When someone says they ran a 5k, what type of measurement are they using? is that a far distance?

Answer:

x = 1.639 in

Step-by-step explanation:

With these instructions, the length of the box would be (14-2x), the width would be (8-2x), and the height would be x, so the equation for volume would be width*length*height, or

\(V=(14-2x)(8-2x)(x)\)

\(V=4x^3-44x^2+112\)

Now we solve for dV/dx because we want to find maximum volume

\(\frac{dV}{dx} =12x^2-88x+112\)

\(\frac{dV}{dx} =4(3x^2-22x+28)\)

Now we let dV/dx equal zero to find critical values

\(0=4(3x^2-22x+28)\)

\(0=3x^2-22x+28\)

\(x=\frac{11+\sqrt{37} }{3}\), \(x=\frac{11-\sqrt{37} }{3}\)

Now we see where dV/dx changes signs:

dV/dx changes from positive to negative at \(\frac{11-\sqrt{37} }{3}\)

and from negative to positive at \(\frac{11+\sqrt{37} }{3}\)

so V(x) has a local maximum when x = \(\frac{11-\sqrt{37} }{3} = 1.639\) in

Answer:

The freezing point of water increases by 0.0001 degrees Fahrenheit when the altitude increases by 1 foot.

Step-by-step explanation:

The model for the freezing point of water T at altitude a is:

T(a)= 0.0001a+32

The slope of this equation is the coefficient of the variable a. Since the slope is positive, it means the freezing point of water increases by 0.0001 degrees Fahrenheit when the altitude increases by 1 foot.

For example, when a=1000, the freezing point is:

T(1000)= 0.0001*1000+32 = 32.1°F

When a=1001, the freezing point is:

T(1001)= 0.0001*1001+32 = 32.1001°F

Note the increase of 1 foot in altitued meant an increase of 32.1001-32.1 = 0.0001°F

Answer:

NONE of these statements are true

\( \frac{d}{dx} (f(x).g(x)) = f'(x).g(x) + g'(x).f(x)\)

\( \frac{d}{dx} ( \sqrt{x {}^{2} + x} ) {}^{2} = \frac{2x + 1}{2 (\sqrt{x {}^{2} + x}) {}^{2} } = \frac{2(2x + 1)(x {}^{2} + x) }{2|x²+x|} = \frac{(2x + 1)(x { }^{2} +x)}{|x²+x|} \)

\( \frac{d}{dx} ( \sqrt{f(x)} ) = \frac{f'(x)}{2 \sqrt{f(x)} } \)

a. The Present value will be  $123.60 (15% nominal rate, semiannual compounding, discounted back 4 years). b. The Present value will be  $122.85 (15% nominal rate, quarterly compounding, discounted back 4 years. c. The Present value will be  $181.96 (15% nominal rate, monthly compounding, discounted back 1 year). d. The differences in the present values (PVs) occur due to the compounding frequency and discounting period.

To find the present value (PV) of $200 due in the future under different conditions, we need to use the formula for present value and consider the compounding frequency and discounting period.
a. 15% nominal rate, semiannual compounding, discounted back 4 years:
In this case, we use the formula PV = FV / (1 + (r/n))^(n*t), where FV is the future value, r is the nominal rate, n is the compounding frequency per year, and t is the number of years.
PV = $200 / (1 + (0.15/2))^(2*4)
PV = $200 / (1.075)⁸
PV = $123.60

b. 15% nominal rate, quarterly compounding, discounted back 4 years:
Using the same formula:
PV = $200 / (1 + (0.15/4))^(4*4)
PV = $200 / (1.0375)¹⁶
PV = $122.85

c. 15% nominal rate, monthly compounding, discounted back 1 year:
PV = $200 / (1 + (0.15/12))^(12*1)
PV = $200 / (1.0125)¹²
PV ≈ $181.96

d. The differences in the present values (PVs) occur due to the compounding frequency and discounting period. When compounding occurs more frequently, such as semiannually or quarterly, the PV decreases because the interest is added more frequently, reducing the impact of compounding. On the other hand, when the discounting period is longer, as in the case of 4 years versus 1 year, the PV decreases because the future value is being discounted over a longer time period.

To know more about Present value refer here

brainly.com/question/29586738

#SPJ11

Answer:

80,023,904

Step-by-step explanation:

Just add all the numbers together.

Answer:

"8023904

Step-by-step explanation:

20 000 + 8 000 000=8020000

4+3000=3004

3004+900=3904

3904+ "8023904"

Answer:

w(15)=112.5

Step-by-step explanation:

All you have to do is put the number in the parentheses in the place of the variable, which in this case is h, and perform the prescribed operation.

In this case, you make the equation w(15)=7.5(15) which you can rewrite as

                                                                                  w(15)= 7.5×15, which gives                        .                                                                                  you 112.5 as the product.

The equation between the number of months Hassan takes voice lessons, x, and the number of pieces he knows, y, is y = 2x+6

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, Hassan knows how to sing 6 vocal pieces, Now he's about to start private lessons. His teacher says he will learn 2 new pieces each month.

Since, he already knows 6 vocal pieces,

And, he is learning 2 each month, so for y month he will know = 2x+6 pieces

Hence, the relationship is y = 2x+6

For more references on equations, click;

https://brainly.com/question/29657988

#SPJ1

Answer:

Step-by-step explanation:

area or rect = l*b

= 4*6/7

= 3.4285

The procedures below must be carried out in order to use a compass and straightedge to create a line through a given point that is parallel to a given line:

1. Position the straightedge on the indicated line, and then draw a line segment through the indicated point.

2. Set the compass on the indicated point and draw two arcs that cross the line segment on either side without adjusting the compass's width.

3. Draw an arc that crosses the original line while maintaining the same compass width by setting the compass on one of the arcs' junction points.

4. Repetition of step 3 using the opposite arc's junction point.

5. Using the straightedge, draw a line between the indicated point to the locations where the

learn more about procedures here :

https://brainly.com/question/27176982

#SPJ11

ANSWER

0.1

EXPLANATION

We want to estimate the quotient of 1.64 ÷ 22.

To do this, we will approximate the two numbers to whole number and solve it.

It becomes:

2 ÷ 20

That is:

Note: since 2 cannot be divided by 20, we write 0. and add a 0 to the back of 2.

The estimate of the quotient is 0.1.

Answer:

Therefore the total amount that Jackson's Bakery made in one week from sheet cakes is: = $2,238

Step-by-step explanation:

Step One:

To arrive at the total amount made from the sheet cakes, we have to assign the prices of each type of cake. They are:

Step Two:

If the new pastry sold 17 small, 11 medium and 20 large sheet cakes respectively, the total money made comes to the following:

= (36 x 17) + (11 x 46) + (56 x 20)

= 612 +  506 + 1120

Therefore the total amount that Jackson's Bakery made in one week from sheet cakes is:

= $2,238

Cheers!

7 L of one solution is mixed with 3 L of another, making a new solution with a total volume of 10 L and concentration 29%. This means the new solution contains

(10 L) * 29% = (10 L) * 0.29 = 2.9 L

of acid.

Let the concentration of the first solution be c%. Each liter of the 15% acid solution contributes 0.15 L, and each liter of the solution of unknown concentration contributes 0.01c L of acid. To end up with a total of 2.9 L of acid, we would get

7 * (0.01c L) + 3 * (0.15 L) = 2.9 L

Solve for c (we can omit the units):

0.07c + 0.45 = 2.9

0.07c = 2.45

c = 35

So the first solution has a concentration of 35%.

Answer:

x 2 + 5 x + 6

Step-by-step explanation:

y = m x + c

y- intercept

x = 0

y = (-2) (0) + 3

=3

(x =0,  y = 3)

Answer: m = -5

Step-by-step explanation:

m = y₂ - y₁ / x₂ - x₁

6 - ( - 3 ) / -1 - 2

6 + 9 / -3

15 / -3

-5

Answer:

0.390625 grams

Step-by-step explanation:

can i get a second opinion on this

Answer:

I'd help you if you gave me the radius or the picture or the diameter...

Step-by-step explanation:

Binding constraints directly influence the optimal solution in a linear Programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution.

binding constraints and positive slack in the context of linear programming. In a linear programming problem, we aim to find the optimal solution for an objective function, given a set of constraints. The terms "binding constraints" and "positive slack" are related to these constraints.

1. Binding constraints: These are constraints that directly impact the optimal solution of the problem. In other words, they "bind" the feasible region (the area where all the constraints are satisfied) and affect the maximum or minimum value of the objective function. Binding constraints are active constraints, as they influence the final solution.

2. Positive slack: Slack is the difference between the left-hand side and right-hand side of a constraint when the constraint is satisfied. If this difference is positive, it means that there is some "extra" or "unused" resource in that constraint. Positive slack indicates that the constraint is non-binding, meaning it does not directly impact the optimal solution. It shows that there is some room for the constraint to be further tightened without affecting the final outcome.

In summary, binding constraints directly influence the optimal solution in a linear programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution. Knowing the difference between these terms can help you better understand and analyze linear programming problems.

To Learn More About Programming

https://brainly.com/question/24361247

#SPJ11

Answer:

Option B

Step-by-step explanation:

There are 1,000 people to start. It's growing by 2% every three year, so that would be 1.02%.

So p=1,000(1.02)^1/3

Answer:

b

Step-by-step explanation:

Answer:

Perpendicular.

Step-by-step explanation:

It's perpendicular because one line is crossing the other two, thus making it perpendicular. Have a great day!

Step-by-step explanation:

\( \tan(26) = \frac{42}{x} \\0.487732588565 \times x = 42 \\ x = 86.11276134633\)

C.x=86.113

Answer:

C (86.113)

Step-by-step explanation:

First, find the missing angle B. Since angles in a triangle add upp to 180,

180-26-90= 64

Then use the formula a/sina = b/sinb

' a' in the formula is the missing length X and sina is the corresponding(opposite) angle of X which is sin64.

B in the formula would be 42 and sinb is sin26 (the angle).

Substitute all values into the formula,

X/sin64 = 42/ sin26

Shift sin64 to the right side:

X= 42(sin64)/ sin26

X= 86.113

Hope this makes sense:)

Answer:

My guess would be the first one

Step-by-step explanation:

Both the 2nd and 3rd are shapes that share a side(back to back), but number one doesn't

Answer:

Step-by-step explanation:

The first one is not provable using any postulate.

You are given 2 sides that are equal. You have an angle that is congruent to another angle that is vertically opposite the first angle.

So you have SA. But the third side is not given nor can it be derived. So that is the odd pair out.

The second set (middle) are proved to be congruent by SAS.

The last set (right) show congruency using SSS.

The calculated length of the segment WX given that TU = 20, UV = 26, and XY = 39 is 30 units

From the question, we have the following parameters that can be used in our computation:

TU = 20, UV = 26, and XY = 39

The length WX can be calculated using the following equivalent ratio

TU : UV = WX : XY

Substitute the known values in the above equation, so, we have the following representation

20 : 26 = WX : 39

Express the ratio as fraction

So, we have

20/26 = WX/39

Make WX the subject

WX = 39 * 20/26

Evaluate the products

WX = 30

Hence, the length is 30 units

Read more about similar shapes at

https://brainly.com/question/14285697

#SPJ1

Complete question

If TU = 20, UV = 26, and XY = 39, find the length of WX. Round your answer to the nearest tenth if necessary.

Figures are not necessarily drawn to scale

The independent set in a graph is a set of vertices that contain no edges. So, no neighboring vertices are included. The max independent set problem is to get an independent set of maximum size in graph G.

The solution for this question is discussed below:

a) The integer linear program for the max independent set problem is as follows:

maximize ∑x_i Subject to: x_i+x_j ≤ 1 {i,j} ∈ E;x_i ∈ {0, 1} ∀i. The variable x_i can represent whether the ith vertex is in the independent set. It can take on two values, either 0 or 1.

b) The LP relaxation for the max independent set problem is as follows:

Maximize ∑x_iSubject to:

xi+xj ≤ 1 ∀ {i, j} ∈ E;xi ≥ 0 ∀i. The variable xi can take on fractional values in the LP relaxation.

c) The family of graphs is as follows:

Consider a family of graphs G = (V, E) defined as follows. The vertex set V has n = 2^k vertices, where k is a positive integer. The set of edges E is defined as {uv:u, v ∈ {0, 1}^k and u≠v and u, v differ in precisely one coordinate}. It can be shown that the size of the max independent set is n/2. Using LP, the value can be determined. LP provides a value of approximately n/4. Therefore, the ratio LP-OPT/OPT is at least c/4. Therefore, the ratio is in for a constant c>0.

d) The size of a max-independent set is equivalent to the number of vertices minus the minimum vertex cover size.

e) The 2-approximation algorithm for vertex cover implies a 2-approximation algorithm for the max independent set.

