Mason's mother wants to make 8 curtains that each require 2 1/5 (two, one over five) metres of material in a standard width, but she only has 16 1/4(sixteen, one over four)metres of material. There are to be no seams in her curtains. She asks Mason to buy more material.
a. How much more material must Mason buy?
B. How much material is left over?

The arithmetic sequence expression for the given sequence 6, 9, 12, 15, 18....... would be aₙ = 6+(n-1)3.

A progression or sequence of numbers known as an arithmetic sequence maintains a consistent difference between each succeeding term and its predecessor.

The common difference of that mathematical progression is the constant difference.

'n' denotes the term's position in the supplied arithmetic sequence in the formula for obtaining the general term: a = a1 + (n - 1) d. For instance, a2 denotes the second phrase in the sequence.

So, the given sequence is:

6, 9, 12, 15, 18

Common difference (d) is: 9 - 6 = 3

Then, the sequence expression would be:

aₙ = 6+(n-1)3

Therefore, the arithmetic sequence expression for the given sequence 6, 9, 12, 15, 18....... would be aₙ = 6+(n-1)3.

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Answer:

the answer is d

Step-by-step explanation:

hope this helps

l will spend $58.40 on gas.

What is Multiplication?

Multiplication is an arithmetic operation that involves combining two or more numbers to produce a third number called the product. The symbol for multiplication is "×" or "*".

For example, if you have 3 apples and want to know how many apples you would have if you tripled the amount, you can multiply 3 by 3 to get the answer: 3 × 3 = 9. So, if you tripled the amount of apples you had, you would have 9 apples in total.

Multiplication can be thought of as repeated addition. For instance, 3 × 4 is the same as 3 + 3 + 3 + 3, which equals 12. In this example, 3 is added to itself four times.

Here given, a car holds 50 litres of gas and the price is 116.8 ($1.168) per litre.

We want to calculate the total cost of the gas.

We can find it by multiplying the number of litres by the price per litre

Total cost = [tex]50 \times 1.168[/tex]

Total cost = $58.40

Therefore, l will spend $58.40 on gas.

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Correct question is "Your car holds 50 litres

of gas. If the price is 116.8 ($1.168) per litre then how much money will you spend on gas?"

Answer: 348 square meters

Step-by-step explanation:

To find the surface area of a rectangular prism, we need to calculate the area of each of the six faces and add them together. A rectangular prism has three pairs of opposite faces: the length (l) and width (w), the length (l) and height (h), and the width (w) and height (h).

Given dimensions: length (l) = 6m, width (w) = 4m, and height (h) = 15m

Area of the length and width faces (lw): 6m * 4m = 24m²

Since there are two opposite faces, the total area of these faces is 2 * 24m² = 48m².

Area of the length and height faces (lh): 6m * 15m = 90m²

Since there are two opposite faces, the total area of these faces is 2 * 90m² = 180m².

Area of the width and height faces (wh): 4m * 15m = 60m²

Since there are two opposite faces, the total area of these faces is 2 * 60m² = 120m².

Now, add the areas of all the faces together:

Surface area = 48m² (lw faces) + 180m² (lh faces) + 120m² (wh faces) = 348m²

The surface area of the rectangular prism is 348 square meters.

Answer:

the surface area of the rectangular prism is 348 square meters.

Step-by-step explanation:

The surface area of a rectangular prism can be found using the formula:Surface Area = 2lw + 2lh + 2whwhere l, w, and h are the length, width, and height of the prism.In this case, the dimensions of the rectangular prism are:l = 6m

w = 4m

h = 15m

Substituting these values into the formula, we get:

Surface Area = 2(6m)(4m) + 2(6m)(15m) + 2(4m)(15m)

Surface Area = 48m^2 + 180m^2 + 120m^2

Surface Area = 348m^2

The ball is in the air for a total of 2 seconds.

We can use the fact that the time it takes for the ball to reach its maximum height is half of the total time the ball is in the air.

The initial vertical velocity of the ball is 32 ft/s and the acceleration due to gravity is -32 ft/s^2 (since it acts in the opposite direction to the initial velocity). We can use the kinematic equation:

y = y0 + v0*t + (1/2)at^2

Where

When the ball reaches its maximum height, its vertical velocity becomes 0. Therefore, we can use the equation:

v = v0 + at

To find the time it takes for the ball to reach its maximum height, since the vertical velocity at that point is 0.

v = v0 + at

0 = 32 - 32t

t = 1 second

So it takes 1 second for the ball to reach its maximum height. At this point, the vertical velocity of the ball is 0, so we can use the equation:

y = y0 + v0*t + (1/2)at^2

to find the maximum height:

y = 5 + 32(1) + (1/2)(-32)(1)^2

y = 21 feet

Now we can use the fact that the time it takes for the ball to fall back to the ground is the same as the time it took to reach its maximum height. Therefore, the total time the ball is in the air is:

2*1 second = 2 seconds

So the ball is in the air for a total of 2 seconds.

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Answer:

Step-by-step explanation:

Volume of a rectangular prism = l x w x h

I am reading the width as 12 1/2 ft

Treat the depth of the ball pit as height

Vol = l x w x h

875 = (20)(12 1/2)(h)

875 = 250(h)

875/250 = 250h/250

3 1/2 = height

depth of the ball pit is 3 1/2 ft

The ball pit is 3.5 feet deep. This can be answered by the concept Surface area.

To find the depth of the ball pit, we can use the equation: Volume = length x width x depth.

The volume of the ball pit is given as 875 cubic feet, the length is 20 feet and the width is 12.5 feet. Let d be the depth of the ball pit. Therefore, the equation we can use is:

875 = 20 x 12.5 x d

To solve for d, we can divide both sides of the equation by (20 x 12.5):

d = 875 / (20 x 12.5)

d = 3.5 feet

Therefore, the ball pit is 3.5 feet deep

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If the pyramid is sliced horizontally (parallel to the base), the resulting cross section would be a regular pentagon with the same side length as the base of the pyramid

If the pyramid is sliced horizontally (parallel to the base), the resulting cross section would be a regular pentagon with the same side length as the base of the pyramid. This is because a horizontal slice would intersect all five sides of the pentagonal base at equal distances from the apex of the pyramid, resulting in a regular pentagon.

If the pyramid is sliced vertically through the top vertex (perpendicular to the base), the resulting cross section would be a triangle. The triangle's shape would depend on the height of the pyramid and the angle of the slice. The base of the triangle would be a regular pentagon, with the height of the pyramid as the altitude. The apex of the triangle would be the top vertex of the pyramid. The shape of the triangle would change depending on the angle of the slice, but it would always be an isosceles triangle since the slice passes through the apex, which is the vertex of the pyramid where all the edges meet.

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The first five terms are 2, 6, 18, 54, 162.

A number is a fundamental building block of mathematics.

Numbers are used for indexing, counting, measuring, and a variety of other tasks.

According to their characteristics, there are various sorts of numbers, including natural numbers, whole numbers, rational and irrational numbers, integers, real numbers, complex numbers, even and odd numbers, etc.

The resultant number can be calculated by using the fundamental arithmetic operations for integers.

Tally marks were formerly used before numbers.

Numbers are a crucial aspect of our daily lives, from the number of rounds we run around the race track to the number of hours we sleep at night, and much more.

According to our question-

a series where each subsequent term is obtained by multiplying the preceding one by a shared ratio.

The order is provided by:

a, ar, ar2, aar3, aar4, aar5,...

What is the nth term provided by-

a_n = ar^(n-1)

Second term = 6

a_2 = ar^(2-1)

6 = ar^1

6 = ar

Hence, The first five terms are 2, 6, 18, 54, 162.

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the first five terms of the geometric sequence can be either [tex]{2, 6, 18, 54, 162} or {-2, 6, -18, 54, -162}.[/tex]

Assume that "a" is the first letter of the geometric sequence and "r" is the common ratio.

According to the problem statement, the second term is 6. Therefore, we have:

[tex]ar = 6 .....(1)[/tex]

Similarly, the fourth term is 54, which gives us:

[tex]ar^3 = 54 .....(2)[/tex]

We must first determine the values of "a" and "r" in the geometric sequence. The two equations mentioned above can be solved simultaneously to achieve this.

The result of dividing equation [tex](2)[/tex] by equation [tex](1)[/tex] is

[tex]r^2 = 9[/tex]

When we square the two sides, we obtain:

r = ±3

Now, using equation (1), we can find the value of "a" as follows:

[tex]ar = 6[/tex]

Substituting r = 3, we get:

[tex]3a = 6[/tex]

[tex]a = 2[/tex]

Substituting [tex]r = -3[/tex], we get:

[tex]-3a = 6[/tex]

[tex]a = -2[/tex]

Therefore, the first term of the geometric sequence is either  [tex]2[/tex] or [tex]-2[/tex]  , and the common ratio is 3 or -3.

If the first term is 2 and the common ratio is 3, then the first five terms of the geometric sequence are: [tex]2, 6, 18, 54, 162[/tex]

The first five terms of the geometric sequence are as follows, if the common ratio is three and the first term is two:

[tex]-2, 6, -18, 54, -162[/tex]

So, the first five terms of the geometric sequence can be either [tex]{2, 6, 18, 54, 162} or {-2, 6, -18, 54, -162}.[/tex]

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Based on both the mean and median values, we can conclude that Wide Awake typically sells more coffee per hour than Coffee Ground.

What are the mean and median?

The mean and median are two measures of central tendency that can be used to describe a set of data. The median is the middle value in the data set when the values are arranged in order from lowest to highest. If there are an even number of values, the median is the average of the two middle values.

To determine which coffee shop typically sells the most amount of coffee per hour, we need to compare the measures of center (mean and median) of the data for each shop.

Calculating the mean of each dataset, we get:

Mean of Coffee Ground = (1.5+20+3.5+12+2+5+11+7+2.5+9.5+3+5) / 12 = 6.5/2 = 5.42 gallons

Mean of Wide Awake = (2.5+10+4+18+4+3+6+5+2.5) / 9 = 56 / 9 = 6.22 gallons

Calculating the median of each dataset, we get:

Median of Coffee Ground = 4.25 gallons

Median of Wide Awake = 4.5 gallons

Comparing the measures of the center, we see that the mean value of coffee sold per hour at Coffee Ground is approximately 5.42 gallons, while the mean value of coffee sold per hour at Wide Awake is approximately 6.22 gallons.

Therefore, on average, Wide Awake sells more coffee per hour than Coffee Ground.

However, we also see that the median value of coffee sold per hour at Wide Awake is 4.5 gallons, while the median value of coffee sold per hour at Coffee Ground is 4.25 gallons.

This suggests that the middle value of coffee sold per hour is higher for Wide Awake than for Coffee Ground.

Therefore, based on both the mean and median values, we can conclude that Wide Awake typically sells more coffee per hour than Coffee Ground.

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Answer:

[tex]3 \: {cm}^{2} [/tex]

Step-by-step explanation:

Given:

h (height) = 1,5 cm

b (base) = 4 cm

Find: A (area) - ?

[tex]a = \frac{1}{2} \times b \times h[/tex]

[tex]a = \frac{1}{2} \times 4 \times 1.5 = 3 \: {cm}^{2} [/tex]

The possible values of |x + 7| are:

-(x + 7), if x < -7

0, if x = -7

(x + 7), if x > -7

What is the inequality equation?

The expression |x + 7| represents the absolute value of x + 7. An inequality equation involving absolute value can be written as:

|x + 7| < a

where "a" is a positive constant. This inequality means that the distance between x + 7 and 0 on the number line is less than "a". In other words, x can be any value within "a" units of -7.

The possible values of |x + 7| depend on the value of x.

If x is negative, then |x + 7| will be equal to -(x + 7), which is negative.

If x is zero or positive, then |x + 7| will be equal to (x + 7), which is non-negative.

Therefore, the possible values of |x + 7| are:

-(x + 7), if x < -7

0, if x = -7

(x + 7), if x > -7

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the length of NR is approximately 22.8, rounded to the nearest tenth.

To find the length of NR, we need to first identify any relationships between the chords and the arcs they intercept in the circle. From the diagram, we can see that chord PQ intersects arc ONR and chord NO intersects arc PQN.

There are two main properties we can use to solve this problem: the chord-chord power theorem and the angle-arc theorem. The chord-chord power theorem states that if two chords intersect in a circle, the product of the lengths of their segments is equal. That is:

(PQ)(QR) = (NO)(NR)

We know that PQ = 48 and NO = 21, so we can plug those values into the equation and solve for NR:

(48)(QR) = (21)(NR)

QR = (21NR)/48

To find QR, we can use the angle-arc theorem. This theorem states that the measure of an angle formed by two intersecting chords is equal to half the sum of the measures of the arcs they intercept. That is:

∠QNR = (arc PN + arc OQ)/2

We know that arc PN is equal to arc PQ (since they are intercepting the same arc), and we know that arc OQ is equal to the entire circumference of the circle minus arc PQ. The circumference of a circle is given by 2πr, where r is the radius. We don't know the radius of the circle, but we can find it using the Pythagorean theorem. We know that NO and PQ are both chords, so they must intersect at the center of the circle. Therefore, the line segment connecting the center of the circle to the midpoint of chord NO is a perpendicular bisector of NO. This gives us a right triangle with legs of 10.5 and 24 (half of 21 and half of 48). Using the Pythagorean theorem, we can find that the radius of the circle is approximately 26.2.

