18. Suppose A (red, blue, yellow), B = (Red, yellow, green), and C= (green, red, purple). Which set is equivalent to (AUB)NC? (a) (purple) (b) (red) (c) {red, green) (d) {yellow, purple)​

According to algebra property of power of a power, the following results are listed below:

Case 1: (x⁵)³ = x¹⁵ (Correct choice: 1)

Case 2: (x⁸)⁷ = x⁵⁶ (Correct choice: 4)

Case 3: (x⁷)¹⁰ = x⁷⁰ (Correct choice: 2)

Case 4: (x¹⁴)³ = x⁴² (Correct choice: 3)

In this question we find four cases of power of a power, whose solution is described by the following algebra property:

(xᵃ)ᵇ = xᵃᵇ, where x, a and b are real numbers.

Now we proceed to determine the solution to each case:

Case 1

(x⁵)³ = x¹⁵

Case 2

(x⁸)⁷ = x⁵⁶

Case 3

(x⁷)¹⁰ = x⁷⁰

Case 4

(x¹⁴)³ = x⁴²

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The unit rate of the shirt is $1.50 per shirt.

Unit rate is a measure of the relationship between two quantities, where the second quantity is expressed as a unit of one. It is often expressed as a ratio, with the unit of the second quantity being 1. Unit rate helps us compare different quantities and make sense of their relative sizes.

The unit rate for the shirts can be calculated by dividing the total cost by the number of shirts. In this case, the unit rate would be:

$6.00 ÷ 4 shirts = $1.50/shirt

So, the unit rate for the shirts is $1.50 per shirt.

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The cost of the skirt and blouse after the discount would be -

$52.8 and $56.1 respectively.

Given is that Laura has bought a skirt and a blouse for 66 euros, both had the same price but they have given her a 20% discount on the skirt and only 15% on the blouse.

The cost skirt would be -

${x} = 66 - {20% of 66}

${x} = 66 - {20/100 x 66}

${x} = 66 - {66/5}

${x} = 66 - 13.2

${x} = 52.8

The cost of blouse would be -

${y} = 66 - {15% of 66}

${y} = 66 - {15/100 x 66}

${y} = 66 - {3/20 x 66}

${y} = 66 - 9.9

${y} = 56.1

Therefore, the cost of the skirt and blouse after the discount would be -

$52.8 and $56.1 respectively.

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{Question in english -

Laura has bought a skirt and a blouse for 66 euros, both had the same price but they have given her a 20% discount on the skirt and only 15% on the blouse. How much did each item cost??

Answer:

Both triangles are congruent by S A S congruent.

Step-by-step explanation:

     In ΔHIG & ΔKJG,

HG = KG                Given

∠GHI ≅ ∠GKJ       Alternate interior angles, HI // KJ and KH is transversal

    HI = KJ               Given

ΔHIG  ≅ ΔKJG       Side Angle Side congruency

To find the area of the base of the column, we need to find the expression for the radius of the column, r, in terms of x.

The volume of a column can be calculated as V = πr²h, where r is the radius, h is the height, and π is pi.

Using the given expression for the volume of the column, we can write:

πr²h = x³ + 37x² - 110x + 400

Since h = x + 40, we can substitute to get:

πr²(x + 40) = x³ + 37x² - 110x + 400

Dividing both sides by π(x + 40) gives us:

r² = (x³ + 37x² - 110x + 400) / (π(x + 40))

Finally, taking the square root of both sides gives us the expression for the radius in terms of x:

r = √((x³ + 37x² - 110x + 400) / (π(x + 40)))

So, the expression that approximates the area of the base of the column in terms of x and π is:

A = πr² = π √((x³ + 37x² - 110x + 400) / (π(x + 40)))²

Answer:

To find the dimensions that would guarantee the greatest possible area, we can use the formula for the area of a rectangle, which is A = l * w, where l is the length and w is the width.

