Nature's Squeeze is a drink stand known for its fresh-squeezed juices. Colin just got his first job working there! During his training, he made 4 drinks in 12 minutes. Today is Colin's first shift, and he will work for 90 minutes.
If Colin makes drinks at the same rate, how many drinks will he make today?

Chenelle can travel at most 160 miles without exceeding her spending limit of $300.

We have,

To determine the maximum number of miles Chenelle can travel without exceeding her spending limit of $300, we need to subtract the flat rate from her budget and divide the remaining amount by the cost per mile.

So,

Subtract the flat rate from Chenelle's budget:

Budget after subtracting the flat rate.

= $300 - $19.95

= $280.05

Divide the remaining budget by the cost per mile to find the maximum number of miles:

Maximum miles = Budget after subtracting the flat rate / Cost per mile

= $280.05 / $1.75

Using division.

Maximum miles = 160.028571

Therefore,

Chenelle can travel at most 160 miles without exceeding her spending limit of $300.

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The Solution:

Representing the given in a diagram, we have

By similarity theorem, we have that:

So,

Substituting these values in the formula above, we get

Solving for x:

We shall cross multiply,

Dividing both sides by o.21, we get

The height of the tower is

Therefore, the correct answer is 138 meters.

Answer:

The equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) is y = (-4/5)x + (8/5) + π.

Step-by-step explanation:

o find the equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) using implicit differentiation, we can follow these steps:

Differentiate both sides of the equation with respect to x:

cos(x+y) * (1 + dy/dx) = 4 - 4dy/dx

Simplify by grouping the terms with dy/dx on one side and the rest on the other side:

cos(x+y) * (1 + dy/dx) + 4dy/dx = 4

Substitute x = π and y = π, since we want to find the equation of the tangent line at the point (π,π):

cos(2π) * (1 + dy/dx) + 4dy/dx = 4

Simplify:

-5dy/dx = 4 - cos(2π)

dy/dx = -4/5

Use the point-slope form of the equation of a line to write the equation of the tangent line:

y - π = (-4/5)(x - π)

Simplify:

y = (-4/5)x + (8/5) + π

The equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) is y = (-4/5)x + (8/5) + π.

The whole given data sets can have their median calculated after being arranged either in an ascending or descending order. That is option A,B,C,D and E.

The median of a data set is defined as the data that is found at the center, otherwise known as the measure of center of a data set, after being arranged in ascending or descending order.

For example the median of option A) is calculated as follows:

Data set= 23,62,68,73,75,77

Median = 68+73/2 = 70.5

Therefore the median is between 68 and 73 which is = 70.5

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Answer:

he is an ordinary man because that is what the speaker is talking about

Answer:

The story develops the character of the speaker's father to keep things simple by not do anything extraordinary, not to compare himself to other fathers, is a devoted father on his devoted job, and is not judged by the community how or what he does in his job or the speaker.

Answer:

Based on the information given, we know that angles 3 and 4 are supplementary (they add up to 180 degrees) and angles 2 and 4 are vertical angles (they are congruent). Therefore, we can write:

m∠4 + m∠3 = 180 (since angles 3 and 4 are supplementary)

m∠4 = m∠2 (since angles 2 and 4 are vertical angles)

Substituting m∠4 = m∠2 into the first equation, we get:

m∠2 + m∠3 = 180

Now we can solve for m∠2 and m∠3:

m∠3 = 43 (given)

m∠2 = 180 - m∠3 = 180 - 43 = 137

Since angles 1 and 2 are also supplementary, we can find m∠1 by subtracting m∠2 from 180:

m∠1 = 180 - m∠2 = 180 - 137 = 43

Therefore, m∠1 = 43 degrees and m∠2 = 137 degrees.

Answer:

47.06%

Explanation:

First, let's calculate the number of miles that Hannah has driven. So:

680 miles - 360 miles = 320 miles

Now, to know what percent represents 320 miles, we need to divide this quantity by the total number of miles and then multiply by 100, so:

Therefore, she has driven 47.06% of the trip.

Answer:

this is a trick question. the answer is most likely just 16 lol

Answer:

Is the answer 15, if not please comment. Thank you....

Answer:

x=-4 is true, x=6 is not

Step-by-step explanation:

5x + 7 < 22

Plug in our X values

5(-4) + 7 < 22 ?

solve

-20 + 7 < 22

-13 < 22 ?

x=-4 is true.

Repeat steps from ^

5(6) + 7 < 22

30 + 7 < 22

37 < 22 ?

x=6 is not true.

Hope this helped

Answer:

False

Step-by-step explanation:

5(-4) + 7 < 22

-20 + 7 < 22

-14 < 22

5(6) + 7 < 22

30 + 7 < 22

37 < 22

The statement would be false because when applying 6 to the equation, the equation becomes false.

On the other hand, when applying -4 to the equation, the equation becomes true, but since both -4 and 6 HAVE to be BOTH solutions to the equation, the statement becomes false.

Answer:

\(21.7 x 10^5\)

Step-by-step explanation:

(6.2 x 10²) x (3.5 x 10³)

First, multiply the coefficients: 6.2 x 3.5 = 21.7.

Then, add the exponents: 10² x 10³ = 10^(2+3) = 10^5.

Therefore, the result is 21.7 x 10^5.

Answer:

3286000

Step-by-step explanation:

The simplification of the given expression results as √5K/3.

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

The given expression is √10K²/√18k.

It can be evaluated as follows,

Write √10 and √18 in terms of prime factors as,

√10 = √(5 × 2)

And, √18 = √(3 × 3 × 2) = 3√2

Plug these values in the given expression to obtain,

⇒ √10K²/√18k

⇒  √(5 × 2)K²/3√2K

⇒ √5K/3

Hence, the given expression can be simplified as √5K/3.

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The surface area of cube and rectangular prism is 384 sq. cm and 100 sq. cm respectively.

The surface area of an object refers to the overall space filled by its surfaces. Different 3D shapes in geometry have various surface areas, which may be quickly estimated using the formulas we shall learn in this lesson. Two categories are used to classify the surface area:

Curved surface area or Lateral surface area

Surface area in total

The surface area of the cube is given as:

SA = 6s²

Substitute the value of s= 8:

SA = 6(8)²

SA = 384 sq. cm

The surface area of the rectangular prism is given by:

SA = 2(lw) + 2(wh) + 2(hl)

Substitute the value of l = 7, w = 2 and h = 4.

SA = 2(7)(2) + 2(2)(4) + 2(4)(7)

SA = 28 + 16 + 56

SA = 100 sq. cm

Hence, the surface area of cube and rectangular prism is 384 sq. cm and 100 sq. cm respectively.

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In multiple regression problem with two independent variables, value of one varible , b₁ is 2 then it means that the estimated mean of Y increases by 2 units for each increase of 1 unit of X₁, holding X₂ constant. So, second option is correct option.

Multiple Regression: Multiple regression is a statistical technique that can be used to analyze the relationship between a single dependent variable and multiple independent variables. The goal of multiple regression analysis is to use independent variables with known values to predict the value of each dependent value.

Y = b₁x₁+ b₂x₂ + … bₙxₙ + a

Here Y is the dependent variable, and X₁,…,Xₙ are the n independent variables. In calculating the weights, a, b₁,…,bₙ,

In the multiple regression b1 shows the coeffcient of independent variable X₁ in fitted model.

Here b₁ =+2.0 shows that for each unit increase in X₁, dependent variable Y is increased by 2 keeping other things constant.

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Answer:

93%

Step-by-step explanation:

651/700 houses were for sale. Write that as a percentage.

651/700=0.93

0.93=93%

Answer:

7 units

Step-by-step explanation:

Answer:

37.7 feet

Step-by-step explanation:

The circumference of a circle can be calculated using the formula: Circumference = 2 * π * radius, where π (pi) is approximately 3.14159.

For example, if we have a circle with a radius of 3 feet, its circumference would be approximately 18.85 feet (rounded to five decimal places).

When we double the radius to 6 feet, the circumference also doubles. In this case, the circumference would be approximately 37.70 feet (rounded to five decimal places).

In summary, when the radius of a circle doubles, the circumference also doubles, maintaining a direct proportional relationship between the two measurements.

Answer:

10

Step-by-step explanation:

∠X = 89°, ∠Y = 90°, ∠Z = 40° ∠X+∠Z=180---------> ∠X=180-∠Z-----> ∠X=180-40°----> ∠X=140°

→ (2b+6)+(3b-1)=90----> 5b+5=90----> 5b=85----> b=17°

→ ∠Z=2b+6---- 2*17+6-----> ∠Z=40°

→ ∠Y=3b-1---> ∠Y=3*17-1---> ∠Y=50°

angle Y and W are supplementary angles

so

→ ∠Y+∠W=180---------> ∠W=180-∠Y------> ∠W=180-50----> ∠W=130°

angle X and Z are supplementary angles

so

→ ∠X+∠Z=180---------> ∠X=180-∠Z-----> ∠X=180-40°----> ∠X=140°

Therefore, the answer is

There are a total of 8 color-wheel size combinations for the kickboard scooter. This means that customers have 8 different options to choose from when selecting the color and wheel size for their scooter.

To determine the total number of color-wheel size combinations for the kickboard scooter, we need to multiply the number of color options by the number of wheel size options.

Given that there are 4 color options (silver, red, blue, and purple) and 2 wheel size options (125mm and 180mm), we can use the multiplication principle to find the total number of combinations:

Total combinations = Number of color options × Number of wheel size options

Total combinations = 4 colors × 2 wheel sizes

Total combinations = 8

There are a total of 8 color-wheel size combinations for the kickboard scooter. This means that customers have 8 different options to choose from when selecting the color and wheel size for their scooter.

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Answer:

942 square millimeters.

Step-by-step explanation:

The formula for the surface area of a cylinder is:

S = 2πr^2 + 2πrh

where S is the surface area, r is the radius, and h is the height.

Substituting the given values, we get:

S = 2 x 3.14 x 10^2 + 2 x 3.14 x 10 x 5

S = 628 + 314

S = 942

Therefore, the surface area of the cylinder is 942 square millimeters.

The scale of the map is that 4 inches on the drawing represents 1 mile in real life

We can use the scale formula:

scale = distance on map / actual distance

In this case, the distance on the map is 8 inches, and the actual distance is 2 miles.

Now we can plug in the values:

scale = 8 inches / 2 miles

scale = 4 inches /1 mile

Therefore, the scale of the map is 4 inches represents 1 mile

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Answer:

1. $34.30

2. $9.60

3. $135.30

4. $8.25

Step-by-step explanation:

Answer:

1. $14.70

2. $1.60

3. $135.30

4. $8.25

Step-by-step explanation:

1. Convert percentage to decimal:

30% = 30/100 = 0.3

So 30% of $49 = 0.3 x 49 = 14.7

Therefore, a discount of 30% = a discount of $14.70

2. Convert percentage to decimal:

20% = 20/100 = 0.2

So 20% of $8 = 0.2 x 8 = 1.6

Therefore, the 20% tip = $1.60

3. Convert percentage to decimal:

20% = 20/100 = 0.2

So 20% of $112.75 = 0.2 x 112.75 = 22.55

Therefore, total cost with the tip = 112.75 + 22.55 = $135.3

4. If a discount of 45% is applied, the new cost of the shirt will be 55% of its original price (as 100% - 45% = 55%)

Convert percentage to decimal:

55% = 55/100 = 0.55

So 55% of $15 = 0.55 x 15 = 8.25

Answer:

B

Step-by-step explanation:

4 is a lot less than the others

yez

The surface integral in terms of ρ and θ ∫∫S.((6y - 5)e^(x^2))

To evaluate ∬s.curl F•nds using Stokes' Theorem, we first need to find the curl of the vector field F and then compute the surface integral over the given surface S.

Given vector field F = (6yz)i + (5x)j + (yz(e^(x^2)))k, let's find its curl:

∇ × F = ∂/∂x (yz(e^(x^2))) - ∂/∂y (5x) + ∂/∂z (6yz)

Taking the partial derivatives, we get:

∇ × F = (0 - 0) i + (0 - 0) j + (6y - 5)e^(x^2)

Now, let's parametrize the surface S, which is the portion of the paraboloid z = (1/4)x^2 + y^2 for 0 ≤ z ≤ 4. We can use cylindrical coordinates for this parametrization:

r(θ, ρ) = ρcos(θ)i + ρsin(θ)j + ((1/4)(ρcos(θ))^2 + (ρsin(θ))^2)k

where 0 ≤ θ ≤ 2π and 0 ≤ ρ ≤ 2.

Next, we need to find the normal vector n to the surface S. Since S is oriented upward, the normal vector points in the positive z-direction. We can normalize this vector to have unit length:

n = (∂r/∂θ) × (∂r/∂ρ)

Calculating the partial derivatives and taking the cross product, we have:

∂r/∂θ = -ρsin(θ)i + ρcos(θ)j

∂r/∂ρ = cos(θ)i + sin(θ)j + (1/2)(ρcos(θ))k

∂r/∂θ × ∂r/∂ρ = (-ρsin(θ)i + ρcos(θ)j) × (cos(θ)i + sin(θ)j + (1/2)(ρcos(θ))k)

Expanding the cross product, we get:

∂r/∂θ × ∂r/∂ρ = (ρcos(θ)(1/2)(ρcos(θ)) - (1/2)(ρcos(θ))(-ρsin(θ)))i

+ ((1/2)(ρcos(θ))sin(θ) - ρsin(θ)(1/2)(ρcos(θ)))j

+ (-ρsin(θ)cos(θ) + ρsin(θ)cos(θ))k

Simplifying further:

∂r/∂θ × ∂r/∂ρ = ρ^2cos(θ)i + ρ^2sin(θ)j

Now, we can calculate the surface integral using Stokes' Theorem:

∬s.curl F•nds = ∮c.F•dr

= ∫∫S.((∇ × F)•n) dS

Substituting the values we obtained earlier:

∫∫S.((∇ × F)•n) dS = ∫∫S.((6y - 5)e^(x^2))•(ρ^2cos(θ)i + ρ^2sin(θ)j) dS

We can now rewrite the surface integral in terms of ρ and θ:

∫∫S.((6y - 5)e^(x^2))

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The class had cleaned x × A square miles before lunch.

Let's assume that the area of the park is A square miles, and the portion of the park cleaned by Mai's class before the lunch break is represented by x (a fraction or decimal between 0 and 1).

If the class had cleaned x portion of the park, then the area they had cleaned is x times the total area of the park:

Area cleaned before lunch = x × A

Since x represents a fraction or decimal, multiplying it by the total area A gives us the corresponding portion of the park that was cleaned.

Let's say the park has an area of A square miles, and the area that Mai's class cleaned up before lunch is denoted by the number x (a fraction or decimal between 0 and 1).

If the class had cleaned a certain percentage of the park, their cleaned area would be x times the park's overall area:

Before lunch, the area was cleaned = x A

We may calculate the proportion of the park that was cleaned by multiplying x by the entire area A because it indicates a fraction or decimal.

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The solution of the given problem of equation comes out to be total cost for 942 minutes is $1044.

The similar symbol (=) is used in arithmetic equations to signify equality between two statements. It is shown that it is possible to compare various numerical factors by applying mathematical algorithms, which have served as expressions of reality. For instance, the equal sign divides the number 12 or even the solution y + 6 = 12 into two separate variables many characters are on either side of this symbol can be calculated. Conflicting meanings for symbols are quite prevalent.

Part A:

Given:

To find an equation,

Where x is number of monthly minutes.

and y is total monthly of splint plan.

So, equation is:

\(\rightarrow \text{y} =\text{mx} +\text{b}\)

For the first case:

\(\rightarrow\bold{173 = 380x + b}\)

Second case:

\(\rightarrow\bold{249= 570x + b}\)

Solve for x:

\(\rightarrow{173 - 380\text{x}=249- 570\text{x}\)

\(\rightarrow{-207=-321\)

\(\rightarrow \text{x} =\dfrac{321}{207}\)

\(\rightarrow \text{x} =\dfrac{107}{69}\)

\(\rightarrow \text{x} \thickapprox1.55\)

For value of b

\(\rightarrow 173 = 380(1.55) + \text{b}\)

\(\rightarrow 173 - 589 = \text{b}\)

\(\rightarrow -416 = \text{b}\)

Part B:

\(\rightarrow \text{y} = 942(1.55) - 416\)

\(\rightarrow \text{y} = 1460.1 - 416\)

\(\rightarrow \text{y} \thickapprox1044\)

Therefore, the solution of the given problem of equation comes out to be total cost for 942 minutes is $1044.

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Answer: a

Step-by-step explanation: