A tank containing 1140.8 gallons can be emptied in 92 minutes. How many gallons is that per minute?

Answer:

a) 0.1138 = 11.38% probability that 14 of them were very confident their major would lead to a good job

b) 0.0483 = 4.83% probability that 10 of them are NOT confident that their major would lead to a good job

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

a. A 2017 poll found that 53% of college students were very confident that their major will lead to a good job. If 30 college students are chosen at random, what's the probability that 14 of them were very confident their major would lead to a good job?

Here, we have that \(p = 0.53, n = 30\), and we want to find \(P(X = 14)\). So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 14) = C_{30,14}.(0.53)^{14}.(0.47)^{16} = 0.1138\)

0.1138 = 11.38% probability that 14 of them were very confident their major would lead to a good job.

b. A 2017 poll found that 53% of college students were very confident that their major will lead to a good job. If 30 college students are chosen at random, what's the probability that 10 of them are NOT confident that their major would lead to a good job?

10 not confident, so 30 - 10 = 20 confident. This is P(X = 20).

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 20) = C_{30,20}.(0.53)^{20}.(0.47)^{10} = 0.0483\)

0.0483 = 4.83% probability that 10 of them are NOT confident that their major would lead to a good job

Answer:

\(Sum = -81\)

Step-by-step explanation:

See the comment for complete question.

Given

\(c = 36\) ----- Constant

No coefficient of x^2

Required:

Determine the sum of all distinct positive integers of the coefficient of x

Reading through the complete question, we can see that the question has 3 terms which are:

x^2 ---- with no coefficient

x ---- with an unknown coefficient

36 ---- constant

So, the equation can be represented as:

\(x^2 + ax + 36 = 0\)

Where a is the unknown coefficient

From the question, we understand that the equation has two negative integer solution. This can be represented as:

\(x = -\alpha\) and \(x = -\beta\)

Using the above roots, the equation can be represented as:

\((x + \alpha)(x + \beta) = 0\)

Open brackets

\(x^2 + (\alpha + \beta)x + \alpha \beta = 0\)

To compare the above equation to \(x^2 + ax + 36 = 0\), we have:

\(a = \alpha + \beta\)

\(\alpha \beta = 36\)

Where: \(\alpha, \beta <0\) and \(\alpha \ne \beta\)

The values of \(\alpha\) and \(\beta\) that satisfy \(\alpha \beta = 36\) are:

\(\alpha = -1\) and \(\beta = -36\)

\(\alpha = -2\) and \(\beta = -18\)

\(\alpha = -3\) and \(\beta = -12\)

\(\alpha = -4\) and \(\beta = -9\)

So, the possible values of a are:

\(a = \alpha + \beta\)

When \(\alpha = -1\) and \(\beta = -36\)

\(a = -1 - 36 = -37\)

When \(\alpha = -2\) and \(\beta = -18\)

\(a = -2 - 18 = -20\)

When \(\alpha = -3\) and \(\beta = -12\)

\(a = -3 - 12 = -15\)

When \(\alpha = -4\) and \(\beta = -9\)

\(a = -4 - 9 = -13\)

At this point, we have established that the possible values of a are: -37, -20, -15 and -9.

The required sum is:

\(Sum = -37 -20 -15 - 9\)

\(Sum = -81\)

Answer:

(d) 18 in.

Step-by-step explanation:

When we're given the three sides of a triangle, one formula we can use for perimeter of a triangle is:

P = s1 + s2 + s3, where

P = 2 + 6 + 10

P = 8 + 10

P = 18

Thus, the perimeter of the triangle is 18 in.

Answer:

c= 70?

a= 66? I think im not too sure

Answer:

32 cm²

Step-by-step explanation:

Area of rectangle

= length × breadth

= 8 cm × 4 cm

= 32 cm²

For the level surface f(x, y, z) = 12, this is the equation of the normal line to the surface f(x, y, z) = 4x² - 2y² + z² at the position (2, 2, 2).

To find the equation of the tangent plane and normal line to the surface f(x,y,z) = 4x² - 2y² + z² at the point (2, 2, 2) for the level surface f(x, y, z) = 12, we need to follow the steps below:

First, we need to find the gradient vector of f(x, y, z) at the point (2, 2, 2) as:

grad(f) = (8x, -4y, 2z)

grad(f) at (2, 2, 2) = (16, -8, 4)

Next, we find the equation of the tangent plane by using the formula:

f_x(x₀, y₀, z₀)(x - x₀) + f_y(x₀, y₀, z₀)(y - y₀) + f_z(x₀, y₀, z₀)*(z - z₀) = 0

Substituting the values, we get:

16(x - 2) - 8(y - 2) + 4(z - 2) = 0

Simplifying, we get:

16x - 8y + 4z = 8

This is the equation of the tangent plane at the point (2, 2, 2).

Finally, we find the equation of the normal line by using the formula:

r(t) = (x₀, y₀, z₀) + t(grad(f) at (x₀, y₀, z₀))

Substituting the values, we get:

r(t) = (2, 2, 2) + t(16, -8, 4)

Simplifying, we get:

r(t) = (16t + 2, -8t + 2, 4t + 2)

This is the equation of the normal line to the surface f(x, y, z) = 4x² - 2y² + z² at the point (2, 2, 2) for the level surface f(x, y, z) = 12.

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ANSWER

Infinitely many solutions (0 = 0)

EXPLANATION

We have the two equations and we are to solve them simultaneously.

We have:

y = 5x + 2 ___(1)

10y - 50x = 20 ___(2)

Put (1) in (2):

We have that:

10(5x + 2) - 50x = 20

50x + 20 - 50x = 20

=> 50x - 50x = 20 - 20

=> 0 = 0

This kind of solution implies that there are infinitely many solutions to this equation.

We can conclude that the hypotheses of the Existence and Uniqueness Theorem are satisfied in any rectangular region in the ty-plane that does not contain the curve t² + y² = -1.

The Existence and Uniqueness Theorem for first-order ordinary differential equations states that if a differential equation of the form y' = f(t, y) satisfies the following conditions in some rectangular region in the ty-plane:

1. f(t, y) is continuous in the region.

2. f(t, y) satisfies a Lipschitz condition in y in the region, i.e., there exists a constant L > 0 such that |f(t, y₁) - f(t, y₂)| ≤ L|y₁ - y₂| for all t and y₁, y₂ in the region.

then there exists a unique solution to the differential equation that passes through any point in the region.

In the case of the differential equation y' = (y cot(2t)) / (t² + y² + 1), we have:

f(t, y) = (y cot(2t)) / (t² + y² + 1)

This function is continuous everywhere except at the points where t² + y² + 1 = 0, which is the curve t² + y² = -1 in the ty-plane. Since this curve is not included in any rectangular region, we can say that f(t, y) is continuous in any rectangular region in the ty-plane.

To check if f(t, y) satisfies a Lipschitz condition in y, we can take the partial derivative of f with respect to y and check if it is bounded in any rectangular region. We have:

∂f/∂y = cot(2t) / (t² + y² + 1) - (2y² cot(2t)) / (t² + y² + 1)²

Taking the absolute value and simplifying, we get:

|∂f/∂y| = |cot(2t) / (t² + y² + 1) - (2y² cot(2t)) / (t² + y² + 1)²|

= |cot(2t) / (t² + y² + 1)| * |1 - (2y² / (t² + y² + 1)))|

Since 0 ≤ (2y² / (t² + y² + 1)) ≤ 1 for all t and y, we have:

1/2 ≤ |1 - (2y² / (t² + y² + 1)))| ≤ 1

Also, cot(2t) is bounded in any rectangular region that does not contain the points where cot(2t) is undefined (i.e., where t = (k + 1/2)π for some integer k). Therefore, we can find a constant L > 0 such that |∂f/∂y| ≤ L for all t and y in any rectangular region that does not contain the curve t² + y² = -1.

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Answer: 24

Step-by-step explanation:63

Huda's error in evaluating (3) squared incorrectly led to the incorrect final result.

The correct answer should be -20, not 34.

Huda's error was that she evaluated (3) squared incorrectly.

Instead of calculating 3 squared as 9, she mistakenly considered it as 3. This error led to incorrect subsequent calculations and the final result of 34, which is not the correct answer.

To evaluate the expression correctly, let's go through the steps:

Negative 3 (8 minus 5) squared minus (negative 7) \(= -3(3)^2 - (-7)\)

First, we simplify the expression within the parentheses:

\(-3(3)^2 - (-7) = -3(9) - (-7)\)

Next, we evaluate the exponent:

-3(9) - (-7) = -3(9) + 7

Now, we perform the multiplication and addition/subtraction:

-3(9) + 7 = -27 + 7 = -20

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Answer:

Sin X = 15/17

Cos X = 8/17

Tan X = 15/8

Step-by-step explanation:

Recall, SOHCAHTOA.

Thus:

Sin X = opp/hyp

opp = 15

hyp = 17

✅Sin X = 15/17

Cos X = adj/hyp

Adj = 8

Hyp = 17

✅Cos X = 8/17

Tan X = opp/adj

Opp = 15

Adj = 8

✅Tan X = 15/8

Answer:

10×6.8 to the 9th power

Answer:

Step-by-step explanation:

21-26. a = v - u / t

=> a = 47 - 19 / 5

=> a = 28 / 5

=> a = 5.6 m/s²

27-32. avg. speed = distance / time

=> 40 m / 10 s

=> 4 m/s

33-38. velocity = distance / time

=> v = 150 / 40

=> v = 15 / 4

=> v = 3.75 m/s

The coefficient of the second term, 6x⁴, is 6.

The terms of the polynomial are:

-4y⁵, 6x⁴, 9w³, -4w, -1

The coefficient of the second term, which is 6x⁴, we look at the number in front of the variable term.

The coefficient is 6.

Therefore, the list of terms is:

-4y⁵, 6x⁴, 9w³, -4w, -1

Each term represents a separate component of the polynomial, where the variable is raised to a certain power and multiplied by its coefficient.

The coefficients indicate the scalar value by which each term is multiplied.

The polynomial's terms are -4y5, 6x4, 9w3, -4w, and -1.

Looking at the number in front of the variable term, we can determine the second term's coefficient, which is 6x4.

There is a 6 coefficient.

As a result, the terms are as follows: -4y5, 6x4, 9w3, -4w, and -1.

Each term represents a different part of the polynomial, where the variable is multiplied by its coefficient and raised to a given power.

The scalar value by which each phrase is multiplied is shown by the coefficients.

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The number of possible selections of the five donuts is; 21

The ample supply contains;

Since he wants to select 5 donuts, the orders could be;

Strawberry = 4, Chocolate = 1, Caramel = 0

or

Strawberry = 4, Chocolate = 0, Caramel = 1

or

Strawberry = 3, Chocolate = 2, Caramel = 0

e.t.c

Now, to solve this, Each option for Jamie is represented by an imaginary picture of five donuts (circles) and two bars (shelf separators).

Thus, the number of ways to select two spaces from 7 is;

7!/(5! × 2!) = 21

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Answer: 118

Step-by-step explanation:

Angle ABC and Angle BCD add up to 180 degrees, because Line AB and line CD are parallel. Because of this, Angle BCD can be moved up the the angle above 3n-47. Because the two angles fall on to a straight line, we can say that (3n-47)+(n+7)=180. Solving, n=55, so angle ABC equals 118 degrees.

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The probability of snow is about 0.75

The probability of snow is greater than 0.5.

It is a branch of mathematics that deals with the occurrence of a random event.

Given that Southern Florida has a mild climate.

We have to check the statement which shows the probability of snow in southern Florida is mostly likely true.

The probability of  snow in June in June southern Florida.

So the probability of snow is greater than 0.5.

Hence, The probability of snow is greater than 0.5.

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13 water stations will be placed every 400 meters of a 5 kilometer.

Given: Water stations will be placed ; every 400 meters

Also the total distance = 5 km = 5000 meters

Thus if a water station is supposed to be kept at every 400 meter distance then that means we can find out this distance by using unitary method

this means by using unitary method we get;

Number of water stations needed is = 5000 divided by 400

12.5 = 13 water stations would be required.

Thus 13 water stations will be placed every 400 meters of a 5 kilometer.

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Answer:

3

Step-by-step explanation:

2 (n + 9) = 24 this is the equation

to solve for n (number):

2(n+9)=24 // Distribute the 2 into parentheses

2n + 18 = 24 // Subtract 18 on both sides of equal sign

      - 18   -18

      2n = 6 // Divide by 2 on both sides of equal sign

        2     2

      n = 3

Hope this helps :)

Answer:

\(\begin{array}{cccc}{} & {Samples} & {Positive} & {Negative} & {Contains\ Organic\ Matter} & {700} & {665} & {[35 ]} & {Does\ not\ contain\ organic\ matter} & {300} & {[60]} & {240} \ \end{array}\)

\(\% Pr= 95\%\)

Step-by-step explanation:

Given

\(\begin{array}{cccc}{} & {Samples} & {Positive} & {Negative} & {Contains\ Organic\ Matter} & {700} & {665} & {[\ ]} & {Does\ not\ contain\ organic\ matter} & {300} & {[\ ]} & {240} \ \end{array}\)

Solving (a): Complete the table

The sum of each row must equal to the samples.

i.e.

\(Positive + Negative = Samples\)

For the samples that contain organic matter, we have:

\(665 + Negative = 700\)

Collect like terms

\(Negative = 700 - 665\)

\(Negative = 35\)

For the samples that do not contain organic matter, we have:

\(Positive + 240 = 300\)

Collect like terms

\(Positive = 300 -240\)

\(Positive = 60\)

So, the complete table is:

\(\begin{array}{cccc}{} & {Samples} & {Positive} & {Negative} & {Contains\ Organic\ Matter} & {700} & {665} & {[35 ]} & {Does\ not\ contain\ organic\ matter} & {300} & {[60]} & {240} \ \end{array}\)

Solving (b): Proportion of samples that are positive if the sample contains organic matter

From the table, we have:

\(Samples = 700\)

\(Contains\ Organic\ Matter\ n\ Positive = 665\)

So, the percentage is:

\(\%Pr = \frac{Contains\ Organic\ Matter\ n\ Positive}{Samples} * 100\%\)

\(\% Pr= \frac{665}{700} * 100\%\)

\(\% Pr= \frac{665* 100}{700} \%\)

\(\% Pr= \frac{66500}{700} \%\)

\(\% Pr= 95\%\)

Answer:

35, 60, 95%

Step-by-step explanation:

correct

Answer:

The general form of the quadratic function f is f(x) = ax2 + bx + c, ... To get the x-intercepts, we opt to set the given formula g(x)=6 − x − x2 = 0.

Step-by-step explanation:The general form of the quadratic function f is f(x) = ax2 + bx + c, ... To get the x-intercepts, we opt to set the given formula g(x)=6 − x − x2 = 0.

Answer:

Solution:

Here,

\(\begin{array}{ | c| c c | } \hline\ \ \text{length \: of \: iron \: rod}& \text{weight} \\ \hline 13 \rm{m}& \rm{23.4kg} \\ \hline \rm{6m}&?\\ \hline\end{array}\)

Weight of 13 m of rod=23.4 kg

Weight of 1 m of rod=23.4/13 kg

[less length,less weight]

Weight of 6 m of rod=23.4/13 ×6 kg=10.8 kg

[more length,more weight]

Thus,the weight of 6 m of rod is 10.8 kg.

Alternative method:

Let,the required weight be x kg.

Then,

\(\begin{array}{ | c| c c | } \hline\ \ \text{length \: of \: iron \: rod}& \text{weight} \\ \hline \rm{13m}& \rm{23.4 \: kg }\\ \hline \rm{6m}& \rm{x =? } \\ \hline\end{array}\)

We know that,

More length of iron rod(\(\red{\uparrow}\)) will have the more weight(\(\red{\uparrow}\)).

So,using the rule of direct proportion;

i.e. Ratio of length=Ratio of weight

\( \displaystyle{ \frac{13}{6} = \rm\frac{23.4}{x} }\)

\( \rm{13x = 6 \times 23.4}\)

\( \rm{x = \displaystyle{ \frac{6 \times 23.4}{13} }}\)

\( \therefore{x = 10.8}\)

Thus,the weight of 6 m long iron rod is 10.8 kg.

In this problem we are given that a person who wants to go to a party would like to bring 3 different bags of chips; and also, that he/she has 13 varieties.

As she has differents options to choose, we see that this one is a problem of permutations or combinations. But the order of the chips the person brings does not matter, and so, we have to find a combination. We remember then that the equation for finding a combination of n objects and k possibilites is given by the following binomial coefficient

Where the symbol ! represents factorial (the product of the number to the number). For example,

Now, in our exercise, we have that the person has 13 varieties and has to choose 3 of them. We have to calculate then:

For doing so, we will start by replacing the values on the formula:

And cancelling the equal terms, we obtain:

This means that the person would be able to do 286 different selections.

To find how many square feet of tile is needed we need to calculate the area of the floor, as you can see, the total surface of the floor is formed by two rectangles, then the total area would be the sum of the areas of them, the area of a rectangle can be calculated by means of the formula:

Where l is the length and w is the width.

Now, let's calculate the area of the new wing:

And the area of the left rectangle:

By summing up these areas we get the area of the whole floor:

A=800+2400 = 3200

Then, we need 3200 square feet of tile.

Step-by-step explanation:

try desmos its a life saver

Answer:

(40,35)

Step-by-step explanation:

Well we can immediacy eliminate 2 options for ow becuase if you add them up they don’t equal 75 and in the equation it asked for x+y=75.

Now we just test out each x and y possibility

We know 5x+3 > 300

So lets try the first one

30 is x

45 is Y

5*30=150

45*3=135

Now if you add them

285

285 is not greater than 300 so thats wrong

SO B is correct

But lets check just in case

5*40=200

3*35= 105

305 IS greater than 300

305 > 300

SO B is correct

The point (40,35)

Answer:

y = 2/x

Step-by-step explanation:

You cannot divide by zero because you will get an undefined value, and this will create a hole in the graph.

Answer:

\(y = \frac{2}{x\\}\)

Explanation:

Let's check all the answers to be sure we are correct!

Choice A)  y = 2x

The domain for y = 2x is represented by the interval (-∞,∞). This shows that the domain is all real numbers.

Choice B)  y = 2 + x

The domain is represented by the interval (-∞,∞). This shows that the domain is all real numbers.

Choice C)  \(y=\frac{2}{x}\)

We know that the denominator can not be equal to zero. You must remember this! So, now we find that the domain is represented by the interval,

                                              (-∞,0) ∩ (0,∞)

This shows that the domain is all real numbers except the number zero.

Choice D) \(y = x^{2}\)

The domain is represented by the interval (-∞,∞). This shows that the domain contains all real numbers.

Therefore, our answer is choice C!

Nice job everyone!