Now we can plug in our values for arc PN and arc OQ:

∠QNR = (arc PQ + (2πr - arc PQ))/2

∠QNR = πr

We know that QR is the side opposite the angle ∠QNR in right triangle QNR. Therefore, we can use the sine function to find QR:

sin(∠QNR) = QR/r

sin(πr) = QR/26.2

QR = 26.2sin(πr)

Now we can substitute this value for QR into our equation from the chord-chord power theorem:

(48)(26.2sin(πr)) = (21)(NR)

NR ≈ 22.8

Therefore, the length of NR is approximately 22.8, rounded to the nearest tenth.

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The area of the kitchen in square feet is 132[tex]ft^{2}[/tex]

To find the area of the rectangular kitchen, we need to multiply the length by the width.

The length of the kitchen can be found by subtracting the x-coordinates of the two points on the same vertical side. So, the length is 8 - (-3) = 11 feet.

The width of the kitchen can be found by subtracting the y-coordinates of the two points on the same horizontal side. So, the width is 4 - (-8) = 12 feet.

Therefore, the area of the kitchen is:

Area = Length x Width = 11 ft x 12 ft = 132 square feet

So the answer is 132[tex]ft^{2}[/tex].

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Answer: The degree of (4by+2b-by) is 2, as it is a quadratic expression with the highest exponent of the variable being 2.

Step-by-step explanation: The degree of a polynomial is the highest exponent of the variable. In this case, the highest exponent of the variable is 2, which appears in the term 4by. Therefore, the degree of (4by+2b-by) is 2.

A sample size of at least 109 GPAs to estimate the population mean with a 90% confidence level

Confidence level = 90%

Standard deviation = 0.88

Mean = 0.1

Calculating the sample size -

[tex]n = [(zα/2σ) / E]^2[/tex]

The crucial value for a confidence level of 90%, denoted by z/2, may be determined using a typical normal distribution table or calculator, where n is the required sample size. The value of z/2 at a 90% degree of confidence is around 1.645. The problem statement specifies that the population standard deviation at 0.88 and that E is the most significant error of the sample mean from the population mean at 0.1.

Therefore, substituting the values -

[tex]n = [(1.645 x 0.88) / 0.1]^2[/tex]

n = 108.25

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Answer:

Step-by-step explanation:

Easy...

a=.5bh

so, .5*18*15= 135 in^2.

It looks like it has about four triangular sides, so just multiply that number four times.

135*4= 540

add the base

a=lw

=15*15

=225

540+225= 765 in^2

Let's hope.  A better photo next time would definitely help....;)

The leading coefficient of the polynomial -4x^3+9  is -4.

The leading coefficient of a polynomial is the coefficient of the term with the highest degree.

In this polynomial, -4x^3+9, the term with the highest degree is -4x^3, and the coefficient of this term is -4.

Therefore, the leading coefficient of the polynomial is -4.

The degree of a polynomial is the highest exponent of the variable in any of its terms. In this polynomial, the variable is x and the highest exponent is 3. So, the degree of this polynomial is 3.

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Let's represent the cost of a cup of corn as 'c' and the cost of a taco as 't'.

From the first statement, we know that:

2c + 4t = 19 (equation 1)

From the second statement, we know that:

3c + 2t = 14.5 (equation 2)

We can solve this system of equations using elimination or substitution. Here, we'll use substitution.

Rearranging equation 2, we get:

3c = 14.5 - 2t

Dividing both sides by 3, we get:

c = 4.83 - 0.67t

Now we can substitute this expression for 'c' into equation 1:

2(4.83 - 0.67t) + 4t = 19

Simplifying, we get:

9.66 - 0.34t = 19

Subtracting 9.66 from both sides, we get:

-0.34t = 9.34

Dividing both sides by -0.34, we get:

t = -27.47 ≈ $-2.75

Since a negative price for a taco doesn't make sense, we made an error somewhere. Checking our calculations, we can see that we made a mistake in the expression for 'c'. It should be:

c = (14.5 - 2t)/3

Substituting this expression for 'c' into equation 1:

2[(14.5 - 2t)/3] + 4t = 19

Multiplying both sides by 3:

2(14.5 - 2t) + 12t = 57

Expanding and simplifying:

29 - 4t + 12t = 57

8t = 28

t = 3.5

Therefore, the tacos cost $3.50.

