The Swamis family went on a vacation. They recorded the number of miles they drove each day. The mileage is shown in the table. Day 1 2 3 4 5 Distance (mi) 248 176 379 263 202

The maximum value of z = 4x + y subject to the given constraints is 180, which occurs at x = 45 and y = 0.

To find the maximum value of z = 4x + y subject to the given constraints, we can use linear programming.

Graph the constraints:

First, we will graph the constraints to visualize the feasible region.

The constraint x + y ≤ 50 represents the region below the line x + y = 50:

The constraint 3x + y ≤ 90 represents the region below the line 3x + y = 90:

The feasible region is the shaded region that satisfies both constraints:

Identify the corner points of the feasible region:

The feasible region has four corner points: (0, 0), (0, 50), (30, 20), and (45, 0).

Evaluate z at each corner point:

z(0, 0) = 4(0) + 0 = 0

z(0, 50) = 4(0) + 50 = 50

z(30, 20) = 4(30) + 20 = 140

z(45, 0) = 4(45) + 0 = 180

Compare the values of z at the corner points:

The largest value of z is 180, which occurs at the corner point (45, 0).

Therefore, the maximum value of z = 4x + y subject to the given constraints is 180, which occurs at x = 45 and y = 0.

To learn more about linear Equation, click here:

brainly.com/question/28243079

#SPJ1

Step-by-step explanation:

Physically, integrating f(x)dx means finding the a. area to the right of point b. b. area to the left of point a . area under the curve and bounded by the lines x= a and x = d. d. area above the curve and bounded by the lines x = a and x = c. b. b.

Answer:

Step-by-step explanation:

means finding the area under the curve from a to b area t0 the left of point area t0 the right of point area above the curve from a to b CelecGne The exact value of xe ' dx is most nearly (A 7.8036 B) 11.807 14.034 19.614 CelecGne

The equivalent value of the inequality is w ≥ 15

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

w/3 - 1 ≥ 4

On simplifying , we get

Adding 1 on both sides , we get

w/3 ≥ 5

Multiply by 3 on both sides , we get

w ≥ 15

Therefore , the value of w is greater than or equal to 15

Hence , the inequality is w ≥ 15

To learn more about inequality equations click :

https://brainly.com/question/11897796

#SPJ1

The equation for the circle graphed in the coordinate axis is:

(x - 5)^2 + (y - 6)^2 = 16

Remember that the equation for a circle whose center is at (a, b) and has a radius R is.

(x - a)^2 + (y - b)^2 = R^2

On the graph, we can see that the center of the circle is at (5, 6), and the radius of the circle is R = 4 units. Then the equation for the circle in the graph is:

(x - 5)^2 + (y - 6)^2 = 4^2

(x - 5)^2 + (y - 6)^2 = 16

That is the equation we wanted to find.

Learn more about circles at:

https://brainly.com/question/1559324

#SPJ1

Answer:

answer is

c. y = 2x - 4

Step-by-step explanation:

y=mx+b is standard, b is also correct but not in standard form, hope this helps

A. not continuous

Continuous functions have no jumps or vertical asymptotes.

Continuity

For a function to be continuous, each point on the function must be defined. This means that there cannot be points on the graph where there is no value or coordinate point. Additionally, all points must be connected by the graph. Sudden jumps in the graph that are not connected by anything are not continuous.

Determining Continuity

The graph above is not continuous. We know this for 2 reasons. Firstly, the graph is not defined at x = -3. Since there is an open circle at x = -3, the value is not defined. Thus, the function cannot be considered continuous. Additionally, there are multiple jumps. At x = -3, the function suddenly jumps to x = -2 without the points being connected. The same thing happens again at x = 1. This also shows that the graph is not continuous.

The value of x is 21.75.

We need to convert from mixed number to decimal number. To do this you can follow the steps shown below:

We must divide the numerator of the fraction by the denominator of the fraction.

Now we must add the quotient obtained to the Whole number part.

So, we get:

7 1/4 = 7.25

Then, the scale image that maps "Figure a" onto "Figure b" is: 1 : 7.25.

