Which could be the first step of an indirect proof of the conditional below? Select all that apply.

If x = 4, then 4x = x2.

A. If 4x ≠ x2, then x ≠ 4.
B. If x = 4, then 4x = x2.
C. Assume if 4x ≠ x2, then x ≠ 4.
D. Assume if x ≠ 4, then 4x ≠ x2.

Answer:

π/4 − x

Step-by-step explanation:

I hope its correct

Answer:

15

Step-by-step explanation:

Red counters = 35

Number of green counters = x

P(picking a green counter) = 0.3

Probability = required outcome / Total possible outcomes

Required outcome = number of green counter

Total possible outcomes = green counter + red counter

Hence,

0.3 = x / (35+x)

0.3(35 + x) = x

10.5 + 0.3x = x

10.5 = x - 0.3x

10.5 = 0.7x

x = 10.5 / 0.7

= 15

Number of green counters = 15

The graphical solution to the inequality is attached below with the solution at coordinate (50, 45).

Groups :

Total of atleast 95 :

Atmost Five less students in Y than in X :

Using graphical inequality solver or calculator :

Hence. The solution to the inequality is (50, 45) and the graph is attached below.

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Answer:

x = 50

Step-by-step explanation:

<c = <e so:

5y - 4 = 76

5y = 80

y = 16

<c = 76

All triangle interior angles add up to 180 so:

x + 8 + 46 + 76 = 180

x + 130 = 180

x = 50

The lesser number is 6 and the greater number is 13, satisfying the given conditions of being 7 apart and fulfilling the equation 10x + 5 = 5y.

Let x represent the lesser number and y represent the greater number. According to the problem, the greater number is 7 more than the lesser number, so we have the equation y = x + 7.

The second condition states that 10 times the lesser number increased by 5 is equal to 5 times the greater number. Mathematically, this can be written as 10x + 5 = 5y.

Now, substitute the value of y from the first equation into the second equation. We have 10x + 5 = 5(x + 7).

Simplifying the equation, we get 10x + 5 = 5x + 35.

Subtracting 5x from both sides, we have 5x + 5 = 35.

Subtracting 5 from both sides, we get 5x = 30.

Dividing both sides by 5, we find x = 6.

Substituting this value back into the first equation, we get y = 6 + 7 = 13.

Therefore, the lesser number is 6 and the greater number is 13.

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The graph represents this system of inequalities:

F. y ≤ −x + 4

G. y ≤ 3x − 1

In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Next, we would determine the linear equation representing the line of f(x) which passes through the points (0, 4) and (4, 0) by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 0 = (4 - 0)/(0 - 4)(x - 4)

y - 0 = -1(x - 4)

y = -x + 4

Therefore, an inequality representing the line of f(x) is y ≤ -x + 4

For the line of g(x), we have:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - (-1) = (5 - (-1))/(2 - 0)(x - 0)

y + 1 = 3(x - 0)

y = 3x - 1

Therefore, an inequality which represents the line of g(x) is y ≤ 3x - 1.

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Complete Question:

In the graph, the area below f(x) is shaded and labeled A, the area below g(x) is shaded and labeled B, and the area where f(x) and g(x) have shading in common is labeled AB. Graph of two intersecting lines. The line f of x is solid and goes through the points 0, 4, and 4, 0 and is shaded below the line. The other line g of x is solid, and goes through the points 0, negative 1 and 2, 5 and is shaded below the line. The graph represents which system of inequalities?

y ≤ −3x − 1

y ≤ −x − 4

y > −3x + 1

y ≤ −x − 4

y < 3x − 1

y ≤ −x + 4

y ≤ 3x − 1

y ≥ −x + 4

Use the slope formula:-

\(\displaystyle\frac{y_2-y_1}{x_2-x_1}\)

Plug in the values:-

\(\displaystyle\frac{2-(-4)}{-5-3}\)

\(\displaystyle\frac{2+4}{-8} =\frac{6}{-8} =-\frac{6}{8}\)

Reduce the fraction by dividing the top & bottom by 2:-

\(-\displaystyle\frac{3}{4}\)

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)

Answer:

Step-by-step explanation:

103.8 seconds

68.11024 inches

1) The probability that all the marbles are red:

There are 8 red marbles out of a total of 20 marbles (8 + 5 + 7). The probability of drawing 4 red marbles without replacement is:

(8/20) * (7/19) * (6/18) * (5/17) = 0.0392
Rounded to 4 decimal places, the probability that all the marbles are red is 0.0392.

