2. Given f(x) = 2x + 3(x – 3), find x, if f(x) = 11.

please hurry

The equation of the linear relationship in slope-intercept form is y = -6x + 303.

Slope intercept is an equation used to describe the relationship between an independent and dependent variable. It is written in the form y = mx + b, where m is the slope, x is the independent variable, and b is the y-intercept. The slope intercept equation can be used to draw a line on a graph, which can then be used to make predictions about the dependent variable given a certain value for the independent variable.

The equation of the linear relationship in slope-intercept form can be determined by looking at the table. The slope of the linear relationship is given by the change in y for a given change in x, which in this case is -6. The intercept can be determined by looking at the y-value when x is 0, which in this case is 303. Therefore, the equation of the linear relationship in slope-intercept form is y = -6x + 303.

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Considering the definition of an inequality and system of inequalities, the correct option is: "No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100."

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

An inequality contains one or more unknown values ​​called unknowns, in addition to certain known data.

Solving an inequality consists of finding all the values ​​of the unknown for which the inequality relation holds.

A system of inequalities is made up of two or more inequalities.

The solution will be formed by the intersection of the half-planes of each of the inequalities, that is, it will be the enclosure that all the inequalities have in common. That is, the solution of the system is given by the region of the common plane of the half-planes that define each one of the inequalities.

In this case:

Then, the system of inequality is:

\(\left \{ {{4c+6a\leq 120} \atop {4c+4a\leq 100}} \right.\)

On the other hand, the company can build 20 child bikes and 6 adult bikes in the week. So, checking the equations, for given c=20 and a=6:

4×20 + 6×6= 116 < 120

4×20 + 4×6= 104 >100

Finally, the correct option is: "No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100."

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Answer:

6+36-4=38/2=19

Answer is 19 for number 1

Step-by-step explanation:

Answer

55

Step-by-step explanation:

let the angle be X so
x + 125=180
so 180 -125=x
180-125=55
so x=55

Answer:

\( 2 \sqrt{71} \: units\)

Step-by-step explanation:

Given is a right angled triangle in which third side is the hypotenuse.

Therefore, by Pythagoras theorem:

\(thid \: side = \sqrt{ {15}^{2} + ( \sqrt{59} )^{2} } \\ \\ = \sqrt{225 + 59} \\ \\ = \sqrt{284} \\ \\ = \sqrt{ {2}^{2} \times 71 } \\ \\ = 2 \sqrt{71} \: units\)

Answer:The answer is below

Step-by-step explanation:

The bottom of a river makes a V-shape that can be modeled with the absolute value function, d(h) = ⅕ ⎜h − 240⎟ − 48, where d is the depth of the river bottom (in feet) and h is the horizontal distance to the left-hand shore (in feet). A ship risks running aground if the bottom of its keel (its lowest point under the water) reaches down to the river bottom. Suppose you are the harbormaster and you want to place buoys where the river bottom is 20 feet below the surface. Complete the absolute value equation to find the horizontal distance from the left shore at which the buoys should be placed

Answer:

To solve the problem, the depth of the water would be equated to the position of the river bottom.

h is=380 or h=100

Step-by-step explanation:

The given problem involves finding the curl of a given vector field and using it to evaluate line integrals over specific curves.

Specifically, we are asked to find the curl of the vector field F = (7z+ 7x^2) i + (3y + 6z + 6 sin(y^2)) j + (7x+6y + 3e^z) k, and use it to evaluate line integrals over a circle and a half circle in the xy-plane, with specific orientations.To find the curl of the vector field, we need to take the cross product of the gradient operator and the vector field. The curl of a vector field measures how much the vector field curls around a point, and it is a vector field itself.

Using the curl of the vector field, we can evaluate line integrals over specific curves by applying Stokes' theorem. Stokes' theorem states that the line integral of a vector field around a closed curve is equal to the surface integral of the curl of the vector field over any surface bounded by the curve.The final answers are numbers, which represent the line integrals of the vector field over the specific curves.Overall, the problem involves applying the principles of vector calculus, including the curl and Stokes' theorem, to evaluate line integrals over specific curves. It also requires an understanding of orientation and the relationship between line integrals and surface integrals.

