e:f=3:7
f:g=2:3
Work out e:g in simplest form

For the regions bounded by y = 6cosx and y = one-fourth x squared minus 7, the limits of integration, the expression representing the total area, and the total area are mathematically given as

A=27.03squnit

What are the limits of integration, the expression representing the total area, and the total area.?

Generally, the equation for expression is mathematically given as

y = 6cosx

y=(1/4)x^2-7

therefore

[tex]A=\int^{b}_a (f(x)-g(x))dx[/tex]

The limits are

a=0 b=2\pi

Hence

[tex]A=\int ^{2\pi}_0 (6cosx -((1/4)x^2-7))dx\\\\solving\\\\A=\int^{2\pi}_0 (6cosx -((1/4)x^2-7))dx[/tex]

A=27.03squnit

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Probability helps us to know the chances of an event occurring. The probability she will do her homework without complaining given that she ate her dinner without complaining is 2/5.

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

Let eating dinner without complaining be A, and doing homework without complaining be B.

Given the probability my daughter will eat her dinner without complaining is 5/7. So, we can write,

P(A) = 5/7

Also, The probability she will eat her dinner and do her homework all without complaining is 2/7. So, we can write,

P(A∩B) = 2/7

Now, the probability she will do her homework without complaining given that she ate her dinner without complaining is,

[tex]P(B|A)= \dfrac{P(A\cap B)}{P(A)}[/tex]

             [tex]= \dfrac{\dfrac{2}{7}}{\dfrac57}\\\\\\= \dfrac25[/tex]

Hence, the probability she will do her homework without complaining given that she ate her dinner without complaining is 2/5.

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Answer:

Obtuse and the rest of the question is incomplete.

Step-by-step explanation:

Answer:

GFC = 4

Step-by-step explanation:

Factors of 20     1   2   4   5   10  20

Factors of 36     1   2  3 4  6  9 12 18 36

Answer:4

Step-by-step explanation:nice and simple

A, -9 ≤ -3X -6 ≤ 6

Inequality is an algebraic statement that shows that two quantities are unequal.

Analysis:

From the above, only A, is the correct inequality represented above.

solving for x in A, we have,

-9 ≤ -3x - 6 ≤ 6

splitting,

-9 ≤ -3x -6

-3 ≤ -3x

1 ≥ x

x ≤ 1

-3x-6 ≤ 6

-3x ≤ 12

x ≥ 12/-3 ≥ -4

-4 ≤x ≤1, A

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Answer:

k(magnitude of vector a).vector a

Step-by-step explanation:

Given question is based on vectors so,

vectors :- Vectors in math is a geometric entity that has both magnitude and direction. Vectors have an initial point at the point where they start and a terminal point that tells the final position of the point. Various operations can be applied to vectors such as addition, subtraction, and multiplication.

To produce an another vector form a given vector we increase its magnitude only not its direction as we have to produce another vector from a given vector.

as its clear from the graph given in the question that only the magnitude of  vector a is increased to produce another vector b

hence we multiply any constant ('k') with the magnitude of vector a to increase its magnitude.

and finally multiply the increased magnitude with the vector 'a' itself.

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As per the question each row must have 6 seats more than the row before it. And there are 11 seats in the first row.

So, the first row has 11 seats

2nd row has 11+6 seats

3rd row has 11+2*6=11+12=23

4th row has 11+3*6=11+18=29

and so on...

We know that the difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. Arithmetic progression can be calculated as

aₙ = a₁ + (n - 1)d,

where aₙ is the nth and a₁ is the first term of this progression respectively and d is the common difference between terms.

So, we can observe the trend and develop the equation for the problem.

There are 11+(n-1)*6 seats in the n-th row.

So, there is 11+(18-1)*6=11+17*6=113 seats in the 18th row.

Therefore, there are 113 seats in the 18th row.

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Answer:

I solved 26 problems correctly.

Answer:

16 and 34

Step-by-step explanation:

The general form = 3n+4

The 4th term = 3(4)+4 = 12+4 = 16

The 10th term = 3(10)+4= 30+4= 34

The population of Tacoma in 2019 would be 1,028,332.

The population can be represented with an exponential equation that has the form:

FV = P (1 + r)^n

200,000 (1.09)^19 = 1,028,332.

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The number of ways Jose can arrange his family members into a row of 5 seats if Jose must sit in the first seat is 840.

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

The number of ways Jose can make his family sit is,

Number of ways = number of ways people can sit on the first sit × number of ways people can sit on the second sit × number of ways people can sit on the third sit × number of ways people can sit on the fourth sit × number of ways people can sit on the fifth sit

Since Jose wants to sit on the first seat there are only options for the first seat, therefore,

Number of ways = 1 × 7 × 6 × 5 × 4 = 840

Hence, the number of ways Jose can arrange his family members into a row of 5 seats if Jose must sit in the first seat is 840.

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Answer:

1/2 is the answers

Step-by-step explanation:

please mark me as brainlest

The slope of the line is = 0.5

one point is =(14,0)

other is =(2,-6)

We can easily solve the question by the formula of a straight line.

The slope is = 0-(-6)/(14-2)

= 1/2

Step-by-step explanation:

[tex] = \tan(5\pi) [/tex]

[tex] = \tan(\pi + 4\pi) [/tex]

[tex] = \tan(\pi) [/tex]

[tex] = \tan(180 \degree) [/tex]

[tex] = 0[/tex]

The answer is A.

Answer:

[tex]y=11[/tex]

Step-by-step explanation:

⇒ [tex]23 - y[/tex]  (Difference means subtraction)

⇒ [tex]23 - y = 12[/tex] (Subtract 12 from 23)

⇒ [tex]y = 11[/tex] (The difference from 23 - 12)

Hii!

___________________________________________________________

Answer:

y=11

Step-by-step explanation:

Let's set up an equation.

"difference between y and 23" tells us to subtract y from 23, so we'll do just that.

23-y=12

Now subtract 23 from both sides

-y=-11

Divide both sides by -1

y=11 "We solved for the variable"

--

Hope that this helped! Best wishes.

--

Answer:

The parent function of linear functions is y=x and it passes through the origin.The domain and range of all linear functions are all real numbers.



Step-by-step explanation:

The remaining elements if Venn diagram is  S= { 4, 9}

A Venn diagram uses overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items.

Given:

E = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 }

S = square numbers

E = even numbers

Element in set S= { 4, 9}

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Answer:

I exactly don't know the answer

[tex]1) \pm 2 \\\\2) \pm 2i\\\\3) \pm i\sqrt{2}\\\\4) \pm \sqrt{2}\\\\5) \pm 3i\sqrt{2}\\\\6) \pm 3\sqrt{2}\\\\7) 2\\\\8) -2[/tex]

Answer:

x=-4,8

Step-by-step explanation:

To solve this, we can take the absolute value sign off -4x+8 and make the right side ±24. This makes the equation -4x+8=±24.

Simplifying, we have

[tex]-4x=\pm24-8\\x=\frac{\pm24-8}{-4} \\x=\frac{+24-8}{-4}, \frac{-24-8}{-4} \\x=-4, 8[/tex]

Answer: 8

Step-by-step explanation:

We are going from a smaller triangle to a larger triangle, so the scale factor is greater than 1.

We know scale factor = (image)/(preimage), so the scale factor is 32/4 = 8

The scale factor of dilation of the triangle is k = 8

Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent

The result of dilation is that the shapes and boundaries of objects in the input image are expanded or thickened. It is often used in conjunction with other morphological operations such as erosion, opening, and closing to manipulate and enhance images.

Given data ,

Let the first triangle be represented as ΔABC

Let the second triangle be represented as ΔDEF

where the measures of sides of ΔABC are

AB = 6 , BC = 6 and AC = 4

The measure of sides of triangle ΔDEF are

DE = 48 , EF = 48 and DF = 32

The scale factor of dilation k = measure of side DE / measure of side AB

k = 48 / 6

k = 8

Hence , the dilation factor is k =8

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The pieces of rope measuring a yard can he divide his rope into1/4 would be 96.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Chad has a rope that is 24 yards long. He wants to divide the rope so each piece will be 1/4 yards

= 24÷1/4

= 24× 4

= 96

Hence he can divide the rope into 96 pieces.

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#1

Find slope

y=-3x+5 is the equation as there is no other having slope -3

#2

slope

y=x-4 as no other have slope m

#3

y intercept is -1

y=2x-1 is the equation as it has y intercept -1

#4

y intercept is -4

All the blanks have been filled , which proves ultimately that Triangle ABC is a right angled Triangle.

A triangle in which one angle is 90 degree is called a Right Angled Triangle.

AB is congruent to DB because segment DE was constructed so that DE = AB , BC is congruent to EF , because segment EF was constructed so that EF = BC , Since Triangle DEF is a right angled triangle .

DE² +EF²  = DF²  by the Pythagoras Theorem .

WE are given that AB²  +BC²  = AC²

Since DE = AB and EF = BC , DE²  +EF²  = AC²  by the given data

Also DF² = AC² by the above equation .

Taking the square root on both the sides of the equation gives DF = AC .

So AC is congruent to DF by the definition of congruency .

Applying SSS Congruency , Triangle ABC is congruent to DEF .Therefore ABC is a right angled triangle.

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A function assigns the values. The correct option is C.

A function assigns the value of each element of one set to the other specific element of another set.

For the given graph, the value of f(0) means the value of function when the value of x is 0. Thus, when the graph intersect with the x-axis is the value of f(0), therefore,the values of f(0) are -2, -1, 1, and 3 only.

Hence, the correct option is C.

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Answer:

1/4 = 0.25

Step-by-step explanation:

I assume you mean

lim((ln(x) - ln(4)) / (x - 4))

ln(x) - ln(4) = ln(x/4)

rule of l'hopital

lim f(x)/g(x) = lim f'(x)/g'(x)

if g'(x) <> 0

f(x) = ln(x/4)

g(x) = x - 4

ln(x)' = 1/x

ln(x/4)' = 1/x/4 × 1/4 = 1/x

(x - 4)' = 1

so,

lim f'(x)/g'(x) = 1/x / 1 = 1/x

which is for x approaching 4 : 1/4 = 0.25

Answer: 1/2

Step-by-step explanation:

Dividing the numerator and denominator by x, we get the limit is equal to:

[tex]\lim_{x \to -\infty} \frac{-\sqrt{1+\frac{5}{x}+\frac{1}{x^2}}+3}{4+\frac{7}{x}}\\\\=\frac{\lim_{x \to -\infty} \left(-\sqrt{1+\frac{5}{x}+\frac{1}{x^2}}+3 \right)}{\lim_{x \to -\infty} \left(4+\frac{7}{x} \right)}\\\\=\frac{2}{4}=\boxed{1/2}[/tex]

Answer:

30.5

Step-by-step explanation:

here :

n represents the number of trials

p represents the probability of success

 In a binomial distribution, The mean

 is equal to the product of those two values.

In other words,

The mean = n × p

                 = 122 × 0.25

                 = 30.5

Answer:

C) 5 units

Step-by-step explanation:

In order to find the distance between points P and Q, we will be using the Distance Formula.

[tex]\sf \textsf{\underline{Distance Formula:}}\ \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Given:

where:

⇒ x₁ = 3, y₁ = -1

⇒ x₂ = -1, y₂ = -4

Substitute these values into the formula:

[tex]\sf\\\implies d=\sqrt{(-1-3)^2+(-4-(-1))^2}\\\\\implies d=\sqrt{(-1-3)^2+(-4+1)^2}\\\\\implies d=\sqrt{(-4)^2+(-3)^2}\\\\\implies d=\sqrt{16+9}\\\\\implies d=\sqrt{25}\\\\\implies d=5[/tex]

The distance from P to Q is 5 units.

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The amount of force is moving the wagon along ground level will be 26.8 pound

A force in physics is an effect that has the power to alter an object's motion. A mass-containing object's velocity can vary, or accelerate, as a result of a force. Intuitively, a push or a pull can also be used to describe force. Being a vector quantity, a force has both magnitude and direction.

Given a wagon is being pulled by a handle making a 40° angle with a force of 35 pounds

We have to find amount of force is moving the wagon along level ground

The angle with force is given 40 degree

So the formula to find amount of force is moving the wagon along level ground will be as follow:

Fₓ = F cosθ

Fₓ = 35 * cos40

Fₓ = 26.8 pound

Hence amount of force is moving the wagon along ground level will be 26.8 pound

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