2) The probability that none of the marbles are red:

There are 12 non-red marbles out of 20 total marbles. The probability of drawing 4 non-red marbles without replacement is:

(12/20) * (11/19) * (10/18) * (9/17) = 0.2614
Rounded to 4 decimal places, the probability that none of the marbles are red is 0.2614.

a) The probability of getting all Tails when tossing a fair coin 4 times is calculated by multiplying the probability of getting a Tail in each toss (which is 0.5). So, the probability is:

0.5 * 0.5 * 0.5 * 0.5 = 0.0625
Rounded to 4 decimal places, the probability is 0.0625.

b) To find the probability of getting at least one Head, we can find the probability of not getting any Heads (i.e., getting all Tails) and then subtract it from 1:

1 - 0.0625 = 0.9375
Rounded to 4 decimal places, the probability of getting at least one Head is 0.9375.

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Answer:

24/25

Step-by-step explanation:

here's your solution

=> perpendicular = 24

=> base = 7

=> hypotenuse = ?

=> firstly we need to find hypotenuse

=> h^2 = p^2 + b^2

=> h^2 = 24^2 + 7^2

=> h^2 = 576 + 49

=> h^2 = 625

=> h = √625

=> h = 25

now sin thita = perpendicular/hypotenuse

=> 24/25

hope it helps

The relationship between a circumference of a circle and its diameter is the circumference is about 3.14 times greater than its diameter.

What is circumference?

A circle's perimeter is known as its circumference. It is the circumference of the circle as a whole.

The formula gives it

\(C = 2\pi r\)

where r is the radius of the circle.

Diameter is defined as the two times the radius

i.e. d = 2r ................. (1)

and the circumference of a circle is \(C = 2\pi r\) ................ (2)

From equations (1) and (2), we get

\(C = \pi d\)

where, \(\pi\) = 3.14

So, the required option is the circumference is about 3.14 times greater than its diameter.

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Check the picture below.

so the area of it, is really the area of a 16x16 square and four triangles with a base of 16 and a height of 15.

\(\stackrel{ \textit{\LARGE Areas}}{\stackrel{ square }{(16)(16)}~~ + ~~\stackrel{ \textit{four triangles} }{4\left[\cfrac{1}{2}(16)(15) \right]}}\implies 256~~ + ~~480\implies \text{\LARGE 736}~cm^2\)

Answer: 21

Step-by-step explanation:

Answer: sorry i cant help but i love the username

Step-by-step explanation:

Lines l and m are parallel; line l will map onto line m with a 90° rotation; line l can map onto line m with a vertical line of reflection.

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The correct statement is "only a and c are correct"  so option g is the answer.

The statement that is true in a normal distribution is "approximately 70% of the values are within one standard deviation from the mean" (a), and "2.1% of the values are between -2 and -3 standard deviations from the mean" (c).

These statements are true because of the properties of a normal distribution, also known as a Gaussian distribution or bell curve. In a normal distribution, the majority of values cluster around the mean, with fewer and fewer values as you move further away from the mean.

The statement "twenty-seven percent of the values are between one and two standard deviations from the mean" (b) is not true, as the correct percentage is approximately 27.7% (68-95-99.7 rule).

The statement "0.1% of the values are 3 or higher standard deviations from the mean" (d) is also not true, as the correct percentage is approximately 0.3%.

Therefore, the correct statement is "only a and c are correct".

