Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
f(x) =
1
8
(7x − 2), x ≤ 3
absolute maximum value

Answer:

150 km I think

Step-by-step explanation:

Using classical probability, we found that the chance of one minority candidate getting hired is 2/5.

What is meant by probability?

The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place. Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. The degree to which something is likely to happen is basically what probability means.

Given,

  Number of total candidates = 5

Number of candidates from minority = 2

a) Probability that one of the minority candidates is hired

= number of favourable events/total events = 2/5

b) Classical probability is used.

   This is because since the candidates are selected by lottery, each candidate has an equal chance of getting selected. So the classical probability is used.

Therefore using classical probability, we found that the chances of one minority candidate getting hired is 2/5.

To learn more about probability, follow the link.

https://brainly.com/question/24756209

#SPJ1

Step-by-step explanation:

The converse is:if the square of the third side of a triangle is equivalent to the sum of its two shorter sides then it's a right triangle

The coordinates of the particle are (0, 6) at t = 0, (-4, 16) at t = 1, and (-100, 630) at t = 5.

the coordinates of the particle at different times. Let's start by identifying the correct path equations for the particle:

x = -4t^2
y = 6 + 10t^3

Now, we'll find the coordinates at t = 0, 1, and 5:

1. For t = 0:
x = -4(0)^2 = 0
y = 6 + 10(0)^3 = 6
Coordinates at t = 0: (0, 6)

2. For t = 1:
x = -4(1)^2 = -4
y = 6 + 10(1)^3 = 16
Coordinates at t = 1: (-4, 16)

3. For t = 5:
x = -4(5)^2 = -100
y = 6 + 10(5)^3 = 630
Coordinates at t = 5: (-100, 630)

So, the coordinates of the particle are (0, 6) at t = 0, (-4, 16) at t = 1, and (-100, 630) at t = 5.

to learn more about coordinates click here:

brainly.com/question/29093485

#SPJ11

Answer:

Given an angle ABC, it is possible to construct a line BF that divides the angle into two equal parts using only a straightedge and compass. Such a line is called an angle bisector. ... If we then construct the line BF, it will divide the original angle ABC into two equal angles.

Given an angle ABC, it is possible to construct a line BF that divides the angle into two equal parts using only a straightedge and compass

An angle bisector or the bisector of an angle is a ray that divides an angle into two equal parts.

Given an angle ABC, it is possible to construct a line BF that divides the angle into two equal parts using only a straightedge and compass.

Such a line is called an angle bisector. ... If we then construct the line BF, it will divide the original angle ABC into two equal angles.

Hence an angle ABC, it is possible to construct a line BF that divides the angle into two equal parts using only a straightedge and compass

To know more about Angle bisector follow

https://brainly.com/question/24334771

#SPJ2

(a) The area that lies between Z = -1.57 and Z = 1.57 under the standard normal curve is 0.8820. (b) The area that lies between Z = -0.93 and Z = 2.00 under the standard normal curve is 0.7912. (c) The area that lies between Z = -2.06 and Z = -1.78 under the standard normal curve is 0.0817.

To calculate the areas under the standard normal curve, we use the standard normal distribution table, also known as the Z-table. The Z-table provides the cumulative probabilities for various values of Z, which represents the number of standard deviations away from the mean.

In each case, we look up the Z-values in the Z-table and find the corresponding probabilities. The area between two Z-values represents the cumulative probability between those values.

For example, in case (a), to find the area between Z = -1.57 and Z = 1.57, we look up the Z-values in the Z-table and find the probabilities associated with those values. The cumulative probability between the two Z-values is 0.8820.

Similarly, we calculate the areas for cases (b) and (c) by looking up the respective Z-values in the Z-table and finding the cumulative probabilities between those values.

Learn more about standard normal curve here:

https://brainly.com/question/29184785

#SPJ11

If the plot of the residuals is fan-shaped, the assumption violated is the equal error variance (homoscedasticity) assumption.

