The temperature at the point (x,y) on a metal plate is
T=x/x2+y2
Find the direction of greatest increase in heat from the point (2, 5).

The smallest number of eggs that could have been in the basket = 301

Given that the basket is filled with an unknown number of eggs.

Let N be the smallest number of eggs in the basket.

When eggs are removed 2, 3, 4, 5, or 6 at a time, one egg is left over at the end which means (N-1) is divisible by 2, 3, 4, 5, or 6, i.e. (N-1) is the least common multiple of 2, 3, 4, 5, and 6.  

Since LCM (2, 3, 4, 5, 6) = 60

So, (N-1) should be a multiple of 60, then only (N-1) will be divisible by 2, 3, 4, 5, and 6. Therefore N is of the form 60k+1 (where k is an integer).

Since no egg is left over when they are removed 7 at a time, N should be a multiple of 7. Smallest multiple of 7 that is of the form 60k+1 (where k is an integer) is 301.

Hence the smallest number of eggs that could have been in the basket = 301.

To learn more about LCM visit : https://brainly.com/question/16054958

#SPJ11

The width of a cuboid is 7 cm

In geometry, a cuboid is a solid shape or a three-dimensional shape. A convex polyhedron that is bounded by six rectangular faces with eight vertices and twelve edges is called a cuboid. A cuboid is also called a rectangular prism. A cuboid with six square faces is called a cube. An example of a cuboid in real life is a rectangular box.

volume = l * b * h = 490

7 * b *10 = 490

b = 7 cm

In Maths, we can observe other shapes which are exactly the same as cuboid, they are rectangular cuboid, rectangular box, right rectangular prism, right cuboid, rectangular parallelepiped, and rectangular hexahedron

know more about cuboid click here;

https://brainly.com/question/29568631

#SPJ4

Voume of marble is 10mL because when you submerged the marble in water equal volume of water flowed out.

m = 60 and n = 24

. . . .

. . . .

. . . .

The coordinates where the fountain will be located is (2, 1/2)

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

The center town forms a parallelogram with the vertices

A = (0, 4); B = (6, 1); C = (4, -3); D = (-2, 0)

The corner points when placed on a coordinate grid can be calculated using

Mid-point = 1/2(x1 + y1, x2 + y2)

So, we have

Center = 1/2 * (0 + 4, 4 - 3) or

Center = 1/2 * (6 - 2, 1 + 0)

Evaluate

Center = (2, 1/2) or Center = (2, 1/2)

Hence, the coordinates where the fountain will be located is (2, 1/2)

Read more about midpoint at

https://brainly.com/question/28462165

#SPJ1

Answer: 0.85 kilograms

Step-by-step explanation:

Answer:

80\(\leq\)20x+0.1(100)

Step-by-step explanation:

x for the number of days you are trying to find.

$20 to rent the car per day.

$0.1 for every mile driven and she wants to drive 100 miles so $0.1(100).

she cannot spend over 80 so the sign should be equal to $80 or less than.

Answer:

500000 x 500000 =250000000000

Step-by-step explanation:

Hope it help and have a great day

Answer: It's 250000000000

Step-by-step explanation:

The equation that shows the relationship is w = 38m.

If Mrs. Lopez types at a constant rate, then the number of words she types is directly proportional to the amount of time she types. We can express this relationship using the formula:

w = km

where w is the number of words typed, m is the number of minutes spent typing, and k is the constant of proportionality.

We are given that k = 38, so we can substitute this value into the formula to get:

w = 38m

Therefore, the equation that shows the relationship between the number of words Mrs. Lopez types and the number of minutes she types is w = 38m.

Read more about proportional relationship at

https://brainly.com/question/28651666

#SPJ1

Answer:

Step-by-step explanation:

Volume of cylinder:  V = π×r² × h

diameter = 20 cm  ⇒  r = 10 cm

h = 2 cm

Volume:

V = π×(10)²×2 = 200π cm³ = 628.318.... cm³ ≈ 628.3 cm³

The coordinate of point O after the dilation  (16, 24).

A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.

Given:

We have center of dilation at (4, 6)

Scale factor = 4

after applying the scale the coordinate will be

= 4(4, 6)

= (4 x 4, 6 x 4)

= (16, 24)

Learn more about scale factor here:

https://brainly.com/question/29144135

#SPJ1

Answer:

x = 2

Step-by-step explanation:

3(4x + 2) = 15x

12x + 6 = 15x

6 = 15x - 12x

6 = 3x

x = 6/3

The minimum required sample size is 47 as it is very important for safety, the 99% confidence interval needs to have a margin smaller than 0.06.

To estimate the mean tensile strength for roof hangers with a 99% confidence interval margin of 0.06, we can use the formula:

Margin of error = z* (standard deviation / sqrt(sample size))

where z is the z-score for the desired confidence level, which for a 99% confidence interval is 2.576.