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The mean class size at Mountain View School is 4.4 and at Seaside School is 4.2.

The median class size is 5 for both schools.

The range for Mountain View School is 12 and for Seaside School is 8.

The IQR for Mountain View School is 6 and for Seaside School is 3.

To find the measures of center, we can calculate the mean and median for both schools.

Mountain View School:

Mean = (2+1+0+5+8+6+9+8+2+0+1+0+6)/15

Mean = 4.4

Median = 5

Seaside School:

Mean = (0+1+2+5+6+8+8+7+6+5+5+4+4+3+1+0)/15

Mean = 4.2

Median = 5

Part B:

To find the measures of variability, we can calculate the range and interquartile range (IQR) for both schools.

Mountain View School:

Range = largest value - smallest value = 12 - 0

Range = 12

IQR = Q3 - Q1 = 8 - 2 = 6

Seaside School:

Range = largest value - smallest value = 8 - 0

Range = 8

IQR = Q3 - Q1 = 7 - 4 = 3

Part C:

If we are interested in a smaller class size, Seaside School would be the better choice. The median class size is the same at both schools, but Seaside School has a smaller mean, which suggests that on average, class sizes are smaller.

Additionally, the range and IQR are both smaller for Seaside School, indicating less variability in class size.

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As per the addition formula, the value of the trigonometric function is -0.809.

In statistics, function is defined as a relationship between inputs where each input is related to exactly one output.

Here we have to find the value of the trigonometric function cos(13/15)cos(-/5)-sin(13/15)sin(-/5)  by using the addition and subtraction formula.

Here we have the following trigonometric function:

=> cos(13/15)cos(-/5)-sin(13/15)sin(-/5)

Now, we have to use the trigonometric addition formula,

=> Cos (A+B) = Cos A Cos B - Sin A Sin B

To solve the given function,

Here let us rewrite the given function based on the addition formula, then we get,

=> Cos ( 13π/15 + (-π/5) )

=> Cos( 12π/5)

=> Cos(144°)

=> -0.809

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Answer:

5/6

Step-by-step explanation:

i know that i tolde you i like you o na-na and ohhhhh baby

The alternative hypothesis (H1) would be that the mean of the bottles of cream is not equal to 8 ounces, indicating that the containers are being filled incorrectly. It can be written as: H1: μ ≠ 8 ounces where μ represents the population mean of the bottle cream fillings.

In the given scenario, the null hypothesis would be that the bottles of cream are being filled correctly with a mean of 8 ounces. The alternative hypothesis would be that the bottles of cream are not being filled correctly, meaning the true mean of the population is different from 8 ounces. However, the specific form of the alternative hypothesis would depend on the direction of the problem. If we are interested in knowing whether the mean filling amount is greater than or less than 8 ounces, we would use a one-tailed alternative hypothesis. If we are interested in determining whether the mean filling amount is simply different from 8 ounces, we would use a two-tailed alternative hypothesis.

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The probability that the Davis boys will occupy the first two seats in the row, the Jones boys will occupy the next three seats, and the Smith boys will occupy the last four seats is 7.937×\(10^{-4}\).

There are \(\left[\begin{array}{ccc}9\\2,3,4\\\end{array}\right]\) potential arrangements for the nine boys if we do not make a distinction amongst boys with the same last name. We are curious in the likelihood of a specific one of these configurations.

Probability = \(\frac{1}{\left[\begin{array}{ccc}9\\2,3,4\\\end{array}\right]}\)

                  = \(\frac{2!3!4!}{9!}\)

                 = 0.0007937

                = 7.937×\(10^{-4}\)

Hence, the probability is 7.937×\(10^{-4}\).

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Answer:

5

Step-by-step explanation:

slopes of the parallel lines are always same this line has slope five

because equation in y intercept form is y=mx+b

where m is the slope.

so the slope of the new line will be five

The distance of the point from the origin is 7.07.

