can someone explain to me what this is in detail P(A∩B) = P(A) · P(B)

Answer:

Step-by-step explanation:

Sin (90 + Ф ) =Cos Ф

135° = 90 + 45

Sin 135° = Sin (90 + 45)

             = Cos 45°

             [tex]= \dfrac{1}{\sqrt{2}}[/tex]

Answer:

six hundred and sixty-two by twenty-six

Step-by-step explanation:

Answer:

333 remainder 6

Step-by-step explanation:

       333   R 6

26/8664

  - 78

     086

     - 78

        084

          -78

              6

I struggled to show the work formatted how I would normally write this problem out, so I'll also talk through how I got the answer.

The first step in long division by hand is to take the number that is furthest to the left and seeing how many times your divisor (26) will go into it.

In this case the digit in the thoudands place (our furthest left) is 8.  Obivously 26 does not fit into 8. So our answer will have a 0 in the thousands place and we move one place to the right.  

We now have 86.  26 fits into 86 three times and leaves a difference of 8 remaining in the hundreds place, and we move the right again to the tens place.

We again have 86. 26 again fits in three time and leaves a difference of 8. As we move to the right to the ones place we are left with 84.  

26 fits into 84 three times, but we have a difference of 6 this time.

We cannot continue as 26 will never fit into our remainder of 6.

We had a 0 in the thousands place, a 3 in the hundreds place, a 3 in the tens place and a 3 in the ones palce with 6 left over.

So the final answer is 333 remainder 6

Answer:

7 (1-6)

Step-by-step explanation:

you find the greatest common factor of 7 and 42.

7

7x1

42

1x42

2x21

3x14

6x7

Based on the amount that Felix deposited in the account and the 5% compounded annual interest, the interest Felix will earn in 2 years is $10.25

First, find the amount the $100 would have accrued to in 2 years:

= Amount deposited x (1 + rate) ^ number of years

Solving gives:

= 100 x (1 + 5%)²

= $110.25

The interest earned is:

= Amount in 2 years - Amount deposited

= 110.25 - 100

= $10.25

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Answer:10.25

Step-by-step explanation:

Answer:

undefined

Step-by-step explanation:

Given points:  (-8, -3) and (-8, -2)

As the x-value of both points is the same, there is no slope.

Therefore, the line that passes through the two given points is a vertical line at [tex]x=-8[/tex]

[tex]\textsf{let}\:(x_1,y_1)=(-8,-3)[/tex]

[tex]\textsf{let}\:(x_2,y_2)=(-8,-2)[/tex]

[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-2-(-3)}{-8-(-8)}=\dfrac{1}{0}[/tex]

Any number divided by zero is undefined.

You should keep 0.97 seconds of distance between you and the vehicle ahead.

The formula for calculating distance is expressed as:

distance  = speed * time

Time = Distance/Speed

Given the following parameters

Distance = 50 feet

Speed = 35mph = 51.3ft/s

Time taken = 50/51.3
Time taken = 0.97

Hence you should keep 0.97 seconds of distance between you and the vehicle ahead.

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Answer:

I think it is (n - 5) x 4 - 7, but I am not sure.

The graph is not symmetric, and it has no vertical or horizontal asymptotes.

Coordinate geometry is a branch of mathematics that combines algebraic and geometric concepts to study the properties of geometric figures using a coordinate system. It involves representing geometric figures such as points, lines, curves, and shapes in a plane or space using numerical values called coordinates.

The graph of the function [tex]f(x)=-3(x+1)^2 (x-3) (x-5)^3[/tex] is a cubic polynomial function with several important characteristics:

Degree: The degree of the function is 7, which means that the graph has 7 x-intercepts.

Symmetry: The function is not symmetric with respect to the y-axis or the origin.

End Behavior: As x approaches negative infinity, the function approaches negative infinity, and as x approaches positive infinity, the function approaches negative infinity.

Zeros: The function has x-intercepts at x = -1, x = 3, and x = 5. The intercept at x = -1 has a multiplicity of 2, while the intercepts at x = 3 and x = 5 have a multiplicity of 3. This means that the graph touches the x-axis at x = -1 and bounces off at x = 3 and x = 5.

