2/4 = 1/2 1/3 circle the equivalent fraction

the maximum height of the equation -16x^2+80x+25=0 is 31.25.

we can use the fact that the maximum height of a quadratic equation occurs at the vertex. The x-coordinate of the vertex can be found using the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic equation. In this case, a = -16 and b = 80, so x = -80/(-32) = 2.5.

To find the corresponding y-coordinate (i.e. the maximum height), we substitute x = 2.5 into the equation and simplify:

-16(2.5)^2 + 80(2.5) + 25 = 31.25

Therefore, the maximum height of the equation is 31.25.

the maximum height of the equation -16x^2+80x+25=0 is 31.25, which occurs at x = 2.5.

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There are probability (6 choose 3) = 20 possible ways to select 3 or more students from 6 students, since the order in which the students are selected is not important.

If 3 or more students must be selected from 6 students, and the order in which the students are selected is not important, then this is an example of a combination problem. Combination problems are used to calculate the number of ways a certain number of objects can be selected from a larger group of objects. To calculate this, the formula that is used is (n choose r) = n!/(r!(n-r)!), where n is the total number of objects, and r is the number of objects that must be selected. In this case, n = 6 and r = 3, so the answer is (6 choose 3) = 6!/(3!(6-3)!) = 20. This means that there are 20 possible ways to select 3 or more students from 6 students, since the order in which the students are selected is not important.

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Answer:

\(\displaystyle \sin\Big(\frac{x}{2}\Big) = \frac{7\sqrt{58} }{ 58 }\)

\(\displaystyle \cos\Big(\frac{x}{2}\Big)=-\frac{3 \sqrt{58}}{58}\)

\(\displaystyle \tan\Big(\frac{x}{2}\Big)=-\frac{7}{3}\)

Step-by-step explanation:

We are given that:

\(\displaystyle \sin(x)=-\frac{21}{29}\)

Where x is in QIII.

First, recall that sine is the ratio of the opposite side to the hypotenuse. Therefore, the adjacent side is:

\(a=\sqrt{29^2-21^2}=20\)

So, with respect to x, the opposite side is 21, the adjacent side is 20, and the hypotenuse is 29.

Since x is in QIII, sine is negative, cosine is negative, and tangent is also negative.

And if x is in QIII, this means that:

\(180<x<270\)

So:

\(\displaystyle 90 < \frac{x}{2} < 135\)

Thus, x/2 will be in QII, where sine is positive, cosine is negative, and tangent is negative.

1)

Recall that:

\(\displaystyle \sin\Big(\frac{x}{2}\Big)=\pm\sqrt{\frac{1 - \cos(x)}{2}}\)

Since x/2 is in QII, this will be positive.

Using the above information, cos(x) is -20/29. Therefore:

\(\displaystyle \sin\Big(\frac{x}{2}\Big)=\sqrt{\frac{1 + 20/29}{2}\)

Simplify:

\(\displaystyle \sin\Big(\frac{x}{2}\Big)=\sqrt{\frac{49/29}{2}}=\sqrt{\frac{49}{58}}=\frac{7}{\sqrt{58}}=\frac{7\sqrt{58}}{58}\)

2)

Likewise:

\(\displaystyle \cos \Big( \frac{x}{2} \Big) =\pm \sqrt{ \frac{1+\cos(x)}{2} }\)

Since x/2 is in QII, this will be negative.

Using the above information, cos(x) is -20/29. Therefore:

\(\displaystyle \cos \Big( \frac{x}{2} \Big) =-\sqrt{ \frac{1- 20/29}{2} }\)

Simplify:

\(\displaystyle \cos\Big(\frac{x}{2}\Big)=-\sqrt{\frac{9/29}{2}}=-\sqrt{\frac{9}{58}}=-\frac{3}{\sqrt{58}}=-\frac{3\sqrt{58}}{58}\)

3)

Finally:

\(\displaystyle \tan\Big(\frac{x}{2}\Big) = \frac{\sin(x/2)}{\cos(x/2)}\)

Therefore:

\(\displaystyle \tan\Big(\frac{x}{2}\Big)=\frac{7\sqrt{58}/58}{-3\sqrt{58}/58}=-\frac{7}{3}\)

Answer:

The last 3 are OR inequalities

Step-by-step explanation:

Because they are not meeting the center, they are going opposite directions.

Hope This works.

