6 minus a number minus 11

Answer:

84, -6

Step-by-step explanation:

y= -x+84

y= x^2+(-6)

The system of equations used to find the value of x is:

y = -x + 84

y = x² - 6

Let x represent the first number and y represent the second number.

The sum of the two numbers is 84, hence:

x + y = 84

y = -x + 84      (1)

The square of the first number is 6 more than the second number. Hence:

x² = 6 + y

y = x² - 6     (2)

The system of equations used to find the value of x is:

y = -x + 84

y = x² - 6

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Answer:

6296.5

Step-by-step explanation:

Cone volume: 622.0

Cylinder Volume: 5674.5

622+5674.5=6296.5

Answer:

0.5 < x < 16.5

Step-by-step explanation:

For a triangle (by the triangular inequality theorem), we know that the sum of any two sides must be larger than the other side.

When we have a triangle and we know two sides, let's define the measures of these sides as S1 and S2.   (such that S2 > S1)

By the first property, we will have that S1 + S2 > S3

Where S3 is the third side, the one that we do not know.

But there is also a lower restriction, given by:

S2 - S1 < S3 < S1 + S2

This is because we also must have:

S1 + S3 > S2

and

S2 + S3 > S1

We can rewrite both of these to get:

S2 - S1 < S3

S1 - S2 < S3

Because S2 > S1, the first inequality is more restrictive, so we need to use that one.

Then we get the inequality:

S2 - S1 < S3 < S1 + S2

Ok, in this case, the shorter side is 8.0 then:

S1 = 8.0

And the longer side is 8.5, then:

S2 = 8.5

And the third side is x, S3 = x

Replacing those in our inequality, we get:

8.5 - 8.0 < x < 8.5 + 8.0

0.5 < x < 16.5

This is the range of possible sizes for side x.

To integrate ∫1/(√x√(1−x)) dx, we can use a trigonometric substitution. Let's consider the substitution x = sin^2θ.

First, we need to find the differentials dx and dθ. Taking the derivative of x = sin^2θ, we have dx = 2sinθcosθ dθ.

Now, substitute x and dx in terms of θ:

∫ 1/(√x√(1−x)) dx = ∫ 1/(√sin^2θ√(1−sin^2θ)) (2sinθcosθ) dθ.

Simplifying the integrand:

∫ 1/(√sin^2θ√(cos^2θ)) (2sinθcosθ) dθ

= ∫ 1/(sinθ cosθ) (2sinθcosθ) dθ

= ∫ 2 dθ.

Integrating 2 with respect to θ gives:

2θ + C, where C is the constant of integration.

Finally, substitute back θ = arcsin(√x):

∫ 1/(√x√(1−x)) dx = 2arcsin(√x) + C.

Therefore, the integral of 1/(√x√(1−x)) dx is 2arcsin(√x) + C.

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Answer:

2 quadrant

Step-by-step explanation:

i think

Answer:

Quadrant 2...

the general solution of the given differential equation is:

y = (1/|x|^2) [(1/5)x^5 - (1/3)x^3 + C]

where C is the constant of integration.

To find the general solution of the given differential equation, we need to solve for y in terms of x. The differential equation is:

What is Integrating factor?

x dy/dx + 2y = x^3 - x

To solve this, we can use an integrating factor. First, we rearrange the equation in the standard form:

dy/dx + (2/x) y = (x^3 - x)/x

The integrating factor (IF) is defined as the exponential of the integral of the coefficient of y. In this case, the coefficient is (2/x), so the IF is:

IF = exp(∫(2/x) dx)

= exp(2 ln|x|)

= exp(ln|x|^2)

= |x|^2

Now, we multiply both sides of the differential equation by the integrating factor:

|x|^2(dy/dx) + (2|x|^2 / x) y = (x^3 - x)|x|^2 / x

Simplifying this expression, we have:

|x|^2(dy/dx) + 2|x|y = (x^3 - x)|x|

Now, we can rewrite the left-hand side as the derivative of (|x|^2y) with respect to x:

d/dx (|x|^2y) = (x^3 - x)|x|

Integrating both sides with respect to x, we get:

∫ d/dx (|x|^2y) dx = ∫ (x^3 - x)|x| dx

|x|^2y = ∫ (x^4 - x^2) dx

Integrating further, we have:

|x|^2y = (1/5)x^5 - (1/3)x^3 + C

Finally, we can solve for y:

y = (1/|x|^2) [(1/5)x^5 - (1/3)x^3 + C]

Therefore, the general solution of the given differential equation is:

y = (1/|x|^2) [(1/5)x^5 - (1/3)x^3 + C]

where C is the constant of integration.