I. In cylindrical polar coordinates the coordinates of the given point are (7.07, 45°, 5.12). To obtain these coordinates we must first find the radius of the circle this point lies on. This is calculated as: radius = √(x² + y²) = √(5.12² + 7²) = 7.07. We then calculate the angle from the x-axis to the point as: angle = tan⁻¹(y/x) = tan⁻¹(7/5.12) = 45°

II. In spherical polar coordinates the coordinates of the given point are (7.07, 45°, 53°). To obtain these coordinates we must first find the radius of the sphere this point lies on.

This is calculated as: radius = √(x² + y² + z²) = √(5.12² + 7² + 0²) = 7.07. We then calculate the angle from the x-axis to the point as: angle1 = tan⁻¹(y/x) = tan⁻¹(7/5.12) = 45°.

Finally, we calculate the angle from the z-axis to the point as: angle2 = cos⁻¹(z/r) = cos⁻¹(0/7.07) = 53°

III. The distance of this point from the origin can be computed using the Pythagorean theorem as: distance = √(x² + y² + z²) = √(5.12² + 7² + 0²) = 7.07.

Hence, the distance of the point from the origin is 7.07.

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A. Prospective observational studies involve collecting data from participants before an event or outcome occurs, while retrospective observational studies collect data after the event has already taken place.

A prospective observational study is a type of observational study that involves collecting data from participants before an event or outcome occurs. This type of study is used to predict and measure outcomes in the future.

In this type of study, the researcher can control the variables, such as when and how the data is collected, and can also observe the effects of any changes in the environment.

On the other hand, a retrospective observational study is a type of observational study that involves collecting data after an event or outcome has already taken place. This type of study is used to study the causes of a given outcome.

In this type of study, the researcher looks back in time and collects data from the past. This type of study is more limited than a prospective observational study, since the researcher cannot control the variables of the study or observe any changes in the environment.

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Your answer is in the above Attachment

Your answer is in the above Attachment Hope It helps :)

The length of Adrian's shadow measured by his friend and the distance directly from Adrian's head to the tip of his shadow can be used to find Adrian's height using Pythagorean Theorem. Using an example of the measurement values, Adrian's height is about 5.5 feet

Pythagorean Theorem states that the sum of the square of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse side.

The diagram in the question appears left out. Please find attached a drawing made using the measurement lengths in the following example, created with MS Word.

The measurements Adrian had his friend to do are;

The length of Adrian's shadow on the sidewalk and the length from Adrian's head to the tip of the shadow.

Let x represent the length of Adrian's shadow, let r represent the distance from Adrian's head to the tip of the shadow, and let y represent Adrian's height

According to Pythagorean Theorem, we get;

r² = x² + y²

Therefore, the Adrian's height, h = √(r² - x²)

When r ≈ 8.14, and x = 6, we get;

h = √(8.14² - 6²) ≈ 5.5

Adrian's height is about 5.5 feet in the example situation

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Answer:

35

Explanation:

The lengths of triangle PQR are 5x the lengths of triangle ABC.

4*5= 20

8*5= 40

7*5= 35

The solution is Option B , Option D.

The equations are z/6 + w = 11 and 5y + 4 = 16 + y

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

( 10 + a ) / ( 3a + 1 )  

Now , it is an expression because the "=" sign and terms on both sides must always be present when writing an equation.

b)

z/6 + w = 11   be equation (1)

Now , the equation is having = sign along with coefficients and variables

c)

( z-2 ) / 3 < 15

The < sign represents an inequality relation

So , it is not an equation

d)

5y + 4 = 16 + y   be equation (2)

Now , the equation is having = sign along with coefficients and variables

e)

x² + 3x + 7

Now , it is an expression because the "=" sign and terms on both sides must always be present when writing an equation.

f)

5y + 1 ≤ y

The ≤ sign represents an inequality relation

So , it is not an equation

Hence , the equations are solved

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Answer:

hope this helps

To find the probability that a participant selected at random found the products favorable, we can calculate the weighted average of the favorable responses from both the industry-sponsored and non-industry-funded studies.