Finally, in order to find the value of "x", you need to multiply the given length of the corresponding side of "Figure a" by 7.25,

Therefore, you get that the result is:

x = 3(7.25)

x = 21.75

Hence the value of x is 21.75.

Learn more about scale factors, click;

https://brainly.com/question/30215044

#SPJ1

The complete question is ;

Figure a is a scale image of figure b the scale that maps figure a onto figure b is 1:7 1/4 enter the value of x

Both figures are triangles

Figure a is smaller than figure b

Figure a to the right has a 3

Figure b to the right has a x

Answer:

Step-by-step explanation:

We can simplify the given product using the properties of radicals:

√10x² √5x = √(10*5)x^(2+1) = √50x^3

We can further simplify the radical by factoring out the largest perfect square from 50, which is 25:

√50x^3 = √(25*2)x^3 = 5x√2

Therefore, the product √10x² √5x is equivalent to 5x√2, when x≥0.

To simplify the product √10x² √5x, we can combine the square roots and simplify:

√10x² √5x = √(10x² * 5x) = √(50x³) = √(25x² * 2x) = 5x√2x

Therefore, the choice that is equivalent to the original product when x≥0 is A. 5x√2x.

The slope from the table is greater than the slope from the graph hence the table shows a greater rate.

The slope of a graph is the measure of how steep a line is. It is the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. Mathematically, slope is represented as:

Slope (m) = (change in y)/(change in x)

The slope from the table is;

y2 - y1/x2 - x1

m = 42 - 30/7 - 5

= 6

The slope from the graph is;

8 - 0/1.5 - 0

m = 5.33

Learn more about slope:https://brainly.com/question/28756431

#SPJ1

The collection of all points in a plane that are equally spaced from a given point, referred to as the circle's center, is referred to as a circle. The radius of the circle is the distance measured from any point on the circle to its center.

A circle is described as the collection of all points on a plane that is at the same distance, or radius, from a fixed point known as the circle's center.

Every location inside the circle is, therefore, closer to the center point than the radius, and any point outside the circle is farther away from the center point than the radius.

Therefore, a circle is made up of points that are spaced out by a particular amount, known as the radius, from the circle's center.

Learn more about Circle here:

https://brainly.com/question/29142813

#SPJ1

Answer: the correct answer is B

Step-by-step explanation:

Remember that the coordinates (4,4π3) tell us the radius r=4 and the angle θ=4π3. So the point should be on the circle labeled 4 and form an angle of 4π3 with the positive x-axis. Point B is the correct point.

Using percentages we know that the bucket which is of 460 grams is made up of 92 grams of recyclable plastic.

A% is a mathematical figure or ratio that denotes a percentage of 100.

Ratios, fractions, and decimals are some of the numerous ways to represent a dimensionless connection between two numbers.

The symbol "%" is generally written after the integer to denote percentages.

A figure or ratio that is stated as a fraction of 100 is referred to as a percentage in mathematics.

So, in the given situation we will use percentages to get what % of recyclable plastic is used as follows:

= 460/100 * 20

= 4.60 * 20

= 92 grams

Therefore, using percentages we know that the bucket which is of 460 grams is made up of 92 grams of recyclable plastic.

Know more about the percentage here:

brainly.com/question/24877689

#SPJ1

The formula and the differences are shown below

The formula to calculate weighted average is:

weighted average = (w1x1 + w2x2 + ... + wnxn) / (w1 + w2 + ... + wn)

Where x1, x2, ..., xn are the values being averaged, and w1, w2, ..., wn are their corresponding weights.

The weighted average gives more importance or weight to certain values than others.

The weights can represent the relative importance, significance, or contribution of each value to the final average.

The main difference between ROR and weighted return is that ROR measures the return of a single investment, while weighted return measures the return of a portfolio or investment that is composed of multiple assets with different weights.

Weighted return takes into account the relative importance of each asset or security in the portfolio, while ROR does not consider the impact of other investments.

Read more about weighted average at

https://brainly.com/question/28293878

#SPJ1

Thus, the interquartile range of the given data set. are -

1st quartile (Q1) = 6.8 ; 2nd quartile (Q2) = 7.6 and 3rd quartile (Q3) = 8.4 .interquartile range = 1.60.

The interquartile range in descriptive statistics reveals the spread of your distribution's middle half.

Each distribution that is sorted from low to high is divided into four equal portions using quartiles. The third and second quartiles, or the centre half of your data set, are contained in the interquartile range (IQR).

The interquartile range provides the range of a middle half of a data set, whereas the range provides the spread of the entire data set.

Given data set:

8.4, 7.1, 6.3, 6.8, 9.2, 7.3, 8.8, 7.9, 5.3, 8.2

arrange the data set in ascending order:

5.3, 6.3, 6.8, 7.1, 7.3, 7.9, 8.2, 8.4, 8.8, 9.2

Total term = 10 (even)

2nd quartile (Q2) 50% quartile - (5th + 6th) /2 = (7.3 + 7.9) /2 = 7.6

Now:

1st quartile (Q1) 25% quartile - 3rd term = 6.8

3rd quartile (Q3) 75% - 8th term = 8.4

Thus, the  interquartile range of the given data set. are -

1st quartile (Q1) = 6.8 ; 2nd quartile (Q2) = 7.6 and 3rd quartile (Q3) = 8.4 .

interquartile range = maximum  - minimum

interquartile range = 8.4 - 6.8 = 1.60.

Know more about the interquartile range:

https://brainly.com/question/4102829

#SPJ1

Answer:

There are 31 days in October, so there are 31 - 15 = 16 days left in October after October 15.

16 days is equivalent to 2 weeks and 2 days (since there are 7 days in a week), so November 11 is 2 weeks and 2 days after October 15.

Therefore, November 11 falls on a Wednesday + 2 weeks + 2 days = Friday.

So November 11 of that same year falls on a Friday.

Yellow to red hence has a 4 to 1 ratio. Solution: B. 4 to 1 as 2 red times 5 purple (Instead of purple).

A percent is a claim that two factors are equal in mathematics. When two quantities are compared by dividing them, the result is expressed as a ratio as a fraction. For instance, the number of girls to boys in a class can be expressed as "girls: boys" or "girls/boys." One way to express a percentage is as follows: a/b = c/d in which a, b, c, and d were four values that prevent b and d from being equal to zero. As a result, the ratio of a to b is the same as the ratio of c to d. The first term (a) is therefore equal to the reelection campaign (b), and the τ (c) is equal to the fourth term.

given

The given equalities can be used to calculate the proportion of yellow to red:

5 green times 6 yellow (Subtract both sides by 5)

(6/5) Yellow is equivalent to green.

3 purple + 4 green (substitute for green)

4 (6/5) Purple x 3 yellow

(24/5) Purple x 3 yellow (divide both sides by 4)

(8/5) Purple x yellow

2 red times 5 purple (Instead of purple)

(5/8) yellow Equals 2 red.

2 red x 8 yellow (divide both sides by 5)

Red + 4 yellows

Yellow to red hence has a 4 to 1 ratio. Solution: B. 4 to 1 as 2 red times 5 purple (Instead of purple).

To know more about proportionality visit:

https://brainly.com/question/29126727

#SPJ1

Adding 5 bonus points to each test grade in Mrs. Matthew's class will increase the mean, median, and mode of the scores by 5 points each.

The addition of 5 bonus points to each test grade will affect the mean, median, and mode in the following ways:

So, in conclusion, adding 5 bonus points to each student's test score will raise the mean, median, and mode of the scores by 5 points each.

https://brainly.com/question/31538429

#SPJ11

The calculated base area of the paperweight is 9.6 square cm.

To calculate the base area of the paperweight, we can use the formula for the volume of a three-dimensional object:

Volume = Base area x Height

In this case, we know that the height of the paperweight is 4cm and the volume is 38.4 cubic cm.

So we can rearrange the formula and solve for the base area:

Base area = Volume / Height

Substituting the values we have:

Base area = 38.4 cubic cm / 4cm

Base area = 9.6 square cm

Therefore, the base area of the paperweight is 9.6 square cm.