To know more about the independent set, visit:

brainly.com/question/31418821

#SPJ11

Answer:

Step-by-step explanation:

given data

mean = 1.9 hours

standard deviation = 0.3 hours

solution

we get here first  random movie between 1.8 and 2.0 hours

so here

P(1.8 < z < 2 )

z = (1.8 - 1.9) ÷ 0.3

z = -0.33

and

z = (2.0 - 1.9) ÷ 0.3

z = 0.33

z = 0.6293

so

P(-0.333 < z < 0.333 )

=  0.26

so random movie is between 1.8 and 2.0 hours long is 0.26

and

A movie is longer than 2.3 hours.

P(x > 2.3)

P( \(\frac{x-\mu }{\sigma}\)  > \(\frac{2.3-\mu }{\sigma}\) )

P (z  > \(\frac{2.3-1.9 }{0.3}\)  )

P (z  > 1.333  )

= 0.091

so chance a movie is longer than 2.3 hours is 0.091

and

length of movie that is shorter than 94% of the movies is

P(x > a ) = 0.94

P(x <  a ) = 0.06

so

P( \(\frac{x-\mu }{\sigma }\) <  \(\frac{a-\mu }{\sigma }\) )

\(\frac{a-1.9 }{0.3 } = -1.55\)

a = 1.43

so length of the movie that is shorter than 94% of the movies about 1.4 hours.

Answer:

hi pls do enter the no.s

Answer:

None

Step-by-step explanation:

−5a + 5a + 9 = 8  is the same as

                 9 = 8 yet this is always false so the equation has no solutions

Answer:

A and C

Step-by-step explanation:

Answer:

The approximate value of the scale is 1:67

or the actual value without approximation is 1: 66 2/3 ( 66 while number , two over three)

Step-by-step explanation:

Here, we want to figure out the scale in inches of the drawing to the actual object.

The actual object is 500 ft by 700 ft

while the drawing is 90 inches by 126 inches

Mathematically, we know that 12 inches = 1 foot

So the actual object will be;

500(12) by 700(12)

= 6000 inches by 8400 inches

Now let’s make a division to get the scale;

6000/90 by 8400/126

we get 66.67 as answers on both ends

This is approximately equal to 67

So the scale we have here is 1:67

Answer:

I would believe that it is A.

Step-by-step explanation:

The fact that A has 5, and x is minus two times, 5/2= 2.5, and that is where the second arrowhead is pointing to on the x axis.

The number of pounds of apples, y, minus two times the number of pounds of oranges, x, is at most 5 which is correct option (A).

A graph can be defined as a pictorial representation or a diagram that represents data or values.

A linear function is defined as a function in the form of f(x) = mx + bc where 'm' and 'c' are real numbers.

It represents the line's slope-intercept form, which is written as y = mx + c.

This is because a linear function represents a line, i.e., its graph is a line. Here,

'm' is the slope of the line

'c' is the y-intercept of the line

'x' is the independent variable

'y' (or f(x)) is the dependent variable

According to given graph,

A has a value of 5, and since x is negative two times, 5/2=2.5, which is where the second arrowhead on the x axis is pointing.

So, the total  number of the pounds of apples, y minus two times, and the pounds of oranges, x, equals at most five pounds.

Hence, the number of pounds of apples, y, minus two times the number of pounds of oranges, x, is at most 5.

Learn more about graph here:

brainly.com/question/16608196

#SPJ5

An equation that mode the relationship between thee two variable is y=2x+3 .

Let x represent the number of 6-month period worked

Let y represent the total number of paid vacation day

According to the question,

When he started work, he was given three paid day of vacation. For each six-month period he pay at the job, his vacation is increased by two day.

Each year has 2 six-month periods. After 4.4 years Roberto will have worked 8.8 six-month periods. He will have been given vacation days for each of the 8 whole working periods he has completed. x=8 y=2*8+3 y=19

An equation that mode the relationship between thee two variable is y=2x+3 (Total vacation time equals 2 days times x plus the 3 days he was given at the start).

Learn more about linear equations in two variables at :

https://brainly.com/question/24085666

#SPJ4