Answer:

5.82

Step-by-step explanation:

rule number 1: if the last digit in 5.275 is less than 5, them remove the last digit.

rule number 2: if the last digit in 5.275 is 5 or more and the second to the last digit in 5.275 is less than 9, then remove the last digit and add 1 to the second to last digit

rule number 3: if the last digit in 5.275 is 5 or more and the second to last digit IS 9, and the 3rd to last digit is LESS THAN 9, then remove the last digit, make the 2nd to last digit 0 and add 1 to the number to the third to last digit.

rule number 4: if the last digit in 5.275 IS 9, and the 3rd to the last digit is 9, then add 1 to the number on the left side of the decimal point and make the right side of the decimal point 00

Answer:

4/13

Step-by-step explanation:

Add the number of eggs which is 13 so it shows that 13 eggs are in the bag and there are 4 white eggs so the probability of taking a white egg is 4/13

Answer:

Y=-1+10/3x

Step-by-step explanation:

The slope is 10/3x and the point is -1. I think this is correct, but I’m not sure

Answer:

y=10/3

Step-by-step explanation:

10x-3y=3

-10x -10x move 10x

-3y=-10x+3

-3. -3. -3. divide

y=10/3x

Answer:

0, -2

Step-by-step explanation:

Can I have brainliest? I hope this helped and have a nice day!

Answer:

(-1, -5)

Step-by-step explanation:

The expressions that show the amount of money Erica saves if she spends $40 are (b) 40 - 2 and (e) 40 ÷ 2.

To calculate the amount of money Erica saves if she spends $40, we need to find the difference between the amount she spent and the amount she saved. The expression 40 - 2 represents the amount Erica saves if she spends $40 and saves $2. By subtracting the amount saved from the amount spent, we can determine the savings.

Similarly, the expression 40 ÷ 2 calculates the amount Erica saves if she spends $40 and saves half of it. Dividing the amount spent by 2 gives us the savings. The expressions 40 ÷ 40 and 40 + 40 do not accurately represent the amount Erica saves.

40 ÷ 40 simplifies to 1, which means Erica would save only $1 if she spends $40. This expression represents a ratio of the amount saved to the amount spent, rather than the actual savings. 40 + 40 equals 80, which is not the correct representation of Erica's savings.

This expression adds the amount spent to itself, resulting in a sum that is double the spending amount, not the savings. Therefore, the expressions that correctly show the amount of money Erica saves if she spends $40 are (b) 40 - 2 and (e) 40 ÷ 2.

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Here is the complete question Which expressions show the amount of

money Erica saves if she spends $40?

Choose ALL that apply.

a. 40 ÷ 40

b. 40-2

c. 40.2

d. 40+ 40

e. 40÷2

The instructional designer should use the procedure of "Confidence interval for a single proportion" to make the estimate of the proportion of learners who use Firefox as their primary browser.  (option 3)

This procedure allows for the estimation of the true proportion of the population within a certain level of confidence based on a sample proportion. It involves calculating a range of values within which the true proportion is expected to fall with a specified level of confidence. The procedure is appropriate when the variable of interest is categorical, and the goal is to estimate the proportion of individuals in a population who have a certain characteristic, in this case, using Firefox as their primary browser.

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9514 1404 393

Answer:

  x = -3±√31 ≈ {-8.568, +2.568}

Step-by-step explanation:

The usual steps are to ...

  group the x-terms

     (x² +6x) -22 = 0

  add and subtract the square of half the x-coefficient

     (x² +6x +(6/2)²) -22 -(6/2)² = 0

  simplify to a binomial square

     (x +3)² -31 = 0

Solve for x.

  (x +3)² = 31

  x +3 = ±√31

  x = -3 ±√31 . . . . . solution to the quadratic

The system of equation has no solution.

Given is a system of equation -x = y+4 and x+2y = 19, we need to change the equations in slop-intercept form and then solve,

So, the slope-intercept form of a line is given by y = mx + c, where m is the slope and c is the y-intercept,

So,

-x = y+4

y = -x - 4................(i)

x+2y = 19

2y = -x + 19

y = -0.5x + 9.5...........(ii)

So, the slope-intercept form of the given equations is eq(i) and eq(ii).

We see since the slope of the system of equation are equal so the lines are parallel.

Hence the system of equation has no solution.

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Answer:

8.4 grams

Step-by-step explanation:

So if there are 1.2 grams of protein in a half cup serving, and you're trying to find how many grams in a 3.5 serving. Find the number of halves in 3.5

That would be 7, because 7 multiplied by 1/2 is 3.5

So then multiply 1.2 with 7

= 8.4 grams

Answer:

24

Step-by-step explanation:

8 * 12 = 96

96 / 4 = 24

Have a great night! :D

Hope this helps.

Answer:

87.5

Step-by-step explanation:

A = base1 + base2/ 2 * h

A = 10 + 15/2 * 7 = 87.5

(a) To find a matrix A ∈ M such that all of its eigenspaces are 1-dimensional, we need to construct a matrix with distinct eigenvalues. Since the characteristic polynomial is given as (λ - 1)(λ - 2)(λ - 3)², we can choose A as a diagonal matrix with the eigenvalues as its diagonal entries. Therefore, A =

⎡

1 0 0 0

0 2 0 0

0 0 3 0

0 0 0 3

⎤

satisfies the condition.

(b) To find a matrix B ∈ M such that at least one eigenspace is 2-dimensional, we need to have a repeated eigenvalue with multiplicity greater than 1. We can choose B as a matrix with the eigenvalues 1, 2, and 3, where 3 is repeated twice. Therefore, B =

⎡

1 0 0 0

0 2 0 0

0 0 3 0

0 0 0 3

⎤

fulfills this requirement.

(c) The invertibility of a matrix C ∈ M cannot be determined solely based on its characteristic polynomial. The characteristic polynomial only provides information about the eigenvalues of a matrix. In general, a matrix C ∈ M may or may not be invertible depending on its specific entries.

(d) The statement is true. For any matrix D ∈ M, the characteristic polynomial is given as (λ - 1)(λ - 2)(λ - 3)². Since the eigenvalues are 1, 2, and 3 with multiplicities, no positive power of D can equal the identity matrix because it would require having distinct eigenvalues.

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The midpoint formula and the normal vector of the plane can be used to determine the equation of the plane that contains all points equidistant from the points (1,0,-2) and (3,4,0).

Given by: The midpoint of the two points is:

M = [(1 + 3)/2, (0 + 4)/2, (-2 + 0)/2] = (2, 2, -1) (2, 2, -1)

The following vector runs between the two points:

V = (3 - 1, 4 - 0, 0 - (-2)) = (2, 4, 2) (2, 4, 2)

The cross product of two non-parallel plane vectors yields the normal vector to the plane. The midpoint M to a point on the plane is one such vector, while the other is the vector V. Consider the point P = (2, 2, -1) + t(2, 4, 2) as an illustration, where t is a scalar.

The normal vector is then provided by:

N = V x (P - M) = (2, 4, 2) x (2t, 4t, 2t -1), which equals (12t, -8t, 4t + 2)

The point-normal form, which makes use of the normal vector N and the point M, can be used to determine the equation for the plane:

(x - 2) * 12t = (y - 2) * -8t = (z + 1) * 4t + 2

The final equation of the plane is obtained by multiplying both sides of the equation by t and setting t 0.

12(x - 2) = -8(y - 2) = 4(z + 1) + 2

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Answer:

In expanded form:

2^3 = 2 * 2 * 2 = 8

In standard form :

2^3

Step-by-step explanation:

Given the numbers in range (0 to 10)

Write an exponential expression :

Choosing from the range for the Base and the exponent

Base = 2

Exponent = 3

where ; 2 = base. ; 3 = exponent

In expanded form:

2^3 = 2 * 2 * 2 = 8

In standard form :

2^3

Answer:

Step-by-step explanation:

The easiest way to think about increasing area is by taking a square, if you double the dimensions, let's say they were 1 by 1 and then was made into a 2x2 square, you can fit four of the original cube (1x1) into the 2x2. So when the dimensions are doubled the area is quadrupled.

Even easier shortcut:

Take the cube idea, when the dimensions are messed with for anything, (works for volume too) always think of the smaller piece as 1x1 or 1x1x1. Then if the dimensions are double make it 2x2 or 2x2x2. If the dimensions are tripled then do 3x3 or 3x3x3, etc... 1x1=1x1x1, they are both equal to 1. So think of that as the numerator. the 2x2 in this case is equal to 4 so the smaller piece is 1/4 of the bigger one. Shown with volume if you double the dimensions of a cube that was 1x1x1 into 2x2x2. 1x1x1 still equals 1 so that's still the numerator and 2x2x2 is equal to 8 so the 1x1x1 cube is 1/8 of the 2x2x2, in other words you can fit eight 1x1x1 cubes into the 2x2x2 cube.

Hope this helps with area and volume.

Answer:

d would be correct

Step-by-step explanation:

A pyramid is a polyhedron formed by connecting a polygonal base and an a a p e x. The basic formula for pyramid volume is the same as for a cone: volume = (1/3) times  base area times height, where height is the height from the base to the a p e x. That formula is working for any type of base polygon and oblique and right pyramids.

The probability of approximately 48% that a player will have a height between 5'2" and 5'6".

To calculate the probability of a player being between 5'2" and 5'6" given that historically, the members of the chess club have had an average height of 5'6" with a standard deviation of 2", we can use the standard normal distribution.

First, we need to convert the heights to z-scores using the formula:

z = (x - μ) / σ

where x is the height we want to find the probability for, μ is the mean height, and σ is the standard deviation.