Read more about area at

https://brainly.com/question/24487155

#SPJ1

Answer:

7

Let's call the width = x

width : x

so (x + 2x-4)2 = 34 (perime formula of a rectangle) x+2x-4 = 7

3x = 21

x = 7

so x is 7

Suppose you are driving a car with the velocity function represented by the following equation: f(x)= 2x^3-3x^2-12x+1. The derivative would be: f'(x) = 6x^2 - 6x - 12

To find the acceleration of the car at a particular moment, we would need to calculate the derivative of the velocity function f(x). In this case, the derivative would be:

f'(x) = 6x^2 - 6x - 12

The result of this calculation would give us the instantaneous acceleration of the car at a given time x.

In terms of the car's motion, a positive value for f'(x) would indicate that the car is accelerating, while a negative value would indicate that the car is decelerating. The magnitude of the value would indicate the rate of change of the car's velocity, with larger values indicating a more rapid change.

Translated question "A derivative problem from everyday life using the following function: f(x)= 2x^3-3x^2-12x+1"

Read more about derivative problem

brainly.com/question/28376218

#SPJ1

The population will be approximately 29,628 people 5 years from now. (Rounded to the nearest whole number)

To calculate the future population, we need to take into account the growth rate over time.

In this case, we know that the population doubled in size over 26 months and the current population is 20,000.

Let's break down the problem step by step:

Calculate the monthly growth rate:

Since the population doubled in size over 26 months, the monthly growth rate can be calculated as the 26th root of 2.

This is because if the population doubles in size over 26 months, each month the population grows by the 26th root of 2.

Monthly growth rate  [tex]= 2^{(1/26) } \approx 1.027[/tex]

Calculate the number of months in 5 years:  

Since there are 12 months in a year, the number of months in 5 years is [tex]5 \times 12 = 60[/tex] months.

Calculate the future population:

We start with the current population of 20,000 and apply the monthly growth rate for 60 months.

Future population  = Current population [tex]\times[/tex]  (Monthly growth rate)^{(Number of months)

Future population [tex]= 20,000 \times (1.027)^60 \approx 29,628.12[/tex]

For similar question on population.

https://brainly.com/question/30412211

#SPJ11

 The third player hit 4 more home runs than the first player. The algebraic expression that shows the relationship between a and b is:  a = 3b. So option A is correct

A linear equation in one variable is an equation that has only one variable. It is of the form Ax B = 0, where A and B are  two real numbers and x is an unknown variable with only one solution. For example, 9x + 78 = 18 is a linear equation in one variable.

 2) Each player's home runs are labeled A, B, C, and D, where A is the first baseman, B is the second baseman, C is the third baseman, and D is the shortstop. We know this:

C = 2B (the third player hit twice as many home runs as the second player)

C/B = D/B = A/C (numbers for first baseman and shortstop are proportional to numbers for third baseman and second baseman)

B = D 4 (second baseman hit 4 more home runs than  shortstop)

To solve for the values ​​of A, B, C, and D, we can use the second equation to write:

C/B = D/B

C = D (multiply both sides by B)

C = B - 4 (using the fourth equation to substitute  D)

2B = B - 4 (using the first equation to substitute  C)

B = 4 (interface to both sides 4)

C = 8 (using the first equation to find C)

D = 4 (using the fourth equation to find D)

A = C/2 = 4 (use another equation to find A)

Therefore the third player (C) hit 8 home runs and the first player (A) hit 4 home runs, so the third player hit 4 more home runs than the first player.

3) The relative relationship between a and b can be expressed as follows:

a/b = 6/2 = 3/1

To write this relationship as an algebraic equation, we can cross multiply to get:

a = 3b

Therefore, the algebraic expression that shows the relationship between a and b is:

a = 3b. So option A is correct

Learn more about  linear equation here

https://brainly.com/question/11897796

#SPJ1

a) [tex]f(x) + xg(x) = x^{3} + 7x^{2} + x - 4.[/tex]

b) [tex][f(x)]² = 4x^{4} - 4x^{3} - 15x^{2} + 8x + 16[/tex]

c) [tex]f^{2}(x) = 4x^{4} - 4x^{3} - 15x^{2} + 8x + 16[/tex]

d) [tex]gf(x) = 2x^{4} + 8x^{3} - 13x^{2} - 3x - 8.[/tex]

what is expression ?

