Rachel works at a lemonade stand at the park on Monday. She used 1 2/5 bags of lemons on Tuesday. She used 1 1/4 times as many lemons as on Monday. How many bags of lemons did Rachel use on Tuesday?

The IQR of the data set is 4.

First, let's arrange the data set in order from smallest to largest:

1, 2, 3, 5, 6, 6, 6, 7, 9

Next, let's find the median (Q2) of the data set. Since there are an odd number of values in the data set, the median is the middle value:

Q2 = 6

Now, let's find the median (Q1) of the lower half of the data set. This includes the values from the minimum (1) up to (but not including) the median (6). There are four values in this lower half, so the median is the average of the two middle values:

Q1 = (2 + 3) / 2 = 2.5

Finally, let's find the median (Q3) of the upper half of the data set. This includes the values from the median (6) up to (and including) the maximum (9). There are also four values in this upper half, so the median is the average of the two middle values:

Q3 = (7 + 6) / 2 = 6.5

Now that we have Q1, Q2, and Q3, we can calculate the IQR as:

IQR = Q3 - Q1

IQR = 6.5 - 2.5

IQR = 4

Therefore, the IQR of the given data set is 5.5.

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Answer:

k = 8.4; j = 13.1

Step-by-step explanation:

We can find the measures of j and k using trigonometric ratios, namely the tangent ratio and the cosine ratio

If we allow 40 to be our reference angle...

Because we're not given the measure of either j or k, we have to use 10 each time

Steps to find j:

[tex]cos(40)=\frac{10}{j}\\ \\j*cos(40)=10\\\\j=\frac{10}{cos(40)}\\ \\j=13.05407289\\\\j=13.1[/tex]

Steps to find k:

[tex]tan(40)=\frac{k}{10}\\ \\10*tan(40)=k\\\\8.390996312=k\\\\8.4=k[/tex]

Answer:

Step-by-step explanation:

29 ft

7  in

The slope of the polar curve at θ = π/4 is 24. Therefore, option D is correct.

To find the slope of the polar curve r = 6cos(2θ) - 5 at θ = π/4, we need to find the derivative of r with respect to θ, and then substitute θ = π/4 into the resulting expression.

Using the chain rule of differentiation, we have:

dr/dθ = dr/d(cos(2θ)) * d(cos(2θ))/dθ

To find the first derivative, we can use the power rule of differentiation:

dr/d(cos(2θ)) = -12sin(2θ)

To find the second derivative, we can use the chain rule again:

d(cos(2θ))/dθ = -2sin(2θ)

Substituting these into the expression for dr/dθ, we get:

dr/dθ = -12sin(2θ) * (-2sin(2θ)) = 24sin^2(2θ)

Now, substituting θ = π/4, we get:

dr/dθ|θ=π/4 = 24sin^2(π/2) = 24

The slope of the polar curve at θ = π/4 is therefore 24.

None of the given options match this result.

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The city with a population of 500,000 would produce 305,000 tons of pollutants.

We have,

Let's call the unknown amount of pollutants in the second city "x".

According to the problem,

The amount of pollution is directly proportional to the number of people. This means that we can set up a proportion:

Pollution/number of people

= pollution/number of people

Using the values we know:

= 21350/35000

= x/500000

Simplifying:

0.61 = x/500000

To solve for x, we can cross-multiply:

0.61 x 500000 = x

x = 305000

Therefore,

The city with a population of 500,000 would produce 305,000 tons of pollutants.

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The probability of at least 8 homes would prefer brand B compare to compare A is given by 0.672.

Sample size 'n'= 25

Proportion of people prefer brand A = 0.4

This implies ,

Proportion of people prefer brand B 'p' = 1 - 0.4

                                                                  = 0.6

Using the binomial distribution.

Let X be the number of homes that prefer brand B out of the 25 homes surveyed.