To find the surface area of a pyramid with a square base, we need to find the area of the square base and the area of each triangular face, then add them together.

The area of the square base is the square of the length of one of its sides. In this case, the side length is 10 inches, so the area of the base is:

[tex] \rm A_{base} = 10^2 = 100 \text{ square inches}[/tex]

To find the area of each triangular face, we need to find the height of the pyramid. The height of the pyramid is the perpendicular distance from the apex (the top of the pyramid) to the base. To find the height, we can use the Pythagorean theorem, since we know the length of the slant height (15 inches) and half the length of the base (5 inches):

[tex] \rm{h = \sqrt{15^2 - 5^2} = \sqrt{200} = 10\sqrt{2} \text{ inches}}[/tex]

Now we can find the area of each triangular face using the formula:

[tex] \rm{A_{face} = \frac{1}{2} \times \text{base} \times \text{height}}[/tex]

where the base is the side length of the square base, and the height is the height of the pyramid. In this case, we have:

[tex] \rm{A_{face} = \frac{1}{2} \times (10 \text{ inches}) \times (10\sqrt{2} \text{ inches}) = 50\sqrt{2} \text{ square inches}}[/tex]

Finally, we can find the surface area of the pyramid by adding the area of the base and the area of the four triangular faces:

[tex] \rm{A_{total} = A_{base} + 4A_{face} = 100\text{ square inches} + 4(50\sqrt{2} \text{ square inches}) \approx 314.16 \text{ square inches}}[/tex]

Therefore, the surface area of the pyramid is approximately 314.16 square inches.

As, AD = BC, the given shape on the graph shows the rectangle found using distance formula.

An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides. A rectangle has two dimensions—length and width—because it is a two-dimensional form. The rectangle's longer side is its length, while its shorter side is its breadth.

From the given graph, The coordinates of A,B, C and D are-

A = (-3,1)

B = (0,3)

C = (4, -3)

D = (1, -5)

Find the distance AD and BC, if both are equal it forms a rectangle:

Using the distance formula:

d = √[(x2 - x1)² + (y2 - y1)²]

AD = √[(- 3 - 1)² + (1 + 5)²]

AD = √(16 + 36)

AD = √53

BC = √[(0 - 4)² + (3 + 3)²]

BC = √(16 + 36)

BC = √53

As, AD = BC, the given shape on the graph shows the rectangle found using distance formula.

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The probability that the next piece of track Carly picks will be straight is 8/24 or 1/3

From the given information, Carly has picked 8 straight, 7 curved, 4 cross, and 5 switch tracks.

The total number of pieces of the track she has picked is 8 + 7 + 4 + 5 = 24

The probability that the next piece of track Carly picks will be straight is calculated as follows:

Probability = Number of straight tracks/Total number of tracks= 8/24= 1/3T

Therefore, the probability that the next piece of track Carly picks will be straight is 1/3.

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Answer: 1/3

Step-by-step explanation: i did this question and got it right

After solving the given equation 1/4b - 2 = -1/2b + 4, the resultant value of b is 8/3 respectively.

An equation is a mathematical expression with two equal sides and an equal sign.

4 + 6 = 10 is an illustration of an equation.

On the left side of the equal sign, you can see 4 + 6, and on the right, you can see 10.

A formula exists in every equation.

Some equations do not have formulae.

Equations are designed to be solved for a variable.

We look over formulas.

So, we have the equation:

1/4b - 2 = -1/2b + 4

Now, solve the equation for b as follows:

1/4b - 2 = -1/2b + 4

1/4b = -1/2b + 6

1/4b + 2/1b = 6

1+8/4b = 6

9/4b = 6

b = 6 * 4/9

b = 2 * 4/3

b = 8/3

Therefore, after solving the given equation 1/4b - 2 = -1/2b + 4, the resultant value of b is 8/3 respectively.

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Brie saves $600 each month.

What is equation?

An equation is a  statement that shows that two expressions are equal. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division

To determine how much money Brie saves each month, we need to subtract her expenses from her income.

Income = $3,000

Expenses = $1,400 + $700 + $200 + $100 = $2,400

Savings = Income - Expenses

Savings = $3,000 - $2,400

Savings = $600

Therefore, Brie saves $600 each month.

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The height of the basketball hoop is 13.32'.

What is law of similarity?

The Law of Similarity in mathematics states that if two geometric figures have the same shape but different sizes, then they are considered similar. This means that the corresponding angles of the two figures are congruent, and the corresponding sides are proportional in length.

