300/15 gallons. Find the unit rate

Answer:

sorry I don't know sis ☹️

Answer:

You can ask your school guidance counselor, a parent, or trusted adult. You can ask them by telling them what is going on and let them tell you what to do. You should thank them too because they helped you with a problem that you have.

Answer:

Triangle DEF was dilated according to the rule DO,One-third(x,y)(one-third x, one-third y) to create similar triangle D'E'F'.

 On a coordinate plane, (0, 0) is the center of dilation. Triangle F D E is dilated to create smaller triangle F prime D prime E prime. Triangle F D E has points (negative 9, 3), (negative 9, 9), (negative 6, 6). Triangle F prime D prime E prime has points (negative 3, 1), (negative 3, 3), and (negative 2, 2).

Which statements are true? Select three options.

right answer   ∠F corresponds to ∠F'.  

wrong answer Segment EE' is parallel to segment FF'.

right answer The distance from point D' to the origin is One-third the distance of point D to the origin.

wrong answer The measure of ∠E' is One-third the measure of ∠E.

right answer△DEF △D'E'F'

Step-by-step explanation:

Answer:

A, C, E

Step-by-step explanation:

EDU

Basis for R^3 = {(1, 0, 2), (0, 1, 1), (2, -1, 1)}

To find a basis for R^3 that includes the vectors (1, 0, 2) and (0, 1, 1), we need to find a third vector that is linearly independent from these two vectors. Here's a step-by-step explanation:

Step 1: Write down the given vectors.
Vector A = (1, 0, 2)
Vector B = (0, 1, 1)

Step 2: Find a third vector C that is linearly independent from A and B.
To do this, let's take the cross product of A and B:

Vector C = A x B = (1, 0, 2) x (0, 1, 1) = (2, -1, 1)

Step 3: Verify that vector C is linearly independent from A and B.
Check if there is no scalar combination of A and B that can form C:

a * A + b * B = C, where a and b are scalars.

If there is no solution for a and b, the vectors A, B, and C are linearly independent.

In this case, there is no solution for a and b that would give us the vector C, so A, B, and C are linearly independent.

Step 4: Form the basis for R^3 using vectors A, B, and C:

Basis for R^3 = {(1, 0, 2), (0, 1, 1), (2, -1, 1)}

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Answer: a prediction of the number of hot cocoas sold when the temperature is 0F

Step-by-step explanation: i did it on delta math

The line's y-intercept represent ''Number of hot cocoas sold''.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Chloe has a part-time job at an ice skating rink selling hot cocoa.

She decided to plot the number of hot cocoas she sold relative to the day's high temperature and then draw the line of best fit.

Now,

Since, She decided to plot the number of hot cocoas she sold relative to the day's high temperature and then draw the line of best fit.

Hence, By the graph we have;

The line's x - intercept represent ''Temperature''.

And, The line's y-intercept represent ''Number of hot cocoas sold''.

Thus, The line's y-intercept represent ''Number of hot cocoas sold''.

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Answer: 169.2cm

Step-by-step explanation:

From the question, we are informed that three equal-sized cardboard boxes are stacked on top of each other and that each box is 56.4 cm in height.

To get the combined height of the 3 stacked boxes, we multiply 56.4cm by 3. This will be:

= 56.4cm × 3

= 169.2cm

Answer:

slope is 2

Step-by-step explanation:

-11-(-1) =-10

4-9=-5

-10/-5

=2

Slope-2x

The area of a rhombus can be found by multiplying the length of one of its sides by the height of a perpendicular line from the center to a side.

The height of the rhombus is the distance from the center of the rhombus to one of its sides, perpendicular to that side.

The formula for the area of a rhombus can be written as A = s*h, where A is the area, s is the length of one of the sides of the rhombus, and h is the height of the rhombus.

It's important to note that this method of finding the area of a rhombus without diagonals can only be used when the rhombus is a regular polygon, a polygon with all sides and angles congruent. When the rhombus is not a regular polygon, then you can find the area by using the diagonals.