Turning Points: The function has two turning points, one at x = -1 and one at x = 3. The turning point at x = -1 is a local maximum, while the turning point at x = 3 is a local minimum.

Behavior near Zeros: Near each of the x-intercepts, the function changes direction. At x = -1, the function changes from decreasing to increasing. At x = 3 and x = 5, the function changes from increasing to decreasing.

Vertical Asymptotes: The function has no vertical asymptotes.

Horizontal Asymptotes: The function has no horizontal asymptotes.

Intercepts: The y-intercept of the function is at y = 0.

Overall, the graph of the function [tex]f(x)=-3(x+1)^2 (x-3) (x-5)^3[/tex] is a complicated cubic polynomial with multiple x-intercepts, turning points, and changing directions near the intercepts.

Therefore, the graph is not symmetric, and it has no vertical or horizontal asymptotes.

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Answer:

According to my calculation it came like this.Hope the picture will help you.

Answer:

5. During the day, the temperature on the surface of Mars rises at a rate of 9 degrees C every hour

a. In 2 hours: 18 a. in 3 hours: 27    in n hours: 9n

b. y=9n

c. 108

d. -540

6. Kaite saves 5 dollars every week, so far she has saved a total of $63

a. y=5x+63

b. 25

hope it helps

Answer:

g(x) = x^2 + 6

Step-by-step explanation:

We are trying to find what is g(x) from the graph. f(x) = x^2 translated to g(x).

g(x) = (x - h)^2 +k

It appears the graph is just translated up by k = 6 and no transition of left/right h = 0.

g(x) = (x-0)^2 + 6

g(x) = x^2 + 6

Answer:

26

Step-by-step explanation:

as the ratio is given you should divide ratio of boys by total ratio and multiply it by the total number of students, kinda like how in percentages you divide partial value/total value x 100, just in this case the total is 45 instead of 100. So [tex]\frac{4}{7} * 45[/tex] = 25.7 which have to be rounded to 26

Answer:

6:7

Step-by-step explanation:

1.5 m=150 cm

ratio of their hight is 150/175=30/35=6/7

=6:7

The proportion equation is A = 6 : 7

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the proportion equation be represented as A

Now , the value of A is

The height of Maisa is P = 1.5 m

The value of 1.5 m = 150 cm

And , the height of Arman = 175 cm

So , the proportion is

A = height of Maisa / height of Arman

Substituting the values in the equation , we get

A = 150 / 175

A = 6/7

Therefore , the value of  A is 6 : 7

Hence , the proportion is 6 : 7

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Answer:

65.2%

Step-by-step explanation:

~Hope this helps~

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{6\% of 12.75}}{\left( \cfrac{6}{100} \right)12.75}\implies 0.765~~\approx 0.77~~\textit{about 77 cents}[/tex]

Answer:

i think that the correct answer would be A or C

Step-by-step explanation:

hope this helps

sorry if the answers that i gave you is incorrect

Answer:

2nd option

Step-by-step explanation:

the nth term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

here a₁ = 64 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{32}{64}[/tex] = [tex]\frac{1}{2}[/tex] , then

[tex]a_{n}[/tex] = 64 [tex](\frac{1}{2}) ^{n-1}[/tex]

Answer:

70 fl oz

Step-by-step explanation:

Find how much is added to the punch bowl.

2 containers and each holds 6 fluid ounces.

2 x 6 = 12

Now find the total amount of liquid by adding the original amount and the amount added.

58 + 12 = 70

Answer:

Step-by-step explanation:

Answer: 28

Step-by-step explanation: 80 x 0.35 = 28

when we multilpy we get 80×0.35 = 28

Without going too much into the proofs angle ACD is congruent to angle DBA.

If ACD is ~= DBA then

ACD = 54 degrees

Explanation:

The figure is a reflection. While orientation isnt preserved in reflections side lengths and angle measures are.

This means that both triangles have the same side length measures and have the same angle measures.

You are given the angle measures of one of the triangles. We also know both triangles are congruent since they both fit perfectly inscribed in the circle.

