An artist can create 4 pieces of pottery in 2 hours. What’s the artist’s unit rate?

The option (b) set y equal to a constant other than zero to get the curve of points where the slope is that constant.

A slope field is a visual representation of the slopes of a function's derivative at different points on the xy-plane. The slope at a particular point in the xy-plane is given by the derivative of the function at that point.

To match the given equations with their corresponding slope fields, you need to analyze the behavior of the slopes and isoclines. An isocline is a curve in the plane along which the slope of a function is constant. Isoclines are useful in constructing slope fields by hand, as they help in determining the slope at different points.

To start with, set y equal to zero and observe how the derivative behaves along the x-axis. Similarly, set x equal to zero and observe the behavior of the derivative along the y-axis. These observations will give you an idea of the direction and magnitude of the slope at different points in the xy-plane.

Next, consider the curve in the plane defined by setting y' = 0. This curve represents the points in the picture where the slope is zero. These points are known as critical points or equilibrium points. They are essential in analyzing the stability and behavior of a system.

These curves are called isoclines and can be used to construct the slope field picture by hand.

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Complete Question:

Match the following equations with their slope field. Clicking on each picture will give you an enlarged view. While you can probably sove this problem by guessing, it is useful to try to predict characteristics of the slope field and then match them to the picture Here are some handy characteristics to start with- you will develop more as you practice. Set y equal to zero and look at how the derivatiwe behaves along the x axis. Do the same for the y axis by setting x equal to 0. Consider the curve in the plane defined by setting y' = 0-this should correspond to the points in the picture where the slope is zero. Setting y equal to a constant other than zero gives the curve of points where the slepe is that constant. These are called isoclines, and can be used to construct the slope field picture by hand.

Solution:

Given the data below:

To evaluate how many more employees worked at BIT Labs than at Boxerville Hardware, we have

Where

Thus, we have

The correct option is D

Answer:

Yes

Step-by-step explanation:

A for loop basically relies on repeating the same code for a pre-set number of times. During which you can make any code repeat inside of it, including indexing through a type of list. Many times a for-loop will use the indexes in a list to calculate the number of times that the loop has to repeat. This is usually done in order to search or apply changes in an array of other types of data structures that have countless values stored in it.

Answer:

= 34

Step-by-step explanation:

(32)-5+7

32 - 5 + 7

= 32 + 2

= 34.

Answer: C

Step-by-step explanation:

The rest of the quadrilaterals provided have 2 pairs of parallel lines.

The choice is:

Explanation:

The quadrilateral that has exactly one pair of parallel lines is called a trapezoid.

Here's what a trapezoid looks like :

\(\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\linethickness{0.3mm}\qbezier(0,0)(0,0)(1,3)\qbezier(5,0)(5,0)(4,3)\qbezier(1,3)(1,3)(4,3)\qbezier(3,0)(8.2,0)(0,0)\put(-0.5,-0.3){$\sf A$}\put(5.3,-0.3){$\sf B$}\put(4.2,3.1){$\sf C$}\put(0.6,3.1){$\sf D$}\end{picture}\)

Answer:

100 inches/1 minute  X  1 foot/12 inches =(100/12) feet/minute = 8 1/3 feet/minute

Answer:

39ft by 34ft

Step-by-step explanation:

4 and 1/3 is equal (by doing 4*3+1)to 13/3 which is equal (by doing 13/3 *3/3)to 39/9 inches which according to the conversion is equal to 39ft

3 and 7/9 is equal (3*9+7)to 34/9 inches which when converted is 34ft

Answer:

B

Step-by-step explanation:

taking test rn ill say if its correct when i finish

Answer:

C reflection over y=x-1 (x+0y-4)

Step-by-step explanation:

Just got it right on the test

Answer:

175

Step-by-step explanation:

Divide. 136.50 divided by 78 then times it by 100 and you get it 175

The percent increase is 56.41%.

We first calculate the difference between the original value and the new value when comparing a rise in a quantity over time. The relative increase in comparison to the initial value is then determined using this difference, and it is expressed as a percentage. The percentage increase formula is provided by:

percentage increase = (increase in amount /original amount ) x 100

Given:

Bill in may month- 78

Bill in June month = 122

So, change in amount= 122 - 78 = 44

So, percent increase = 44/ 78 x 100

percent increase = 0.5641 x 100

percent increase = 56.41%

Hence, the percent increase is 56.41%.

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To find the average rate of change of f(x) = 3x + 10, simply compare with f(x) = mx + 10 where m is the average rate of change

Comparing the two equation, average rate of change = m = 3

The remaining credit after 63 minutes of calls is $19.92.

From the information illustrated, the remaining credit after 36 minutes of calls is $24.24, and the remaining credit after 55 minutes of calls is $21.20.

The rate will be:

= (24.24 - 21.20) / (55 - 36)

= 3.04 / 19

= 0.16

The remaining credit after 63 minutes of calls will be:

= $21.20 - ((63 - 55) × $0.16)

= $21.20 - $1.28

= $19.92

The credit is $19.92.

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Answer:

21.V=1746.1

22.V=1922.7

23.V=54.4

Step-by-step explanation:

V=h*w*l                V=pir^2*h

V=12*8*14 .           V=pi*4^2*8

V=1344 .               V=402.1

V1+V2=1344+402.1=1746.1

V=pi*r^2*h             V=2/3*pi*r^3

V=pi*6^2*13           V=2/3*pi*6^3

V=pi*36*13             V=2/3*pi*216

V=1470.3                V=452.4

V1+V2=1470.3+452.4=1922.7

V=1/3pi*r^2*h           V=1/3pi*r^2*h

V=1/3pi*2^2*6          V=1/3pi*2^2*7

V=8pi                       V=28/3pi

V=25.1 .                    V=29.3

V1+V2=25.1+29.3=54.4

It will take 150 minutes for the two containers to have the same amount of water.

To find the number of minutes it will take for the two containers to have the same amount of water, we need to use the following formula:

m = |A - B| / (a - b)

where m is the number of minutes, A is the initial amount of water in Container A, B is the initial amount of water in Container B, a is the rate at which water is being added to Container A, and b is the rate at which water is being drained from Container B.

In this case, the initial amount of water in Container A is 300 liters, the initial amount of water in Container B is 900 liters, the rate at which water is being added to Container A is 6 liters per minute, and the rate at which water is being drained from Container B is 2 liters per minute. Substituting these values into the formula, we get:

m = |300 - 900| / (6 - 2)

m = |-600| / 4

m = 600 / 4

m = 150 minutes

Therefore, it will take 150 minutes for the two containers to have the same amount of water.

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The person is approximately 8.43 miles from home, and they need to walk in the direction of approximately 26.6 degrees east of north to head directly home.

To determine the distance from home, we can use the concept of vector addition. The person walks 4 miles west, which can be represented as a vector (-4, 0) in a coordinate plane. Then, they walk 5 miles southwest, which can be represented as a vector (-3.54, -3.54) since southwest is a combination of west and south. Adding these two vectors together gives us (-7.54, -3.54).

To find the magnitude or distance from home, we use the Pythagorean theorem. The distance is given by sqrt((-7.54)^2 + (-3.54)^2) = 8.43 miles (approximately).

To determine the direction to head directly home, we need to find the angle between the vector (-7.54, -3.54) and the positive x-axis. We can use trigonometry to find this angle. The tangent of the angle is given by the ratio of the y-coordinate to the x-coordinate, which is -3.54 / -7.54. Taking the inverse tangent of this value gives us approximately 26.6 degrees.

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The value of secant XY is 37.5 units.

The Secant-Secant Theorem states that "if two secant segments which share an endpoint outside of the circle, the product of one secant segment and its external segment is equal to the product of the other secant segment and its external segment".

Using the theorem above, we can say:

VZ * VW = VX * VY

30 * 45 = 22.5 * VY

22.5VY = 1350

VY = 1350/22.5

VY = 60 units

Since VY = VX + XY. We have:

60 = 22.5 + XY

XY = 60 - 22.5

XY = 37.5 units

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ANSWER and EXPLANATION

To find the compound inequality represented by the phrase, we first have to write the two inequalities in the phrase.

Let x represent the values.

All values less than or equal to -1 is:

All values greater than 1 is:

Therefore, combining them, we have:

That is the compound inequality.

The graph is:

Answer:

The answer is no this number is not rational.

Step-by-step explanation:

Because, To show that the rational numbers are dense:

It cannot be expressed as a fraction with integer values in the numerator and denominator. When an irrational number is expressed in decimal form, it goes on forever without repeating.

Answer:

C and D

multiply the 6 and -3 to the numbers inside the parenthesis

The sale price of the shoe is given as follows:

P3,436.

The sale price of the shoe is obtained applying the proportions in the context of the problem.

The initial price is of:

P 4,295.

The shoe is sold at a discount of 20%, meaning that the sale price is 80% of the initial price, and the value is given as follows:

0.8 x 4295 = P3,436.

The problem asks for the selling price of the shoe.

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Answer:

x < 6

Step-by-step explanation:

2 x -9 < 3

     +9 .     +9

2x < 3 + 9

2x < 12

__ .   __

2 .     2

x <  6

Answer:

381 bacteria

Step-by-step explanation:

\(\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function with base $e$}\\\\$y=Ae^{kt}$\\\\where:\\\phantom{ww}$\bullet$ $A$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $e$ is Euler's number. \\ \phantom{ww}$\bullet$ $k$ is some constant.\\ \phantom{ww}$\bullet$ $t$ is the independent value time.\\\end{minipage}}\)

If the initial population is 240 bacteria, then A = 240:

\(\implies y=240e^{kt}\)

Create equations for the population after 1 hour and 7 hours:

\(t=1\implies y=240e^{k}\)

\(t=7\implies y=240e^{7k}\)

Given the population after 7 hours is double the population after 1 hour:

\(\implies 240e^{7k}=2 \cdot 240e^k\)

\(\implies e^{7k}=2e^k\)

Solve the equation to find the value of k:

\(\implies e^{7k}=2e^k\)

\(\implies \dfrac{e^{7k}}{e^k}=2\)

\(\implies e^{6k}=2\)

\(\implies \ln e^{6k}=\ln 2\)

\(\implies 6k \ln e = \ln 2\)

\(\implies 6k=\ln 2\)

\(\implies k=\dfrac{1}{6}\ln 2\)

Therefore, the equation that models the given parameters is:

\(y=240e^{\frac{1}{6}t\ln 2}\)

To find how many bacteria there will be after 4 hours, substitute t = 4 into the equation:

\(\implies y=240e^{\frac{1}{6}(4)\ln 2}\)

\(\implies y=240e^{\frac{2}{3}\ln 2}\)

\(\implies y=240(1.58740105...)\)

\(\implies y=380.9762525\)

\(\implies y=381\)

Therefore, there will be 381 bacteria after 4 hours

The parallelogram with the parametric equations 1 + 2u + v is the surface integral.

The surface element is

dS is equal to || r/u x r/dv || du dv.

where

r (u, v) is equal to x (u, v) I plus y (u, v) j plus z (u, v) k

r (u, v) = (u + v) I plus (u -v) j plus (1 + 2u + v) k

is the surface S's vector parameterization.

The surface's normal vector is

R / u x R / d

= I + j + k + 2) x I - j + k)

= 3 I + j - 2 k

as well as norm

|| r/dv x u r/u || = √(3² + 1² + (-2)²) = √(14) (14)

Calculate the integral now:

∫∫ (x + y + z) dS = √(14) ∫₀¹ ∫₀² (1 + 2u + v) = ((u + v) + (u - v)) du dv

= (14)... 01... 02 (3u + v + 1) du dv

= (14), 01 (3/2 u2, uv, and u), |02 dv

= √(14) ∫₀¹ (8 + 2v) dv

= √(14) (8v + 2v²) |₀¹

= 10 √(14) (14).

The parallelogram with the parametric equations x = u + v, y = u â' v, and z = 1 + 2u + v is the surface integral.

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The obtuse angles from the given list are D (between 90° to 180°) and E (111° angle). Thus, the answer is D, E.

The angles are given as follows:

A: less than 45°

B: greater than 270°

C: right angle

D: between 90° to 180°

E: A 111° angle

F: A 222° angle

G: A 0.180° angle

H: A 180.180° angle

To identify which angles are obtuse, we need to determine the angles that are greater than 90 degrees but less than 180 degrees.

Among the given angles:

A: less than 45° (not obtuse)

B: greater than 270° (not obtuse)

C: right angle (not obtuse)

D: between 90° to 180° (obtuse)

E: 111° angle (obtuse)

F: 222° angle (not obtuse)

G: 0.180° angle (not obtuse)

H: 180.180° angle (not obtuse)

Therefore, the obtuse angles from the given list are:

D (between 90° to 180°)

E (111° angle)

The answer is D, E.

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The landing space per step for the indoor staircase is solved to be

The vertical rise from first floor to second floor is 14 feet

The figure defined to be a right triangle and the dimensions are worked using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The right angle triangle comprises of

opposite = total vertical height

adjacent = total horizontal height = 13 feet

The total vertical height is calculated using tan, TOA

let the angle be x

tan x = opposite / adjacent

tan 47 = opposite / 13

opposite = (13 * tan 47) feet

opposite = 12 * (13 * tan 47) inch

opposite = 167.2895 inch

For a 14 inch vertical rise per step say number of step is y

14 y = total vertical height

14 y = 167.2895

y = 11.9493 steps ≈ 12 steps

The landing space for 12 steps is solved by

= horizontal space total in inch / number of steps

= 13 * 12 / 12

= 13 inches

vertical rise from the 1st floor to the 2nd floor

opposite = (13 * tan 47) feet

opposite = 13.94 feet

opposite = 14 feet (to the nearest foot)

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By using the number line above, the answer choice which has statements that are all true include the following: A. Point A represents -4, Point D represents 1 3/4, and 1 3/4 > -4.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

By critically observing the number line (see attachment), the first point A would be located at -4 and the open arrow circle should point to the left because it represent the less than inequality symbol.

On the other hand (conversely), the last point A would be located at 1 3/4 and the open arrow circle should point to the right because it represent the greater than inequality symbol. Therefore, we have:

Point D > Point A

1 3/4 > -4

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Answer:

b. a statistic.

Step-by-step explanation:

the value 1670 is regarded as a statistic. this is because it is a representation of the value of a sample. from the question we get that destructive testing is being done this shows is that what we have here is a sample.

the mean force 1670 is not a parameter, a point estimate, a confidence interval or interval estimate. therefore option b is the answer.