ASAP Two points ___________ create a line. A. sometimes B. always C. never D. not enough information

Answer:

(a) P(E∪F)= 0.8

(b) P(Ec)= 0.4

(c) P(Fc)= 0.7

(d) P(Ec∩F)= 0.8

Step-by-step explanation:

(a) It is called a union of two events A and B, and A ∪ B (read as "A union B") is designated to the event formed by all the elements of A and all of B. The event A∪B occurs when they do A or B or both.

If the events are not mutually exclusive, the union of A and B is the sum of the probabilities of the events together, from which the probability of the intersection of the events will be subtracted:

P(A∪B) = P(A) + P(B) - P(A∩B)

In this case:

P(E∪F)= P(E) + P(F) - P(E∩F)

Being P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.1

P(E∪F)= 0.6 + 0.3 - 0.1

P(E∪F)= 0.8

(b)  The complement of an event A is defined as the set that contains all the elements of the sample space that do not belong to A.  The Complementary Rule establishes that the sum of the probabilities of an event and its complement must be equal to 1. So, if P (A) is the probability that an event A occurs, then the probability that A does NOT occur is  P (Ac) = 1- P (A)

In this case: P(Ec)= 1 - P(E)

Then: P(Ec)= 1 - 0.6

P(Ec)= 0.4

(c) In this case: P(Fc)= 1 - P(F)

Then: P(Fc)= 1 - 0.3

P(Fc)= 0.7

(d)  The intersection of two events A and B, designated as A ∩ B (read as "A intersection B") is the event formed by the elements that belong simultaneously to A and B. The event A ∩ B occurs when A and B do at once.

As mentioned, the complementary rule states that the sum of the probabilities of an event and its complement must equal 1. Then:

P(Ec intersection F) + P(E intersection F) = P(F)

P(Ec intersection F) + 0.1 = 0.3

P(Ec intersection F)= 0.2

Being:

P(Ec∪F)= P(Ec) + P(F) - P(Ec∩F)

you get:

P(Ec∩F)= P(Ec) + P(F) - P(Ec∪F)

So:

P(Ec∩F)= 0.4 + 0.3 - 0.2

P(Ec∩F)= 0.8

Answer:

red

Step-by-step explanation:

Since the bag contains more red marbles than any other color, you are most likely to pick a red marble

Answer:

Yes

Step-by-step explanation:

you would do 2(5x-10) + 2(8x+4)= 26x-12

Answer:

26x - 12

Step-by-step explanation:

The perimeter is the sum of all the exterior sides of a figure.

Here, we have a parallelogram, and its sides are 5x - 10, 8x + 4, 5x - 10, and 8x + 4. Adding these, we get:

(5x - 10) + (8x + 4) + (5x - 10) + (8x + 4) = 26x - 12

Thus, the answer is 26x - 12. Note that since the problem doesn't give a value for x, this cannot be simplified further.

~ an aesthetics lover

Answer:

Step-by-step explanation:

[tex] \frac{2}{5} + p = \frac{4}{5} + \frac{3}{5} p[/tex]

Multiply through by the LCM

The LCM for the equation is 5

That's

[tex]5 \times \frac{2}{5} + 5p = 5 \times \frac{4}{5} + \frac{3}{5}p \times 5[/tex]

We have

2 + 5p = 4 + 3p

Group like terms

5p - 3p = 4 - 2

2p = 2

Divide both sides by 2

We have the final answer as

Hope this helps you

Answer:

The value of the expression when [tex]m = 3.48[/tex] and [tex]b = 96.52[/tex] is 323.779.

Step-by-step explanation:

Let be [tex]f(m, b) = m\cdot b - m^{2}[/tex], if [tex]m = 3.48[/tex] and [tex]b = 96.52[/tex], the value of the expression:

[tex]f(3.48,96.52) = (3.48)\cdot (96.52)-3.48^{2}[/tex]

[tex]f(3.48,96.52) = 323.779[/tex]

The value of the expression when [tex]m = 3.48[/tex] and [tex]b = 96.52[/tex] is 323.779.

Answer:

3x+2+x-3+2x+1+2(2x+5)=360

10x+10=360

x=35

Answer:

65 ft

Step-by-step explanation:

The area of a rectangle is

A = lw

6045 = 93*w

Divide each side by 93

6045/93 = 93w/93

65 =w

Answer:

[tex]\huge \boxed{\mathrm{65 \ feet}}[/tex]

Step-by-step explanation:

The area of a rectangle formula is given as,

[tex]\mathrm{area = length \times width}[/tex]

The area and length are given.

