A study tested the effects of sleep deprivation and alcohol consumption on reaction time. Which of the following would be considered responsible for the interaction effect of this study? a. reaction time b. how sleep deprivation and alcohol consumption react together on the participant's reaction time
c. the results for only alcohol consumption d. the results for only sleep deprivation

Answer: 10/40 or 1/4

Step-by-step explanation:

Add up all the amount of rolls, so 10+6+4+8+6+6=40

then add the probability of rolling a 3 or 6 = 10

divide that quantity out of the whole

answer is 10/40 and simplified is 1/4

hope it helps

Answer:

angle b

Step-by-step explanation:

let's assume the triangle is a right angle triangle . either angle a or c can be equal to 60 degree

it is located in the y axis.

You already answered yourself. If its coordinates are (-3,0) then it's located at (-3,0) on the graph. It's on the x-axis between quadrant 2 and quadrant 3. It's 3 units away from the origin of the graph.

a) The fraction of chocolate distributed is given as follows: 4/3.

b) The fraction of chocolates left with Paul is given as follows: 8/3.

The fractions are obtained applying the proportions used in the context of this problem.

He distributes 1/3 of each bar to 4 children, hence the total number of bars distributed is given as follows:

4 x 1/3 = 4/3.

(multiplication of fractions, multiply the numerators and the denominators, keeping the quotient).

The total number of bars that Paul had initially is given as follows:

4 bars.

Then the fraction of chocolate remaining with Paul is given by the subtraction of the total amount of bars by the amount given to the children, as follows:

4 - 4/3 = 12/3 - 4/3 = 8/3 bars.

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Answer:

Attached is an example of a circle with a radius of 5 and a diameter of 10.

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Answer:

Triangle sum of equation: x° + 109° = 180°

value of x = 71°

Answer:

The Comparison Test is inconclusive because of our choice of g(x).

Step-by-step explanation:

1 / (√x + eˣ) < 1 / √x

1 / √x diverges (p series with p = ½).  So comparison test is inconclusive.  The larger series diverging doesn't tell us whether the smaller series converges or diverges.

The result of the matrix 4|D| -3|B|

\(\left[\begin{array}{ccccc}31&6&36&-14&-57\\-19&-27&-18&18&27\\47&14&-1&-40&9\\10&12&-19&-15&-58\\-14&-23&10&-8&19\end{array}\right]\)

To solve the 5 x 5 matrix, we have to multiply and subtract the matrix this way;

4 x 7 - 3 x -1 = 31

4 x -6 - 3 x-10 = 6

4 x 3 - 3 x-8 = 36

4 x -8 - 3 x-6 = -14

4 x -9 - 3 x 7 = -57

Therefore 31, 6, 36, -14, and -57 makes the first role of the matrix 4|D| - 3|B|

4 x 2 - 3 x 9 = -19

4 x -9 - 3 x -3 = -27

4 x -6 - 3 x -2 = -18

4 x 6 - 3 x 2 = 18

4 x 9 - 3 x 3 = 27

Therefore -19, -27, -18, 18, and 27 make the second role of the matrix 4|D| - 3|B|

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Answer:

if the base is on the x-axis, the width of the rectangle is = xif the height is based on the parabola, the length = 7-x^2

the area of a rectangle = length * width

thus, area = x*(7-x^2)= 7x-x^3

in order to maximize the area, you would need to take the derivative of the area and set it equal to 0

Area = 7x-x^3Area' = 7 - 3x^2

7-3x^2 = 0thus, x = 1.5275

this x represents the x needed to create the largest possible area with the given parameters.

Thus:Width (x-axis) = 1.5275Length (y-axis) = 7 - (1.5275)^2 = 4.6667

Length of scarf before unraveling = 4.75 + 0.75 = 5.5.

Equation: Length before unraveling = 4.75 + 0.75

Sadie is knitting a striped scarf for her grandfather for his birthday, but discovers a mistake and has to unravel 0.75 of the scarf. After unraveling, the remaining part of the scarf is 4.75 long. To calculate the length of the scarf before it was unraveled, we can use an equation. The equation we will use is Length before unraveling = 4.75 + 0.75. We can interpret this equation as the length before unraveling being equal to the length after unraveling plus the amount unraveled. Therefore, the length of the scarf before unraveling is 4.75 + 0.75, which is equal to 5.5. This equation is useful for finding the original length of the scarf, as it takes into account the amount that was unraveled. Therefore, the original length of the scarf is 5.5.

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Answer:

\(\begin{cases}a_1 = 10\\a_{n+1} = a_n + 4\end{cases}\)

==================================================

Explanation:

The first row \(a_1 = 10\) indicates the first term is 10. The small "1" is the index number. That means \(a_2\) is next followed by \(a_3\) and so on.

To generate the next term, we follow this recursive step: \(a_{n+1} = a_n + 4\)

It means "whatever the nth term \(a_n\) is, we add 4 to it to get the next term \(a_{n+1}\)"

In other words, we add 4 to each term to get the next term.

Eg: 10+4 = 14 and 14+4 = 18

The recursive step could be rewritten as \(a_n = a_{n-1}+4\) based on how you frame things.

Answer:

\(5 { \times 54}^{2} \)

Answer:

Minimum--> 250

Q1--> 255

Q2--> (Median): 307

Q3--> 433

Maximum-->507

Step-by-step explanation:

To find the five-number summary of this data set, we need to determine the minimum value, maximum value, and three quartiles (Q1, Q2, Q3) which divide the data into four equal parts.

First, we need to sort the data set in ascending order:

{ 250, 253, 255, 267, 307, 425, 433, 435, 507 }

Minimum: 250

Maximum: 507

To find the quartiles, we need to find the median of the entire data set (Q2) and then the medians of the two halves of the data set, which will give us Q1 and Q3.

Q2 (Median): The median of the entire data set can be found by averaging the two middle numbers.

Q1: The median of the lower half of the data set is 255, which is the middle value of { 250, 253, 255, 267, 307 }. Therefore, Q1 = 255.

Q3: The median of the upper half of the data set is 433, which is the middle value of { 425, 433, 435, 507 }. Therefore, Q3 = 433.

Answer:

=3np2−3pz

Step-by-step explanation:

Answer:

  4264 cm³

Step-by-step explanation:

The formula is properly written as ...

  V = (4/3)πr³

So, the logarithm of the volume is ...

  log(V) = log(4/3) +log(π) +3·log(r)

  = log(1.333) +log(3.142) +3·log(10.06)

  = 0.12483 +0.49721 +3·1.00260

  = 3.62984

  V = 10^3.62984 ≈ 4264 . . . . cm³

_____

Comment on this solution

We don't have your log tables. We have assumed that a 4 significant-figure number is used to find a 5-significant-figure logarithm, and vice versa. Rounding results in a result slightly different from using the volume formula directly. That gives 4265 cm³.

Answer:

Check the proof below

Step-by-step explanation:

try to verify from RHS to LHS

(Tan a + tan b) / (tan a - tan b)

= (sin a / cos a + sin b /cos b) / ( sin a/ cos a - sin b/ cos b)

= (sin a cos b + cos a sin b)/ (sin a cos b - cos a sin b)

= sin (a+b) / sin (a-b)

Fyi

sin(A+B) = sinAcosB+cosAsinB

sin(A-B) = sinAcosB-cosAsinB

Answer:

Hi, this is not really a question it is a statement but if you really need help with math then you can provide an actual question.

Step-by-step explanation:

Answer:

Then you must improve to get more things in your life

Answer:

20 Pizza

Step-by-step explanation:

Let the number of vegetable pizza be x

Given that

Manuel ordered four times as many cheese pizzas as vegetable pizzas

the number of cheese pizza = 4x

1. no of slice in 1 vegetable pizza pie = 6

no of slice in x vegetable pizza pie = 6x

2. no of slice in 1 cheese pizza pie = 8

no of slice in 4x cheese pizza pie = 8*4x = 32x

Total no of slice for x vegetable pizza and 4x cheese pizza = 6x+32x = 38x

Given that

total no. of 152 slices, therefore

38x = 152

=> x = 152/38 = 4

Thus, no. of vegetable pizza ordered = 4

no. of cheese pizza ordered = 4x = 4*$ = 16

Total no of pizza ordered = 16+4 = 20 (answer)

Answer:

B

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

2

The circumference of circle is 150.72 millimetres.

In simpler terms, circumference in the perimeter of circle. Thus, it will represent the measure of length of the line of circle. The relationship between circumference of circle and it's diameter will be represented as formula -

C = πd, where C is circumference and d is diameter.

Keep the value of diameter in the formula to find the exact circumference of the circle.

Circumference = 3.14×48

Performing multiplication to find the circumference of the circle

Circumference = 150.72 millimetres.

Therefore, the circumference of the circle with 48 millimetres diameter is 150.72 millimetres.

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Answer:

A and B look identical, so perhaps there was a typo?

The equations are:

\(y\geq1/3x+3\)

\(3x-y>2\)

Step-by-step explanation:

To find the system of linear inequalities represented by the graph, we need to find the equation of each line.

Red Line:

To find the equation of the red line, we need to first find the slope and the y-intercept.

Let's pick two points from the red line. We can use (0, 3) and (3, 4).

The slope formula is:

\(m=\frac{y_2-y_1}{x_2-x_1}\)

Let (0, 3) be (x₁, y₁) and let's let (3, 4) be (x₂, y₂). So, our slope is:

\(m=\frac{4-3}{3-0}\)

Subtract:

\(m=1/3\)

So, our slope is 1/3.

Note that (0,3) is also our y-intercept. So, our y-intercept is y=3.

Now, we can use the slope-intercept form:

\(y=mx+b\)

Where m is the slope and b is the y-intercept.

Substitute 1/3 for m and 3 for b. This yields:

\(y=1/3x+3\)

Now, we need to determine which sign to use.

Note that the red line is not dotted, meaning we need "or equal to."

Also, note that the shaded region is above our line. In other words, y must be greater than our equation.

So, our sign is "greater than or equal to."

This, the red inequality is represented by the equation:

\(y\geq1/3x+3\)

Blue Line:

Again, let's first find the slope and the y-intercept.

We can use the points (0, -2) and (1,1). Let (0,-2) be (x₁, y₁) and let's let (1, 1) be (x₂, y₂). Substitute them into the slope formula:

\(m=\frac{1-(-2)}{1-0}\)

Evaluate:

\(m=3/1=3\)

So, our slope is 3.

(0, -2) is also our y-intercept. So, our y-intercept is y=-2.

Again, we can use the slope-intercept form:

\(y=mx+b\)

Substitute 3 for m and -2 for b:

\(y=3x-2\)

Now, we need to find our inequality sign.

Notice that the line is dotted. So, we won't have any "or equal to."

Also, notice that our shaded region is below our line. Thus, y is less than our equation. Therefore:

\(y<3x-2\)

However, all of our choices are in standard form. So, we need to convert this to standard form.

To do so, subtract 3x from both sides:

\(-3x+y<-2\)

The first term is traditionally positive. So, multiply both sides by -1. Since we're multiplying by a negative, flip the inequality sign:

\(3x-y>2\)

We can see that the answer choice that matches this is A (or B?)

And we're done!

Answer: A and B are identical so pick one of them

Step-by-step explanation:

Replacing x with x + 2 means that the graph of f(x) = |x - 4| will be translated 2 units left.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The change from x to x + 2 means that we calculated f(x + 2), thus the graph is translated 2 units left.

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To solve this problem one must be aware of the concepts of standard deviation and variance of raw data.

There is a direct formulae to calculate the variance of the data,

Variance = \(σ^{2} =\frac{Sigma(xi-m)^{2}}{n}\)

Now here we need to verify ∑x and ∑\(x^{2}\).

∑x = 21+19+15+32+27

     = 114

and ∑\(x^{2}\) = \(21^{2} +19^{2} +15^{2} +32^{2} +27^{2}\)

             = 441+361+225+1024+729

             = 2780

So, the given relation is true.

Now the variance of the given data by putting the values in the formulae is  equal to 45.2.

And Standard deviation=\(\sqrt{Variance}\)

                                     = \(\sqrt{45.2}\)

                                      = 6.72

And for population α²=36.16 and deviation=6.01.

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Answer:4/5

Step-by-step explanation: thats the slope

Answer:

Total surface area = 510.2 cm^2

Step-by-step explanation:

When we have the slant height and radius, one formula for the surface area of a cone we can use is given by:

SA = B + LA, where

B = πr^2 and LA = πrs, where

Because the radius of the cone's circular base is 7 cm and the cone's slant height is 16.2 cm, we can plug in 7 for r and 16.2 for s in the cone surface area formula and round to find the total surface area of the cone to 1 decimal place:

SA = π(7)^2 + π(7)(16.2)

SA = 49π + 113.4π

SA = 162.4π

SA = 510.1946469

SA = 510.2 cm^2

Thus, the total surface area of the cone is about 510.2 cm^2.

The correct option for the given question is c) lim x→a¯ f(x) = f(a) when the function f(x) is said to have jump discontinuity at a point x=a.

Jump continuity is a concept in calculus that describes the behaviour of a function at a specific point where the function jumps from one value to another value without any intermediate values. In other words, a function is considered jump continuous at a point if the function approaches a finite limit from both the left and right sides of that point, but the function values on the left and right sides of the point are not equal.

According to the given information:

The correct notation for the left-hand limit as x approaches a from the left side is lim x→a¯, where the horizontal line above the "a" indicates approaching from the left side.

The statement "lim x→a¯ f(x) = f(a)" means that the limit of f(x) as x approaches a from the left side is equal to the value of f(a) at x = a. This indicates that the function f(x) has a jump discontinuity at x = a, where the function jumps from one value to another value at that specific point.

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The value of y is 4√3

Similar triangles have the same corresponding angle measures and proportional side lengths. The corresponding angles of similar triangles are congruent or equal.

Also , the ratio of corresponding sides of similar triangles are equal.

There are two triangles that are similar

Therefore;

y /16 = 4/y

y² = 48

y = √48

y = √16 × √ 3

y = 4√3

Therefore, the value of y is 4√3

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Answer: An implicit function is a function, written in terms of both dependent and independent variables, like y-3x2+2x+5 = 0. Whereas an explicit function is a function which is represented in terms of an independent variable.

Step-by-step explanation: To find the implicit derivative,

Differentiate both sides of f(x, y) = 0 with respect to x.

Apply usual derivative formulas to differentiate the x terms.

Apply usual derivative formulas to differentiate the y terms along with multiplying the derivative by dy/dx.

Solve the resultant equation for dy/dx (by isolating dy/dx).

The equation that represents the condition is m° + 66° + m° = 120°. Then the value of m is 27°.

When two lines intersect, then their opposite angles are equal. Then the equation is given as,

m° + 66° + m° = 120°

Simplify the equation for m, then the value of 'm' is calculated as,

m° + 66° + m° = 120°

2m° = 120° - 66°

2m° = 54°

m° = 27°

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