It is possible to do mathematical operations like addition, subtraction, division, and multiplication. An expression is put together as follows: Number, expression, and mathematical operator.

a) f(x) + xg(x)

First, we need to find xg(x), which is x multiplied by g(x):

[tex]xg(x) = x(x^{2} + 5x + 2) = x^{3} + 5x^{2} + 2x\\\\f(x) + xg(x) = 2x^{2} - x - 4 + x^{3} + 5x^{2} + 2x\\\\f(x) + xg(x) = x^{3} + 7x^{2} + x - 4[/tex]

Therefore, [tex]f(x) + xg(x) = x^{3} + 7x^{2} + x - 4.[/tex]

b) [f(x)]²

To square f(x), we can simply multiply it by itself:

[f(x)]² = (2x² - x - 4)(2x² - x - 4)

[tex][f(x)]² = 4x^{4} - 4x^{3} - 15x^{2} + 8x + 16[/tex]

c) f²(x)

Since f²(x) means f(x) times f(x), we can use the distributive property of multiplication:

[tex]f^{2} (x) = f(x) * f(x)\\\\f^{2}(x) = (2x^{2} - x - 4)(2x^{2} - x - 4)[/tex]

[tex]f^{2}(x) = 4x^{4} - 4x^{3} - 15x^{2} + 8x + 16[/tex]

d) gf(x)

To find gf(x), we need to multiply g(x) by f(x):

[tex]gf(x) = (x^{2} + 5x + 2)(2x^{2} - x - 4)[/tex]

Multiplying each term of g(x) by each term of f(x), and simplifying:

gf(x) = 2x⁴ + 8x³ - 13x² - 3x - 8

Therefore, [tex]gf(x) = 2x^{4} + 8x^{3} - 13x^{2} - 3x - 8.[/tex]

To know more about expressions visit,

brainly.com/question/14083225

#SPJ1

Answer:

To determine if the given equations are symmetric with respect to the origin, we need to check if replacing x with -x and y with -y results in the same equation.

For the equations given:

y=7x-4 is not symmetric with respect to the origin since replacing x with -x and y with -y gives y=-7x+4, which is not the same equation.

y= -x+7 is not symmetric with respect to the origin since replacing x with -x and y with -y gives y=x-7, which is not the same equation.

y = -7x^2 is symmetric with respect to the origin since replacing x with -x and y with -y gives -y = -7(-x)^2, which simplifies to -y = -7x^2. Thus, the equation remains the same.

y = 6x^2 - 9 is not symmetric with respect to the origin since replacing x with -x and y with -y gives -y = 6(-x)^2 - 9, which simplifies to -y = 6x^2 - 9. Thus, the equation is not the same.

x=1/4 y^2 is not symmetric with respect to the origin since replacing x with -x and y with -y gives -x = 1/4 (-y)^2, which simplifies to -x = 1/4 y^2. Thus, the equation is not the same.

x = -y^2 + 9 is symmetric with respect to the origin since replacing x with -x and y with -y gives -x = -(-y)^2 + 9, which simplifies to -x = -y^2 + 9. Thus, the equation remains the same.

y=-1/6 x^3 is symmetric with respect to the origin since replacing x with -x and y with -y gives -y=-1/6(-x)^3, which simplifies to -y=-1/6 x^3. Thus, the equation remains the same.

y=x^3-1 is not symmetric with respect to the origin since replacing x with -x and y with -y gives -y=(-x)^3-1, which simplifies to -y=-x^3-1. Thus, the equation is not the same.

y=sqrt(x) is not symmetric with respect to the origin since replacing x with -x and y with -y gives -y=sqrt(-x), which is not the same equation.

y=sqrt(x)-6 is not symmetric with respect to the origin since replacing x with -x and y with -y gives -y=sqrt(-x)-6, which is not the same equation.

Therefore, the only equation that is symmetric with respect to the origin is y = -7x^2.

Answer:

i can only see b not c

Step-by-step explanation:

The required value of impulse is 88 N-s and the mass of the cart is 8.8 kg.

Newton's Second Law relates an object's acceleration as a function of both the object's mass and the applied net force on the object.

Given data:

The speed of cart is, v = 10 m/s.