Formally, if we have two geometric figures A and B, and if every angle of figure A is congruent to the corresponding angle of figure B, and if the ratio of the length of any pair of corresponding sides of A and B is constant, then we can say that A and B are similar figures.

Here we can see two triangle and base of two triangle is given.

Here base of small triangle is 12' and the base of big triangle is (12'+25') = 37'.

It is also given that height of small triangle is 4'3.84".

Now we want to find the height of the basketball hoop which is equal to height of big triangle.

Let the height of the basketball hoop be x.

So, by law of similarity ratios,

12'/37' = 4'3.84"/x

Now, 4'3.84" = 4.32'

So, 12'/37' = 4.32'/x

Therefore, x = 13.32'

Therefore, the height of the basketball hoop is 13.32'.

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With the confidence interval, it can be concluded with 99% confidence that the true proportion of teenage drivers in Atlanta who text while driving lies between 35.89% and 75.23%.

The confidence interval (CI) is equal to the sample proportion (p) plus or minus the product of the critical value (z*) and the standard error of the proportion, where the standard error is calculated by taking the square root of the product of the sample proportion, its complement (1 - p), and the reciprocal of the sample size (n), formed in an equation.

where:

p is the sample proportion (15/27 in this case)

z* is the critical value from the standard normal distribution for the desired confidence level (99% in this case, which corresponds to a z* value of 2.576)

n is the sample size (27 in this case)

Substituting the given values, we get:

CI = 0.5556 ± 2.576*√((0.5556(1-0.5556))/27)

Simplifying this expression, we get:

CI = 0.5556 ± 0.1967

So the 99% confidence interval for the population proportion of teens who text while driving is:

(0.3589, 0.7523)

Therefore, we can be 99% confident that the true proportion of teenage drivers in Atlanta who text while driving lies between 35.89% and 75.23%.

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Answer:

3 and 5

Step-by-step explanation:

|x-4| = 1 is the same as x-4 = 1 and -x+4 = 1

x-4=1

x = 5

-x+4 = 1

-x = -3

x = 3

The least of the integers in arithmetic mean of n consecutive odd integers is 3.

The formula to calculate average or arithmetic mean of evenly distributed set is -

Average = sum of first and last term/2

Keep the values in formula to find the least integer. Since these are consecutively arranged, the first number will be the least number.

10 = first number + 17/2

First number + 17 = 10×2

Performing multiplication on Right Hand Side

First number + 17 = 20

First number = 20 - 17

Performing subtraction

First number = 3

Hence, the least integer is 3.

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The clock that shows the time Mr. Walsh left his house to go to the store would be 3:42 pm.

Mr. Walsh's journey consisted of driving from his house to the store, shopping for 28 minutes, and then driving back home. The total time for his journey would be:

10 minutes (driving to the store) + 28 minutes (shopping) + 10 minutes (driving back home) = 48 minutes

If Mr. Walsh arrived home at 4:30 pm, and we subtract the 48 minutes it took for his entire journey, we can determine the time he left his house to go to the store:

4:30 pm - 48 minutes = 3:42 pm

Therefore, the clock that shows the time Mr. Walsh left his house to go to the store would be 3:42 pm.

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The domain of f is [0, π/2]. The range of [tex]f^-1[/tex] is also [0, /2].

The domain of a function is the set of all possible values for the input variables (usually denoted as x) for which the function is defined. It is the set of all real numbers or other possible values that can be used as input to the function.

To find the inverse function [tex]f^-1[/tex] of f(x) = 2cos(2x), we follow these steps:

Step 1: Replace f(x) with y.

y = 2cos(2x)

Step 2: Swap x and y and solve for y.

x = 2cos(2y)

cos(2y) = x/2

2y = [tex]cos^(-1)[/tex](x/2)

y = (1/2)[tex]cos^(-1)[/tex](x/2)

Therefore, the inverse function of f is [tex]f^-1[/tex](x) = (1/2)[tex]cos^(-1)[/tex](x/2).

To find the range of f, we notice that the range of cos(2x) is [-1, 1]. Multiplying this by 2 gives us the range of f: [-2, 2].

To find the domain of [tex]f^-1[/tex], we notice that the range of [tex]cos^-1[/tex](x) is [0, pi]. Multiplying this by (1/2) and replacing x with x/2, we get the domain of [tex]f^-1[/tex]: [0, π/2].

To find the range of [tex]f^-1[/tex], we notice that the domain of f is [0, π/2]. Therefore, the range of [tex]f^-1[/tex] is also [0, /2].

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