Since one side of the garden is already boarded by a river, we only need to use 600ft of fencing for the other three sides. This means that the length and width of the garden must add up to 600ft. We can write this as:

l + w = 600

Since we want to find the dimensions that would give us the greatest possible area, we want to maximize l * w. Using the formula for the area of a rectangle, we can write this as:

A = l * w = l * (600 - l) = 600l - l^2

To find the maximum area, we can differentiate this equation and set it equal to zero:

dA/dl = 600 - 2l = 0

Solving for l, we get:

l = 300/2 = 150ft

So, the shorter side is 150ft and the longer side is 450ft (600 - 150).

Finally, we can use the formula for the area of a rectangle to find the greatest possible area:

A = 150 * 450 = 67,500ft^2

Therefore, the greatest possible area for the garden is 67,500ft^2 when the shorter side is 150ft and the longer side is 450ft.

Step-by-step explanation:

Answer:

Step-by-step explanation:

4ft : $24 -> 1ft = $6

so 7ft = 6X7 = $42

and 6X10 = $60

The coordinates of the intercepts of the depreciation equation are (9, 0) and (0, 22,995).

The x intercept is the x coordinate of a point where the line touches the X axis.

The y intercept is the y coordinate of a point where the line touches the Y axis.

Here, there are two variables.

The independent variable x is the number of years.

The dependent variable y is the value of the car.

x intercept is the year when the value of the car is 0.

Given that, model of a car loses all of it's marketable value after 9 years.

x intercept = 9

y intercept is the value of the car in the 0th year.

Initial value of the car = $22,995

y intercept = 22,995

Hence the intercepts are (9, 0) and (0, 22,995).

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Answer:

the answer is E

Step-by-step explanation:

your welcome

The average speed of the tsunami was approximately 496.45 km/hr.

To find the average speed of the tsunami, we need to know the distance it traveled (7546 kilometers) and the time it took to travel that distance (15 hours and 12 minutes).

First, we need to convert the time to a single unit of measurement. For this calculation, we'll use hours. To do this, we'll convert the minutes to hours:

15 hours + 12 minutes ÷ 60 minutes/hour

= 15.2 hours

Next, we can divide the distance traveled by the time it took:

7546 km ÷ 15.2 hours

= 496.45 km/hr

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Using a system of equations, the unit cost of one roll of plain wrapping paper and one roll of holiday wrapping paper is as follows:

A system of equations is two or more equations solved at the same time, concurrently, or simultaneously.

A system of equations is otherwise known as simultaneous equations.

                         Plain Wrapper   Holiday Wrapper     Total Cost

Cody sales               5                           8                      $174.00

Aliyah                       5                          10                      $210.00

Let the unit cost of Plain Wrapper = x

Let the unit cost of Holiday Wrapper = y

5x + 8y = 174... Equation 1    

5x + 10y = 210... Equation 2

Subtract Equation 1 from Equation 2:

5x + 10y = 210

-

5x + 8y = 174

2y = 36

y = 18

y = $18

Substitute y = 18 in either equation:

5x + 8y = 174

5x + 8(18) = 174

5x +144 = 174

5x = 174 - 144

5x = 30

x = 6

x = $6

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Answer:

[tex]1) p = 205 - 3 = 202 \ 2)2x \div 7 = 4 \\ 2x = 28 \\ x = 14 \\ \\ 3)3y - 6 = 9 \\ 3y = 9 + 6 \\ 3y = 15 \\ y = 5[/tex]

Therefore , the solution of the given problem of function comes out to be  f(x) = 1.1f(x + 1) is the solution for the graph.

The study of mathematics includes looking at numbers, their variables, the world around us, buildings, and both real and imagined places. An illustration of the relation between the quantity of inputs and the appropriate outputs for each is called a function. A function, simply described, is a group of inputs who, when combined, provide distinct outputs for each input. Every function has a city, province, or scope—also referred to as a domain—assigned to it. Functions are usually indicated with the letter f. (x). The input contains an x.

Here,

Given:

The parent function f(x) is translated left by one unit and slightly stretched vertically to form g(x).