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The gradient of the function \(\(f\)\) at the point \(\((-1, -3)\)\) is:

\(\[\nabla f(-1, -3) = \left(-3e^{-3} \sin(12), 4e^{-3} \cos(12)\right)\]\)

To find the gradient of the function \(\( f(x, y) = e^{3x} \sin(4y) \)\) at the point \(\((-1, -3)\)\), we need to compute the partial derivatives with respect to \(\(x\) and \(y\)\) and evaluate them at that point.

The gradient of a function is given by:

\(\[\nabla f(x, y) = \left(\frac{{\partial f}}{{\partial x}}, \frac{{\partial f}}{{\partial y}}\right)\]\)

Let's calculate the partial derivatives:

\(\[\frac{{\partial f}}{{\partial x}} = \frac{{\partial}}{{\partial x}}\left(e^{3x} \sin(4y)\right) = 3e^{3x} \sin(4y)\]\)

\(\[\frac{{\partial f}}{{\partial y}} = \frac{{\partial}}{{\partial y}}\left(e^{3x} \sin(4y)\right) = 4e^{3x} \cos(4y)\]\)

Now, we can evaluate these derivatives at the point \(\((-1, -3)\):\)

\(\[\frac{{\partial f}}{{\partial x}}\Bigr|_{(-1, -3)} = 3e^{3(-1)} \sin(4(-3)) = 3e^{-3} \sin(-12)\]\)

\(\[\frac{{\partial f}}{{\partial y}}\Bigr|_{(-1, -3)} = 4e^{3(-1)} \cos(4(-3)) = 4e^{-3} \cos(-12)\]\)

Simplifying further:

\(\[\frac{{\partial f}}{{\partial x}}\Bigr|_{(-1, -3)} = 3e^{-3} \sin(-12) = -3e^{-3} \sin(12)\]\)

\(\[\frac{{\partial f}}{{\partial y}}\Bigr|_{(-1, -3)} = 4e^{-3} \cos(-12) = 4e^{-3} \cos(12)\]\)

Therefore, the gradient of the function \(\(f\)\) at the point \(\((-1, -3)\)\) is:

\(\[\nabla f(-1, -3) = \left(-3e^{-3} \sin(12), 4e^{-3} \cos(12)\right)\]\)

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The water level drop each​ hour by 0.0384 inch

Firstly, the deacrease in water level is takes as per the question

Decrease = 3/8 inches

Decrease=0.375 inches

Then the time interval is calculated

From 10 pm to  7:45 hours will be 9.45 hours

Time interval= (9 + 45/60) hours

Time interval=9.75 hours

Now, the drop in water level per hour is determined, to do so, total water level decreased is divided by the time taken to decrease that water level

that is 0.375/9.75 inches/hour

= 0.03846 inches/hour

Therefore, if between 10 P.M. and 7:45 A.M.​, the water level in a swimming pool decreased by 3/8 inches and the water level decreased at a constant​ rate, the water level drop each​ hour is 0.03846

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Answer:

(-3*4)^3= -1728

Step-by-step explanation:

remember that

(-3*4)^3 is the same as (-3)^3 * (4)^3

Therefore,

-3^3 * 4^3

-27 * 64

= -1728

hope this helps :)

Using geometric sequences, 20,480 rabbits are grown during the 12th month.

A geometric sequence is a sequence of numbers in which each term after the first is found by multiplying the preceding term by a fixed non-zero number called the common ratio.

At the end of the first month, there are 10 x 2 = 20 rabbits.

At the end of the second month, there are 20 x 2 = 40 rabbits.

Similarly, at the end of the third month, there are 40 x 2 = 80 rabbits.

This is a geometric sequence with a common ratio of 2 and a first term of 10. The number of rabbits at the end of the 12th month would be:

10 x 2^12 = 10 x 4096 = 40,960 rabbits

To find the number of rabbits grown during the 12th month, we need to subtract the number of rabbits at the end of the 11th month from the number of rabbits at the end of the 12th month:

\(40,960 - (10 x 2^{11}) = 40,960 - 20,480 = 20,480\)

Hence, 20,480 rabbits are grown during the 12th month.

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Answer:

i got 45 but I'm not sure

Step-by-step explanation:

so if he is saving up fot the skate board,

you would need to multiply 40 × 3 that will give you 120, then after that I subtracted 85 from 120 and got 45 but like I said I'm not so sure

False. The columns of matrix P are not necessarily eigenvectors of matrix A. While the diagonal matrix D contains the eigenvalues of A, the eigenvectors are not explicitly determined by the columns of P.

False. The columns of matrix P are not guaranteed to be eigenvectors of the transpose of matrix A (A.T).

In the given equation, \(a = PDP^(-1),\)

where D is a diagonal matrix and P is an invertible matrix.

The diagonal elements of D represent the eigenvalues of matrix A, while the columns of P correspond to the eigenvectors of A.

When considering the transpose of matrix A (A.T), we have \((A.T) = (PDP^(-1)).T = (P^{(-1)})^T D^T P^T.\)

Taking the transpose of a product involves reversing the order of the matrices and transposing each matrix individually.

Therefore, we have \((A.T) = P^T D^T (P^{(-1)})^T.\)

Since P is an invertible matrix, its transpose \(P^T\) is also invertible. Similarly, the transpose of the inverse of \(P, (P^{(-1)} )^T,\) is also invertible.

However, the key point is that the diagonal matrix\(D^T\) is not guaranteed to have the same eigenvalues as matrix A.

The eigenvalues of A are present in D, but they may not remain on the main diagonal after transposing.

Thus, the columns of matrix P, which correspond to the eigenvectors of A, may not necessarily be the eigenvectors of A.T.

In conclusion, the statement is false.

The columns of matrix P do not have to be eigenvectors of the transpose of matrix A (A.T).

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Answer:

y = 3x - 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 3 , then

y = 3x + c ← is the partial equation

To find c substitute (2, 3) into the partial equation

3 = 6 + c ⇒ c = 3 - 6 = - 3

y = 3x - 3 ← equation of line

Using the solution of Algebraic expression,

we get that total 28 games won by sports team.

We have given that,

let a sports team lost be x games .

then, total number of games won by sports team

= 2x

total number of games played by sports team

= 42

i.e , 2x + x = 42

=> 3x = 42

=> x = 42/3

=> x = 14

so, number of games lost by sports team is 14

but we have to calculate the total number of games won by spots team .

using the value of x , we get 2x = 2×14

=> 28 games

Hence, total 28 games out of 42 games are won by sports team.

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Answer:

12.5 L of grape juice is needed in 5L of cranberry juice.

Step by step explanation:

We can solve this situation by using proportional relationships:

Now, solve for x:

Answer:

1, 2, 5, 12, 13

Step-by-step explanation:

∠1 = 90 is given, which is a right angle

∠3 = 90 as well because ∠1 and ∠3 are vertically opposite

∠3 = ∠8, because ∠1 and ∠8 are same side exterior angles, which are the same

Therefore ∠3 must be congruent to ∠8  

Answer:

The answer to the question provided is -70.

a. all of their children will have blood type O. b. The probability of their next child having blood type O is 50%, since each parent has a 50% chance of passing down an O allele.

For the first question:

(a) Emily and Michael both have alleles O, which means that they can only pass down an O allele to their children. Therefore, all of their children will have blood type O.

(b) The probability of their next child having blood type O is 100%, since both parents only have O alleles to pass down.

For the second question:

(a) Andreona and Caleb both have alleles A and O, which means that they each have a 50% chance of passing down either an A or an O allele to their children. The possible blood types their children can have are A and O.

(b) The probability of their next child having blood type A is 50%, since Andreona has a 50% chance of passing down an A allele, and Caleb has a 50% chance of passing down an A allele. The probability of their next child having blood type O is 50%, since each parent has a 50% chance of passing down an O allele.

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Answer:

10

Step-by-step explanation:

160-80/12-4= 80/8= 10

Answer:

-20x^2+8x

Step-by-step explanation:

That is -20x squared by the way

You’re welcome :)