With this in mind you can prove that all the angles of each triangle are congruent.

Thus

ACD = 54 degrees

To calculate the area of a parallelogram

 ⇒ we must know the formula

     ⇒ Area = base * height

What are we given:

Thus:

   Area = 3ft * 4ft = 12 [tex]ft^2[/tex]

Hope that helps!

Answer:

43.98229 ft

Step-by-step explanation:

The diameter is 14ft, meaning the radius, which is half of it, is 7ft. Plug 7 into the r. C= 2pi(7) which 14pi. Now you multiply 14 by 3.14, which is the value of pi, and round it to whatever you need to give you your value.

The value of circumference of this circle is,

⇒ circumference = 14π ft

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Diameter = 14 ft

Hence, We get;

Radius = 7 ft

Thus, The value of circumference of this circle is,

⇒ circumference = 2πr

⇒ circumference = 2 × π × 7

⇒ circumference = 14π ft

Thus, The value of circumference of this circle is,

⇒ circumference = 14π ft

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Answer:

One solution

Step-by-step explanation:

Discriminant

[tex]\textsf{Discriminant}:b^2-4ac}\quad\textsf{when}\:ax^2+bx+c=0[/tex]

[tex]\textsf{If}\quad b^2-4ac=0 \implies \textsf{one solution}[/tex]

[tex]\textsf{If}\quad b^2-4ac > 0 \implies \textsf{two solutions}[/tex]

[tex]\textsf{If}\quad b^2-4ac < 0 \implies \textsf{no solutions}[/tex]

Given equation:

[tex]-8x^2-8x-2=0[/tex]

Swap sides:

[tex]\implies 8x^2+8x+2=0[/tex]

Using discriminant:

[tex]\implies b^2-4ac=8^2-4(8)(2)=0[/tex]

Therefore, there is one solution

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

Proof

[tex]8x^2+8x+2=0[/tex]

Divide both sides by 2:

[tex]\implies 4x^2+4x+1=0[/tex]

Separate the middle term:

[tex]\implies 4x^2+2x+2x+1=0[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies 2x(2x+1)+1(2x+1)=0[/tex]

Factor out the common term [tex](2x+1)[/tex]:

[tex]\implies (2x+1)(2x+1)=0[/tex]

Therefore:

[tex]\implies 2x+1=0[/tex]

[tex]\implies x=-\dfrac12[/tex]

Thus proving there is one solution.

Here

Discriminate

Roots are equal hence one solution

Step-by-step explanation:

The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables and c is the constant term. The other different forms to find and represent the equation of a line are slope-intercept form, point-slope form, two-point form, intercept form, and normal form.

Answer:

[tex]\boxed{\sf{x=\dfrac{21}{4}=5.25 }}[/tex]

Step-by-step explanation:

Isolate the term of x from one side of the equation.

Use the distributive property.

Distributive property:

[tex]\Longrightarrow: \sf{A(B+C)=AB+AC}[/tex]

Expand the form multiply.

4*x=4x

4*3=12

Rewrite the problem down.

4x-12=9

Add by 12 from both sides.

4x-12+12=9+12

Solve.

Add the numbers from left to right.

9+12=21

4x=21

Divide by 4 from both sides.

4x/4=21/4

Solve.

Divide the numbers from left to right.

x=21/4

21/4=5.25

x=21/4=5.25

I hope this helps you! Let me know if my answer is wrong or not.

The answer is B. Apply the distributive property to get 4x−12=9. You would do 4 times x to get 4x and then 4x3 to get 12. Then apply that information to the equation to get 4x−12=9.

Answer:

5

x

2

+

20

x

−

60

Factor

5

out of

5

x

2

+

20

x

−

60

.

Tap for more steps...

5

(

x

2

+

4

x

−

12

)

Factor.

Tap for more steps...

5

(

x

−

2

)

(

x

+

6

)

Step-by-step explanation:

ANSWER IS =5X2+20X-60

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

THIS ANSWER IS CORRECT

Answer:

x=4

Step-by-step explanation:

3x+8 = 20

subtract 8 both sides

3x=12

divide 3 both sides

x=4