A babysitter earns $8 an hour for babysitting 2 children and an additional $3 tip when both children are put to bed on time. If the babysitter gets the children to bed on time, what expression could be used to determine how much the babysitter earned?

The gradient of f(x, y, z) = log(x2 + y2 + z2) at (1, 0, 1) is (2/1, 0, 2/1)

This gradient is a vector that points in the direction of the greatest rate of increase of the function f(x, y, z) = log(x2 + y2 + z2). To evaluate this gradient, the partial derivatives of the function with respect to x, y, and z must be calculated.

The partial derivative of the function with respect to x is (2x / (x2 + y2 + z2)). When x is 1, this simplifies to 2/1. Similarly, the partial derivative with respect to y is 0, and the partial derivative with respect to z is (2z / (x2 + y2 + z2)), which simplifies to 2/1 when z is 1. Therefore, the gradient of f(x, y, z) = log(x2 + y2 + z2) at (1, 0, 1) is (2/1, 0, 2/1).

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Answer:

Your answer is 1 more student.

Step-by-step explanation:

For the class to be held it need 16.25 students.

I got that number by multiplying 25 by .65

Because we can't have .25 of a student, and were talking about the minimum requirement. Having less than 16.25 would mean that we wouldn't have the class, so we need 17 students.

Answer:

Fraction: 97/100

Decimal: 0.97

Percentage: 97%

Step-by-step explanation:

Hope this helped.

97% you just need to substract

The average rate of the given function is 2.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given function is h(x)=-x²-x+5 and the interval is -6≤x≤2.

x={-6, -5, -4, -3, -2, -1, 0, 1, 2}

y=-x²-x+5

When x=-2

y=-(-2)²-(-2)+5

y=-4+4+5

y=5

When x=-1

y=-(-1)²-(-1)+5

y=5

When x=0

y=5

When x=1

y=-1-1+5

y=3

When x=2

y=-(2)²-(2)+5

y=-1

Now, rate using (1, 3) and (2, -1), we get

m =(-1-1)/(2-3)

m=2

Therefore, the average rate of the given function is 2.

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Answer:

E

Step-by-step explanation:

Imagine you cut the figure into two rectangles. This would leave you with a rectangle with the following variables(h=4, w=3, l=9), and a rectangle  with the following variables(H=7, l=3 w=3)

Answer:

the total number of shares in the shelf is 11 and their two white shirts in the shelf so the probability of not choosing a white shirt is the total which is 11 minus the two white shirts which will give you nine

the probability of a particular site is given by the formula

required outcome / sample space and the sample space here is 11.

Therefore, it is 9/11 that is the probability of not choosing a white shirt.

Answer: 565.2cm3

Step-by-step explanation:

The volume of the cone with a height of 6 cm and a base diameter of 6 cm is 169.56 cubic cm.

Suppose that the radius of the considered right circular cone is 'r' units.

And let its height be 'h' units.

Then, its volume is given as:

[tex]V = \dfrac{1}{3} \pi r^3 h \: \rm unit^3[/tex]

The right circular cone is the cone in which the line joining peak of the cone to the center of the base of the circle is perpendicular to the surface of its base.

Given a cone with a height of 6 cm and a base diameter of 6 cm.

r = 3 cm

h = 6 cm

The volume of the cone

[tex]V = \dfrac{1}{3} \pi r^3 h \: \rm unit^3[/tex]

[tex]V = \dfrac{1}{3} \times 3.14 \times3 ^3 \times 6 \: \rm unit^3\\\\V = 3.14\times 54\\\\V = 169.56[/tex]

Therefore, the volume of the cone is 169.56 cubic cm.

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Answer:

So for the first one I got two answer for both actually 1( I got 12 And 120)

2( I got the same 12 and 120) sorry if it ain’t very helpful ;^;

Step-by-step explanation:

Answer:

720°, 2340°, 180°

Step-by-step explanation:

Look at the attached image of a regular hexagon.  I drew all possible lines from a vertex to other vertices (AC, AD, AE).  Drawing in all those diagonals splits the hexagon into 4 triangles, and adding up the measures of all the triangle angles would account for all the interior angles of the hexagon.

♦  Four triangles have an angle sum of 180° x 4 = 720° (180° in each triangle).

See attached image2 to see what happens in an octagon.  There are six triangles formed, so the total of all interior angle measures is 6 x 180° = 1080°.

