What is the unit price for 12 apples for $3.12?

394 subscribers are represented in the venn diagram.

Venn diagrams are charts that are used to visually represent relationships between sets, operations on those relationships, and set relationships. The Venn diagram, which uses circles that are overlapped, intersected, and not intersected to depict the relationship between sets, was created by John Venn. A set diagram or a logic diagram is another name for a Venn diagram, which shows a variety of set operations such the intersection, union, and difference of sets.

Additionally, it can be used to set items. a depiction of each relationship between several sets. Any closed figure, such as a circle or a polygon (square, hexagon, etc.), can be used to represent a Venn diagram. However, each group is typically represented as a circle.

according to the venn diagram

196+41+21+52+84 = 394

There are 394 subscribers

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Answer:

\(x=12\)

Step-by-step explanation:

Simplify:

\(6x-20=x+40\\5x=60\\x=12\)

The Volume of the box is 3.75in³

The volume of the box is dependent on the volume of the cube in it.

To obtain the volume of a cube, we use the relation, V = s³

s = side of the cube

Volume = 0.5³ = 0.125 in³

Number of cubes in box = 30

Volume of each cube × Number of cubes

0.125 × 30 = 3.75 in³

Hence, the volume of the box is 3.75in³

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Answer:

The answer is 54.

Step-by-step explanation:

You add all these numbers up.

The percentage population increase from 2001 to 2011 is 50%.

To calculate the percentage population increase from 2001 to 2011, you need the population figures for both years. Let's assume the population in 2001 was 100,000 and in 2011 it was 150,000.

The formula to calculate the percentage increase is:

Percentage Increase = ((New Value - Old Value) / Old Value) * 100

Plugging in the values:

Percentage Increase = ((150,000 - 100,000) / 100,000) * 100 = (50,000 / 100,000) * 100 = 0.5 * 100 = 50%

Therefore, the percentage population increase from 2001 to 2011 is 50%.

Please note that the actual population figures for the respective years need to be used in the calculation to obtain an accurate result. The example above is for illustrative purposes.

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Answer:

209/1040

Step-by-step explanation:

= 20.9/1040

= 209/1040  /  0.200961  

Answer:

Step-by-step explanation

Okay so lets solve step by step/

15% can be written as a  fraction: 15/100

The of in the equation means multiplying.

15/100= 3/20

3/20*9= 270/20

27/2 is answer

Answer:

Step-by-step explanation:

X: -2, -1, 0, 1, 2,...

Y: -2, -1, 0, 1, 2,...

(y=x)

Answer:

The demand d as a function of price is \(d=\frac{800}{3} -\frac{40p}{3}\)

The demand if the price is $ 8 per gallon is 160 millions of gallons.

Step-by-step explanation:

You know that the price-demand equation for gasoline is 0.3d + 4p = 80

To write demand d as a function of price p, you must solve for or isolate demand d, remembering that:

So:

0.3d + 4p = 80

0.3d = 80 - 4p

\(d=\frac{80 - 4p}{0.3}\)

\(d=\frac{80}{0.3} -\frac{4p}{0.3}\)

\(d=\frac{800}{3} -\frac{40p}{3}\)

The demand d as a function of price is \(d=\frac{800}{3} -\frac{40p}{3}\)

To determine how much is the quantity demanded if the price is $ 8 per gallon, you simply plug that value into the previously determined expression and perform the corresponding calculations:

\(d=\frac{800}{3} -\frac{40*8}{3}\)

\(d=\frac{800}{3} -\frac{320}{3}\)

d= 160

The demand if the price is $ 8 per gallon is 160 millions of gallons.

The Simple Interest on Principal amount: $1,000 is $100.

Simple interest is, by definition, the amount of interest paid on a specific principal sum of money when an interest rate is applied.

Given:

Principal amount: $1,000

Interest rate: 10%

Time: 12 months

So, the Simple Interest

= P x R x T/100

= 1000 x 10 x 1 / 100

= 10000/100

= $100

and, Amount = P + I

Amount = $1100

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Answer:

x > -5, so the correct answer is C.

The value of the angle B from the trigonometric ratios is 53.13 degrees

The Pythagorean theorem is a powerful tool for solving various problems involving right triangles. It allows us to find the length of a missing side in a right triangle when the lengths of the other two sides are known. It is also used to identify whether a triangle is a right triangle or not.

We have that;

TanB = 4/3

B= Tan-1(4/3)

B = 53.13 degrees

Hence we are going to have by the use of tan that the angle is 53.1 degrees

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Answer:

4x25/100=1

Step-by-step explanation:

How I came up with it

4÷100=25

25÷25=1

Julie will only get a 1% discount

Hope it helps

Answer:

1. Given

2. Subtraction P.O.E

3. Addition P.O.E

4. Division P.O.E

5. Symmetric P.O.E

Step-by-step explanation:

P.O.E stands for Property of Equality

Answer:

Part A

The amplitude of a cosine function is the distance between its highest and lowest points. In this case, the highest point is 8 feet and the lowest point is 8 - 12 = -4 feet, so the amplitude is 8 - (-4) = 12 feet.

The period of a cosine function is the time it takes for the function to complete one cycle of its movement. In this case, the bird completes one cycle of its movement every 16 seconds, so the period is 16 seconds.

Part B

The cosine function that could represent the situation is:

y = 6 cos(2πt / 16) + 8

This function has an amplitude of 6 feet and a period of 16 seconds. It also passes through the point (0, 8) when t = 0, which is the condition given in the problem.

Part C

The bird will reach its lowest height when the cosine function is equal to -6. This happens when 2πt / 16 = π / 2, or t = 4 seconds.

Here is a graph of the function:

[Image of a cosine function with an amplitude of 6 feet and a period of 16 seconds. The graph reaches its lowest point at t = 4 seconds.]

I hope this helps! Let me know if you have any other questions.

Step-by-step explanation:

Answer:

26.46

Step-by-step explanation:

24.50 x .08 = 1.96 (this is our sales taxes)

1.96 + 24.50 = 26.46

The measure of angle ADC in the geometric system is equal to 55°.

In this question we find a geometric system formed by a quadrilateral and an angle vertical to a vertex of the quadrilateral. Angle CDE is supplementary to angles EDF and ADC. Two angles are supplementary whose sum of measures equals 180°. Therefore:

m ∠ CDE + m ∠ EDF = 180°

(2 · x + 1) + (x - 7) = 180°

3 · x - 6 = 180°

3 · x = 186°

x = 62

m ∠ CDE = 2 · x + 1

m ∠ CDE = 2 · 62 + 1

m ∠ CDE = 125°

m ∠ ADC = 180° - 125°

m ∠ ADC = 55°

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The given function y = sec⁻¹(x³) is differentiated as dy/dx = 3x/√(x² - 1).

The differentiation of a function is defined as rate of change of its value at a point. It can be written as f'(x) = Lim h --> 0 (f(x + h) - f(x)) /(x + h - x).

Its geometric meaning is the slope of tangent of the function at a given point.

The given function is as below,

y = sec⁻¹(x³)

The given function is a composite function of sec⁻¹x and x³.

In order to differentiate it, first differentiate x³ and then sec⁻¹x as follows,

dx³/dx = 3x²

And, dsec⁻¹x /dx = 1/x√(x² - 1)

Now, differentiation of sec⁻¹(x³) is given as,

d sec⁻¹(x³)/dx = 3x²/(x√(x² - 1))

                      = 3x/√(x² - 1)

Hence, the differentiation of the given function is 3x/√(x² - 1).

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Alaska occupies 17.22% of the surface area of the United States. Rounding to the nearest whole number, we get 17%. Hence, the answer is:17%

We are given that the surface area of the United States is 3.797 million square miles and the state of Alaska occupies 655,400 square miles. We need to determine what percentage of the surface area of the United States is occupied by Alaska using ratios.To find the percentage, we need to first find the ratio of Alaska's surface area to the surface area of the United States. We can do this by dividing the surface area of Alaska by the surface area of the United States. That is,655,400 / 3,797,000 = 0.1722We can express this ratio as a percentage by multiplying by 100. That is,0.1722 × 100 = 17.22%

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Answer:

a) Particle has a constant speed of 4, b) Velocity and acceleration vector are orthogonal to each other, c) Clockwise, d) False, the particle begin at the point (0,1).

Step-by-step explanation:

a) Let is find first the velocity vector by differentiation:

\(\vec v = \frac{dr_{x}}{dt} i + \frac {dr_{y}}{dt} j\)

\(\vec v = 4\cdot \cos 4t\, i - 4 \cdot \sin 4t \,j\)

\(\vec v = 4 \cdot (\cos 4t \, i - \sin 4t\,j)\)

Where the resultant vector is the product of a unit vector and magnitude of the velocity vector (speed). Velocity vector has a constant speed only if magnitude of unit vector is constant in time. That is:

\(\|\vec u \| = 1\)

Then,

\(\| \vec u \| = \sqrt{\cos^{2} 4t + \sin^{2}4t }\)

\(\| \vec u \| = \sqrt{1}\)

\(\|\vec u \| = 1\)

Hence, the particle has a constant speed of 4.

b) The acceleration vector is obtained by deriving the velocity vector.

