1. [10 pts.] A fair four-sided die and a fair six-sided die are tossed and the sum of their faces is recorded. Second Die (a) Complete the table of all possible sums. Find the following probabilities. Write your final answers as fraction in lowest terms. (b) P(Sum > 6) (c) P(First Die is even AND Second Die = 5) (d) P(First Die is even OR Second Die = 5) (e) P(one of the die shows 2 | Sum= 6) First Die 1 2 3 4 1 2 3 4 5 6​

Answer:

3-a

Step-by-step explanation:

it involves variables like x, y, z

in this case a

By differentiation rules, the expression for the derivative of the function h(x) = u(x)^v(x), where u(x) = x² + 4 and v(x) = 5 · x is h'(x) = [(x² + 4)^(5 · x)] · [[(5 · x) / (x² + 4)] · (2 · x) + ㏑ (x² + 4) · 5].

In this question we find a differentiation rule for a function of the form h(x) = u(x)^v(x). Herein we find a function whose components are u(x) = x² + 4 and v(x) = 5 · x. First, determine the derivatives of u(x) and v(x):

u'(x) = 2 · x, v'(x) = 5

Second, substitute in the expression of the differentiation rule:

h'(x) = [u(x)^v(x)] · [[v(x) / u(x)] · u'(x) + ㏑ [u(x)] · v'(x)]

h'(x) = [(x² + 4)^(5 · x)] · [[(5 · x) / (x² + 4)] · (2 · x) + ㏑ (x² + 4) · 5]

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Answer:

9.95h + 5  ≤ 125

Step-by-step explanation:

let 'h' = number of hats

Answer:

7.6ft

Step-by-step explanation:

Answer:

7.6

Step-by-step explanation:

3.8 + 3.8 = 7.6

The radius of a circle is half of the diameter

The radius is half of the circle length and the diameter is the whole length

remember that :)

Answer:

y = 2

Step-by-step explanation:

6y - 5 = 7

~Add 5 to both sides

6y = 12

~Divide 6 to both sides

y = 2

Best of Luck!

Answer:

2.16

Step-by-step explanation:

6y - 5 = 7

7 + 5 = 13

6y = 13

6y/6 = 13/6

y = 2.16

Answer:

C. -4 = 16x

Step-by-step explanation:

That is the graph i got when I typed -4 = 16x.

Brainliest Please!!!

- Hermionia

The list of elements in the sets are as follows:

A.  A ∩ B = {2, 9}

B. B ∩ C = {2, 3}

C. A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}

D. B ∪ C = {2, 3, 5, 7, 9, 10}

Set are defined as the collection of objects whose elements are fixed and can not be changed.

Therefore,

universal set = U = {1,2,3, 4, 5, 6, 7, 8, 9, 10​}

A = {1, 2, 7, 8, 9}

B = {2, 3, 5, 9}

C = {2, 3, 7, 10}

Therefore,

A.

A ∩ B = {2, 9}

B.

B ∩ C = {2, 3}

C.

A ∪ B ∪ C = {1, 2, 3, 5, 7, 8, 9, 10}

D.

B ∪ C = {2, 3, 5, 7, 9, 10}

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Answer:

y=2/3x+4

Step-by-step explanation:

to find x, count the rise over run between two points. to find your b value, find where the line crosses the y axis

The answer is D. No, they are not independent, because P(girl) = 0.46 and P(girl | plays a sport) = 0.54.

What is independent event ?

In probability theory, two events A and B are said to be independent if the occurrence of one event does not affect the probability of the occurrence of the other event. That is, the probability of A occurring does not change based on whether B occurs or not, and vice versa.

Mathematically, two events A and B are independent if and only if the probability of their joint occurrence is the product of their individual probabilities:

P(A and B) = P(A) x P(B)

If this equation holds true, then we can say that A and B are independent events. Otherwise, they are dependent events.

According to the question:
The answer is D. No, they are not independent, because P(girl) = 0.46 and P(girl | plays a sport) = 0.54.

Two events A and B are independent if the occurrence of one event does not affect the probability of the occurrence of the other event. In this case, we want to know if being a girl and playing a sport are independent events.

We are given that P(girl) = 0.46, which means that 46% of the students surveyed are girls. We are also given that P(girl | plays a sport) = 0.54, which means that 54% of the students who play a sport are girls.

If being a girl and playing a sport were independent events, then we would expect P(girl | plays a sport) to be equal to P(girl). However, we see that P(girl | plays a sport) = 0.54, which is different from P(girl) = 0.46.

This means that the probability of a student playing a sport is dependent on their gender. Therefore, being a girl and playing a sport are not independent events.

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Step-by-step explanation:

it seems you solved the tricky part yourself already.

just to be sure, let's do the first derivative here again.

the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...

f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =

= 3t⁴ + 18t³ + 24t² + 18t + 21

f'(t) = 12t³ + 54t² + 48t + 18

and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).

we simply put the input number (2) at every place of the input variable (t).

so,

f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =

= 426

Answer:

7. slope= 1

y-intercept= 0

8. slope= -3/2

y-intercept= -2

9. slope= 0

y-intercept= 4

10. slope= undefined

y-intercept= 0

11. slope= 2/9

y-intercept× 1

12. slope= -1/2

y-intercept= 2

Step-by-step explanation:

hope this helps!