What about a 15-sided regular polygon?  How many triangles would be formed by putting in all the diagonals coming from one vertex?  There will be 2 fewer triangles than the number of vertices, 13.

♦  The total of interior angle measures in a 15-gon is 13(180°) = 2340°

♦  A polygon with 3 sides is a single triangle; interior angle sum = 180°

The original amount placed in the account is $320.

What is simple interest ?

Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.

The simplest way to compute interest is as a percentage of the principal. For instance, if you borrow $100 from a friend and agree to pay back the money with 5% interest, the interest you would have to pay would simply be 5% of $100, or $5.

Simple Interest is the amount repaid for using the borrowed funds over a predetermined amount of time.

The interest earned is calculated as follows:

I = P*r*t

Where:

I = Interest

P = initial principal balance

r = interest rate

t = time

Marvin is saving money in a savings account with a simple interest rate of r=7.5%=0.075. It's known that after t=12 years, the account had earned $288 interest.

Substituting in the formula:

288 = P*0.075*12

Calculating:

288 = 0.9P

Dividing by 0.9:

P = $320

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Answer:

D I took this today math 6th grade

Step-by-step explanation:

Answer:

Nitrogen is needed for plant growth the energy to grow, and produce fruit or vegetables. Nitrogen is part of the chlorophyll molecule, which gives plants their green color and is involved in creating food for the plant.

With too much nitrogen, plants produce excess biomass, or organic matter, such as stalks and leaves, but not enough root structure.

Plants take nitrogen from the soil by absorption through their roots as amino acids, nitrate ions, nitrite ions, or ammonium ions. Plants do not get their nitrogen directly from the air.From here, various microorganisms convert ammonia to other nitrogen compounds that are easier for plants to use.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The steps in order are: 4, 1,  5, 6, 3, 2

Answer:

Yes

Step-by-step explanation:

I think its yes.I think It's Yes.

Answer:first one .

Step-by-step explanation:

n/a

The condition of the parabola opening upward with a center at and a directrix will be f(x) = 1/32(x - 9)^2 + 19. so alternative D option correct.

What is the equation of the parabola?

The equation can be written as

f(x) = 1/(4p)(x -h)^2 +(k-p)

where (h, k) is the focus, and p is half the distance between focus and directrix.

Here, We have the upward parabola;

Focus at (9,27)

P/2 = 27-19 = 8        Nature of focus

P = 16

so (x-9)^2 = 2py = 32y

y = 1/32(x-9)^2 + 19

The condition of the parabola opening upward with a center at and a directrix will be f(x) = 1/32(x - 9)^2 + 19. so alternative D option correct.

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The graph of the function f(x) = 2x² + 2x - 2 is plotted and attached

The graphs of the function is plotted by making a table of value for a number of the x values and the corresponding y values as done below

Using the function the table is created as f(x) = 2x² + 2x - 2

For x = -4, y =  2 * (-4)² + 2 * (-4) - 2 =  22

For x = -2, y =  2 * (--2)² + 2 * (-2) - 2 =  4

For x = 0, y =  2 * (0)² + 2 * (0) - 2 =  -2

For x = 2, y =  2 * (2)² + 2 * (2) - 2 =  10

For x = 4, y =  2 * (4)² + 2 * (4) - 2 =  38

The table of values

x     y

-4   22

-2   4

0    -2

2     10

4    38

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Answer:

The distance beween the points located 7 and 112 on the number line is -7 i hope this is right

Step-by-step explanation:

Answer: Five Days

Step-by-step explanation:

Isabella can hike 8 miles per day. So:

[tex]\frac{30miles}{8miles} = 3.75 days[/tex]

It will take:

[tex]\frac{70 miles}{8 miles} = 8.75 days[/tex]

..in total to hike 70 miles.

So, subtracting the two values:

[tex]8.75 - 3.75 = 5[/tex]

She still needs to hike five days in order to finish the trail.

Answer:

A≈96.07

Step-by-step explanation:

area of a circle is PiXr^2

Answer:

9

Step-by-step explanation:

27 divided by 3 equal 9

The combined gas law for a gas is discussed below.

Given is the combined gas law.

The ideal combined gas law is given by →

PV = nRT

Where -

{P} = pressure     {T} = temperature     {V} = volume    

{n} = number of moles   {R} = gas constant

Non ideal gases are often modelled by the Van der Waals equation as →

(p + n²a/V²)(V - nb) = nRT

Where -

{a} and {b} = constants for a particular gas

{p} = pressure       {v} = volume    

{n} = number of moles       {t} = temperature  

{R} = gas constant

Therefore, the combined gas law for a gas is discussed above.