Plugging in the given values, we get:

0.06 = 2.576 * (0.25 / sqrt(sample size))

Solving for the sample size, we get:

sample size = (2.576 * 0.25 / 0.06)^2

sample size = 89.59

Rounding up to the nearest whole number, the minimum required sample size is 90.

Therefore, we need to take a sample of at least 90 roof hangers to estimate the mean tensile strength with a 99% confidence interval margin of 0.06.

To estimate the mean tensile strength for roof hangers with a 99% confidence interval and a margin of error smaller than 0.06, you'll need to determine the minimum required sample size.

For a 99% confidence level, the Z-score (critical value) is approximately 2.576.

The known standard deviation is 0.25. The desired margin of error is less than 0.06. Use the formula:

Margin of Error = Z-score * (Standard Deviation / sqrt(Sample Size))

Rearrange the formula to find the sample size:

Sample Size = (Z-score * Standard Deviation / Margin of Error)^2

Sample Size = (2.576 * 0.25 / 0.06)^2

Sample Size ≈ 46.24

Since you cannot have a fraction of a sample, round up to the nearest whole number. The minimum required sample size is 47.

Visit here to learn more about Standard Deviation:

brainly.in/question/55758939

#SPJ11

An irrational number could not be written as a fraction.

We need to clasify the following numbers in rational or irrational:

Answer:

We can determine that Option A, y = 0.4x - 2 is the correct answer

Step-by-step explanation:

Step 1:  Plug in 30 into the x-value to see if the y-value matches

Equation 1 --> y = 0.4(30) - 2 = 10

Equation 2 --> y = 0.3(30) + 2 = 11  <--  WRONG Y-VALUE

Equation 3 --> y = 0.3(30) + 1 = 10

Step 2:  Plug in 50 into the x-value to see if the y-value matches

Equation 1 --> y = 0.4(50) - 2 = 18

Equation 3 --> y = 0.3(50) - 2 = 13  <--  WRONG Y-VALUE

Answer: We can determine that Option A, y = 0.4x - 2 is the correct answer

Answer:

x=50

Step-by-step explanation:

67=x+17

67-17=50

x=50

Answer:

Solving the equation \((5^2 -4) \cdot 2 -18\) we get 24

Step-by-step explanation:

We need to solve the equation \((5^2 -4) \cdot 2 -18\)

We will solve using DMAS rule i.e first bracket will be solved, then multiplication and at the end subtraction will be done.

First we will solve the bracket

\((5^2 -4) \cdot 2 -18\\=(25-4) \cdot 2-18\\=21 \cdot 2-18\)

Now multiply 21 by 2

\(=42-18\)

Now subtract

\(=24\)

So, solving the equation \((5^2 -4) \cdot 2 -18\) we get 24

The equation is: G = -⁵/₄t + 15

The slope of the function represents that ⁵/₄ gallons of gas is consumed to drive the car for one hour.

The formula for the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

From the graph, we see that:

y-intercept = 15 gallons

Now, the slope is gotten from the formula:

Slope = (y₂ - y₁)/(x₂ - x₁)

Slope = (10 - 5)/(4 - 8)

Slope = -⁵/₄

Thus, equation is:

G = -⁵/₄t + 15

The slope of the function represents that ⁵/₄ gallons of gas is consumed to drive the car for one hour.

Read more about Linear equation graph at: https://brainly.com/question/28732353

#SPJ1

Answer:

Let's first represent the number of years since 2000 with 't'. The initial milk consumption in the year 2000 was 8.38 gallons per person per year. After that, it decreases by 0.3 gallons per year. Therefore, the number of gallons of milk consumed 't' years after 2000 is given by 8.38 - 0.3t. Now we need to find the number of years since 2000 when milk consumption was greater than 6.06 gallons per person per year.

Let's represent this inequality with 't':8.38 - 0.3t > 6.06

We need to solve this inequality for 't':8.38 - 0.3t > 6.06-0.3t > 6.06 - 8.38-0.3t > -2.32t < (-2.32)/(-0.3)t < 7.73

Therefore, the inequality that can be used to find the number of years, t, since 2000 when whole milk consumption was greater than 6.06 gallons per person per year is t < 7.73.

Linear inequality: https://brainly.com/question/11897796

#SPJ11

To determine the probability that Paul will not eat the pizza Chef Carl has made, we need to calculate the probability of Chef Carl selecting mushrooms as one of the toppings.

First, let's calculate the total number of possible combinations of two different toppings that Chef Carl can choose from the given options. Since order does not matter, we can use the combination formula:

C(n, r) = n! / (r! * (n-r)!),

where n is the total number of options and r is the number of choices. In this case, n = 5 (the number of toppings) and r = 2 (the number of choices).

C(5, 2) = 5! / (2! * (5-2)!) = 5! / (2! * 3!) = (5 * 4) / (2 * 1) = 10.