The value of ∠A in triangle ΔABC is 119° with ∠B = 44° and ∠C = 17° .

A polygon having three edges and three vertices is called a triangle. It is one of the fundamental geometric forms. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

The properties of a Triangle are :

The six types of triangles are: isosceles, equilateral, scalene, obtuse, acute, and right.

In triangle ΔABC

∠B = 44° and ∠C = 17°

So, The sum of angles of a triangle is 180°

Therefore,

∠A + ∠B + ∠C = 180°

⇒∠A + 44° + 17° = 180°

⇒∠A = 180° - 61°

⇒∠A = 119°

The value of ∠A in triangle ΔABC is 119° with ∠B = 44° and ∠C = 17° .

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Answer: x = 5

The step-by-step explanation is below.

Combine like terms

8x-6x = 2x

4+5=9

2x+9=19

Subtract 9

2x=10

Divide by 2

x = 5

Hope this helps!

Answer: Inductive Reasoning

Step-by-step explanation: The process of arriving at a general conclusion based on observations of specific examples. When you try to find the pattern for a list of numbers or visuals, you are using inductive reasoning.

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The costs as being relevant to Mrs. Ojeda's decision are Rent of display space 900.000 advertisement 3000 and irrelevant costs are commission,

We should know that the cost that differs from other costs in terms of alternative decision is called relevant cost, the irrelevant cost does not change as the result of a management decision.

Sales commission by brand 1.00    ........ Irrelevant to number of boxes

Rent of display space =900.000 ............ Relevant to number of boxes

Advertising cost = 3,000.00........................ Relevant to number of boxes

Cost per unit = 6.00 .................................. irrelevant to number of boxes

cost per unit of $4.00 ...................... Relevant to number of boxes

Fixed cost include the following

Rent of display  900.000

Variable costs are

Sales commission    1.00

Advertisement      2000

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Answer:

2469.6 Joules

Step-by-step explanation:

The hourly wage, the number of hours and the number of days Jaxon works indicates that the amount Jaxon gets paid is $192

The formula for hourly wage can be presented as follows;

Hourly wage  = Total earnings/Total hours worked

The question in the link is presented as follows;

Jaxon gets paid $6 an hour. He works for 8 hours each day for four days. How much will Jaxon get paid

The amount Jaxon gets paid per hour (his hourly wage) = $6

The number of hours he works each day = 8 hours

The number of days Jaxon works = Four days

The amount Jaxin gets paid = Hourly wage × Hours per day × Number of days

Therefore we get;

Amount he gets paid = $6 per hour × 8 hours/day × 4 days = $192

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The diameter of the tin in the picture is  \(3d/5\) where 'd' is the diameter of the tin in reality.

Determining the diameter of tin:

Since there is no indication of dimensions, represent the diameter with a variable 'd' and find the diameter of the tin according to the given condition in the problem.

Here we have assumed that the diameter of the tin is 'd' in reality and the diameter of the tin picture can be calculated as given below.  

Here we have

A ricoffy tin container with no dimensions indicated

Let d and h be the diameter and height of the tin

Given that the container is 2/5 times smaller than d

then the diameter of the tin in the picture \(= d - 2/5(d)\)

\(= [5d - 2d]/5 = 3d/5\)

Therefore, The diameter of the tin in the picture is  \(3d/5\) where 'd' is the diameter of the tin in reality.

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

Work Shown:

A = old price = 320

B = new price = 400

C = percent change

C = [ (B-A)/A ] * 100%

C = [ (400-320)/320 ] * 100%

C = (80/320)*100%

C = 0.25*100%

C = 25%

The positive C value indicates a percent increase.

--------------------------------

A slightly alternative method:

A = old price = 320

B = new price = 400

C = change in price

C = B-A

C = 400-320

C = 80 is the price increase

D = percent change

D = (C/A)*100%

D = (80/320)*100%

D = 0.25*100%

D = 25%

We get the same result as before.

Step-by-step explanation:

scatter plot s are similar to line graphs in that they start with mapping quantitive data points. The difference is that with a scatter plot, the decision is made the the individual points should not be connected directly together with a line but, instead express a trend

The diagonal of the rectangular box will be 9.7 inches.

Given that:

Length, L = 3 inches

Width, W = 2 inches

Height, H = 9 inches

The diagonal of the rectangular prism is given as,

d² = L² + W² + H²

The diagonal of the rectangular box will be calculated as,

d² = 3² + 2² + 9²

d² = 9 + 4 + 81

d² = 94

d = √94

d = 9.7 inches

The diagonal of the rectangular box will be 9.7 inches.

