Tyler has entered a buffet line in which he chooses one kind of meat, two different vegetables and one dessert. If the order of food items is not important, how many different meals might he choose? Meat: beef, chicken, pork Vegetables: baked beans, corn, potatoes, tomatoes Dessert: brownies, chocolate cake, chocolate pudding, ice creama.4 b.24 c.72 d.80 e.144

If two events are collectively exhaustive, then the probability that both occur at the same time is 0 .(option-a)

Tossing a coin is an illustration of two occurrences that are both mutually exhaustive and mutually exclusive. When we flip a coin, we can only obtain either a head (H) or a tail (T), never both (H) and (T). As the events are mutually exclusive in this situation, the probability of receiving both a head and a tail is equal to P(H and T) = 0, and the chance of getting either a head or a tail is equal to P(H or T) = 1 since the occurrences are mutually exhaustive.

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Answer:y varies directly as x if y = kx for some constant, k. In other words, y/x is constant. y varies inversely as x if y = k/x for some constant, k.

Step-by-step explanation:

Let u=x-4 ⇒ du=dx Putting x=u+4$ in the integral,

\(\int\limits^5_1 {(x-4)^{\frac{3}{2} } } \, dx\)  =     \(\int\limits^1_{-3} {u}^{\frac{3}{2} } \, du\)

We integrate using the power rule of integration and  get ;

\(\int\limits^1_{-3} {u}^{\frac{3}{2} } \, du\)    =   \([\frac{2}{5}u^{\frac{5}{2}}]\limits^1_{-3}\)    = \(\frac{2}{5}(1^{\frac{5}{2} }-(-3)^{\frac{5}{2} } )\)   = \(\frac{40}{5}\)    = 8

Since this integral exists, and it is finite, the integral is convergent.

We are given

\(\int\limits^5_1 {(x-4)^{\frac{3}{2} } } \, dx\)

We note that this integral is improper at x= ∞ but not at x=-∞; so we only need to check whether this integral exists or not.Using u-substitution,

we let u=x-4 ⇒ du=dx.

Then, putting x=u+4 in the integral, we get

\(\int\limits^1_5 {(x-4)}x^{\frac{3}{2} } \, dx\)   =   \(\int_{-3}^{1}ux^{\frac{3}{2} }\, du\)  

We can then use the power rule of integration to solve the integral as follows:

\(\int_{-3}^{1}u^{\frac{3}{2} }\, du\)  =  \(\left[\frac25u^{\frac52}\right] _{-3}^1\) =  \(\frac25(1^{\frac52}-(-3)^{\frac52})\)   =   \(\frac{40}{5}\) =  8

Since this integral exists, and it is finite, the integral is convergent. Therefore, the given integral converges.Therefore, the given integral

\(\int_1^5(x-4)^{\frac32}dx\)   is convergent.

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The probability of choosing a 5 and then a 6 is 1/49

From the question, we have the following parameters that can be used in our computation:

The tiles

Where we have

Total = 7

The probability of choosing a 5 and then a 6 is

P = P(5) * P(6)

So, we have

P = 1/7 * 1/7

Evaluate

P = 1/49

Hence, the probability of choosing a 5 and then a 6 is 1/49

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Question

You randomly choose one of the tiles. Without replacing the first tile, you choose a second tile. Find the probability of the compound event. Write your answer as a fraction or percent rounded to the nearest tenth. The probability of choosing a 5 and then a 6

Answer:

The perimeter is 12 :) hope that helped and brainiest answer would be greatly appreciated!

Check the picture below.

Answer:

a) As sides of squares are always equal.

So,

BC=CD

2b+CF=a+b

CF= a+b-2b

CF= a-b

b) Area of rectangle CDEF= CDxCF

=(a+b)(a-b)

=(a²-b²)

Hope it helps :-)

Answer: x = 70

Step-by-step explanation: the sum of the angle 2x-5  and 45 deg should equal 180 deg, so 2x-5 should be equal to 135 because 180 - 45 = 135

So 2x -5 = 135. Add 5 to both sides to cancel it out. 2x = 140. divide both sides by 2 to cancel 2 on x. Answer is X=70

I think this is how you do it lol but I don't know for sure.

Answer:

2

Step-by-step explanation:

The answer is "The graph is incorrect. He should have shaded ro the right"

Answer:

16.2

Step-by-step explanation:

4*2.8+5=

Answer:

16.2

Step-by-step explanation:

4x + y

Let x = 2.8 and y = 5 ​

4(2.8) + 5

11.2+5

16.2

The solution set of the example inequality, 2•x + 3 ≤ -3, is the option;

A possible inequality that can be used to get one of the options, (the inequality is not included in the question) is as follows;

Solving the above inequality, we have;

2•x + 3 ≤ -3

2•x ≤ -3 - 3 = -6

2•x ≤ -6

Therefore;

x ≤ -6 ÷ 2 = -3

x ≤ -3

Which gives;

-∞ < x ≤ -3 in interval notation is (-∞, -3]

The solution set of the inequality, 2•x + 3 ≤ -3, is therefore the option;

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Answer:

The square root of 20 is 4.472.

Step-by-step explanation:

Answer:

225%

Step-by-step explanation:

250*.1 = 25

250-25=225$

The central angle of a circle when you know the radius and arc length, you can use the formula:

Central angle (in radians) = Arc length / Radius

To find the central angle of a circle when you know the radius and arc length, you can use the formula:

Central angle (in radians) = Arc length / Radius

If you want the central angle in degrees, you can convert it using the fact that there are 2π radians in a full circle (360 degrees):

Central angle (in degrees) = (Arc length / Radius) * (180 / π)

Make sure to use consistent units for the arc length and radius, such as meters or centimeters, to obtain accurate results.

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Answer:

y=-2, x=7

Step-by-step explanation:

x=−3y+1;−9x−10y=−43

Solve x=−3y+1for x:

Substitute−3y+1forxin−9x−10y=−43:

−9x−10y=−43

−9(−3y+1)−10y=−43

17y−9=−43

17y−9+9=−43+9

17y=−34

17y/17=-34/17

y=-2

Substitute−2 for y in x=−3y+1

x=−3y+1

x=(−3)(−2)+1

x=7

Using substitution method, the solution to the system of equation is

x = 7 and y = -2.

The substitution method is "an algebraic method is used to solve simultaneous linear equation".

According to the question,

x = -3y + 1                  →(1)

-9x - 10y = -43          → (2)

Substitute equation (1) in equation (2)

- 9 (-3y + 1) - 10y = -43

27y - 9 -10y = -43

             17y = -43 + 9

             17y = -34

                y = -2.

Substitute y= -2 in equation (1)

x = -3 (-2) + 1

x =  6 +1

x = 7

Hence, using substitution method, the solution to the system of equation is x = 7 and y = -2.

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Answer:

x= 5 ........................ .......

Answer:  I believe A is the correct answer

Step-by-step explanation:

Step-by-step explanation:

-4x - 28 = -4(x + 7) or 4(-x - 7)

Topic: Algebraic factorization

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You can use the Alternate Exterior Angle Theorem to prove that the 2 angles shown on the drawing are congruent to each other.

The solution of the function \(\rm \int{sin(t) (1 + cos(t) )} \, dt\) is - cos t - ¹/₄cos 2t + c.

An indefinite integral is a function that practices the antiderivative of another function.

It can be visually represented as an integral symbol, a function, and then a dx at the end.

The given function is;

\(\rm \int{sin(t) (1 + cos(t) )} \, dt\)

Multiply by sint in the function and simplify;

\(\rm \int{sin(t) (1 + cos(t) )} \, dt\\\\\rm \int{sin(t) + sin(t)cos(t) \, dt\)

Use trigonometric formulas for double angles:

\(\rm 2sintcost =sin2t\\\\sin t cost =\dfrac{1}{2} sin2t\)

Substitute the values in the function

\(\rm \int{sin(t) (1 + cos(t) )} \, dt\\\\\rm \int{sin(t) + sin(t)cos(t) \, dt}\\\\ \int{sin(t) + \dfrac{1}{2} sin2t \, dt}\\\\\)

And now we integrate this trigonometric form.