=>g(x) is:

=> f(x) = 1.1f(x + 1)

Thus , f(x) = 1.1f(x + 1) is the given function which is graphed here.

Therefore , the solution of the given problem of function comes out to be  f(x) = 1.1f(x + 1) is the solution for the graph.

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m∠FHG is given as 120 degrees

100 + ∠FJG = 180 degrees

∠FJG = 80 degrees

∠BGD = ∠AGJ They are vertically opposite

∠HGI + ∠GIH + ∠IHG = 180

40 + 80 + ∠IHG = 180

∠IHG = 60 degrees

∠IHG + m∠FHG = 180 degrees

60 + m∠FHG = 180

m∠FHG = 120 degrees

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Answer: 5n+30

( The problem was incomplete on my end )

( Hope this helps )

Answer:

Non-linear

Explanation below

Step-by-step explanation:

The relationship is clearly non-linear

If it where a linear relationship then the temperature change per hour would be constant throughout the time period when the observations were made.

The resultant graph would be a straight line

Here the graph rises at a decreasing rate until it almost flattens out. This means the temperature reaches a maximum and stays at that maximum.

Trapezoidal Rule: [tex](b-a)^3 / 96n^2,[/tex] Simpson's Rule: [tex](b-a)^5 / 2880n^4\\[/tex].  Both approximations have error of 0.0208.

For the Trapezoidal Rule, the formula for estimating the error is |E| ≤ (b − a)3/12n2[max |f ''(x)|], a ≤ x ≤ b. In this case, the integral is from x=1 to x=3, so b-a = 2. Plugging in all the values, we get [tex]|E| ≤ 2^3/12(4)^2(2)[/tex] or |E| ≤ 0.0208. For the Simpson's Rule, the formula for estimating the error is |E| ≤ (b − a)5/180n4[max |f (4)(x)|], a ≤ x ≤ b. Again, b-a = 2. Plugging in all the values, we get[tex]|E| ≤ 2^5/180(4)^4(2)[/tex] or |E| ≤ 0.0208. Therefore, the error in approximating the integral with n = 4, using the Trapezoidal Rule and Simpson's Rule, is 0.0208.

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Histograms are commonly used to visualize the distribution of a dataset by grouping the data into bins and representing the frequency of each bin by the height of a bar.

They are useful for observing the spread or variability of the data and determining the shape of the data, such as whether it is symmetrical or skewed. They cannot be used to observe individual data points, but they provide a good visual representation of the overall pattern of the data. Histograms are not appropriate for multiple choice questions as they do not display individual data points in a clear manner. To display parts of a whole, pie charts are a better choice as they show the proportion of each category as a sector of a circle

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Answer: 0.75 :D Hope this helps

Step-by-step explanation:

Solution:

Area=15400mm^2

Now,

Area=pi×r^2

or,15400=22/7×r^2

or,15400×7=22×r^2

or,107800=22r^2

or,107800/22=r^2

or,4900=r^2

or,r=70

Also,

Diameter (d)=r×2

=70×2

=140

Answer: 29.8 feet

Step-by-step explanation:

To solve this, the first step is to make the imaginary triangle (look at the picture below). Now, we use the basic trigonometry functions. Since we have to find tge base part of the triangle (which is the adjacent one to the angle, and we already have the opposite to the angle. So, now we know we have to use the tan ratio. We now solve it with the following method:

[tex]tan(Angle) = \frac{Opposite}{Adjacent} \\[/tex]

Now we sub in our values and use the calculator to solve it:

[tex]tan(40) = \frac{25}{x}\\\\x = \frac{25}{tan(40)} \\\\x = 29.8 (1 d.p)[/tex]

The area of the square block is 48,881 m2, which is calculated by multiplying the length of each side (221 m) by itself.

The area of a square can be calculated by multiplying the length of one side by itself. In this case, the length of each side is 221 m. To find the area of the square block, we need to multiply 221 m by itself. This gives us 48,881 m2 as the final answer. To summarize, the area of the square can be found by multiplying the length of one side by itself. In this case, the length of each side of the block was 221 m, so 221 m multiplied by 221 m results in a total area of 48,881 m2.