So there are a total of 10 possible combinations of two different toppings that Chef Carl can choose.

Next, we need to calculate the number of combinations that include mushrooms. Since Paul will not eat pizza with mushrooms, we want to exclude this option.

To choose one topping from the remaining four (excluding mushrooms), there are C(4, 1) = 4 possible choices.

Therefore, the probability that Chef Carl selects a combination with mushrooms is 4/10.

Finally, the probability that Paul will not eat the pizza Chef Carl has made is the complement of this probability, which is 1 - 4/10 = 6/10 = 3/5.

So, the probability that Paul will not eat the pizza is 3/5.

learn more about probability here

https://brainly.com/question/31828911

#SPJ11

Answer:

144

Step-by-step explanation:

sense you have the line in the triangle you would add that to the 16 (length) and multiply that by the 6 (hight) and that would be the area (144)

Answer:

Simplify the expression.

3x2/2

hope this makes sense lol

Step-by-step explanation:

Answer:

1.5 : 1 (or) 3/2

Step-by-step explanation:

Given expression,

→ 3x/2x

Let's simplify the expression,

→ 3x/2x

→ (3 ÷ 2)(x ÷ x)

→ (1.5)(1)

→ 1.5

Now the required ratio will be,

→ 3 : 2

→ 1.5 : 1

Hence, required ratio is 1.5 : 1.

Answer:

Graph the line using the slope and y-intercept, or two points.

Slope: Undefined

y-intercept: No y-intercept

x         y

-3        0

-3        1

Step-by-step explanation:

Below is a picture of the graph.    PLEASE MARK BRAINlIST

Answer:

5 cups is 2.5 pts

Step-by-step explanation:

cups pts

5.00 2.5

5.01        2.505

5.02 2.51

5.03 2.515

Answer:

Infinitely many solutions

Step-by-step explanation:

Step by Step Solution

More Icon

System of Linear Equations entered :

[1] 3x + y + 2z = 5

[2] 2x + 3y + 3z = 3

[3] x - 2y - z = 2

Solve by Substitution :

// Solve equation [3] for the variable x

[3] x = 2y + z + 2

// Plug this in for variable x in equation [1]

[1] 3•(2y+z +2) + y + 2z = 5

[1] 7y + 5z = -1

// Plug this in for variable x in equation [2]

[2] 2•(2y+z +2) + 3y + 3z = 3

[2] 7y + 5z = -1

// Solve equation [2] for the variable z

[2] 5z = -7y - 1

[2] z = -7y/5 - 1/5

// Plug this in for variable z in equation [1]

[1] 7y + 5•(-7y/5-1/5) = -1

[1] 0 = 0 => Infinitely many

To minimize the amount of tin used, the height of the can must be 4 inches (option D).

The volume of a cylindrical tin can is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height. To minimize the amount of tin used, we need to minimize the surface area, which is given by the formula A = 2πrh + 2πr².

Given the volume is 16π cubic inches, we have:

16π = πr²h

Now, we can find the relationship between r and h:

h = 16/r²

Now, substitute this into the surface area formula:

A = 2πr(16/r²) + 2πr²
A = 32π/r + 2πr²

To minimize the surface area, we can take the derivative with respect to r and set it to 0:

dA/dr = -32π/r² + 4πr

0 = -32π/r² + 4πr

Solving for r:

r³ = 8
r = 2 (since r > 0)

Now, substituting r back into the relationship between r and h:

h = 16/(2²)
h = 16/4
h = 4

Therefore, the height of the can must be 4 inches (option D) to minimize the amount of tin used.

Learn more about minimizing surface area here: https://brainly.com/question/29897121

#SPJ11

Answer:

1) 169.7

2) 678.6

3) 84.9

Hope it helped!!!

Answer:

Step-by-step explanation:

4, 9, 0, 1,1, 2, 0, 0, 2, 8, 8, 3, 1.

Arrange in ascending order:

0, 0, 0, 1, 1, 1, 2, 2, 3, 4, 8, 8, 9.

The median = middle value = 2.

Lower quartile = 0.5

Upper quartile = 6.

Answer:

False

Step-by-step explanation:

The answer is False

The given statement is false, as the letters are used as keys in the dictionary.

The dictionary used in counting letters examples to keep track of letter frequencies uses the letters as the key and the count as the value. This means that for each letter encountered in a string, the value corresponding to the key (letter) in the dictionary is incremented by 1.

For example, if the string is "hello", the dictionary would initially be empty, and for each letter encountered in the string, the value for the corresponding key in the dictionary would be incremented by 1, resulting in a dictionary like {"h": 1, "e": 1, "l": 2, "o": 1}.

Therefore, the correct answer is false, as the letters are used as keys in the dictionary.

To learn more about dictionary here:

brainly.com/question/547574#

#SPJ11