Then X follows a binomial distribution with parameters n = 25 and p = 0.6

Probability that at least 8 homes would state a preference for brand B. expressed as,

P(X ≥ 8) = 1 - P(X < 8)

Using the binomial distribution, compute P(X < 8) as follows,

P(X < 8) = Σ [²⁵Cₓ] × 0.6ˣ × 0.4²⁵⁻ˣ, for x = 0, 1, 2, ..., 7

where ²⁵Cₓ is the binomial coefficient which represents the number of ways to choose k homes out of 25.

Use a binomial calculator ,

⇒P(X < 8) = [²⁵C₀] × 0.6⁰× 0.4²⁵⁻⁰ + [²⁵C₁] × 0.6¹× 0.4²⁵⁻¹ + [²⁵C₂] × 0.6²× 0.4²⁵⁻² + .......+ [²⁵C₇] × 0.6⁷× 0.4²⁵⁻⁷  

⇒P(X < 8) ≈ 0.328

This implies,

P(X ≥ 8) = 1 - P(X < 8)

             ≈ 1 - 0.328

             = 0.672

Therefore,  the probability that at least 8 homes would state a preference for brand B is approximately 0.672.

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The above question is incomplete , the complete question is:

A manufacturer of floor wax has developed two new brands, A and B.  which she wishes to subject to homeowners' evaluation to determine which of the two is superior. Both waxes are applied to the floor surfaces in each of a sample of 25 homes. It is known that the proportion of people that prefer A is 0.4 while the rest prefer brand B.

Find the probability that at least 8 homes would state a preference for brand B.

Using synthetic division, the value at w(-3) of the expression w(x)=11x³ -6x² +2 is -349

Synthetic substitution is a mathematical method that is used for evaluating the algebra polynomial in the simpler process.

To determine the value of the polynomial at w = -3, we need to carry out the synthetic division.

Then, the value of the remainder is taken as the value of the expression at the particular value

We have the expression as;

w(x)=11x³ -6x² +2/x-3

Let's carry out the synthetic division

Then, this is represented as;

-3)  11     -6      0      2

             -33    -117   -351

     11     -39    -117   -349

The value is -349

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Answer:

x = - [tex]\frac{3}{5}[/tex]

Step-by-step explanation:

consider the right triangle formed by the x- axis, the y- coordinate of the given point and the radius of the circle 1 , to the point from the centre.

using Pythagoras' identity

x² + ( [tex]\frac{4}{5}[/tex] )² = 1²

x² + [tex]\frac{16}{25}[/tex] = 1 ( subtract [tex]\frac{16}{25}[/tex] from both sides )

x² = 1 - [tex]\frac{16}{25}[/tex] = [tex]\frac{9}{25}[/tex] ( take square root of both sides )

x² = ± [tex]\sqrt{\frac{9}{25} }[/tex] = ± [tex]\frac{\sqrt{9} }{\sqrt{25} }[/tex] = ± [tex]\frac{3}{5}[/tex]

since the given point is in the second quadrant , then

x = - [tex]\frac{3}{5}[/tex]

The relationships between the figures is a dilation of 3.5 from the small triangle to the big triangle

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

The two triangles

From the figure, we can see that

These mean that the triangles are related by dilation

The constant of dilation is then calculated as

k = (7, 7)/(2, 2)

Evaluate

k = 3.5

Hence, the scale factor is 3.5

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Answer:

(2,0)

Step-by-step explanation:

Answer:

26,225.3 = 3.14(12^2)h + (2/3)(3.14)(12^3)

26,225.3 = 452.16h + 3,617.28

452.16h = 22608.02

h = 50 feet

26,225.3 = π(12^2)h + (2/3)π(12^3)

26,225.3 = 144πh + 1,152π

144πh = 26,225.3 - 1,152π

h = (26,225.3 - 1,152π)/(144π)

h = 49.97 feet = 50 feet

Answer:

V = π(19.1^2)(11.8) = 13,523.8 cubic mm

V = 3.14(1.91^2)(11.8) = 13,516.9 cubic mm

Answer:

The graph of the function appears to be a cosine function that has been shifted to the left by π/2 units, and has an amplitude of 4.

Option (a) is a cosine function that has been shifted to the left by π units, but does not have the amplitude of 4.

