Tegan was hit on the head during a ball game. Her coach had her tap her finger for 20 seconds. She tapped her finger 90 times. The mean is 100 taps with a standard deviation of 20 taps. Her coach decides to send her to the hospital to see if she has neurological damage. Why might this be a good idea, even though almost one-third of all neurologically healthy people tap this slow or slower

The cheapest alternative that Valentino can select is to make the computation and discover which is less expensive when compared to others.

The area of mathematics known as algebra is used to portray situations or problems using mathematical expressions.

Given that the info is incomplete, Valentino needs to analyze the three options and make additions for extra charges or deductions for discount and make a purchase of the cheapest alternative.

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Answer:

I think its 0.69508 hours.

Step-by-step explanation:

The formula for calculating the mean of a probability distribution is mean = (x * P(x)), where x denotes a potential result and P(x) denotes its probability.

Distribution of Probabilities F(x) = P (X x) is a formula that describes it. Additionally, if the interval (a, b) is semi-closed, the probability distribution function is provided by the equation P(a X b) = F(b) - F (a). The range of a random variable's probability distribution function is always from 0 to 1.

Therefore, the mean for this distribution is: (0 * 0.04) + (1 * 0.24) + (4 * 0.35) + (5 * 0.16) + (7 * 0.21). mean = 0 + 0.24 + 1.4 + 0.8 + 1.47 mean = 4.81

Standard deviation = ((x - mean)2 * P(x)), where x is a conceivable outcome and P(x) is the probability of that outcome, gives the standard deviation of a probability distribution.

This gives us the following standard deviation for this distribution: standard deviation = ((((0 - 4.81)2 * 0.04) + ((1 - 4.81)2 * 0.24) + ((4 - 4.81)2 * 0.35) + ((5 - 4.81)2 * 0.16) + ((7 - 4.81)2 * 0.21)) (23.0461) 4.8114 is the standard deviation.

To two decimal places, round:

mean = 4.81 4.81 is the standard deviation.

Therefore, the provided probability distribution's mean and standard deviation are 4.81 and 4.81, respectively.

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Answer:

Step-by-step explanation:

Hope this helps u!!

We can write the scale factor for the table as {K} = y/x.

Given is to determine the scale for the given table.

Therefore, we can write the scale factor for the table as {K} = y/x.

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Hi

let's call X the initial deposit.

the interest rate is 5.2 %

so each year X increase by 1.052.

so we have : X *1.052^7 =2300

X = 2300/1.052^7

X = 1612,94

please note that the deposit was rounded to the next cent. as the result would be 1612,937...

Answer:

1686.22

Step-by-step explanation:

1686.22

 2300=P(1+(0.052x7))  

2300=P1.364  

P=2300/1.364  

=1686.217...  

=1686.22..

=1686 for the nearest dollar

Answer:

A. 1/8x +1/8x

Step-by-step explanation:

1/8x +1/8x =2/8x = 1/4x

Answer:

A: 1/8x+1/8x

Step-by-step explanation:

The only one that makes sense

Step-by-step explanation:

points on the line: (4, -2) & (-5, 3)

gradient of the line = -5/9

general equation for all straight lines: y = mx + c

substitute one coordinate and the gradient into the equation. 3 = (-5/9)(-5) + c

therefore, c = 2/9

so the general equation is y = (-5/9)x + 2/9

The amount of budget cut from last year's budget which was $166,245 will be $54860.85 which is nearly  $55,415 from the given option. Hence the correct option is (B).

The percentage is the 1 of the hundred or simply the amount or value of any number or data in the range of 100 called percentage.

For example, if Ramesh got 87 marks out of 150 then it required a lot of attention to drawing a conclusion about Ramesh's marks but if I say Ramesh got 58% then it will be easier to think and draw any conclusion.

Given that last year budget was $166,245 and the cut was 33% so it means it will be 0.33 of the $166,245 so

$166,245 × .33 = $54860.85 but in option, it is not mentioned so the nearest answer among the option will be (B).

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Answer:

$15.48

Explanation:

100 ÷ 6.46 = 15.479876

Answer: 18.75 lb.ft

Step-by-step explanation:

Given

Force required to stretch spring 8 in. is 18 lb

it can be written

\(\Rightarrow F=kx\\\Rightarrow 18=k(8)\\\\\Rightarrow k=\dfrac{18}{8}=\dfrac{9}{2}\ lb/in.\)

Work done in stretching from its natural length to 10 in.

\(\Rightarrow W=\dfrac{1}{2}kx^2\\\\\Rightarrow W=0.5\times \dfrac{9}{2}\times (10)^2\\\\\Rightarrow W=225\ lb.in.\ or\\\Rightarrow W=18.75\ lb.ft\)

For the statement "Integer x divisible by 6" the option C is correct.

Either statements are NOT sufficient, but BOTH together are sufficient.

What is integer?

The Latin term "Integer," which implies entire or intact, is where the word "integer" first appeared. Zero, positive numbers, and negative numbers make up the particular set of numbers known as integers.

(1) x + 3 is divisible by 3

This means that x is a multiple of 3.

Hence x + 3 is a multiple of 3.

But x could be 0, 3, 6. If x = 3, x is not divisible by 6.

Otherwise it is.

So, this statement is insufficient.

(2) x + 3 is an odd number

This means that x is an even number.

X can be 6, or 10.

So, this statement is insufficient.

Together -

From (1) it is known that x is a multiple of 3.

Hence X can be 0,3,6,9,12,15,18,21,24,27,30.

From (2) it is known that x is even.

Hence X can be 0,6,12,18,24,30.

Therefore, x is divisible by 6.

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So the new coordinates of point C are (1, 2), and the image of Triangle ABC is congruent to the original triangle.

A triangle is a closed, two-dimensional geometric figure with three straight sides and three angles. It is one of the basic shapes in geometry and can be classified based on the length of its sides or the size of its angles. A triangle with all sides of equal length is called an equilateral triangle, while a triangle with two sides of equal length is called an isosceles triangle. A triangle with no sides of equal length is called a scalene triangle. Triangles can also be classified based on the size of their angles, with an acute triangle having all angles less than 90 degrees, a right triangle having one angle equal to 90 degrees, and an obtuse triangle having one angle greater than 90 degrees.

Here,

To find the new coordinates of point C after the rotation and translation, we need to perform each transformation separately and then combine them.

Rotation:

To rotate a point 180° counterclockwise about the origin, we switch the sign of both coordinates. Therefore, the new coordinates of point C after the rotation are (-3, -2).

Translation:

To translate a point to the right 4 and up 4, we add 4 to the x-coordinate and 4 to the y-coordinate. Therefore, the new coordinates of point C after the translation are (1, 2).

To determine if the image of Triangle ABC is similar or congruent to the original triangle, we need to compare the corresponding sides and angles of both triangles.

Since we performed a rotation of 180°, all the angles in the image triangle are congruent to the corresponding angles in the original triangle. Additionally, since we performed a translation, the sides of the image triangle are congruent to the corresponding sides of the original triangle. Therefore, the image triangle is congruent to the original triangle.

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Micah bought 11 gallons of gas and 8 gallons of gas in the first and second week of the month.

Let x represent how many gallons Micah purchased during the first week. He purchased ( x - 3 ) gallons of gas in the second week, which is 3 fewer than the first week's purchase of x gallons.

He spent $2.39x in the first week purchasing x gallons of gas at $2.39 a gallon. He paid $2.49( x - 3) in the second week at a price of $2.49 a gallon (x-3). He has spent a total of $46.21 on gas so far this month.

Therefore,

$46.21 = $2.39 × x + 2.49 × ( x- 3)

46.21 = 2.39x + 2.49x - 7.47

46.21 = 4.88x - 7.47

46. 21 + 7.47 = 4.88x

53.68 = 4.88x

x = ( 53.68 / 488 )

x = 11

Now, for the second week:

x - 3 = 11 - 3 = 8

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Answer: To solve the problem, we need to subtract the number of points scored on touchdowns from the total number of points to find out how many points were scored on field goals.

133 points - (number of touchdowns x 7 points per touchdown) = points scored on field goals

We don't know the number of touchdowns, but we can use the fact that each touchdown is worth 7 points to write:

133 points - 7x = points scored on field goals

Now we can divide the points scored on field goals by the value of each field goal to find the number of field goals:

(points scored on field goals) / (3 points per field goal) = number of field goals

Putting it all together:

133 points - 7x = points scored on field goals

(points scored on field goals) / (3 points per field goal) = number of field goals

We need to solve for x, the number of touchdowns. We can start by isolating points scored on field goals:

133 points - 7x = points scored on field goals

points scored on field goals = 133 points - 7x

Now we can substitute this expression into the second equation:

(133 points - 7x) / (3 points per field goal) = number of field goals

Simplifying:

44.33 - 2.33x = number of field goals

Since the number of field goals must be a whole number, we can try different values of x until we find an integer solution. For example, if we assume that the Bobcats scored 16 touchdowns, then:

133 points - 7(16) = 21 points scored on field goals

21 points scored on field goals / 3 points per field goal = 7 field goals

Therefore, the Bobcats kicked 7 field goals.

Step-by-step explanation:

The number in the problem whose result is 40, will be 3,600 and 90.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Division means the separation of something into different parts, sharing of something among different people, places, etc.

Use the digits nine, six, and three one time each in the following Multi-digit division problem then rewrite the problem.

Then the problem whose result is 40 will be given as the division of 3600 by 90.

3,600 / 90 = 40

The number in the problem whose result is 40, will be 3,600 and 90.

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Answer:

x=4

Step-by-step explanation:

x+3=7

subtract 3 from both sides

simplify

Answer:

Quadrilaterals

Step-by-step explanation:

Answer:

multiply 0.85x40

Step-by-step explanation:

Step-by-step explanation:

75 = 3 x 5 x 5    in prime factorization

Answer:

Step-by-step explanation:

3x5x5

The statement that is not true: The arc is not a semicircle.

The diagram shows an arc that is formed by two points, point a and point b, with the same radius. The arc does not appear to be a semicircle because it is not a complete circle and the two points, a and b, do not appear to be the same distance from each other.

This means that the statement “The arc is a semicircle” is not true. Additionally, the arc could be an ellipse or some other curved shape, depending on the location of the two points, a and b, relative to each other.

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Answer:

C f(x) = 4(x+1)2-1

Step-by-step explanation:

factor of 4 = 2^2

(x+1)2-1 = 4(x+1) 2-1 = with x

           =   4(+1) 2-1  = without x

           =  (4 - 4) 2 = individual products of -1

           =  (8 - 8 ) = individual products of 2

           =   8 - 8  = 2^2 -2^2

           =  2^2 - 2^2

(x+1)2-1 = 4(x+1)2-1 = with x

            = 2x^2 -2^2

          -x = 2^2 -2^2

            x = -2^2-2^2

            x = 4

which proves f(x) is a factor of 4

Using Maxwell's equations, we can determine the magnetic flux density. One of the Maxwell's equations is:

\(\displaystyle \nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial \mathbf{D}}{\partial t}\),

where \(\displaystyle \nabla \times \mathbf{H}\) is the curl of the magnetic field intensity \(\displaystyle \mathbf{H}\), \(\displaystyle \mathbf{J}\) is the current density, and \(\displaystyle \frac{\partial \mathbf{D}}{\partial t}\) is the time derivative of the electric displacement \(\displaystyle \mathbf{D}\).

In this problem, there is no current density (\(\displaystyle \mathbf{J} =0\)) and no time-varying electric displacement (\(\displaystyle \frac{\partial \mathbf{D}}{\partial t} =0\)). Therefore, the equation simplifies to:

\(\displaystyle \nabla \times \mathbf{H} =0\).

Taking the curl of the given magnetic field intensity \(\displaystyle \mathbf{R} =2\cos( 10^{10} t-600x)\hat{a}_{z}\, \text{Am}\):

\(\displaystyle \nabla \times \mathbf{R} =\nabla \times ( 2\cos( 10^{10} t-600x)\hat{a}_{z}) \, \text{Am}\).

Using the curl identity and applying the chain rule, we can expand the expression:

\(\displaystyle \nabla \times \mathbf{R} =\left( \frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial y} -\frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial z}\right) \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Since the magnetic field intensity \(\displaystyle \mathbf{R}\) is not dependent on \(\displaystyle y\) or \(\displaystyle z\), the partial derivatives with respect to \(\displaystyle y\) and \(\displaystyle z\) are zero. Therefore, the expression further simplifies to:

\(\displaystyle \nabla \times \mathbf{R} =-\frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial x} \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Differentiating the cosine function with respect to \(\displaystyle x\):

\(\displaystyle \nabla \times \mathbf{R} =-2( 10^{10}) \sin( 10^{10} t-600x)\hat{a}_{z} \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Setting this expression equal to zero according to \(\displaystyle \nabla \times \mathbf{H} =0\):

\(\displaystyle -2( 10^{10}) \sin( 10^{10} t-600x)\hat{a}_{z} \mathrm{d} x\mathrm{d} y\mathrm{d} z =0\).

Since the equation should hold for any arbitrary values of \(\displaystyle \mathrm{d} x\), \(\displaystyle \mathrm{d} y\), and \(\displaystyle \mathrm{d} z\), we can equate the coefficient of each term to zero:

\(\displaystyle -2( 10^{10}) \sin( 10^{10} t-600x) =0\).

Simplifying the equation:

\(\displaystyle \sin( 10^{10} t-600x) =0\).

The sine function is equal to zero at certain values of \(\displaystyle ( 10^{10} t-600x) \):

\(\displaystyle 10^{10} t-600x =n\pi\),

where \(\displaystyle n\) is an integer. Rearranging the equation:

\(\displaystyle x =\frac{ 10^{10} t-n\pi }{600}\).

The equation provides a relationship between \(\displaystyle x\) and \(\displaystyle t\), indicating that the magnetic field intensity is constant along lines of constant \(\displaystyle x\) and \(\displaystyle t\). Therefore, the magnetic field intensity is uniform in the given medium.

Since the magnetic flux density \(\displaystyle B\) is related to the magnetic field intensity \(\displaystyle H\) through the equation \(\displaystyle B =\mu H\), where \(\displaystyle \mu\) is the permeability of the medium, we can conclude that the magnetic flux density is also uniform in the medium.

Thus, the correct expression for the magnetic flux density in the given medium is:

\(\displaystyle B =6\cos( 10^{10} t-600x)\hat{a}_{z}\).

The correct answer is that the data set {3, 7, 4} is represented in the given histogram.(option-a)

The given histogram represents the number of children in each age group who need to travel to school. Since the histogram has only three bars, we can conclude that there are only three age groups.

The first bar represents children aged 5-10, of which there are 3. The second bar represents children aged 11-13, of which there are 7. The third bar represents children aged 14-18, of which there are 4.

Therefore, the data set that is represented in the histogram is:

{3, 7, 4}

None of the other data sets given match the values in the histogram. The first data set has duplicate values and is not sorted by age group. The second data set includes ages that are not represented in the histogram. The third data set has values for ages 6, 11, 12, 13, 14, 15, 17, and 18, but the histogram does not have bars for all those ages. (option-a)

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Answer:

  True

Step-by-step explanation:

Lines in three dimensions can be one of ...

Lines are coplanar when a plane can be defined that includes the entirety of both of them. In the attached image, lines m₁ and n intersect and both lie in the gray plane. They are coplanar.

Lines m and m₁ are parallel, and both are contained in the turquoise plane. They are coplanar. A plane can always be drawn that will contain a pair of parallel lines. That is, any two parallel lines must be coplanar.

The lines m and n in the figure are skew, non-intersecting and non-parallel. They cannot be contained in a single plane.

__

Additional comment

Three or more parallel lines may not be coplanar. They will only definitely be coplanar when considered in pairs.

The area of the composite figure is  54 inches².

The perimeter of the figure is 35 inches.

A composite figures is a figure with 2 or more 2 dimensional figures. The composite figure can be divided into three shapes.

Let's find the area of the composite figure as follows:]

area of the composite figure = area of the trapezium + area of the square + area of the rectangle

area of the trapezium  = 1 / 2 (a + b)h

area of the trapezium  = 1 / 2 (5 + 8)4

area of the trapezium  = 1 / 2 × 4 × 13

area of the trapezium  = 52 / 2

area of the trapezium  = 26 inches²

Therefore,

area of the square = 4² = 16 inches²

area of the rectangle = 4 × 3 = 12 inches²

Therefore,

area of the composite figure = 12 + 16 + 26

area of the composite figure = 54 inches²

Let's find the perimeter of the composite figure as follows:

perimeter of the composite figure = 12 + 7 + 4 + 3 + 5 + 4

perimeter of the composite figure = 35 inches

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Answer:

c=5+1/2

Step-by-step explanation:

We move all terms to the left:

4c+5-(27)=0

We add all the numbers together, and all the variables

4c-22=0

We move all terms containing c to the left, all other terms to the right

4c=22

c=22/4

c=5+1/2

Answer:

5 & 60

Step-by-step explanation:

s * 12 = g

s + 55 = g

12s = s + 55

11s = 55

s = 5

Answer:

The factors of given polynomial    x =-1 , -2 and x =3

Step-by-step explanation:

Step(i):-

Given the polynomial  

                    f(x) =  x³ - 7x -6

 put x =-1

               f(-1) = (-1 )³- 7(-1) - 6 = -1+7-6=0

(x+1) is a one factor

By using synthetic division

                   x³    x²      x      constant

     x=-1  ↓   1      0      -7        -6

             ↓   0     -1      1          6

                  1       -1      -6       0    

The polynomial    x² - x - 6

Step(ii):-

The factors ( x+1)(x² - x - 6 ) = 0

     x = -1 and x² - x - 6 =0

    x =-1    and  x² - 3x + 2 x - 6 =0

   x =-1     and  x (x -3) + 2( x-3) =0

   x =-1     and  (x+2)(x-3) =0

Final answer:-

The factors of given polynomial    x =-1 , -2 and x =3