[tex]6045=93 \times w[/tex]

Solve for w.

Divide both sides by 93.

[tex]65=w[/tex]

The width of the rectangular garden is 65 feet.

Answer:

$2,589.52

Step-by-step explanation:

[tex] A = P(1 + \dfrac{r}{n})^{nt} [/tex]

We start with the compound interest formula above, where

A = future value

P = principal amount invested

r = annual rate of interest written as a decimal

n = number of times interest is compound per year

t = number of years

For this problem, we have

P = 2000

r = 0.026

n = 2

t = 10,

and we find A.

[tex] A = $2000(1 + \dfrac{0.026}{2})^{2 \times 10} [/tex]

[tex] A = $2589.52 [/tex]

Compound interest formula:

Total = principal x ( 1 + interest rate/compound) ^ (compounds x years)

Total = 2000 x 1+ 0.026/2^20

Total = $2,589.52

Answer:

A)0.126775 B)0.000004325376 C) 0.07548

Step-by-step explanation:

Given the following :

A.) a. n = 15, p = 0.4, find P(4 successes)

a = number of trials p=probability of success

P(4 successes) = P(x = 4)

USING:

nCx * p^x * (1-p)^(n-x)

15C4 * 0.4^4 * (1-0.4)^(15-4)

1365 * 0.0256 * 0.00362797056

= 0.126775

B)

b. n = 12, p = 0.2, find P(2 failures),

P(2 failures) = P(12 - 2) = p(10 success)

USING:

nCx * p^x * (1-p)^(n-x)

12C10 * 0.2^10 * (1-0.2)^(12-10)

66 * 0.0000001024 * 0.64

= 0.000004325376

C) n = 20, p = 0.05, find P(at least 3 successes)

P(X≥ 3) = p(3) + p(4) + p(5) +.... p(20)

To avoid complicated calculations, we can use the online binomial probability distribution calculator :

P(X≥ 3) = 0.07548

Answer:

Step-by-step explanation:

Since the figure above is a right angled triangle we can use trigonometric ratios to find GV

To find GV we use cosine

cos∅ = adjacent / hypotenuse

From the question

GV is the adjacent

GC is the hypotenuse

So we have

GC = 55°

GV = 55 cos 37

GV = 43.92495

We have the final answer as

Hope this helps you

Answer: 3.41x10^3

Step-by-step explanation:

At the beginning of the year, we have:

R = 6.2x10 rats.

And we know that, in one year, each rat produces:

O = 5.5x10 offsprins.

Then each one of the 6.2x10 initial rats will produce 5.5x10 offsprings in one year, then after one year we have a total of:

(6.2x10)*(5.5x10) = (6.2*5.5)x(10*10) = 34.1x10^2

and we can write:

34.1 = 3.41x10

then: 34.1x10^2 = 3.41x10^3

So after one year, the average number of rats is:  3.41x10^3

Answer:

x = 1, y = -1

Step-by-step explanation:

If we have the two equations:

[tex]4x+3y=1[/tex] and [tex]-3x - 6y = 3[/tex], we can look at which variable will be easiest to eliminate.

[tex]y[/tex] looks like it might be easy to get rid of, we just have to multiply [tex]4x+3y=1[/tex]  by 2 and y is gone (as -6y + 6y = 0).

So let's multiply the equation [tex]4x+3y=1[/tex]  by 2.

[tex]2(4x + 3y = 1)\\8x + 6y = 2[/tex]

Now we can add these equations

[tex]8x + 6y = 2\\-3x-6y=3\\[/tex]

------------------------

[tex]5x = 5[/tex]

Dividing both sides by 5, we get [tex]x = 1[/tex].

Now we can substitute x into an equation to find y.

[tex]4(1) + 3y = 1\\4 + 3y = 1\\3y = -3\\y = -1[/tex]

Hope this helped!

Answer:

100°

Step-by-step explanation:

We know that angles EFD and AEF are the same as they are alternate interior angles.

We also can note that BEF and AEF are supplementary, meaning their angle lengths will add up to 180°.

So we can create an equation:

(2x + 60) + (3x + 20) = 180

Combine like terms:

5x + 80 = 180

Subtract 80 from both sides

5x = 100

Divide both sides by 5

x = 20.

Now we can use this to find the measure of BEF.

[tex]2\cdot20 + 60[/tex]

[tex]40 + 60 = 100[/tex]

Hope this helped!

Answer:

BEF = 100

Step-by-step explanation:

The angles are same side interior angles and same side interior angles add to 180 degrees

2x+60 + 3x+20 = 180

Combine like terms

5x+80 = 180

Subtract 80

5x = 100

Divide by 5

5x/5 = 100/5

x = 20

We want BEF

BEF = 2x+60

      = 2x+60

      = 2*20 +60

     = 40+60

     = 100

Answer:

a) Compatibility of Equality with Addition, b) Compatibility of Equality with Multiplication

Step-by-step explanation:

a) This expression can be solved by using the Compatibility of Equality with Addition, that is:

1) [tex]3+x = 27[/tex] Given

2) [tex]x+3 = 27[/tex] Commutative property

3) [tex](x + 3)+(-3) = 27 +(-3)[/tex] Compatibility of Equality with Addition

4) [tex]x + [3+(-3)] = 27+(-3)[/tex] Associative property

5) [tex]x + 0 = 27-3[/tex] Existence of Additive Inverse/Definition of subtraction

6) [tex]x=24[/tex] Modulative property/Subtraction/Result.

b) This expression can be solved by using the Compatibility of Equality with Multiplication, that is:

1) [tex]\frac{x}{6} = 5[/tex] Given

2) [tex](6)^{-1}\cdot x = 5[/tex] Definition of division

3) [tex]6\cdot [(6)^{-1}\cdot x] = 5 \cdot 6[/tex] Compatibility of Equality with Multiplication

4) [tex][6\cdot (6)^{-1}]\cdot x = 30[/tex] Associative property

5) [tex]1\cdot x = 30[/tex] Existence of multiplicative inverse

6) [tex]x = 30[/tex] Modulative property/Result

Answer:

3 + x = 27

✔ subtraction property of equality with 3

x over 6  = 5

✔ multiplication property of equality with 6

Answer:

2 * (x + 2) = 50

Step-by-step explanation:

Let's call the unknown number x. "A number and 2" means that we need to add the numbers, therefore it would be x + 2. "Twice" means 2 times a quantity so "twice a number and 2" would be 2 * (x + 2). "Is" denotes that we need to use the "=" sign and because 50 comes after "is", we know that 50 goes on the right side of the "=" so the final answer is 2 * (x + 2) = 50.

Answer:

[tex]a = 6m/s^2[/tex]

Step-by-step explanation:

Given

When mass = 4kg; Acceleration = 15m/s²

Required

Determine the acceleration when mass = 10kg, provided force is constant;

Represent mass with m and acceleration with a

The question says there's an inverse variation between acceleration and mass; This is represented as thus;

[tex]a\ \alpha\ \frac{1}{m}[/tex]

Convert variation to equality

[tex]a = \frac{F}{m}[/tex]; Where F is the constant of variation (Force)

Make F the subject of formula;

[tex]F = ma[/tex]

When mass = 4kg; Acceleration = 15m/s²

[tex]F = 4 * 15[/tex]

[tex]F = 60N[/tex]

When mass = 10kg; Substitute 60 for Force

[tex]F = ma[/tex]

[tex]60 = 10 * a[/tex]

[tex]60 = 10a[/tex]

Divide both sides by 10

[tex]\frac{60}{10} = \frac{10a}{10}[/tex]

[tex]a = 6m/s^2[/tex]

Hence, the acceleration is [tex]a = 6m/s^2[/tex]

Answer:

The cumulative frequency plot is also attached below.

Step-by-step explanation:

The data provided is as follows:

Age Group Frequency

   0 - 9             34.9

  10 - 19             35.7

20 - 29             36.8

30 - 39             38.1

40 - 49             37.8

50 - 59             37.8

60 - 69             34.5

70 - 79             27.2

80 - 89             18.8

90 - 99               7.7

100 - 109       1.7

Consider the Excel output attached.

The cumulative frequency are computed in the Excel sheet.

The cumulative frequency plot is also attached below.

From the cumulative frequency plot it can be seen that in the future most people will belong to a higher age group rather then the lower ones.

Answer:

The removed number is 11.

Step-by-step explanation:

Given that the average of 5 numbers is 7. So you have to find the total values of 5 numbers :

[tex]let \: x = total \: values[/tex]

[tex] \frac{x}{5} = 7[/tex]

[tex]x = 7 \times 5[/tex]

[tex]x = 35[/tex]

Assuming that the total values of 5 numbers is 35. Next, we have to find the removed number :

[tex]let \: y = removed \: number[/tex]

[tex] \frac{35 - y}{4} = 6[/tex]

[tex]35 - y = 6 \times 4[/tex]

[tex]35 - y = 24[/tex]

[tex]35 - 24 = y[/tex]

[tex]y = 11[/tex]

Okay, let's slightly generalize this

Average of [tex]n[/tex] numbers is [tex]a[/tex]

and then [tex]r[/tex] numbers are removed, and you're asked to find the sum of these [tex]r[/tex] numbers.

Solution:

If average of [tex]n[/tex] numbers is [tex]a[/tex] then the sum of all these numbers is [tex]n\cdot a[/tex]

Now we remove [tex]r[/tex] numbers, so we're left with [tex](n-r)[/tex] numbers. and their. average will be [tex]{\text{sum of these } (n-r) \text{ numbers} \over (n-r)}[/tex] let's call this new average [tex] a^{\prime}[/tex]

For simplicity, say, sum of these [tex]r[/tex] numbers, which are removed is denoted by [tex]x[/tex] .

so the new average is [tex]\frac{\text{Sum of } n \text{ numbers} - x}{n-r}=a^{\prime}[/tex]

or, [tex] \frac{n\cdot a -x}{n-r}=a^{\prime}[/tex]

Simplify the equation, and solve for [tex]x[/tex] to get,

[tex] x= n\cdot a -a^{\prime}(n-r)=n(a-a^{\prime})+ra^{\prime}[/tex]

Hope you understand it :)

Answer:

Step-by-step explanation:

vertical stretching / shrinking has the following transformation.

f(x) -> a * f(x)

when a >  1, it is stretching

when 0< a < 1, it is shrinking.

when  -1 < a < 0, it is shringking + reflection about the x-axis

when a < -1, it is stretching + reflection about the x axis.

Here it is simple shrinking, so 0 < a < 1.

I expect the answer choice to show (1/3) f(x).

However, if the question plays with the words

"shrink by a factor of 1/3" to actually mean a "stretching by a factor of three", then B is the answer (stretch by a factor of three).

Answer:

-23

Step-by-step explanation:

-8+(-15) means that you are subtracting 15 from -8. So you end up with -8-15=-23.

Answer:

(7 x 2.85) + 5v = 28.70. 19.95 + 5v = 28.70. 5v = 28.70 - 19.95. 5v = 8.75. v = 8.75/5. v = 1.75. A pint of veggies costs $1.75.

False!

The answer is: False.

Whomever stated the answer is "true" is wrong.

Answer:

87 mph

Step-by-step explanation:

Total distance needed is 120 mi + 300 mi and that is 420 mi.

Driving at 65 mph means that it would take

420 / 65 hours to reach his destination.

6.46 hours .

at the first phase, he drove at 40 mph for 120 mi, this means that it took him

120 / 40 hours to complete the journey.

3 hours.

the total time needed for the whole journey is 6.46 hours, and he already spent 3 hours in the first phase. To keep up with the 6.46 hours required, in the second phase, he has to drive at a speed of

6.46 - 3 hours = 3.46 hours.

300 mi / 3.46 hours => 86.71 mph approximately 87 mph

Therefore, he needs to drive at not more than 87 mph to keep up with the journey while not breaking his speed limit

Answer:

a ≈ 1.59

b ≈ 6.69

Step-by-step explanation:

Law of Sines: [tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex]

Step 1: Find c using Law of Sines

[tex]\frac{6}{sin58} =\frac{c}{sin13}[/tex]

[tex]c = sin13(\frac{6}{sin58})[/tex]

c = 1.59154

Step 2: Find a using Law of Sines

[tex]\frac{6}{sin58} =\frac{a}{sin109}[/tex]

[tex]a = sin109(\frac{6}{sin58} )[/tex]

a = 6.68961

Answer:

A; The first choice.

Step-by-step explanation:

We have the equation [tex]x^4+6x^2+5=0[/tex] and we want to solve using u-substitution.

When solving by u-substitution, we essentially want to turn our equation into quadratic form.

So, let [tex]u=x^2[/tex]. We can rewrite our equation as:

[tex](x^2)^2+6(x^2)+5=0[/tex]

Substitute:

[tex]u^2+6u+5=0[/tex]

Solve. We can factor:

[tex](u+5)(u+1)=0[/tex]

Zero Product Property:

[tex]u+5=0\text{ and } u+1=0[/tex]

Solve for each case:

[tex]u=-5\text{ and } u=-1[/tex]

Substitute back u:

[tex]x^2=-5\text{ and } x^2=-1[/tex]

Take the square root of both sides for each case. Since we are taking an even root, we need plus-minus. Thus:

[tex]x=\pm\sqrt{-5}\text{ and } x=\pm\sqrt{-1}[/tex]

Simplify:

[tex]x=\pm i\sqrt{5}\text{ and } x=\pm i[/tex]

Our answer is A.

Answer:

The hypotenuse is the longest side in a triangle.

a^2=b^2+c^2.

14^2=9^2+c^2.

c^2=196-81.

c^2=115.

c=√115.

c=10.72~11cm

Answer:

Following are the answer to this question:

Step-by-step explanation:

Let, In the Bth place there are 8 values.

In point a:

There is no case, where it generally manages its next groom is = 7 and it will be arranged in the 2, that can be arranged in 2! ways. So, the total number of ways are: [tex]\to 7 \times 2= 14\\\\ \{(1,2),(2,1),(2,3),(3,2),(3,4),(4,3),(4,5),(5,4),(5,6),(6,5),(6,7),(7,8),(8,7),(7,6)\}\\[/tex][tex]\therefore[/tex] required probability:

[tex]= \frac{14}{8!}\\\\= \frac{14}{8\times7 \times6 \times 5 \times 4 \times 3\times 2 \times 1 }\\\\= \frac{1}{8\times6 \times5 \times 4 \times 3}\\\\= \frac{1}{8\times6 \times5 \times 4 \times 3}\\\\=\frac{1}{2880}\\\\=0.00034[/tex]

In point b:

Calculating the leftmost position:

[tex]\to \frac{7!}{8!}\\\\\to \frac{7!}{8 \times 7!}\\\\\to \frac{1}{8}\\\\\to 0.125[/tex]

In point c:

This option is false because

[tex]\to P(A \cap B) \neq P(A) \times P(B)\\\\\to \frac{12}{8!} \neq \frac{14}{8!}\times \frac{1}{8}\\\\\to \frac{12}{8!} \neq \frac{7}{8!}\times \frac{1}{4}\\\\[/tex]

Answer:

1078

Step-by-step explanation:

The product of 22 and 49 is 1078.

Answer:

1078 is the product

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given that:

[tex]T(x,y) = \dfrac{100}{1+x^2+y^2}[/tex]

This implies that the level curves of a function(f) of two variables relates with the curves with equation f(x,y) = c

here c is the constant.

[tex]c = \dfrac{100}{1+x^2+2y^2} \ \ \--- (1)[/tex]

By cross multiply

[tex]c({1+x^2+2y^2}) = 100[/tex]

[tex]1+x^2+2y^2 = \dfrac{100}{c}[/tex]

[tex]x^2+2y^2 = \dfrac{100}{c} - 1 \ \ -- (2)[/tex]

From (2); let assume that the values of c > 0 likewise c < 100, then the interval can be expressed as 0 < c <100.

Now,

[tex]\dfrac{(x)^2}{\dfrac{100}{c}-1 } + \dfrac{(y)^2}{\dfrac{50}{c}-\dfrac{1}{2} }=1[/tex]

This is the equation for the  family of the eclipses centred at (0,0) is :

[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1[/tex]

[tex]a^2 = \dfrac{100}{c} -1 \ \ and \ \ b^2 = \dfrac{50}{c}- \dfrac{1}{2}[/tex]

Therefore; the level of the curves are all the eclipses with the major axis:

[tex]a = \sqrt{\dfrac{100 }{c}-1}[/tex]  and a minor axis [tex]b = \sqrt{\dfrac{50 }{c}-\dfrac{1}{2}}[/tex]  which satisfies the values for which 0< c < 100.

The sketch of the level curves can be see in the attached image below.