Option (b) is a cosine function that has a period of π/2, which is much shorter than the period of the graph.

Option (c) is a sine function that has been shifted to the right by π units, but does not have the amplitude of 4.

Option (d) is a cosine function that has been shifted to the left by π units and has the correct amplitude of 4.

Option (e) is not a cosine or sine function, so it cannot be the correct answer.

Therefore, the function represented by the graph is:

f(x) = -4 cos(x + π)

which is Option (d).

Step-by-step explanation:

Answer:

[tex]12 \times 10 \times h = 3600[/tex]

[tex]120h = 3600[/tex]

[tex]h = 30[/tex]

The height is 30 millimeters.

The explicit rule for the situation whereby a new car that costs $30,000 depreciates at an average rate of 14% per year, giving the depreciated value of the car after n years, is given by B. an = 30,000 × 0.86^n-1.

The depreciated value of an asset in any year can be determined using the exponential decay function or equation.

An exponential decay equation shows the value of an asset given a constant rate of periodic decrease.

The cost of the new car = $30,000

The average depreciation rate per year = 14%

Depreciation factor = 86% or 0.86 (1 - 14%)

Let the number of years after the purchase = n

Let the depreciated value after n years = an

an = 30,000 × 0.86^n-1.

Thus, the correct explicit rule is Option B.

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The calculated value of the prime fractorization of the number 130 is 2 * 3 * 5

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

Number = 130

When the above number is expanded, we have

Number = 2 * 5 * 13

The above product of numbers cannot be further simplified

This means that 2 * 5 * 13 is the prime fractorization of the number 130

Hence, the prime fractorization of the number 130 is 2 * 3 * 5

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Answer:174

Step-by-step explanation:

209-22=187

361-22=174

In this example of heart attack, it would be appropriate to calculate Conditional row percentages. Therefore, the correct option is option A.

When the blood supply for the heart is significantly impeded or blocked, a heart attack happens. The accumulation of fat, cholesterol, and other chemicals in the heart's (coronary) arteries is typically what causes the obstruction. Plaques are the name given to the fatty, cholesterol-containing deposits.

Atherosclerosis is the name for the phenomenon of plaque accumulation. A plaque may occasionally burst and generate a clot that restricts blood flow. A portion for the heart muscle can be harmed or destroyed by a shortage of blood flow. In this example, it would be appropriate to calculate Conditional row percentages.

Therefore, the correct option is option A.

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Your question is incomplete but most probably your full question was,

The value of variable θ would be,

⇒  θ = 5π/3 and θ = 4π/3

We have to given that;

Expression is,

⇒ - 10sin θ - 8 = 5√3 - 8

Now, We can simplify as;

⇒ - 10sin θ - 8 = 5√3 - 8

⇒ - 10sin θ = 5√3

⇒ sin θ = - 5√3/10

⇒ sin θ = - √3/2

We know that sinθ = -√3/2 when θ = 4π/3 and θ = 5π/3 (among other angles).

However, since 0 ≤ θ < 2π, only the angles in the second and third quadrants are valid solutions for sinθ = -√3/2.

Therefore, the solutions are θ = 5π/3 and θ = 4π/3, option D is correct.

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The given statement, "Signed numbers are also called directed numbers" is true.

Signed numbers are numbers that can be positive, negative, or zero, and they are sometimes referred to as directed numbers because they have a direction or orientation on the number line. Positive numbers are usually associated with movements to the right on the number line, while negative numbers are associated with movements to the left.

Therefore, the given statement, "Signed numbers are also called directed numbers" is true.

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The value of length BD is 3.0 units

Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

since AC is a radius that joins a tangent, the angle between them is 90°. Therefore ∆ABC is a right triangle and Pythagoras theorem can be applied.

therefore c² = a²+b²

c² = 4.5²+6²

c²= 20.25+36

c²= 56.25

c = √7.5

AC = CD(radii of a circle)

therefore BD = BC -CD

= 7.5-4.5

= 3.0units

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Answer:

[tex]\frac{2}{5}[/tex]

Step-by-step explanation:

If the question is asking you to add the two fraction you would need to follow these steps:

Step 1: find a common denominator (both of the number 20 in common

Step 2: add the numerators ( 7/20 + 1/20 would = 8/20 )

Step 3 simply the fraction ( 8/20 will be simplyed to 2/5)

Answer:

33/20

Step-by-step explanation:

First find the Least common denominator

Then you check how many times each denominator goes into de Least common denominator

After multiply the number you got when you checked for the times the denominator will go into the LCM with the numerator then simplify

The polar coordinate (3, 45°) lies in the same location on the polar plane as (-3, Ø), where -360° < Ø < 0. Then, the value of Ø is 45°.

The polar coordinates (r, θ) represent a point on the polar plane, where r is the radial distance from the origin (in this case, 3 units) and θ is the angle measured counterclockwise from the positive x-axis (in this case, 45°).

According to the given statement, the polar coordinate (-3, Ø) lies in the same location on the polar plane as (3, 45°). This means that these two points represent the same location, and their radial distances and angles must be equivalent.

Comparing the radial distances;

|r| = 3 (for (3, 45°))

|-r| = 3 (for (-3, Ø))

Since |-r| = |r|, we can conclude that r = -r, which implies r = 0, as r cannot be negative in polar coordinates.

Comparing the angles;

θ = 45° (for (3, 45°))

θ = Ø (for (-3, Ø))

Since the angles are equivalent, we can equate them:

45° = Ø

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The length of the intercepted arc is 4π unit.

We have,

Angle = 2π/3 = 2(180)/ 3 = 120 degree

r = 6 unit

So, length of Arc

= θ /360 x 2πr

= 120/360 2 π(6)

= 1/3 (12)π

= 4π unit

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Using the translation vector of 3 units up and 1 unit right resulted to image coordinate of

(3, 7)

(3, 5)

(2, 5)

The image is attached

The translation vector is of the rule 3 units up and 1 unit to the right

The coordinate of the preimage are

(2, 4)

(2, 2)

(1, 2)

The translation is done as below

(2 + 1, 4 + 3) = (3, 7)

(2 + 1, 2 + 3) = (3, 5)

(1 + 1, 2 + 3) = (2, 5)

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The surface area of the figure = 2733.3 sq. in.

First we fine the surface area of the top surface of the figure.

The top surface is an rectangle with length = 19 in. and width = 17 in

Using the formula for the area of rectangle, the area of top face would be,

A₁ = 19 × 17

A₁ = 323 sq. in.

The slant face of the figure is a rectangle with  length = 22 in. and width = 17 in

Using the formula for the area of rectangle, the area of slant surface of the figure would be,

A₂ = 22 × 17

A₂ = 374 sq. in.

There are two parallel trapezoidal surface of the figure with bases 35 in. and 19 in. respectively.

The height of the trapezoid = 20.3 in.

Using the formula for that area of trapezoid, the area of two trapezoidal surface of the figure would be,

A₃ = 2 × (sum of lengths two bases/2) × height

A₃ = 2 × (35 + 19/2) × 20.3

A₃ = 1096.2 sq. in.

The area of the bottom surface would be,

A₄ = 35 × 17

A₄ = 595 sq. in.

The area of right surface would be,

A₅ = 20.3 × 17

A₅ = 345.1 sq. in.

So, the total surface area would be,

A = A₁ + A₂ + A₃ + A₄ + A₅

A = 323 + 374 +  1096.2 +  595 + 345.1

A = 2733.3 sq. in.

Therefore, the surface area of the figure = 2733.3 sq. in.

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Find the complete question below.

The quantity of pasta is served to Olivia is 60 in³.

Olivia's mother packed her lunch in a lunch box which is in the shape of rectangular prism, with dimension = length= 5 in, width= 4 in, height= 3 in,

We need to find the quantity of the lunched packed in the box,

So, we will find the volume of the box = length × width × height

= 5 × 4 × 3

= 60 in³

Hence the quantity of pasta is served to Olivia is 60 in³.

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