For 5'2":

z = (62 - 66) / 2 = -2

For 5'6":

z = (66 - 66) / 2 = 0

Next, we can use a standard normal distribution table or calculator to find the area under the curve between these two z-scores.

Using a standard normal distribution table, we can find that the area to the left of z = -2 is 0.0228 and the area to the left of z = 0 is 0.5. Therefore, the area between z = -2 and z = 0 is:

0.5 - 0.0228 = 0.4772

Multiplying this by 100 gives us a probability of approximately 48% that a player will have a height between 5'2" and 5'6".

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(a) If f is an injective function from set A to set B and E is a subset of A, then f^(-1)(f(E)) = E. This is because an injective function assigns a unique element of B to each element of A.

Therefore, f(E) will contain distinct elements of B corresponding to the elements of E. Now, taking the inverse image of f(E), f^(-1)(f(E)), will retrieve the elements of A that were originally mapped to the elements of E. Since f is injective, each element in E will have a unique pre-image in A, leading to f^(-1)(f(E)) = E.

Example: Let A = {1, 2, 3}, B = {4, 5}, and f(1) = 4, f(2) = 5, f(3) = 5. Consider E = {1, 2}. f(E) = {4, 5}, and f^(-1)(f(E)) = {1, 2} = E.

(b) If f is a surjective function from set A to set B and H is a subset of B, then f(f^(-1)(H)) = H. This is because a surjective function covers all elements of B. Therefore, when we take the inverse image of H, f^(-1)(H), we obtain all the elements of A that map to elements in H. Applying f to these pre-images will give us the original elements in H, resulting in f(f^(-1)(H)) = H.

Example: Let A = {1, 2}, B = {3, 4}, and f(1) = 3, f(2) = 4. Consider H = {3, 4}. f^(-1)(H) = {1, 2}, and f(f^(-1)(H)) = {3, 4} = H.

In conclusion, when f is injective, f^(-1)(f(E)) = E holds true, and when f is surjective, f(f^(-1)(H)) = H holds true. However, these equalities may not hold if f is not injective or surjective.

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Las personas encargadas de plasmar el guion en una puesta en escena son los directores.

El director es la persona que se encarga de dirigir la puesta en escena de una película, obra de teatro u otra presentación artística. Su función principal es la de interpretar el guion y dar instrucciones al equipo de actuación para obtener el mejor resultado.

El director es una de las personas más importante en la realización de una puesta en escena porque es quien desarrolla la idea general de cómo se va a transmitir un mensaje y cómo lo va a recibir el público.

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Answer:

fingers

Step-by-step explanation:

The number of people who don't use any alternative transportation mode is 18 people.

To find the number of people who don't use any alternative transportation mode we can use the principle of inclusion and exclusion (PIE) method.

adding the number of people who use each mode:

walk = 144

bus = 102

bicycle = 105

Next, subtract the number of people who use two modes:

walk and bus = 78

walk and bicycle = 65

bus and bicycle 45

adding people who use all three modes:

all three modes of transportation = 34

Therefore, the total number of people who use at least one alternative mode of transportation is:

= 144 + 102 + 105 - 78 - 65 - 45 + 34

= 197

To find the number of people who don't use any alternative transportation. we need to subtract the number of people who use at least one alternative mode of transportation from the total number of people in the survey:

= 215 - 197

= 18

Therefore, The number of people who don't use any alternative transportation mode is 18.

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Random variable X is normally​ distributed, with mean μ = 53 and standard deviation σ = 7. We need to calculate the probability P(X ≤ 42)P(X ≤ 42) = ?
The standard score, or z-score, can be calculated using the following formula:z = (X - μ)/σ

Here, X = 42, μ = 53, and σ = 7.z = (42 - 53)/7 = -1.57Using a normal distribution table or calculator, we can find that the probability of a z-score less than or equal to -1.57 is 0.0584.

Hence, P(X ≤ 42) = 0.0584 (rounded to four decimal places).

The normal curve is given below:Normal curve with area corresponding to P(X ≤ 42) shaded as follows:Normal distribution curve for the given problem

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A shear transformation in R2 is a linear transformation that displaces points in a shape. It is represented by a 2x2 matrix that captures the effects of the transformation. In the case of vertical shear, the matrix will have a non-zero entry in the (1,2) position, indicating the vertical displacement along the y-axis. For the given matrix | 1 k |, | 0 1 |, where k represents the shearing factor, the presence of a non-zero entry in the (1,2) position confirms a vertical shear. This means that the points in the shape will be shifted vertically while preserving their horizontal positions. In contrast, if the non-zero entry were in the (2,1) position, it would indicate a horizontal shear. Shear transformations are useful in various applications, such as computer graphics and image processing, to deform and distort shapes while maintaining their overall structure.

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Answer:

Informative!

Step-by-step explanation: