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WILL GIVE BRAINLIEST AND 40 POINTS TO CORRECT ANSWER (URGENT)chef daniels places her favorite recipes in a bag for 4 pasta dishes, 5 casseroles, 3 types of chili, and 8 desserts. If Chef Daniel chooses two recipes at random (but replaces the first one before drawing the second), what is the probability that the first recipe she selects is a casserole and the second recipe she selects is a dessert?

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A tank contains 22 gallons of water when all of a sudden the water begins draining at a constant rate of 2 gallons per hour. Let t represent the number of hours since the water begun draining and let v represent the volume of water in the tank. Write a formula that expresses y in terms of t .

Answers

Answer:

V= 22-2t

Step-by-step explanation:

I guess the alphabet should be v instead of y. So I am working using v

The rate at which water is draining from the tank is 2gallons/hour. This is the rate of water removal from the tank. So after an hour, 2 × 1= 2 gallons would have drained. After 5 hours, 2×5 =10 gallons would have drained

Therefore to obtain the amount of water in gallons that have been removed from the tank, you will multiply the rate by the time in hours after which the draining started.

Amount (gallons) =2×t

The amount of water remaining in the tank will be obtained by subtracting the amount of water drained after some hour (2×t) from the initial amount of water in the tank (22)

Therefore, the amount of water present in the tank (v)= 22-2t or 2(11-t) gallons

Final answer:

The formula to express volume of the water v in terms of time t is v = 22 - 2t, where 22 is the initial volume and 2t represents the rate at which the water is draining.

Explanation:

This problem is a mathematical representation of a real-world scenario using a linear equation. The volume of water v in the tank can be represented in terms of time t through the equation v = 22 - 2t. This equation illustrates the initial volume of water in the tank (22 gallons) and accounts for the constant rate at which the water is draining (2 gallons per hour).

When time t = 0 (meaning no time has passed since the water started draining), the volume of water v = 22 (the initial volume). As time increases, the volume gradually decreases at a rate of 2 gallons per hour, represented by the term -2t.

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Which expression is the simplest form -(4x^3+x^2)+2(x^3-3x^2)

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The simplest form of the given expression $(4x^(3) +x^(2) )+2 (x^(3) -3x^(2) )$ is,

$6x^(3) - 5x^(2)$ .

Here, given expression is,

$(4x^(3) +x^(2) )+2 (x^(3) -3x^(2) )$

What is simplest form of equation?

The simplest form is the smallest possible equivalent fraction of the number.

Now,

Simplest form of expression,

$(4x^(3) +x^(2) )+2 (x^(3) -3x^(2) )\n4x^(3) +x^(2) +2 x^(3) -6x^(2) \n6x^(3) - 5x^(2)$

Hence, The simplest form of the given expression $(4x^(3) +x^(2) )+2 (x^(3) -3x^(2) )$ is, $6x^(3) - 5x^(2)$ .

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Answer:

6x^3-5x^2

Step-by-step explanation:

(4x^3+x^2)+2(x^3-3x^2)

4x^3+x^2+2x^3-6x^2

4x^3+2x^3+x^2-6x^2

6x^3+x^2-6x^2

6x^3-5x^2

49, 34, and 48 students are selected from the Sophomore, Junior, and Senior classes with 496, 348, and 481 students respectively. Identify which type of sampling is used and why?A) Convenience
B) Cluster
C) Random
D) Systematic
E) Stratified

Answers

Answer:

Stratified sampling

Step-by-step explanation:

In the question, students are selected from subgroups of Sophomore, Junior, and Senior classes.

We are told that 49, 34, and 48 students are selected from the Sophomore, Junior, and Senior classes with 496, 348, and 481 students respectively.

This means that the sample numbers of 49, 34 and 48 students were selected in proportion to the subgroup sizes of 496, 348, and 481 students respectively.

Thus, due to the fact that subgroups were selected & that sample number of students were also selected in proportion to their respective subgroup sizes, this is therefore a stratified sampling.

Final answer:

The type of sampling used in this scenario is stratified sampling. The type of sampling in this case is E) Stratified sampling.

Explanation:

The type of sampling used in this scenario is stratified sampling. Stratified sampling is a method where the population is divided into different groups or strata, and then a sample is randomly selected from each stratum. In this case, the sophomore, junior, and senior classes are the different strata, and the sample sizes are proportional to the size of each stratum.

To further explain, let's consider the sophomore class with 496 students. If we are selecting a sample size of 49 from this class, it means that approximately 10% of the students (49/496 = 0.098) will be selected. Similarly, for the junior class with 348 students, approximately 10% (34/348 = 0.098) of the students will be selected. The same applies to the senior class with 481 students and a sample size of 48 students.

In stratified sampling, the goal is to ensure that the sample represents the characteristics of each stratum in proportion to their size in the population. By sampling from each of the classes, we can obtain a representation of the entire student population.

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Evaluate the given integral by changing to polar coordinates. sin(x2 y2) dA R , where R is the region in the first quadrant between the circles with center the origin and radii 2 and 4

Answers

Answer:

I = 1.47001

Step-by-step explanation:

we have the function

$f(x,y)=sin(x^2y^2)\n$

In polar coordinates we have

$x=rcos\theta\ny=rsin\theta$

and dA is given by

$dA=rdrd\theta$

Hence, the integral that we have to solve is

$I=\int \limt_2^4 \int \limit_0^(\pi /2)sin(r^4cos^2\theta sin^2\theta)rdrd\theta$

This integral can be solved in a convenient program of your choice (it is very difficult to solve in an analytical way, I use Wolfram Alpha on line)

I = 1.47001

Hope this helps!!!

How many #5 cans of potato salad are required to serve 210 people if each can has 3 pounds 8 ounces of potato salad and each serving is 5 ounces

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210 times 5 then divided by 3.8
so rounding up, 277 cans

Look at the square pyramid shown below. Which of the equation best represents volume of this pyramid terms of H?F. V = 2h cubic units

G. V = 36h cubic units

H. V = 18h cubic units

J. V = 12h cubic units