The assumption of equal error variance (homoscedasticity) states that the variability of the residuals should be constant across all levels of the predictor variables. In other words, the spread of the residuals should be the same throughout the range of the predictors. When this assumption is violated, the plot of the residuals tends to exhibit a fan-shaped pattern.

A fan-shaped plot of residuals indicates that the variability of the errors is not constant. This violation of homoscedasticity can lead to problems in statistical inference and can affect the reliability of the model's estimates and predictions. It suggests that the variability of the response variable is not adequately captured by the model, and there may be unaccounted factors that influence the spread of the residuals.

Therefore, if the plot of the residuals is fan-shaped, the assumption of equal error variance (homoscedasticity) is violated.

To learn more about variance  click here

brainly.com/question/31432390

#SPJ11

Answer:

x = 3

Step-by-step explanation:

If B is the midpoint of the line A to C then that means A to B and B to C are equal to one another.

Therefore, to find x you would set the 2 line equations equal to each other:

4x + 2 = 3x + 5

Move the terms around. Start by subtracting the 3x from both sides.

4x - 3x + 2 = 5

Then subtract the 2 from both sides.

4x - 3x = 5 - 2

Then combine like terms.

4x - 3x is x. 5 - 2 is 3.

So that leaves you with:

x = 3

Answer:

Step-by-step explanation:

Answer:

Question 3

First option:
\(\dfrac{\ensuremath{\dfrac{4}{5}\;in}}{\dfrac{2}{3}\;hr}\)

Question 4
Third option:
\(\dfrac{1}{4} \div \dfrac{2}{5}\)

Question 5

Second Option:
\(\dfrac{7}{10}\)

Step-by-step explanation:

Question 3

If  \(\dfrac{4}{5}\) inches of rain falls every  \(\dfrac{2}{3}\) hours then the unit rate in inches per hour is inches \(\div\) hours

This would be:
\(\dfrac{\ensuremath{\dfrac{4}{5}\;in}}{\dfrac{2}{3}\;hr}\)

This is the first option in Question 3 answer choices

Question 4

\(\dfrac{\dfrac{1}{4}\;km}{\dfrac{2}{5}\;min}\)

is nothing but the numerator ÷ denominator which would be:

\(\dfrac{1}{4} \div \dfrac{2}{5}\)

This is the third option in Question 4 answer choices

Question 5

\(\dfrac{1}{2} \div \dfrac{5}{7}\\\)

Flip the divisor \(\dfrac{5}{7}\); it comes \(\dfrac{7}{5}\)

Multiply:
\(\dfrac{1}{2} \times \dfrac{7}{5}\)

The result is
\(\dfrac{7}{10}\)

This is the second option in Question 4 answer choices

Answers:

Question 3: \(\frac{\frac{4}{5}in.}{\frac{2}{3}hr.}\)

Question 4: \(\frac{1}{4}\) ÷ \(\frac{2}{5}\)

Question 5: \(\frac{7}{10}\)

Explanations:

Question 3: We're told that rain is falling at a rate of  \(\frac{4}{5} in.\) every  \(\frac{2}{3} hr.\), and the unit rate we're looking for is inches per hour (or more precisely, inches per 1 hour). Based on these parameters, we know that you have to divide the unit inches by the unit hours. So using the numbers above, the correct complex fraction to represent this situation would be \(\frac{\frac{4}{5} in.}{\frac{2}{3} hr.}\) .

Question 4: In this question, we are given a complex fraction and asked to rewrite it as a simple division problem. The complex fraction is \(\frac{\frac{1}{4} km.}{\frac{2}{5} min.}\), so in order to write this as a division expression, you simply take the numerator fraction and divide it by the denominator fraction, which will end up being \(\frac{1}{4}\) ÷ \(\frac{2}{5}\). Therefore, that will be your answer.

Question 5: Now, we have a division expression and are asked to use the Keep, Change, Flip method to solve the problem. First and foremost, the Keep, Change, Flip method is essentially telling you that when you are dividing by a fraction, you keep the dividend the same, you change the divisor - specifically switching the numerator with the denominator, which is creating the reciprocal of that fraction - and multiply by the reciprocal of the original divisor instead.

                   A good example of the Keep, Change, Flip method from above would be \(\frac{1}{2}\) ÷ \(\frac{1}{3}\). You keep the dividend, change the divisor, specifically flip the function around to create its reciprocal, and instead multiply by the divisor's reciprocal. Following those steps, \(\frac{1}{2}\) ÷ \(\frac{1}{3}\)  will become \(\frac{1}{2}\) × \(\frac{3}{1}\) or \(\frac{1}{2}\) × \(3\).

                  Now that we understand how to use the Keep, Change, Flip method, we can use it to solve the expression \(\frac{1}{2}\) ÷ \(\frac{5}{7}\). We keep \(\frac{1}{2}\) the same, flip \(\frac{5}{7}\) to make its reciprocal, and multiply \(\frac{1}{2}\) by that instead. So the final answer will be \(\frac{1}{2}\) ÷ \(\frac{5}{7}\) = \(\frac{1}{2}\) × \(\frac{7}{5}\) = \(\frac{7}{10}\).

Have a great day! Feel free to let me know if you have any more questions :)

The value of n when y m is the area of a square of length x m, is  2

The value of n when y cm is the  volume of a cube of length x cm, is 3

For area of square, the formula is given by

= length *  length

assuming the length is equal to x

= x * x

= x²

comparing with given formula shows that n = 2

For volume of a cube of length x cm, the formula is given by

= length *  length * length

= x * x * x

= x³

comparing with given formula shows that n = 3

complete question

It is given that y is directly proportional to x".

Write down the value of n when

(i) y m? is the area of a square of length x m,

(ii) y cm is the volume of a cube of length x cm.

Learn more about direct proportionality at:

https://brainly.com/question/1266676

#SPJ1

The two positive numbers are 6 and 11

From the question, we understand that:

There are two positive numbers

Represent these numbers with x and y

So, we have the following equations

x = y - 5

6x - 3y = 3

Substitute x = y - 5 in 6x - 3y = 3

6(y - 5) - 3y = 3

Open the brackets

6y - 30 - 3y = 3

Evaluate the like terms

3y = 33

Divide by 3

y = 11

Substitute y = 11 in x = y - 5

x = 11 - 5

So, we have

x = 6

hence, the numbers are 6 and 11

Read more about positive numbers at

https://brainly.com/question/2253939

#SPJ1

The length of the line segment whose endpoints are A(-1,9) and B(7,4) is 9.43.

We have to determine, the length of the line segment whose endpoints are A(-1,9) and B(7,4).

According to the equation,

The length of the line segment is determined by using the distance formula following all the steps given below.

\(Distance \ formula = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

Where Endpoints of the line segment are A(-1,9) and B(7,4).

\(AB= \sqrt{(7-(-1))^2 + (4-9)^2}\\\\AB= \sqrt{(8)^2 + (-5)^2}\\\\AB = \sqrt{64+25}\\\\AB = \sqrt{89}\\\\AB = 9.43\)

Hence, The length of the line segment whose endpoints are A(-1,9) and B(7,4) is 9.43.

To know more about Geometry click the link given below.

https://brainly.com/question/25841655

The data set contains the variable height (giving a person's height) and the variable gender (coded O=female, 1=male). Then the y-intercept of the regression equation predicting height from gender is given by: option c) the average height of females in the data set.

The y- intercept of a direct retrogression relationship represents the value of one variable when the value of the other is zero. Non-linear retrogression models also live, but are far more complex. Retrogression analysis is a important tool for uncovering the associations between variables observed in data, but can not fluently indicate occasion. The data set contains the variable height (giving a person's height) and the variable gender (enciphered O = womanish, 1 = manly). also the y- intercept of the retrogression equation prognosticating height from gender is given by option c) the average height of ladies in the data set.

To learn more about y-intercept, click here:

brainly.com/question/14180189

#SPJ4

Answer:

y=x-1

Step-by-step explanation:

Answer:

544 acres

Step-by-step explanation:

There is 100% in a whole.

1% is 1/100th of the whole, or 0.01 of it. We get this because 1/100 = 1/100 = 0.01

Similarly, 0.8/100 = 0.008. We then multiply the decimal by the total to get

(0.008) ( 68000) = 544 acres

It is horizontally compressed by a factor of 3 and reflected over the x-axis.

The parent function is given as:

y = 1/x

When the above function is compressed by a factor of 3, the function becomes

y = 1/3x

Next, when the above function is reflected over the x-axis or the y-axis, the function becomes

y = -1/3x

Hence, the transformation is (b) it is horizontally compressed by a factor of 3 and reflected over the x-axis.

Read more about transformation at:

https://brainly.com/question/4289712

#SPJ1

Answer:

The qzz answers to whole thing for "transformations of functions" on Edg. is the following:

1) B

2) A

3) A

4) B

5) B

6) C

7) C

8) A

9) D

10) B

Step-by-step explanation:

Trust me! I got 100% :)

Answer:

13

Step-by-step explanation:

(12) - (3) + (4) = 13

you just insert the numbers into the equation

Answer:

460

Step-by-step explanation:

Answer: multiply 4.2 and 3.4 together for your answer then subtract 5 from your answer

Step-by-step explanation:

Answer:

x=-1

Step-by-step explanation:

54x+64=49x+59

subtract 64

54x=49x-5

subtract 49x

5x=-5

divide by 5

x=-1

Respuesta:

x = 5.656854249

Explicación paso a paso:

[NOTA: Solo quería disculparme de antemano por cualquier mala gramática, ya que estoy usando un traductor para esto.]

x/Sen30°= 8/Sen45° [Multiplica ambos lados por Sen30°]

x = (8/Sen45°) * Sen30° [Resuelve usando una calculadora]

x = 5.656854249

The probability that a light bulb of that brand lasts between 1360 hr and 1840 hr is approximately 0

The probability that a light bulb of that brand lasts between 1360 hr and 1840 hr, we need to calculate the area under the normal distribution

Mean (μ) = 1600 hr Standard deviation (σ) = 150 hr

z = (x - μ) / σ

For 1360 hr

z1 = (1360 - 1600) / 150 = -1.6

For 1840 hr

z2 = (1840 - 1600) / 150 = 1.6

We can use a standard normal distribution table or a calculator to find the cumulative probabilities associated with these z-scores

P(z < -1.6) ≈ 0.054799

P(z < 1.6) ≈ 0.054799

The probability of the light bulb lasting between 1360 hr and 1840 hr, we subtract the smaller probability from the larger probability

P(1360 < x < 1840) = P(z < 1.6) - P(z < -1.6) ≈ 0.054799 - 0.054799

P(1360 < x < 1840) ≈ 0

Therefore, the probability that a light bulb of that brand lasts between 1360 hr and 1840 hr is approximately 0 .

To know more about probability click here:

https://brainly.com/question/31939091

#SPJ4

1. Since triangle ABC and DEF are congruent, the value of x is -3

2. length AB = 24

length DE = 24

If the three angles and the three sides of a triangle are equal to the corresponding angles and the corresponding sides of another triangle, then both the triangles are said to be congruent.

Since triangle ABC is congruent to triangle DEF , then we can say that line AB is equal to line DE

therefore;

12- 4x = 15-3x

collect like terms

12 -15 = -3x +4x

x = -3

therefore the value of x is -3 and

AB = 12 - 4x

AB = 12 -4( -3)

AB = 12 +12 = 24

DE = 15-3x

= 15-3(-3)

= 15 + 9

= 24

learn more about congruent triangles from

https://brainly.com/question/2938476

#SPJ1

To derive the analytical expressions for the optimal portfolio weights of the first and second assets, we need to maximize the expected utility function.

Let's assume the weights of the first and second assets are denoted by w1 and w2, respectively. Since there is no risk-free security available, the sum of weights must be equal to 1: w1 + w2 = 1.

To find the optimal portfolio weights, we need to maximize the expected utility function with respect to w1 and w2. This can be done using optimization techniques, such as Lagrange multipliers or calculus.

We can start by taking the derivative of the expected utility function with respect to w1 and set it equal to zero to find the critical points. Similarly, we take the derivative with respect to w2 and set it equal to zero.

Next, we solve these equations to find the values of w1 and w2 that satisfy the equations. These values will give us the optimal portfolio weights for the first and second assets.

Ihe analytical expressions for the optimal portfolio weights of the first and second assets can be derived by maximizing the expected utility function and solving the resulting equations.

To know more about weights , visit ;

https://brainly.in/question/9873207

#SPJ11

Therefore, the total distance Gabe will paddle is 2x + 400 meters. The exact value of x depends on the width of the river, which is not provided in the given information.

To find the total distance Gabe will paddle, we need to consider the distance he will travel from Q to P, then from P to R, and finally from R back to Q.

First, let's consider the distance from Q to P. Since Gabe will paddle in a diagonal line across the river, this distance can be calculated using the Pythagorean theorem.

The length of the bridge (PR) is given as 400 meters, which is the hypotenuse of a right triangle. The width of the river can be considered as the perpendicular side, and the distance Gabe will paddle from Q to P is the other side. Let's call this distance x.

Using the Pythagorean theorem, we have:

x^2 + (width of the river)^2 = PR^2

Since the width of the river is not given, we'll represent it as w. Therefore:

x^2 + w^2 = 400^2

Next, let's consider the distance from P to R. Gabe will paddle along a route beside the bridge, which means he will travel the length of the bridge (PR) again. So, the distance from P to R is also 400 meters.

Finally, Gabe will paddle back from R to Q along the shore. Since he will follow the shoreline, the distance he will paddle is equal to the distance from Q to P, which is x.

To find the total distance, we add up the distances:

Total distance = QP + PR + RQ

= x + 400 + x

= 2x + 400

For more suchy questions on distance visit:

https://brainly.com/question/28551043

#SPJ8

Y=2x+1 is an equation used in mathematics to calculate the relationship between two variables, X and Y.

An equation is a physical and mathematical statement that describing physical phenomena are describe the relationship between different physical quantities it typically consists of two or more variable which are simple representing physical quantity and then equal sign the variable may be quantity such as force velocity or energy.

This equation is a linear equation, meaning it is a straight line when graphed. It is a very basic equation and one of the most commonly used equations.

To use this equation, you will need to know the value of X. Once you have determined the value of X, you can plug it into the equation to calculate the value of Y. For example, if X=3, then the equation would look like this: Y=2(3)+1, which equals 7. Therefore, when X=3, Y=7.

The equation Y=2x+1 is often used in a variety of math problems, such as determining the slope of a line, calculating the area of a triangle, and finding the equation of a circle. It is also used in physics to calculate velocity or acceleration. As you can see, this equation is quite versatile and can be used in a variety of situations.

To know more about equation click-
https://brainly.com/question/26408808
#SPJ1

The number of tractors lent by the first, second and third stations results in a system of three simultaneous equations which indicates;

The first originally station had 39 tractors, the second station had 21 tractors and the third station originally had 12 tractors

Simultaneous equations are a set of two or more equations that have common variables.

Let x represent the number of tractors at the first station, let y represent the number of tractors at the second tractor station, and let z, represent the number of tractors at the third tractor station

According to the details in the question, after the first transaction, we get

Number of tractors at the first station = x - y - z

Number of tractors at the second station = y + y = 2·y

Number of tractors at the third station = z + z = 2·z

After the second transaction, we get;

Number of tractors at the first station = 2·x - 2·y - 2·z

Number of tractors at the second station = 2·y - (x - y - z) - 2·z = 3·y - x - z

Number of tractors at the third station = 2·z + 2·z = 4·z

After the third transaction, we get;

Number of tractors at the first station = 2 × (2·x - 2·y - 2·z) = 4·x - 4·y - 4·z

Number of tractors at the second tractor station = 6·y - 2·x - 2·z

Number of tractors at the third tractor station = 4·z - (2·x - 2·y - 2·z) - (3·y - x - z) = 7·z - x - y

The three equations after the third transaction are therefore;
4·x - 4·y - 4·z = 24...(1)

6·y - 2·x - 2·z = 24...(2)

7·z - x - y = 24...(3)

Multiplying equation (2) by 2 and subtracting equation (1) from the result we get;

12·y - 4·x - 4·z - (4·x - 4·y - 4·z) = 16·y - 8·x = 48 - 24 = 24

16·y - 8·x = 24...(4)

Multiplying equation (3) by 2 and multiplying equation (2) by 7, then adding both results, we get;

14·z - 2·x - 2·y = 48

42·y - 14·x - 14·z = 168

42·y - 14·x - 14·z + (14·z - 2·x - 2·y) = 48 + 168

40·y - 16·x = 216...(5)

Multiplying equation (4) by 2 and then subtracting the result from equation (5), we get;

40·y - 16·x - (32·y - 16·x) = 216 - 48 = 168

8·y = 168

y = 168/8 = 21

The number of tractors initially at the second station, y = 21

16·y - 8·x = 24, therefore, 16 × 21 - 8·x = 24

8·x = 16 × 21 - 24 = 312

x = 312 ÷ 8 = 39

The number of tractors initially at the first station, x = 39

7·z - x - y = 24, therefore, 7·z - 39 - 21 = 24

7·z = 24 + 39 + 21 = 84

z = 84/7 = 12

The number of tractors initially at the third station, z = 12

Learn more about simultaneous equations here:

https://brainly.com/question/21902579

#SPJ1

To determine whether the exponential function represents growth or decay, we need to examine the base of the exponent, which is 0.909 in this case.

If the base is greater than 1, it represents growth. If the base is between 0 and 1, it represents decay.

In this case, the base is 0.909, which is less than 1. Therefore, the exponential function represents decay.

To determine the percentage rate of decrease, we can calculate the percentage decrease per unit change in x. In this case, the base of the exponent represents the rate of decrease.

The percentage rate of decrease can be found by subtracting the base from 1 and multiplying by 100.

Percentage rate of decrease = (1 - 0.909) * 100 = 0.091 * 100 = 9.1%

Therefore, the exponential function represents decay with a percentage rate of decrease of 9.1%.

Learn more about exponential function here:

https://brainly.com/question/29287497

#SPJ11

Answer:

a) Name the transversal connecting 1 and 5. Line r b) Name the transversal connecting 7 and 14. Line q c) Name the transversal connecting 8 and 11. Line s d) Name the transversal connecting 6 and 15. Line q e) Name the transversal connecting 3 and 9. Line p

Step-by-step explanation:

The angles pairs and the transversal connecting them are:

a. <1 and <5: transversal r.

b. <7 and <14: transversal q

c. <8 and <11: transversal s

<6 and <15: transversal q.

<3 and <9: transversal p.

Note the following about what a transversal is:

Let's determine the transversal connecting the following given angles:

a. <1 and <5: transversal r.

b. <7 and <14: transversal q

c. <8 and <11: transversal s

<6 and <15: transversal q.

<3 and <9: transversal p.

Learn more here:

https://brainly.com/question/14067960