Additionally, it's important to mention that a rhombus can be defined as a parallelogram with all sides congruent or a square with its angles not 90 degrees.

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The price that maximizes revenue is p = 120.

The price that maximizes revenue, we need to find the value of price (p) that corresponds to the maximum value of revenue (R). Revenue is calculated by multiplying the quantity (q) sold by the price (p), so we can express revenue as R = p × q.

Given the demand function q = -5p + 1200, we can substitute this expression for q into the revenue equation:

R = p × q

R = p × (-5p + 1200)

To find the price that maximizes revenue, we can take the derivative of the revenue function with respect to price (p), set it equal to zero, and solve for p.

dR/dp = -10p + 1200 = 0

Solving this equation for p:

-10p + 1200 = 0

-10p = -1200

p = -1200 / -10

p = 120

Therefore, the price that maximizes revenue is p = 120.

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Answer:

Step-by-step explanation:

Converting to decimal (nearest hundredth if needed)

Hey there!

Convert to decimals,

1/4 = 0.25

1/5 = 0.20

1/2 = 0.50

1/9 = 0.11

2/11​ = 0.18

Greatest to least = 1/2 > 1/4 > 1/5 > 2/11 > 1/9.

Greatest = 1/2

Least = 1/9

Hope this helps ya!

In the event that linear regression is required, we have two options: (1) change the delay column 2) ignore them.

A variable's value can be predicted using linear regression analysis based on the value of another variable. The dependent variable is the one you want to be able to forecast. The independent variable is the one you're using to make a prediction about the value of the other variable.

Given,

You want to run a regression to predict the probability of a flight delay, but there are flights with delays of up to 12 hours that are really messing up your model.

I immediately think of grouping delays into ranges such as those under 40 minutes, those between 40 minutes and 2 hours, those between 2 hours and 10 hours, and those above 10 hours. But doing so requires the use of a classification model, such as logistic regression. We frequently consider whether there will be a delay rather than how long it might last when thinking about delays. In the event that linear regression is required, we have two options: (1) change the delay column 2) ignore them.

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Answer:

Answer: 27:8

Step-by-step explanation:

There are 24 + 16 + 14 = 24+16+14= 54

54 marbles in total.

The ratio of total marbles to red marbles is 54 : 16, which simplifies to 27 : 8.

Answer: 27:8

Answer:

My reasonable answer would be that it was a translation and then dilation

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

B. \(\frac{x^2}{3^2} +\frac{y^3}{2^2} =1\)

Step-by-step explanation:

The equation of the osculating plane is 24x + 12√10(y-π) - 3z - 6π√10 = 0.

Given curve,  x=5sin(3t), y=t, z=5cos(3t); (0, π,-5).

To find the normal plane equation, the unit normal vector of the curve at the point must first be found. The unit tangent and unit binormal vectors are both derived from the unit tangent vector.

To calculate the tangent vector, the following steps are taken:

Equation of the curve is given as,

x=5sin(3t),

y=t,

z=5cos(3t).

Differentiating above equation with respect to t, we get;

dx/dt = 15 cos(3t)

dy/dt = 1

dz/dt = -15 sin(3t)

The unit tangent vector T is given by,

T = 1/√(dx/dt² + dy/dt² + dz/dt²) (dx/dt i + dy/dt j + dz/dt k)

Substituting the given values, we get

T = (3√10/10) i + (1/√10) j - (3/√10) k

Since we have to find the normal vector, we will differentiate the unit tangent vector,T, to get the unit normal vector N.

Let's differentiate T to obtain N:

dn/dt = 1/√(dx/dt² + dy/dt² + dz/dt²) [d²x/dt² i + d²y/dt² j + d²z/dt² k] + {(-1/2)(2t)(2t')/√(dx/dt² + dy/dt² + dz/dt²)³} [dx/dt i + dy/dt j + dz/dt k]

On substituting, we get,

N = (-9/√10) i + (3√10/10) j + (9/√10) k

Therefore, the normal plane equation is given by,(-9/√10)(x) + (3√10/10)(y-π) + (9/√10)(z+5) = 0.

To find the osculating plane equation, the coordinates of the point of tangency (P) and the principal normal vector, N, are required.

The equation of the osculating plane is then written as follows:

xT + yN = c,

where c is a constant value that is calculated by substituting the coordinates of P into the equation.Let us calculate the value of P and N,

To find the value of P, we substitute t=π in the given curve,

Thus,

x(π) = 5sin(3π) = 0,y(π) = π,z(π) = 5cos(3π) = -5

Therefore, the point of tangency P is (0, π, -5).

From the above derivation, we know that the unit normal vector N is(-9/√10) i + (3√10/10) j + (9/√10) k

Therefore, the unit principal normal vector is given by,

B = T x N= [(3√10/10) i + (1/√10) j - (3/√10) k] x [- (9/√10) i + (3√10/10) j + (9/√10) k]

= [(3√10/10) (9/√10) + (3/√10) (3/√10)] i + [(9/√10) (1/√10) - (3√10/10) (- 3/√10)] j + [(1/√10) (- 3/√10) - (3√10/10) (3√10/10)] k

= (24/√10) i + (12√10/10) j - (3/√10) k

The osculating plane equation is given by,

xT + yB = c

Now substituting x=0, y=π and z=-5 in above equation, we get

c = π(12√10/10) = (6π√10/5)

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Angle 4 and 7= Interior angles

Angle 12 and 16= Corresponding angles

Angle 1 and 14= Alternate exterior angles

Angle 5 and 10=Alternate angles

angle 6 and 7 are alternate angles I think.

The (g·g)(t) of the function is (g·g)(t) = 16t - 15

A function is an expression, rule, or law that defines a relationship between an independent variable and a dependent variable

Since g(t) = -4t + 5

What (g·g)(t) means is that you should replace t with the value of g(t)  (i.e. -4t + 5) in the same equation. That is:

(g·g)(t) = g(g(t))

(g·g)(t) = -4(-4t + 5) + 5

(g·g)(t) = 16t - 20 + 5

(g·g)(t) = 16t - 15

Thus, the value of g·g)(t) is 16t - 15

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first of all let's check how much each one had when it was 5:8 hmmm well, the total amount was $221, let's divide that by (5 + 8) and distribute accordingly to each.

\(\stackrel{Steve}{5\cdot \cfrac{221}{5+8}} ~~ : ~~ \stackrel{Marion}{8\cdot \cfrac{221}{5+8}}\implies \stackrel{Steve}{5\cdot 17} ~~ : ~~ \stackrel{Marion}{8\cdot 17}\implies \stackrel{Steve}{85} ~~ : ~~ \stackrel{Marion}{136}\)

then Steve got 11 bucks more, so he's got now 85 + 11, so

\(\cfrac{\stackrel{Steve}{85~~ + ~~11}}{\underset{Marion}{136}}\implies \cfrac{\stackrel{Steve}{96}}{\underset{Marion}{136}}\implies \cfrac{8\cdot 12}{8\cdot 17}\implies \cfrac{8}{8}\cdot \cfrac{12}{17}\implies 1\cdot \cfrac{12}{17}~\hfill \boxed{\stackrel{Steve}{12}:\stackrel{Marion}{17}}\)

Answer:

Step-by-step explanation:

Firstly, Steve and Marlon shared 221 dollars and their ratio is 5:8

Since a every sector in the ratio is worth the same. We can do 221 / (5+8) and that means we can figure out that every sector in 221 dollars is worth $17.

Currently, Steve then has $17 * 5 = $85. And Marlon has $17 * 8 = $136.

In the second half of the question it says Steve has been given $11 more.  So Steve now has $85 + $11 which is $96.

So the ratio is 96 : 136 but we have to simplify the ratio to get it first.

The highest common factor (HCF) between them is 8 so the simplified ratio is 96/8 : 136/8 which is 12 : 17

The correct answer would be 12 : 17.

The volume of a chlorine atom is approximately 1.5376×10^(-24) cubic centimeters. The volume of a cube can be calculated using the formula V = L × W × H, where L, W, and H represent the lengths of the three sides of the cube.

In this case, the edge length of the cube is given as 4.50×10^(-3) cm. Since a cube has equal sides, we can substitute this value for L, W, and H in the formula.

V = (4.50×10^(-3) cm) × (4.50×10^(-3) cm) × (4.50×10^(-3) cm)

Simplifying the calculation:

V = (4.50 × 4.50 × 4.50) × (10^(-3) cm × 10^(-3) cm × 10^(-3) cm)

V = 91.125 × 10^(-9) cm³

Therefore, the volume of the cube is 91.125 × 10^(-9) cubic centimeters.

Moving on to the second part of the question, the volume of a spherical object, such as an atom, can be calculated using the formula V = (4/3) × π × r^3, where r is the radius of the sphere. In this case, the radius of the chlorine atom is given as 1.05×10^(-8) cm.

V = (4/3) × π × (1.05×10^(-8) cm)^3

Simplifying the calculation:

V = (4/3) × π × (1.157625×10^(-24) cm³)

V ≈ 1.5376×10^(-24) cm³

Therefore, the volume of a chlorine atom is approximately 1.5376×10^(-24) cubic centimeters.

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The percentage of Country A women weigh between 110 and 200 pounds is 80%.

The percentage is the value of one quantity compared to a larger quantity.

The percentage is the quotient multiplied by 100.

Five-number summary for the weights of women in Country A = 100, 110, 120, 160, 200

The class value of women who weigh between 110 and 200 pounds = 4

The class value of women who weight less than between 110 and 200 pounds = 1

The ratio of women who weight between between 110 and 200 pounds and those who weigh less is 4:1

The sum of ratios = 5 (4 + 1)

The percentage of women weighing between between 110 and 200 pounds = 80% (4/5 x 100).

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The area of the surface obtained by rotating the curve x = 8 cos³(θ), y = 8 sin³(θ), 0 ≤ θ ≤ π/2, about the y-axis is 32π/3 square units.

To find the area of the surface obtained by rotating the curve about the y-axis, we can use the formula for surface area of revolution. The formula is given by:

A = 2π∫[a, b] x × √(1 + (dx/dy)²) dy,

where [a, b] is the interval of integration along the y-axis.

Let's start by finding the expression for dx/dy:

x = 8 cos³(θ)

dx/dθ = -24 cos²(θ)sin(θ)

dx/dy = (dx/dθ) / (dy/dθ)

y = 8 sin³(θ)

dy/dθ = 24 sin²(θ)cos(θ)

dx/dy = (-24 cos²(θ)sin(θ)) / (24 sin²(θ)cos(θ))

= - cos(θ) / sin(θ)

= -cot(θ)

Now, we need to determine the interval of integration, [a, b], which corresponds to the given range of θ, 0 ≤ θ ≤ π/2. In this range, sin(θ) and cos(θ) are always positive, so we can express the interval as [0, π/2].

Using the given information, the formula for the surface area of revolution becomes:

A = 2π∫[0, π/2] (8 cos³(θ)) × √(1 + (-cot(θ))²) dy

= 16π∫[0, π/2] cos³(θ) × √(1 + cot²(θ)) dy

To simplify the integral, we can use the trigonometric identity: 1 + cot²(θ) = csc²(θ).

A = 16π∫[0, π/2] cos³(θ) × √(csc²(θ)) dy

= 16π∫[0, π/2] cos³(θ) × csc(θ) dy

Now, let's proceed with the integration:

A = 16π∫[0, π/2] (cos³(θ) / sin(θ)) dy

To simplify further, we can express the integral in terms of θ instead of y:

A = 16π∫[0, π/2] (cos³(θ) / sin(θ)) (dy/dθ) dθ

= 16π∫[0, π/2] cos³(θ) dθ

Now, we need to evaluate this integral:

A = 16π∫[0, π/2] cos³(θ) dθ

This integral can be solved using various methods, such as integration by parts or trigonometric identities. Let's use the reduction formula to evaluate it:

\(∫ cos^n(θ) dθ = (1/n) × cos^(n-1)(θ) × sin(θ) + [(n-1)/n] × ∫ cos^(n-2)(θ) dθ\)

Applying this formula to our integral, we have:

\(A = 16π * [(1/3) * cos^2(θ) * sin(θ) + (2/3) * ∫ cos(θ) dθ]\\= 16π * [(1/3) * cos^2(θ) * sin(θ) + (2/3) * sin(θ)]

\)

Now, let's evaluate the definite integral

for the given range [0, π/2]:

\(A = 16π * [(1/3) * cos^2(π/2) * sin(π/2) + (2/3) * sin(π/2)] \\= 16π * [(1/3) * 0 * 1 + (2/3) * 1]\\= 16π * (2/3)\\= 32π/3\)

Therefore, the area of the surface obtained by rotating the curve x = 8 cos³(θ), y = 8 sin³(θ), 0 ≤ θ ≤ π/2, about the y-axis is 32π/3 square units.

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Answer:

Step-by-step explanation:

The iota is a complex notation represented by the letter i in complex number.

iota power 2 can also be written as;

i^2

In complex number, the square root of -1 is iota. This can be expressed as;

\(\sqrt{-1} = i\)

Take the square of both sides

\((\sqrt{-1})^2 = i^2\\-1 = i^2\\Rearrange\\i^2 = -1\)

Hence the iota power 2 is equal to ​-1

Answer:

Yes

Step-by-step explanation:

The difference of 18 and 3 is 15 which can be expressed as fraction, so its a rational number.

Answer:

Yes, it is a rational number.

Step-by-step explanation:

A rational number is a number that can be expressed in fractional form. A rational number consists of:

Since the difference of 18 and 3 is 15 and the number 15 can be expressed as 15/1. Therefore, 15 or the difference of 18 and 3 is a rational number.

The dimensions of the printed area  is: 200 cm x 120 cm

Total area of the printed area is:

A = (l + 20) (w + 12)

where l and w is the length and width of the printed area

3480 = (l + 20) (w + 12)

l = [3480/(w + 12)] – 20

The printed area is simply:

a = l w

substituting l:

a = ([ 3840/(w + 12)] – 20) w

a = ( 3840w)(w + 12)^-1 – 20 w

Taking the first derivative da/dw:

da/dw = ( 3840)(w + 12)^-1 - ( 3840w)(w + 12)^-2 – 20

Set da/dw = 0:

( 3840)/(w + 12) - ( 3840w)/(w + 12)^2 – 20 = 0

Multiply everything by (w + 12)^2:

3840 (w + 12) –  3840w - 20(w + 12)^2 = 0

3840w + 288000 – 3840w – 20 (w^2 + 24w + 144) = 0

-20 w^2 – 480 w + 285120 = 0

w^2 + 24 w = 14256

Completing the square:

(w + 12)^2 = 14256 + 12^2

w + 12 = ±120

w = 108 cm

l = [ 3840/(w + 12)] – 20

l = [ 3840/(108 + 12)] – 20

l = 180 cm

Therefore the dimensions of the whole poster are:

w + 12 = 120 cm

l + 20 = 200 cm

The poster should be 200 cm x 120 cm

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Step-by-step explanation:

we simply need to get the total distance and the total time and put them into relation, norming it to distance in 1 hour. after all, speed is always an average number over a period of time (even if it is a tiny period of time).

the total distance is

72 + 69 = 141 km

he drove 69 km going 60 km/h.

how much time did he need ?

we need to get the hours out of an expression of km and h.

so, we need to do

69 km × 1/60 km/h = 69 h / 60 = 69 minutes = 1.15 hours =

= 1 h 9 minutes

so, the total time was

48 + 69 = 117 minutes = 117/60 = 1.95 hours

the average speed for the whole trip was then

141 km / 1.95 h = 141/1.95 km / 1 h = 72.30769231... km/h

Answer: 17 boxes

Step-by-step explanation: 53-2=51 (subtract 2 from 53 as they are left at home)

51/3=17 ( divide by 3 as one box contains 3 lemon cupcakes)

so the answer is 17 boxes