The complete question: In one city there are four straight streets that form  a square block. The length of each side of the block is 221 m. Find the area of the square defined by this city block.

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The p-value is 0.063, which indicates that there is not strong evidence to reject the null hypothesis that the percentage has stayed the same.

The p-value can be calculated by using a one-proportion z-test. The null hypothesis would be that the percentage has stayed the same from last year, and the alternative hypothesis is that the percentage has decreased.

The formula for the z-score is (x-p)/√(p(1-p)/n), where x is the observed proportion (39/260), p is the expected proportion (0.20), and n is the sample size (260). The p-value is then calculated using the z-score and the cumulative distribution function.

Therefore p-value, in this case, is 0.063, which indicates that there is not strong evidence to reject the null hypothesis that the percentage has stayed the same.

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The value of x for the equation is -10.

To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. By eliminating all common factors from the numerator and denominator and putting the fraction in its simplest/lowest form, we can simplify fractions.

Given equation,

-3/4(x + 2) = 6

both sides multiply by -4/3

-3/4(x + 2) * -4/3 = 6 * -4/3

x + 2 = -8

subtract 2 from both sides

x + 2 - 2 = -8 - 2

x = -10

Hence the value of x is -10.

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The probability that Juan will choose a kind of plant his mother would want is 6/30, which is equal to 0.2 or 20%

To calculate the probability that Juan will choose a kind of plant his mother would want, out of 30 plants, six of them are a kind that his mother would want, first divide the number of plants his mother would want (6) by the total number of plants (30). This will give you a decimal, 0.2. To turn this decimal into a percent, multiply it by 100. This will give you 20%, or a 20% chance of Juan choosing a kind of plant his mother would want. To summarize, therefore, the probability that Juan will choose a kind of plant his mother would want is 0.2 or 20%.

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Answer: 4 / 3

Step-by-step explanation:

Soh Cah Toa

In this case, we'll use Toa

Tangent = Opposite / Adjacent

Tan A = 40 (opposite) / 30 (adjacent)

Tan A = 40 / 30 = 4 / 3 (simplified)

Answer:

              The correct scale faction the first pentagon dilated by to create the second pentagon is 1.25.

Step-by-step explanation:

              Since the second pentagon is a dilation of the first pentagon, we can conclude these pentagons are similar, meaning the shape retained all of its previous angles, and all the corresponding sides are dilated by a common scale factor. Since we know the values of a pair of corresponding sides, we can use those to find the scale factor of dilation.

             The corresponding side of the original pentagon is 4 units, and the corresponding side of the dilated pentagon is 5 units. Since the first pentagon dilated to become the second, in order to solve the scale factor the pentagon dilated by, we'd have to divide the side given on the second pentagon by the corresponding side of the first, which will be 5 ÷ 4 = 1.25. Therefore, that will be the scale factor the pentagon dilated by.

Have a great day! Feel free to let me know if you have any more questions :)

Answer:

8 m

Step-by-step explanation:

All the sides of a square are equal.

let x = length of one side

A = x² = 64 m²

√x² = x = √64 = 8

The equation of the parabola is x² - 8x + 16 = 0

To find the equation of the parabola with focus (4, -3) and directrix y = -3, we can use the definition of a parabola.

A parabola is the set of all points that are equidistant to the focus and the directrix.

The distance from a point (x, y) to the directrix y = -3 is simply the vertical distance between the point and the line, which is |y - (-3)| = |y + 3|.

The distance from a point (x, y) to the focus (4, -3) can be found using the distance formula:

d = √[(x - 4)² + (y + 3)²]

Since the point is equidistant to the focus and the directrix, we have:

d = |y + 3|

Squaring both sides, we get:

(x - 4)² + (y + 3)² = (y + 3)²

Simplifying, we get:

(x - 4)² = 0

Thus, the equation of the parabola is simply:

x² - 4x - 4x + 16 = 0

x² - 8x + 16 = 0

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