We are given the Force-time graph for which the area of the force-time graph will provide the value of impulse. So from the graph, the maximum force is,

F = 22 N

And time interval is,

t = 4.5 s - 0.5 s

t = 4 s

So, the impulse is,

I = Area of graph

I = F × t

I = 22 × 4

I = 88 N-s

Now the standard expression for the impulse as per the impulse-momentum theorem is,

I = ΔP (Change in momentum)

I = m ×( v - u )

Here, u is the final velocity, and since the cart stops finally, then u = 0 m/s. And m is the mass of the cart.

Solving as,

88 = m ×( v - u )

88 = m ×( 10 - 0 )

m = 8.8 kg

Thus, we can conclude that the required value of impulse is 88 N-s and the mass of car is of 8.8 kg.

Read more on value of impulse  on https://brainly.com/question/11424771

#SPJ1

y = 3(x-1)^2 - 8

y = 3(x^2 - 2x + 1) - 8 [Using the identity (a-b)^2 = a^2 - 2ab + b^2]

y = 3x^2 - 6x + 3 - 8 [Distributing the 3]

y = 3x^2 - 6x - 5 [Simplifying]

*IG:whis.sama_ent

Answer:

y=3x^(2)-6x-5

[tex]y=3x^2 -6x-5[/tex]

hope this helps ;)

Based on the information provided, the polygon can be classified as a trapezoid.

Learn more about trapezoids in https://brainly.com/question/8643562

#SPJ1

1. A  back-to-back stem-and-leaf plot for the data would be

Mowed by you          stem           mowed by your friend

       8   7   5  4            0              

       7   2   2  0            1                  9

            5   1   0           2                  7    8    9

                      0           3                  0    1     2     2   5   5   8

                                    4                  4

KEY: 3 | 1 ⇒ 31

2.  The mean for you = 14.25 and your friend 31.3. This means that your friend has a higher mean than you. The median for you is 11 and your friend is 30.5. Given that both the mean and median of your friend is higher than yours, it means that your friend mowed more lawns than you

3. The range of data for you is 26 and for your friend is 21.

To find the mean for each data set, add all the number together and divide it by the set number. For example;

4 + 5 + 7 + 8 + 10 + 12 + 12 + 17 + 20 + 21 + 25 + 30

= 171 / 12

= 14.25

To find the range for the data set, simply take the highest number of a set and minus it by the lowest number. For Example;

For your data set, it is 30 - 4 = 26

To find the median for the data sets, simply look for the number in the middle. However, in your data set, there are two middle numbers. take the sum of the two numbers and divide it by 2.

            (10 + 12) / 2 = 11

Find more exercises on calculating mean, median and range;

https://brainly.com/question/16073893

#SPJ1

Answer:

26π

Step-by-step explanation:

radius=13

double radius to find diameter

diameter=26

equation for circumference= π×d

circumference= 26π

After five years, her IRA account's net worth (after taxes) will indeed be $14,322.88 ($10,000 + $4,322.88).

Sarah will be required to file taxes just on interest received each year if she places the $10,000 inside a standard savings account, which will lower her net worth.

She will have earned $800 in pre-tax interest every year, assuming she receives nominal interest of 8% annually.

She will, however, be liable for $240 in taxes just on interest generated each year (30% of $800) since she falls into the 30% tax bracket.

Her pre-tax interest earnings after five years will total $4,000 ($800 x five years). She will still have paid $1,200 in total in taxes just on interest generated ($240 x 5)

She will therefore have a net worth of $12,800 ($10,000 + $4,000 - $1,200) in the normal savings account after five years (after taxes).

Sarah won't have to pay taxable income on the $10,000 invested in such an IRA account or the interest accrued until she starts taking distributions in retirement.

She will have earned $800 in pre-tax interest every year, assuming she receives nominal interest of 8% annually.

She will have the whole $800 to reinvest & compound each year, though, as she is not subject to income taxation on the interest gained each year.

She will have earned $4,322.88 in pre-tax interest after five years, and she won't have to pay any taxes until she starts taking withdrawals in retirement.

To know more about taxation visit:

https://brainly.com/question/28170783

#SPJ1