\(\vec a = \frac{dv_{x}}{dt} i + \frac {dv_{y}}{dt} j\)

\(\vec a = 16\cdot (-\sin 4t \,i -\cos 4t \,j)\)

Velocity and acceleration are orthogonal to each other only if \(\vec v \bullet \vec a = 0\). Then,

\(\vec v \bullet \vec a = 64 \cdot (\cos 4t)\cdot (-\sin 4t) + 64 \cdot (-\sin 4t) \cdot (-\cos 4t)\)

\(\vec v \bullet \vec a = -64\cdot \sin 4t\cdot \cos 4t + 64 \cdot \sin 4t \cdot \cos 4t\)

\(\vec v \bullet \vec a = 0\)

Which demonstrates the orthogonality between velocity and acceleration vectors.

c) The particle is rotating clockwise as right-hand rule is applied to model vectors in 2 and 3 dimensions, which are associated with positive angles for position vector. That is: \(t \geq 0\)

And cosine decrease and sine increase inasmuch as t becomes bigger.

d) Let evaluate the vector in \(t = 0\).

\(r(0) = \sin (4\cdot 0) \,i + \cos (4\cdot 0)\,j\)

\(r(0) = 0\,i + 1 \,j\)

False, the particle begin at the point (0,1).

The probability of -20 < x < 15, where x be a normal random variable with a mean of 5 and a standard deviation of 10 is approximately 0.8351.

To solve this problem, we need to find the area under the normal distribution curve between -20 and 15, with a mean of 5 and a standard deviation of 10.

We can standardize the normal distribution by subtracting the mean and dividing by the standard deviation, which gives us the standard normal distribution with a mean of 0 and a standard deviation of 1.

So, we can first calculate the z-scores for -20 and 15:

z1 = (-20 - 5) / 10 = -2.5

z2 = (15 - 5) / 10 = 1

Next, we use a standard normal distribution table or calculator to find the probabilities associated with these z-scores:

P(z < -2.5) = 0.0062

P(z < 1) = 0.8413

To find the probability of -20 < x < 15, we subtract the probability associated with the lower z-score from the probability associated with the higher z-score:

P(-20 < x < 15) = P(-2.5 < z < 1) = P(z < 1) - P(z < -2.5)

P(-20 < x < 15) = 0.8413 - 0.0062 = 0.8351

Therefore, the probability of -20 < x < 15 is approximately 0.8351.

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The inequality, -7x ≤ -21, has the solution set as same in the graph.

The inequality is the relationship between two values that are not equal.

The graph shows that the value x ranges from 3 to less than 3 values.

i.e x ≤  3

To solve the inequality, -7x -21, we divide both sides by (-7).

i. e (-7x ≤ -21) / (-7)

x≤ 3

Hence, the inequality suitable for the given graph is -7x ≤ -21

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The answer is B.

Step-by-step explanation:

Yes

Answer:

The probability that one marble drawn at random is not blue is 70%

The monthly cell phone bill when shared data equals zero is given as follows:

$26.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

The intercept of the line in this problem is given as follows:

b = 26.

Hence $26 is the monthly cell phone bill when shared data equals zero.

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The probability that the sample mean is between 1.8 hours and 2.2 hours. is; 0.99535

We are given;

Sample size; n = 50

Standard deviation; σ = 0.5

Mean; μ = 2

The formula to find the z-score for each sample mean is;

z = (x' - μ)/(σ/√n)

Thus, for x' = 1.8, we have;

z = (1.8 - 2)/(0.5/√50)

z = -2.83

For x' = 2.2, we have;

z = (2.2 - 2)/(0.5/√50)

z  = 2.83

Thus, the probability that the sample mean is between 1.8 hours and 2.2 hours. is;

P(-2.83 < Z < 2.83) = 0.99535

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Answer:

Step-by-step explanation: 37/56

Answer:

30.48cm

Step-by-step explanation:

The best way to perform conversion is by the multiplication of fractions to keep track of units. You'll see in the equation below that inches cancels out. Leaving you with cm in 1 ft.

\(\frac{2.54 cm}{1in}* \frac{12 in}{1ft} = \frac{30.48cm}{1ft}\)

Answer:

30.48 centimeters

Step-by-step explanation:

To answer this question, keep in mind 1 foot = 12 inches. If 2.54 cm = 1 in., and you are trying to find how many centimeters there are in 12 inches (1 ft), you need to multiply (2.54)(12)=30.48