For the industry-sponsored studies, 65% of participants found the products favorable, and for the non-industry-funded studies, 47% found the products favorable. Since there were 65 industry-sponsored studies and 35 non-industry-funded studies, the overall probability is:

(65/100) * 0.65 + (35/100) * 0.47 = 0.4225 + 0.1645 = 0.587 or 58.7%

If a randomly selected participant found the product favorable, we can use Bayes' theorem to calculate the probability that the study was sponsored by the food industry given this favorable response. The calculation is:

P(Industry-sponsored | Favorable) = (P(Favorable | Industry-sponsored) * P(Industry-sponsored)) / P(Favorable)

P(Favorable | Industry-sponsored) = 0.65

P(Industry-sponsored) = 65/100

P(Favorable) = 0.587

P(Industry-sponsored | Favorable) = (0.65 * (65/100)) / 0.587 ≈ 0.719 or 71.9%

Similarly, if a randomly selected participant found the product unfavorable, we can use Bayes' theorem to calculate the probability that the study had no industry funding given this unfavorable response. The calculation is:

P(No industry funding | Unfavorable) = (P(Unfavorable | No industry funding) * P(No industry funding)) / P(Unfavorable)

P(Unfavorable | No industry funding) = 0.36

P(No industry funding) = 35/100

P(Unfavorable) = 1 - P(Favorable) = 1 - 0.587 = 0.413

P(No industry funding | Unfavorable) = (0.36 * (35/100)) / 0.413 ≈ 0.305 or 30.5%

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Based on the given informations, the angle between the ladder and the ground is decreasing at a rate of 0.009 radians/second when the ladder is 5.8 feet away from the house.

Let's call the distance between the base of the ladder and the house "x". The length of the ladder is 24 feet, so the height it reaches up the house is given by the Pythagorean theorem:

h² = 24² - x²

Differentiating both sides with respect to time:

2h dh/dt = -2x dx/dt

We want to find dh/dt when x = 5.8 feet and dx/dt = 0.25 feet/second. First, we need to solve for h:

h² = 24² - 5.8² = 557.84

h = 23.63 feet

Substituting x = 5.8 feet, h = 23.63 feet, and dx/dt = 0.25 feet/second:

2(23.63) dh/dt = -2(5.8)(0.25)

dh/dt = -0.06 feet/second

So the tip of the ladder is slipping down the side of the house at a rate of 0.06 feet/second.

To find the rate of change of the angle, we can use the formula:

tan(Θ) = h/x

Differentiating both sides with respect to time:

sec²(Θ) d(Θ)/dt = (1/x) dh/dt - (h/x²) dx/dt

We already know x = 5.8 feet, h = 23.63 feet, and dx/dt = 0.25 feet/second. We just calculated dh/dt to be -0.06 feet/second. To find sec(theta), we can use the fact that cos(Θ) = x/h:

cos(Θ) = x/h = 5.8/23.63 = 0.245

sec(Θ) = 1/cos(theta) = 4.0816

Substituting these values into the formula above:

(4.0816)² d(Θ)/dt = (1/5.8)(-0.06) - (23.63/5.8²)(0.25)

d(Θ)/dt = -0.009 radians/second (rounded to 3 decimal places)

Therefore, the angle between the ladder and the ground is decreasing at a rate of 0.009 radians/second when the ladder is 5.8 feet away from the house.

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Answer:

what are you asking, I need more information.

The account value, y(t), accruing continuously at a 5% annual rate, is modeled by the differential equation dy/dt = 0.05y. After 10 years, with P = $2000, the account value is approximately $3263.18.

(a) To model the value of the account, y(t), as it accrues continuously at a 5% annual interest rate, we use a differential equation. The rate of change of y with respect to time, t, is given by dy/dt, and it is equal to the interest rate times the current value of the account, which is 0.05y.