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Step one =

-3/4x + 25 -1/8x = 1/8x = 1/8x -3 - 1/8x

-7/8x + 25 = -3

Step two =

-7/8x + 25 - 25 = -3 - 25

-7/8x = -28

Step three =

(8/-7) * (-7/8x) = (8/-7) * (-28)

Answer

X = 32

Answer:

6

Step-by-step explanation:

Since its theoretical, i believe itll be 1/6 x 36 which is 6 times.

hope I helped :)

Answer:

If you were to roll the cube 36 times, theoretically, you would expect that number 1 will be rolled 6 times.

Step-by-step explanation:

The probability of getting a 1 after rolling the number cube is equal to [tex]\frac{1}{6}[/tex]. Now we just multiply the probability by the number of rolls and get...

[tex](\frac{1}{6})(36) = 6[/tex]

Therefore, if we were to roll the cube 36 times, theoretically we would expect that number 1 will be rolled 6 times.

Answer:

D) 4

Step-by-step explanation:

Take the square root of Miriam's starting bacteria to get your answer [tex](\sqrt{16})[/tex]because the exponent in Jessica's equation is the square of Miriam's.

The perimeter expression of a rectangle has a perimeter represented by the expression 4x−8 is 2(2x - 4)

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

Perimeter = 4x - 8

Factor out 2 from the expression

So, we have the following representation

Perimeter = 2 * 2x - 2 * 4

So, we have

Perimeter = 2(2x - 4)

Hence, the perimeter is 2(2x - 4)

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Step-by-step explanation:

5 (18 - y) when y=6

5 (18 - 6)

5 × 18 - 5× 6

90 - 30

60

Answer:

-44

Step-by-step explanation:

7×-5y

7(-2)-5(6)

-14-30

-44

The if __name__ == '__main__' syntax allows a programmer to specify that certain code should only be executed when the script is run directly, rather than when it is imported as a module into another script.

This can be useful for running code that you only want to execute when you're running the script for testing or development, rather than when you're using it as a library in another program. It also allows to use the same code in multiple script without running the main code.

When a Python script is run, the interpreter assigns the name __main__ to the script's global namespace. Therefore, when the script is run directly, __name__ will be set to __main__. When the script is imported as a module into another script, __name__ will be set to the name of the module, rather than __main__.

So, when a programmer uses the if __name__ == '__main__' syntax, they are essentially checking whether the script is being run directly or imported as a module. If the script is being run directly, the code within the if block will be executed. If the script is being imported as a module, the code within the if block will not be executed.

This allows the programmer to separate code that should only be run when the script is executed directly from code that is intended to be used as a library when the script is imported as a module. It also allows to use the same code in multiple script without running the main code.

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Using the linear function given, the tree will have a height of 5.25 feet in 3 years

Linear functions are mathematical functions where the output values are in direct proportion to the input values. A linear function has the form

y = mx + c, where m is the slope of the line and c is the y-intercept.

In this problem, the function given already models y = mx + c

Since y = 3/4x + 3;

The height of the tree in 3 years can be solved as;

y = 3/4(3) + 3

y = 9/4 + 3

y = 5.25

The height of the tree in 3 years is 5.25 feet

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Answer:

Use the Pythagorean Theorem to calculate the length of the sides of a right triangle. A TV cut in half on the diagonal is a right triangle.

a^2 + b^2 = c^2

a is the width of the TV

b is the height of the TV

c is the diagonal size of the TV

a is equal to the length of b plus 15, and c is equal to 75. If we out those values into the formula, we get this:

(b+15)^2 + (b)^2 = (75)^2

Factoring that out, we get:

(b)^2 + 225 + (b)^2 = 5625

Then..

2b^2 = 5625 - 225

2b^2 = 5400

b^2 = 5400/2

b^2 = 2700

b = ✓2700

b = 51.9615242271 (round it to an even 52)

Next, we know that a = b + 15, so a = 67.

Therefore, the width of the TV is 67 inches, the height is 52 inches, the diagonal is 75 inches, and you have a very strangely shaped television with a 1.288 (approximately 5:4) aspect ratio. Older “square” TVs mostly had a 1.33 (4:3) ratio, and new TVs are usually either 16:9 (1.77) or 21:9 (2.33). While it's not impossible that you have an old square TV with a 75 inch diagonal, it's pretty unlikely…

Step-by-step explanation: