Hannah charges an hourly babysitting fee of $6 for two children, $7 for three children, and $8 for four or five children.


Which is true about the table when c = the number of children and f = the fee per hour?



c 1 2 3 4 5
f 6 6 7 8 8




The relationship is not linear between c and f.

The relationship is linear between c and f.

The relationship is not linear for c and linear for f.

The relationship is linear for c but not f.

Well, let us solve this step by step.

We know that Michelle earns 349 plus 3% of the Purchase price. Let us call the Purchase price as P, so that:

Earnings, E = 349 + 0.03 P

So if she earns 8,965 (E = 8,965) so we can find P:

8,965 = 349 + 0.03 P

0.03 P = 8,616

P = $287,200

Michelle's total commission from a house sale was $8,965, from which $349 is a fixed commission. The rest, $8616, represents the 3% of the selling price of the house. By solving the simple equation $8616 = 0.03 * X, we find that the home price is $287,200.

This problem is a simple, but common, practice in the world of linear equations. The first step is to understand that the base commission of $349 is a constant that Michelle earns every time, whilst the remaining part of her commission comes from the 3% percentage of the sale price. After subtracting the base commission from the total commission, we get a value of: $8965 - $349 = $8616. This value is equal to 3% of the house price.

We can express this as: 8616 = 0.03 * X, where X is the value of the house. By isolating X (the house price), we divide both sides by 0.03 to get the house price. Therefore, the home price would be $8616 / 0.03 = $287,200.

https://brainly.com/question/32634451

#SPJ11

A is your anwser. Hope this Helps

a) The three terms have variables m, n, n. The two like terms are the last two terms, which both have variable n: -3n, n.

b) The 5 terms have variables c, c, c, c, -. The like terms are the first four, which all have variable c: c, 2c, c, -5c.

Normal rate: $10/hr

Time and a half= $15/hr

Double pay: $20/hr

Hours to be paid at $10/hr =32 hours

$10/hr x 32hrs= $320

$20/hr x 8hrs= $160

$15/hr x 15hrs=$225

Total gross pay: $705

To calculate your gross base pay for the week working extra hours including a holiday, you need to consider regular pay, overtime pay, and holiday pay. The gross base pay for the week will be $785.00.

To calculate your gross base pay for the week, you need to consider your regular hours, overtime hours, and holiday pay. Here's how you can calculate it:

Therefore, your gross base pay for the week will be $785.00.

https://brainly.com/question/32256486

#SPJ11

To calculate the volume of a solid bounded by two functions, set up an integral in polar coordinates. The volume is found by integrating the difference of the two volumes described by the functions (50 - sqrt(x²+y²) - sqrt(x²+y²)) over r, θ, and z within their appropriate limits.

The subject of the question is mathematics, more specifically, integral calculus in spherical or polar coordinates. Calculating the volume of a solid bounded by two functions can be done by taking the difference of the two function volumes.

The integrals, using polar coordinates (r and θ), are set up as follows:

Volume = ∫∫∫(50 - sqrt(x²+y²) - sqrt(x²+y²)) r dr dθ dz,

where the limits for r are [0, sqrt(50)], for θ are [0, 2π], and for z are [0, 50]. Also, note that 'x²+y²' is replaced with 'r²' because in polar coordinates, 'r' represents the square root of x^2 plus y^2.

This integral, when solved, gives the volume of the ice cream cone-shaped solid.

https://brainly.com/question/32822827

#SPJ12

The volume of the ice cream shaped solid can be found by converting the limits of the cone to polar coordinates and performing a double integral. The limits of the cone are represented by the expressions z = r and z = sqrt(50 - r^2). The volume integral will be ∫ _(theta=0 to 2*pi) ∫ _(r=0 to sqrt(50)) [(sqrt(50 - r^2)) - r] r dr dθ.

To evaluate the volume of the solid resembling an ice cream cone, we can use the method of double integration in polar coordinates. Because we're dealing with a cone, polar coordinates are suitable as they're related to circular symmetry.

The limits of the cone are given by the functions z = sqrt(x^2 + y^2) and z = sqrt(50 - x^2 - y^2). In polar coordinates these become z = r and z = sqrt(50 - r^2).

To evaluate the volume of the cone, we need to subtract the volume of the lower cone (given by z = r) from the volume of the upper cone (given by z = sqrt(50 - r^2)). We convert the values to polar coordinates and use double integration as follows:

V = ∫ _(theta=0 to 2*pi) ∫ _(r=0 to sqrt(50)) [(sqrt(50 - r^2)) - r] r dr dθ

This integral, once solved, will give the volume of the ice cream shaped solid.

https://brainly.com/question/32065747

#SPJ11

2:9 means for every 2 men there are 9 women

36/9 =4

4*2 = 8

 there are 8 men

Answer:

Option 3 -   [tex]0.45\times2.3= 1.035[/tex]

Step-by-step explanation:

To find : Which number sentence shows the correct placement of the decimal point in the product, based on the two factors?

Solution :

The correct placement of decimal in product is based on the number of digits after decimals as the number of digits after decimal of one number added to number of digits after decimal of second number is the required place in the result a decimal place.

1) [tex]7.98\times 45.67 = 3,644.466[/tex]

Not correct, decimals are 4 so place after 4 numbers.

2) [tex]12.3\times3.8= 467.4[/tex]

Not correct, decimals are 2 so place after 2 numbers.

3) [tex]0.45\times2.3= 1.035[/tex]

Correct, decimals are 3 so place after 3 numbers.

4) [tex]14.22\times2.8= 398.16[/tex]

Not correct, decimals are 3 so place after 3 numbers.

Therefore, option 3 is correct.

Final answer:

The second partial derivatives of v = e⁵x * ey are ∂²v/∂x² = 25e⁵x * ey and ∂²v/∂x² = 5e⁵x * e^y.

Explanation:

To find the second partial derivatives of the function v = e⁵x * ey, we need to differentiate twice with respect to x and y. Let's start with the first partial derivative with respect to x:

∂v/∂x = ∂(e⁵x * ey)/∂x

= 5e⁵x * ey

Next, we differentiate the first partial derivative with respect to x to find the second partial derivative with respect to x:

∂²v/∂x² = ∂(5e⁵x * ey)/∂x

= 25e⁵x * ey

Similarly, the second partial derivative with respect to y is:

∂²v/∂x² = ∂(5e⁵x * ey)/∂y

= 5e⁵x * e^y

negative 2 is where it crosses

Answer:

Sues problem would be - 8×3,209 :8×3,209

A parallelogram, the opposite sides have equal slopes.

To graph the parallelogram ABCD on a coordinate plane, we can plot the given points A(3,4), B(6,1), C(0,-2), and D(-3,1), and then connect them in order to form the parallelogram.

Here are the steps to find the slope of each side:

Plot the Points:

Plot the points A(3,4), B(6,1), C(0,-2), and D(-3,1) on the coordinate plane.

Connect the Points:

Connect the points in order (A to B to C to D to A) to form the parallelogram.

Find the Slope:

The slope of a line passing through two points

(x_1 ,y_1 ) and (x_2 ,y_2 ) is given by the formula m= y_2 -y_1/ x_2- x_1

​Calculate the slope for each pair of consecutive points:

Slope of AB: mAB​ = 1−4/6−3

​Slope of BC: mBC = −2−1/0−6

​Slope of CD: mCD = 1−(−2)/−3−0

​Slope of DA: mDA = 4−1/ 3−(−3)

​Now, observe the slopes:

mAB  and mCD

​are the slopes of opposite sides. They should be equal for a parallelogram.

mBC and mDA are the slopes of the other pair of opposite sides. They should also be equal for a parallelogram.

So, for a parallelogram, the opposite sides have equal slopes.

To estimate the error in the hypotenuse length of a right triangle using differentials, we use the trigonometric identity sin(θ) = opposite/hypotenuse, finding the derivative, and then apply the angle error to get an error estimate of
±0.31 cm in the hypotenuse length.

The question asks to use differentials to estimate the error in computing the length of the hypotenuse of a right triangle when one side is 9 cm and the opposite angle is 30° with a possible error of ±1°. To calculate the hypotenuse (c) when dealing with problems involving right triangles, you can use the trigonometric identity sin(θ) = opposite/hypotenuse, which can be rearranged to c = opposite/sin(θ). The differential of c with respect to θ is dc/dθ = -opposite * cos(θ)/sin2(θ). Given that the opposite side is 9 cm and the angle θ is 30°, we can find dc/dθ and then multiply by the possible angle error of ±1° to estimate the error in the hypotenuse length.

Plugging in the given values and converting the angle to radians (since the derivative is taken with respect to radians), we find

dc/dθ ≈ -9 cm × cos(30°)/sin2(30°) ≈ -18 cm.

The possible change in angle is ±1°, which in radians is approximately ±0.0175 radians, thus

Estimated error in hypotenuse ≈ -18 cm × ±0.0175 ≈ ±0.315 cm.

Therefore, the estimated error in the length of the hypotenuse, rounded to two decimal places, is ±0.31 cm.

The unit price of Starbucks Coffee, when 0.5 lb costs $6.48, is calculated by dividing the total cost by the pounds, resulting in $12.96 per pound.

If 0.5 lb of Starbucks Coffee costs $6.48, to find the unit price for Starbucks Coffee, we perform a simple division. You want to know how much 1 lb would cost, given that 0.5 lb costs $6.48. To do this, you divide the total cost by the number of pounds.

$6.48 ÷ 0.5 = $12.96 per pound

This means that the unit price of Starbucks Coffee, when given a price of $6.48 for a half-pound, is $12.96 per pound. This calculation is crucial in understanding how to break down costs into more manageable, standard units, making price comparisons easier and more straightforward.

The missing side length of the second triangle is 8.

To find the missing side length of the second triangle, we can use the property that similar triangles have proportional side lengths.

Given:

First triangle: ( 3, 4, 5 )

Second triangle: ( 6, x, 10 )

Since the triangles are similar, the ratios of corresponding sides are equal:

[tex]\[ \frac{6}{3} = \frac{x}{4} = \frac{10}{5} \][/tex]

From the first ratio, [tex]\( \frac{6}{3} = \frac{x}{4} \)[/tex], cross multiply:

[tex]\[ 6 \times 4 = 3 \times x \][/tex]

[tex]\[ 24 = 3x \][/tex]

Divide both sides by 3 to solve for ( x ):

[tex]\[ x = \frac{24}{3} \][/tex]

[tex]\[ x = 8 \][/tex]

So, the missing side length of the second triangle is 8.

Here's a detailed calculation step-by-step:

1. Set up the ratios of corresponding sides: [tex]\( \frac{6}{3} = \frac{x}{4} = \frac{10}{5} \).[/tex]

2. Use the first ratio to find [tex]\( x \): \( 6 \times 4 = 3 \times x \)[/tex].

3. Solve for [tex]\( x \): \( 24 = 3x \)[/tex].

4. Divide both sides by 3: [tex]\( x = \frac{24}{3} = 8 \)[/tex].

5. Therefore, the missing side length of the second triangle is 8.

Complete Question:

Two triangles have side lengths 3, 4, 5 and 6, _____, 10, respectively. The triangles are similar to each other. Find the missing side of the triangle.