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Find the inverse Laplace transforms of the following functions. First, perform partial-fraction expansion on G(s); then, use the Laplace transform table. (a). G(s)= 1 / s(s+2)(s+3) (b). G(s)= 10 / (s +1)^2(s+3) (c). G(s)= [100(s+2) / s(s^2 + 4)(s+1)] e^-x

(d). G(s)= 2(s+1) / s(s^2+s+2) (e). G(s)= 1 / (s+1)^3 (f). G(s)= 2(s^2+s+1) / s(s+1.5)(s^2 +5s+5)

(g). G(s)= [2+2se^(-x) + 4e^(-2x)] / [s^2 + 3s + 2] (h). G(s) = 2s+1 / (s^2 + 6s^2 +11s +6)

(i). G(s) = (3s^3 + 10s^2 + 8s + 5) / (s^4 + 5s^3 + 7s^2 + 5s +6)

Answer:

0 represents the water level.

Step-by-step explanation:

The ring started out at -10 and moved upwards to 0.

Answer:20

Step-by-step explanation: my man

Answer:

20

Step-by-step explanation:

1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 10

+ 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 10

= 20

In straight line ABC. O is a point on line AB, then OC = a+b in its simplest form.

ABC is a straight line. Assuming O is a point on the line AB, we can proceed as follows

Let AB = 2a and BC = 3a, where a is some constant. Then, AC = AB + BC = 5a.

Let O be a point on AB such that BO = b. Then, AO = AB - BO = 2a - b.

Since ABC is a straight line, we have:

AO + OC = AC

Substituting the values we obtained above, we get:

(2a - b) + OC = 5a

Simplifying this equation for OC, we get:

OC = 3a + b - 2a

OC = a + b

Therefore, OC is equal to a + b in its simplest form.

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At a significance level of 0.05, the sample data is not consistent with the null hypothesis that the proportion of population who would respond "yes" is 0.5. The P-value of 0.0005 is less than 0.05, and also the sample proportion 0.4616 is not in the interval (0.477, 0.523) which we found as 95% Confidence interval.

Therefore, we reject the null hypothesis and conclude that the population proportion of "yes" responses is different from 0.5.

The P-value for a score test for H0: π = 0.5 can be found using the z-score and a standard normal table. The z-score is calculated as

\(z = \frac{x-0.5}{0.5\sqrt{\frac{x-0.5}{n} } }\), that is

z = (x - 0.5) / (√(0.5(1 - 0.5) / n)

where x is the sample proportion of "yes" responses (842 / (842 + 982) = 0.4616), π is the population proportion of "yes" responses, and n is the sample size (842 + 982 = 1824).

\(z = \frac{0.4616-0.5}{0.5\sqrt{\frac{0.4616-0.5}{1824} } }\)

= (0.4616 - 0.5)/ (√(0.5(1 - 0.5) / 1824)

This gives a z-score of -3.28.

To find the P-value, we can use the standard normal table to find the probability of observing a z-score less than -3.28. This P-value is approximately 0.0005, which is less than the commonly used significance level of 0.05. Therefore, we would reject the null hypothesis that π = 0.5.

To construct a 95% confidence interval for π, we can use the formula for a normal approximation interval:

π ± z×(√(π(1-π) / n)) that is

\(\pi \frac{+}{} z\frac{\pi (1 -\pi )}{n}\)

Where π = 0.5, z = 1.96 (for a 95% confidence level), and n = 1824.

This gives a 95% confidence interval of (0.477, 0.523)

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In regards to the question above, It is difficult to determine which type of vehicle has the most expensive transmission to rebuild, as the cost of rebuilding a transmission can vary greatly depending on a number of factors such as the make and model of the vehicle, the age of the vehicle, the extent of the damage to the transmission, and the cost of labor in the area where the work is being done.

There are many factors that can affect the cost of rebuilding a transmission. Some of the most important include:

The make and model of the vehicle: Different vehicles have different transmissions, and some types of transmissions may be more expensive to rebuild than others.

The specific transmission type: There are several different types of transmissions, including manual, automatic, continuously variable, and dual-clutch.

In all, luxury vehicles and high-performance vehicles may have more expensive transmissions to rebuild due to the use of more complex and costly components. It is a good idea to get a quote from a reputable mechanic or transmission repair shop before deciding to have work done on your vehicle's transmission.

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The months in which the depths decreased are:

Between April and May

Between June and July

The change in depth between April and May is calculated as:

Change in depth = -0.28 - (-0.15) = -0.13 m

Thus, there was a decrease in depth between april and may

The change in depth between May and June is calculated as:

Change in depth = -0.08 - (-0.28) = 0.20 m

Thus, there was an increase in depth between May and June

The change in depth between June and July is calculated as:

Change in depth = -0.01 - (-0.05) = 0.07 m

Thus, there was a decrease in depth between June and July.

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The complete question is:

A scientist measures the depth of the water in a pond each month. The pond is considered full at 0 m. She compares her measures to the height of the water when the pond is considered full and records the change in depth in a table

Between which months did the depth of water decrease?

By engaging in these exercises, students can develop a deeper understanding of conditional statements and logical reasoning, which are essential skills for further studies in mathematics and logic.

In Unit 2 of a logic and proof course, homework 3 focuses on conditional statements.

Conditional statements are fundamental concepts in logic and mathematics, representing logical implications between two statements.

They are typically expressed in "if-then" format, where the "if" part is the hypothesis and the "then" part is the conclusion.

The homework may involve tasks such as:

Identifying conditional statements: Students are given a set of statements and asked to identify which ones are conditional statements.

They need to recognize the "if-then" structure and correctly identify the hypothesis and conclusion.

Analyzing the truth value of conditional statements:

Students may be given conditional statements and asked to determine whether they are true or false.

They need to evaluate the hypothesis and conclusion to determine if the implication holds in each case.

Writing converse, inverse, and contrapositive statements:

Students may be required to manipulate given conditional statements to form their converse, inverse, and contrapositive statements.

This involves switching the positions of the hypothesis and conclusion or negating both parts.

Applying the laws of logic:

Students may need to apply logical laws, such as the Law of Detachment or the Law of Modus Tollens, to deduce conclusions based on conditional statements.

Constructing counterexamples:

Students may be asked to provide counterexamples to disprove statements that are falsely claimed to be universally true based on a given conditional statement.

They also help students develop critical thinking and problem-solving abilities, as they have to analyze and manipulate logical structures.

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Answer:

a) 984.6080 = 984.61 to 2 decimal places

b) 984.6080 = 984.6 to 4 significant figures

c) 984.6080 = 984.608 to 3 decimal places

d) 984.6080 = 984.61 to the nearest h

Step-by-step explanation:

a. the mean is 200.31 cm. b. The height of the new player is 210 cm.

The mean, commonly referred to as the average, is a statistic that depicts the usual value of a group of data and measures central tendency. It is calculated by adding up all of the data set's values and dividing the result by the total number of values. Since it offers a single value that summarises the complete set of data, the mean is an effective statistical tool. It may, however, be vulnerable to outliers or extremely high or low values that affect the mean's value. As a result, while examining data, it is crucial to take additional measures of central tendency into account, such as the median or mode.

The mean or average is given as:

mean = (sum of all heights) / (number of players)

The total number of players are:

1 + 3 + 2 + 5 + 2 = 13

Sum of heights is:

(198 x 1) + (199 x 3) + (200 x 2) + (201 x 5) + (202 x 2) = 198 + 597 + 400 + 1005 + 404 = 2604

Thus,

mean = 2604 / 13 = 200.31 cm

b. For the new player the number of players are 14:

201 = (2604 + height of new player) / 14

201 x 14 = 2604 + height of new player

2814 = 2604 + height of new player

height of new player = 2814 - 2604 = 210 cm

Hence, a. the mean is 200.31 cm. b. The height of the new player is 210 cm.

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To find the markup price you need to multiply the 83% by the cost:

83%=0.83

16*0.83=13.28

and the selling price is the cost plus the markup price so

16+13.28=29.28

So the answer is:

The mark up is $ 13.28 and the final selling price is $ 29.28

Answer:

8.1 s=8.1 it could be 8 because it is based on shoe size

Step-by-step explanation:

1.7f - 7.2

1.7(9) - 7.2

15.3 - 7.2

8.1

Yes, there is the relationship a function.

b. From the table, all the outputs are found to be either 3, 4 or 5.

The relationship is a function, with each input mapping to one output. Table has a function mapping each input to a single output. However, in option b) some inputs map to the same output.

The numbers 5 and 3 are repeated as outputs for "Kabir" and "Ethan", indicating a non-one-to-one function.

This function's rule is based on the length of the input name and assigned values for each letter, which are added together to find the output.

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Consider the relationship shown in the table.

Input   Output

Kabir       5

Eve           3

Ethan        5

Maya          4

Shawn       5

*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆

Answer: 42 minutes

Explanation:

0.40x + 3.20 = 20

0.40x = 16.8

x = 42 minutes

I hope this helped!

<!> Brainliest is appreciated! <!>

- Zack Slocum

*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆

hello

to solve for x, let's cross multiply both sides

step 2

divide both sides by -2

x = - 6

Answer:

x = -6

Step-by-step explanation:

The surface integral can be evaluated becomes

∬S y^2z^2 dS = ∫[0 to 5] ∫[0 to 2π] (r^4 sin^2θ cos^2θ) r√(2) dθ dr.

To evaluate the surface integral ∬S y^2z^2 dS, where S is the part of the cone y = sqrt(x^2 + z^2) and 0 < y < 5, we need to parameterize the surface S and calculate the necessary components.

The cone can be parameterized using cylindrical coordinates as:

x = r cosθ,

y = r,

z = r sinθ,

where r ≥ 0 and 0 ≤ θ ≤ 2π.

To find the surface element dS, we use the cross product of the partial derivatives of the parameterization:

dS = |∂r/∂θ × ∂r/∂r| dθ dr,

where ∂r/∂θ and ∂r/∂r are the partial derivatives of r with respect to θ and r, respectively.

Taking the cross product:

∂r/∂θ = (-r sinθ, 0, r cosθ),

∂r/∂r = (cosθ, 1, sinθ),

we have:

∂r/∂θ × ∂r/∂r = (-r cosθ, -r sinθ, r).

The magnitude of the cross product is:

|∂r/∂θ × ∂r/∂r| = √[(-r cosθ)^2 + (-r sinθ)^2 + r^2] = r√(2).

Now we can rewrite the surface integral in terms of cylindrical coordinates:

∬S y^2z^2 dS = ∫∫S (r^2 sin^2θ)(r^2 cos^2θ) r√(2) dθ dr.

The limits of integration for θ are from 0 to 2π, and for r, it is from 0 to the maximum value of r for the given y range (0 < y < 5). The cone equation gives y = r, so the maximum value of r is 5.

Therefore, the surface integral becomes:

∬S y^2z^2 dS = ∫[0 to 5] ∫[0 to 2π] (r^4 sin^2θ cos^2θ) r√(2) dθ dr.

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Answer:

I need answer choices to help you

Step-by-step explanation:

Answer:

The volume is;

3951.8 cm^3

Step-by-step explanation:

As we can see, the sphere diameter is 19 cm

Radius is half of this which is 19/2 = 9.5 cm

Putting this in the area , we have

4/3 * 3.142 * 9.5^3 = 3951.8

cm^3

Answer:

C.14ײ+5

Step-by-step explanation:

Hope It Help

Brainliest please

Answer:

Step-by-step explanation:

if we consider mod then the negative turns to positive and positive remains positive so it will be

279 < 282 which is l279l < l-282l

a) The values of X and Y that maximize the utility are X = 250 and Y = 125.

b) T he values of X and Y that maximize the utility using the Lagrangean method are X = 250 and Y = 125.

a) To find the values of X and Y that maximize the utility using the substitution method, we can start by substituting the budget constraint into the utility function.

Since the budget constraint is given by 2X + 4Y = 1000 (kr), we can rearrange it to solve for X: X = (1000 - 4Y)/2 = 500 - 2Y.

Now substitute this expression for X in the utility function: U(Y) = 100(500 - 2Y)Y + (500 - 2Y) + 2Y.

Expand and simplify the expression: U(Y) = 50000Y - 200Y^2 + 500 - 2Y + 2Y.

Combine like terms: U(Y) = -200Y^2 + 50000Y + 500.

To maximize the utility, we need to find the critical points. Take the derivative of U(Y) with respect to Y and set it equal to zero:

dU(Y)/dY = -400Y + 50000 = 0.

Solve for Y: Y = 50000/400 = 125.

Now substitute this value of Y back into the budget constraint to find the corresponding value of X:

2X + 4(125) = 1000,
2X + 500 = 1000,
2X = 500,
X = 250.



b) To find the values of X and Y that maximize the utility using the Lagrangean method, we need to set up the following equation:

L(X,Y,λ) = U(X,Y) - λ(2X + 4Y - 1000),

where λ is the Lagrange multiplier.

Taking the partial derivatives of L with respect to X, Y, and λ, we have:

dL/dX = 100Y + 1 - 2λ,
dL/dY = 100X + 2 - 4λ,
dL/dλ = -(2X + 4Y - 1000).

Setting these derivatives equal to zero, we have the following system of equations:

100Y + 1 - 2λ = 0,
100X + 2 - 4λ = 0,
2X + 4Y - 1000 = 0.

Solving this system of equations, we find:

λ = 1/2,
X = 250,
Y = 125.

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The total cost for 10 hours of work would be 25 + 50(10) = 525.

Cost is the monitorial associated with the purchase of production of food or service if can include the prices of material of which is over it and other expenses that are related to the production of the code of service cost is a major fraction of when deciding whether to purchase a product something as it is and indicator of the value of the product of sound service.
The marginal cost of producing 5 items can be calculated using the equation C(x)=1300+4x/10. The marginal cost is the cost associated with producing one additional item. To calculate the marginal cost, we can plug in x=5 into the equation.

The equation in slope-intercept form for cost, c, after h hours of service is c = 25 + 50h.

The total cost for 8 hours of work would be 25 + 50(8) = 425.

The total cost for 10 hours of work would be 25 + 50(10) = 525.

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Answer:

-3

Step-by-step explanation:

x - y = 12 is the same as -2x = -24 - 2y

                                         2x = 27 + 3y

                                     +  --------------------

                                         0 =   3  +  y

                                        -3 = y

The rate at which water is coming into the tank is 5,700 gallons/hr.

Let the amount of water going out of the tank be x gallons/hr. Hence, the amount of water coming into the tank is 3x gallons/hr.

Therefore, the net rate of inflow into the tank is:

Rate of inflow - Rate of outflow = (3x - x) gallons/hr = 2x gallons/hr

Given that the tank contains 11,400 gallons of water after one hour. Hence, the amount of water that went into the tank is equal to the net rate of inflow multiplied by the time.

We have:

Amount of water coming into the tank = Net rate of inflow × Time

Therefore, 11,400 gallons = 2x × 1 hr or 11,400 gallons/hr = 2x gallons/hr x = 5,700 gallons/hr

So, the rate at which water is coming into the tank is 5,700 gallons/hr. Therefore, the answer is:

Water is coming into the tank at the rate of 5,700 gallons/hr.

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