(b) Solving the differential equation dy/dt = 0.05y, we separate variables and integrate:
∫(1/y)dy = 0.05∫dt
ln|y| = 0.05t + C
Taking the exponential of both sides, we have |y| = e^(0.05t + C)
Since y represents the value of the account, we can write the general solution as y = Ae^(0.05t), where A is the constant of integration.

(c) If P = 2000, then we have the initial condition y(0) = 2000. Substituting these values into the general solution, we obtain 2000 = Ae^(0.05(0))
Simplifying, we find A = 2000. Therefore, the specific solution is y = 2000e^(0.05t).
To find the amount of money in the account after 10 years, we substitute t = 10 into the equation:
y(10) = 2000e^(0.05(10))
y(10) ≈ 2000e^(0.5)

Therefore, After 10 years, with P = $2000, the account value is approximately $3263.18.

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Answer:

600cm3 the 3 is ment to be cubed

Step-by-step explanation:

The weighted average of a data set is 36.

Here,

Given data set;

20 has a weight of 3, 40 has a weight of 5, and 50 has a weight of 2.

We have to find the weighted average of a data set.

What is Weighted Average?

Weighted average is a calculation that takes into account the varying degrees of importance of the numbers in a data set.

Now,

Given data set;

20 has a weight of 3, 40 has a weight of 5, and 50 has a weight of 2.

The weighted average is given by the formula;

\(x = \frac{f_{1} x_{1} + f_{2} x_{2}+ f_{3} x_{3}+ ...... f_{n} x_{n}}{f_{1} +f_{2} + f_{2}}\)

Hence,

The weighted average of a data set;

x = 20 x 3 + 40 x 5 + 50 x 2 / 3+5+2

x = 360/10 = 36

Hence, The weighted average of a data set is 36.

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Answer:

1 : \(\frac{2}{3}\)

Step-by-step explanation:

Given the ratio

9 : 6 ← divide both parts of the ratio by 9

= \(\frac{9}{9}\) : \(\frac{6}{9}\) ← simplify

= 1 : \(\frac{2}{3}\)

Answer:

9a^3b^3.

Step-by-step explanation:

The GCF of 9 and 27 is 9.

For a^4 and a^3 it is a^3.

For b^4 and b^3 it is b^3.

Answer is therefore:

9a^3b^3.

Answer:

9a^3 b^3

Step-by-step explanation:

hope this helps you have a nice day :)

i use to use this but its whatever works for you the second picture for prime factors

Answer:

Step-by-step explanation:

To determine if there is a positive linear association between the hours worked and the daily wages of waiters in a restaurant, you can create a scatter plot of the data and look for a pattern.

Once you have the data, you can use a statistical software or a spreadsheet program to create a scatter plot. You can then visually inspect the scatter plot to see if there is a clear pattern of a positive linear association between the two variables.

If there is a positive linear association, the data points on the scatter plot will form a roughly straight line that slopes upwards from left to right. The closer the data points are to the line, the stronger the association.

So, the data table that indicates a positive linear association between the hours worked and the daily wages of waiters in a restaurant is the one where the scatter plot shows a clear upward trend.

The group of volunteers can make a total of 200 masks out of 25 yards of fabric.

To calculate the number of masks that can be made, we divide the total amount of fabric (25 yards) by the amount of fabric required per mask (1/8 yard). To do this, we first convert the fraction 1/8 to decimal form, which is 0.125. Then, we divide the total fabric (25 yards) by the fabric required per mask (0.125 yards). This can be done by dividing 25 by 0.125, which equals 200. Therefore, the group of volunteers can make a total of 200 masks out of 25 yards of fabric. Each mask requires 1/8 yard of fabric, so dividing the total fabric by the fabric required per mask gives us the total number of masks that can be made.

Calculation steps:
1. Convert the fraction 1/8 to decimal form: 1/8 = 0.125.
2. Divide the total fabric (25 yards) by the fabric required per mask (0.125 yards):
  25 / 0.125 = 200.


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