A painter starts with a blank 30 inch by 18 inch piece of rice paper. The painter wants to leave a uniform border x inches wide along the outer edges so that the painting can be framed. Write a polynomial in standard form that represents the area of paper that can be painted

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

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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Answer: 5n+30

( The problem was incomplete on my end )

( Hope this helps )

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.

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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:

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

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: 0.75 :D Hope this helps

Step-by-step explanation:

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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the magnitude of the resultant is [tex]\sqrt{2}[/tex] times the magnitude of each individual vector, not one-third.

No, that is incorrect. The magnitude of the resultant of three vectors having equal magnitudes and making an angle of 120 degrees with each other is not one-third the magnitude of the component vectors.

The magnitude of the resultant of three vectors depends on the angle between them, as well as their magnitudes. In general, the magnitude of the resultant of three vectors can be calculated using the law of cosines, which states that the square of the magnitude of the resultant (R^2) is equal to the sum of the squares of the magnitudes of the individual vectors ([tex]A^2, B^2, and C^2[/tex]), plus twice the product of the magnitudes of two of the vectors multiplied by the cosine of the angle between them.

For three vectors of equal magnitude (A = B = C = m), the magnitude of the resultant can be calculated as:

[tex]R^2 = 3m^2 + 2m^2 * cos(120) = 3m^2 - m^2 = 2m^2[/tex]

[tex]R = \sqrt{2} * m[/tex]

Therefore, the magnitude of the resultant is sqrt(2) times the magnitude of each individual vector, not one-third.

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Question: Three Vectors Have Equal Magnitudes And Make 120° With Each Other. We Can Say That The Magnitude Of The Resultant Is One-Third The Magnitude Of The Component Vectors. The Resultant Is Zero. The Magnitude Of The Resultant Is Equal To The Magnitude Of The Component Vectors. The Magnitude Of The Resultant Is More Than Three Times The Magnitude Of Each component Vector.

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 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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Answer:

arc BAC = 276°

Step-by-step explanation:

the sum of the angles around point D is 360°

sum the central angles and equate to 360

7n + 12 + 6n + 13n - 16 = 360

26n - 4 = 360 ( add 4 to both sides )

26n = 364 ( divide both sides by 26 )

n = 14

Then

∠ ADB = 7n + 12 = 7(14) + 12 = 98 + 12 = 110°

∠ ADC = 13n - 16 = 13(14) - 16 = 182 - 16 = 166°

• the arc of a circle is equal to the central angle it subtends

arc BA = ∠ ADB = 110°

arc AC = ∠ ADC = 166°

Then

arc BAC = arc BA + arc AC = 110° + 166° = 276°

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

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:

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:

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 correct response is A since this triangle has a dilatation of (0,0),(1,0),(1,1)) by a factor of 1/3 with respect to the origin.

A figure will dilate if its sides are scaled (multiplied) by the same amount. The scale factor of that dilatation is the name given to that figure.

It is also known as scaling a figure, but since coordinates are involved, it also requires the center of a dilation, which is similar to a pinned point and remains in the same location after dilation.

It appears as though we are adjusting the size of the figure (or leaving it the same when the scale factor is 1).

The positions (0, 0), (3, 0), (3,3)

1/3 scale factor

Now

the GPS coordinates;

(0,0),(1,0),(1,1)

Thus, required dilation is (0,0),(1,0),(1,1).

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Complete question:

A right triangle is drawn on the coordinate plane. Which is a dilation of this triangle with respect to the origin by a factor of 1/3?

Answer:

The positions (0, 0), (3, 0), (3,3)

1/3 scale factor

Now

the GPS coordinates;

(0,0),(1,0),(1,1)

Thus, required dilation is (0,0),(1,0),(1,1).

Step-by-step explanation:

option a

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 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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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:

the answer is E

Step-by-step explanation:

your welcome

Answer:your mom

Step-by-step explanati

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:

[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]

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.

Answer:

Step-by-step explanation:

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

so 7ft = 6X7 = $42

and 6X10 = $60

Answer:

55

Step-by-step explanation:

80% ^ 2 = 0.64

so f(2) = 86*0.64 = 55