed function is translated to the right along the x-axis and stretched by a scale factor of 2.
For more references on transformation, click;
https://brainly.com/question/11709244
#SPJ2
What is the following product? (3 startroot 16x^7 endroot) (3 startroot 12x^9 endroot)
Answer:
72x^8
Step-by-step explanation:
Product of ;
3 √(16x^7) * 3 √(12x^9)
Let’s factor out all perfect squares in the roots
3 √(16 * x^4 * x^3) * 3 √(4 * 3 * x^8 * x)
Taking out the perfect squares, we have;
3 * 4 * x^2 * √(x^3) * 3 * 2 * √3 * x^4 * √(x)
72 * x^(2 + 4) * √(x^3 * x)
72 * x^6 * √(x^4)
72 * x^6 * x^2
72 * x^8
Help!!!!! please!!!!!
Hey there! :)
Answer:
B. The volume of Cylinder B is larger.
Step-by-step explanation:
Find the volumes of each cylinder using the formula V = πr²h:
Cylinder A:
V = π3² · 5
V = 9π · 5
V = 45π units³
Cylinder B:
V = π5²· 3
V = 25π · 3
V = 75π units³
75π u³ > 45π u³, so the volume of Cylinder B is larger.