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\((\stackrel{x_1}{-4}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{7}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{(-4)}}}\implies \cfrac{-10}{5+4}\implies -\cfrac{10}{9}\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{-\cfrac{10}{9}}(x-\stackrel{x_1}{(-4)})\implies y-7=-\cfrac{10}{9}(x+4)\)

The three pairs are (AB = 6, BC = 6) (AB = 4, AC = 4√2) and (BC = 2√2, AC = 4). So, First option, Option 5. and Option 6 are correct answers.

Trigonometry is the branch of mathematics which set up a relationship between the sides and angle of the right-angle triangles.

The formula for a 30-60-90 triangle is this:

1) Side opposite to 30 will be value a.

2) Side opposite to 60 will be value a√3

3) Hypotenuse will be 2a.

AB is opposite of the angle with 30 degree measurement.

BC is opposite of the angle with 60 degree measurement.

The sides of an isosceles right triangle are in the ratio,

1:1:√2

where √2 is the hypotenuse.

For the example, BC = 2√2, then AC = 2√2  x √2 = 4.

Therefore, the three pairs are;

1. (AB = 6, BC = 6)

5. (AB = 4, AC = 4√2)

6.(BC = 2√2, AC = 4).

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The rate at which the volume of the cylinder is changing is 600 mm^3/min, and the rate at which the surface area is changing is 240π mm^2/min.

To find the rate at which the volume and surface area of the cylinder are changing, we can use the given formulas for volume and surface area and differentiate them with respect to time. Let's calculate the rates at the moment when the radius of the base is 10 mm.

Given:

Radius rate of change: dr/dt = 3 mm/min

Height: h = 20 mm

Radius: r = 10 mm

Volume of the cylinder (V) = \(r^2h\)

Differentiating with respect to time (t), we have:

dV/dt = 2rh(dr/dt) + \(r^2\)(dh/dt)

Since the height of the cylinder is constant, dh/dt = 0.

Substituting the given values:

dV/dt = 2(10)(20)(3) + (10^2)(0)

dV/dt = 600 + 0

dV/dt = 600 mm^3/min

Therefore, the rate at which the volume of the cylinder is changing at the given moment is 600 mm^3/min.

Surface area of the cylinder (SA) = 2πrh + 2π\(r^2\)

Differentiating with respect to time (t), we have:

dSA/dt = 2πr(dh/dt) + 2πh(dr/dt) + 4πr(dr/dt)

Again, since the height of the cylinder is constant, dh/dt = 0.

Substituting the given values:

dSA/dt = 2π(10)(0) + 2π(20)(3) + 4π(10)(3)

dSA/dt = 0 + 120π + 120π

dSA/dt = 240π mm^2/min

Therefore, the rate at which the surface area of the cylinder is changing at the given moment is 240π mm^2/min.

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Answer:

91.6667%

Step-by-step explanation:

1/3 of 1/4 = 1/12

11/12 = 91.6667%

Have a great day <3

Answer:

50% of the donuts are plain

Step-by-step explanation:

out of 12 donuts, 1/4 have sprinkles. This results in 3 donuts having sprinkles. 3 out of 12 is 9. 1/3 of 9 is 3. 3 donuts have cherry filling. The rest, which is 6 are plain. 6 is 50% of 12.

Answer:

first one

Step-by-step explanation:

Answer: The answer is C or the third answer choice because the absolute value of nine is equivalent to the absolute value of nine. The meaning of absolute value is the number of places away from zero on the number line, and both 9 and -9 are equal distance from zero.

Step-by-step explanation:

Answer:

Grogg's dad is 22

Step-by-step explanation:

Let D = dad's current age

Let g = Grogg's current age

6(d - 7) = g - 7 → 6d - 42 = g - 7 → 6d -35 = g

4(d - 3) = g - 3 → 4d -12 = g - 3 → 4d -9 = g

Set the two equations equal to each other and solve for d

6d - 35 = 4d - 9  Subtract 4d from both sides

2d -35 = -9  Add 35 to both sides

2d = 44  Divide both sides by 2

d = 22

Helping in the name of Jesus.

Answer:

Step-by-step explanation:

d = current dad age

g = current grogg age

d-7 = 6(g-7)

d-3 = 4(g-3)

Let's solve the first equation first:

Add 7 to both sides: d - 7 +7 = 6g - 42 + 7 so d = 6g - 35

Substitude d = 6g - 35 for d in d - 3 = 4g - 12

(6g-35)-3 = 4g-12 = 6g-38 = 4g-12

Subtract 4g from both sides: 2g - 38 = -12

Add 38 to both sides: 2g = 26

Easy: g = 13

And now substitude g in for any equations.

d-3 = 52-12

d = 43

Answer: Root 7 would equal 2.64575131106 and would go on forever.

Step-by-step explanation: It isn't one of the perfect squares. For example, the first 10 perfect square are 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.

Answer:

it is an irrational number and here is why

Step-by-step explanation:

So think of square root as it's answer is something that you you multiply its self by its self and you get that answer. Ex: 8 x 8 = 64 square root of 64 is 8. So in that case there is nothing you can exactly multiply by itself to get 7 so in that case it's a decimal or an irrational number.

HOPE THIS HELPS!