\(\rm \int{sin(t) + \dfrac{1}{2} sin2t \, dt}\\\\ \int{sin(t) dt } +\dfrac{1}{2}\int{sin(2t)\, dt}\\\\-cost -\dfrac{1}{2} \times \dfrac{1 \times -cos2t}{2}\\\\-cost -\dfrac{{1 \times -cos2t}}{4}+c\)

Hence, the solution of the given function is - cos t - ¹/₄cos 2t + c.

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Answer:-10.75

Step-by-step explanation:

Answer:

Confidence Level z*-value

90% 1.645 (by convention)

95% 1.96

98% 2.33

99% 2.58

Step-by-step explanation:

the difference in sample means is 0.1, and the upper end of the confidence interval is 0.1 + 0.1085 = 0.2085 while the lower end is 0.1 – 0.1085 = –0.0085.

it is proven that there are no integers x, y, z such that x² + y² = 8z + 3.

What is Integers?

A whole number is a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5+, and √2 are not. The set of integers consists of zero, positive natural numbers, also called integers or counting numbers, and their additive inverses.

To prove that there are no integers x, y, z such that x² + y² = 8z + 3, we can use the concept of modulo arithmetic.

First, let's consider the possible values of x² and y² modulo 8:

For any integer n, n² modulo 8 can only be 0, 1, or 4.

Now, let's examine the possible values of 8z + 3 modulo 8:

8z modulo 8 is always 0.

3 modulo 8 is equal to 3.

Therefore, the possible values of x² + y² modulo 8 can only be 0, 1, or 4, while 8z + 3 modulo 8 is equal to 3. Since 0, 1, and 4 are not equal to 3 modulo 8, there are no integers x, y, z that satisfy the equation x² + y² = 8z + 3.

Hence, it is proven that there are no integers x, y, z such that x² + y² = 8z + 3.

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The solution to the systems of equations graphically is (2, 4)

From the question, we have the following parameters that can be used in our computation:

y = 2x

y = -x + 6

Next, we plot the graph of the system of the equations

See attachment for the graph

From the graph, we have solution to the system to be the point of intersection of the lines

This points are located at (2, 4)

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If Mohammad leaves home walks 5 blocks to the library and he then walks 2 blocks toward home to meet up with his friend and then together, he and his friend walk to the library together, then Mohammad walked for 9 blocks.

To calculate how far Mohammad walked we use addition.

Total blocks Mohammad walked = blocks to the library + blocks towards home to meet up with friend + blocks back to the library together

blocks to the library = 5

blocks towards the home to meet up with friend = 2

blocks back to the library together = 2 (As he walked 2 blocks towards home from the library, he will walk the same number of blocks again to reach the library)

Therefore,

total blocks Mohammad walked = 5 + 2 + 2

total blocks Mohammad walked = 9

Hence, the number of blocks Mohammad walked for is calculated to be 9.

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Answer:

7.6 cm²

Step-by-step explanation:

Area of rectangle= l x w

3 x 4 = 12 cm

Area of circle= πr²

π x 2.5²= 19.625

Area of shaded= Area of circle - area of rec

19.625- 12= 7.625 cm²

≈7.6

I HOPE THIS HELPED

Joaquin will need 1 and two fifths cups to make his famous chocolate chip cookies for his friend's birthday party

To solve this problem we will use a rule of three with the problem information:

5 people-------- 1/4 cup of butter

28 people -------- x

Applying the rule of three we get:

x = ( 28 people * 1/4 cup of butter) / 5 people

x = 1,4 cup of butter

x = 1 + 2/5 cup of butter = 1 and two fifths cups

It describes the proportionality of 3 known data and an unknown data. When you have more than 3 known facts that are involved in the proportionality, it is known as a compound rule. The rule of three is also known as a direct proportions.

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Let J be Jasmine age and S the sister's age. Then, we have

this equality means Jasmine is 5 years younger than twice her sister's age. Now, we also know that J=39 years then by substituying this value into the last equality, we have

and now, we can solve this equation for S. First, we must move -5 to the right hand side as 5. It reads

and finally, we obtain

therefore, Jasmine's sister has 22 years old.

Answer:

16 (NOT SURE )

Step-by-step explanation: