Find the measure of 5

The fraction expression 9 ÷ 2 is 4.5

To evaluate an expression like (9/2), we need to perform the arithmetic operation indicated by the mathematical operator, which in this case is the division symbol "/".

So, we divide the number 9 by the number 2:

9 ÷ 2 = 4.5

The quotient we obtain from this division is 4.5, which means that (9/2) is equal to 4.5.

Therefore, the correct answer to the given question is D. 4.5.

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If a rectangular prism has a length of 2 meters, a width of 4 meters, and a height of 2 meters. The volume of the prism is 16 cubic meters.

The volume of a rectangular prism is given by the formula:

Volume = length x width x height

Substituting the given values, we get:

Volume = 2 meters x 4 meters x 2 meters

Simplifying this expression, we get:

Volume = 16 cubic meters

Therefore, the volume of the prism is 16 cubic meters.

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Given

Let P = Percentage of people using signal

[tex]\text{P} = 78\%[/tex]

Let Q = Percentage of people not using signal

[tex]\text{P + Q} = 1[/tex] ---- Make Q the subject of formula

[tex]\text{Q} = 1 - 78\%[/tex]

[tex]\text{Q} = 1 - 0.78[/tex]

[tex]\text{Q} = 0.22[/tex]

The expected number of people is calculated as 1/Q

[tex]= \dfrac{1}{0.22}[/tex]

[tex]= 4.54[/tex]

[tex]= 5[/tex] ---- Approximated

Hence, the expected number of people a police officer expects to pull over until she finds a driver not using the turn signal is 5

Answer:

They should expect to pull over 5 people.

Answer: width is 12 m

Step-by-step explanation:

Let [tex]x[/tex] be the length of the rectangle. Then the width is [tex]x-4.[/tex] The area of a rectangle is base times height, so our variable [tex]x[/tex] satisfies the equation:

[tex]x(x-4)=192.[/tex]

After a bit of algebraic manipulation, we get [tex]x^2-4x-192=0,[/tex] and we can solve this using the quadratic formula.

This gives us [tex]x = \frac{4 \pm \sqrt{16+4\times192}}{2} = \frac{4 \pm 28}{2} = 2 \pm 14.[/tex] However, we must take the positive solution, as lengths in geometry are always positive. Hence, [tex]x = 2+14=16,[/tex] and width is just [tex]x-4[/tex] which is equal to [tex]\boxed{12}[/tex].

Answer:

the statement 'the dilation changed the orientation of the figure' is NOT true

Step-by-step explanation:

the only transformations that can change a figure's orientation is a reflection, not a dilation like is shown.

the first statement is true because it is an enlargement of the shape

the third is true (look at point I and I', point I is (2,2) and becomes (4,4) which follows 2x 2y)

and the fourth is true because the ratios are 1:1:1:1 for both shapes

Answer:

the root index is 4 the radical is the expression under the radical. (2^7)

Step-by-step explanation:

The circles are similar because you can translate circle 1 using the transformation rule (x + 10, y) and then dilate it using a scale factor of 2/5.

First analyze the centers, the original center is at (-3, 5) and the new center is at (7, 5)

The change is in the x-value, the change is:

7 - (-3) = 10

So there is a translation of 10 units to the right,

And the original radius is R = 10, the new one is R' = 4

if the scale factor of the dilation is k we can write:

10*k = 4

k = 4/10 = 2/5

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To create a scatter plot using the data in the table, we can plot the year on the x-axis and the winning height on the y-axis.

What is scatter plot?

A scatter plot, also known as a scatter chart or scatter diagram, is a graph used in statistics to visually display the relationship between two variables. It is a collection of points on a two-dimensional plane, where each point represents the value of two different variables. One variable is plotted on the x-axis (horizontal) and the other variable is plotted on the y-axis (vertical).

To create a scatter plot using the data in the table, we can plot the year on the x-axis and the winning height on the y-axis. Here is a properly labeled scatter plot using the given data:

In this scatter plot, each data point is represented by a circle (o) located at the corresponding year and winning height.

The x-axis is labeled with the years 1912, 1932, 1952, 1972, 1982, and 2002, and the y-axis is labeled with the winning height in meters. The plot shows that the winning height increased steadily over time, with the largest jump being achieved by Australia in 2002.

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Note that the statement "the dihedral group Dn of a polygon is generated by {r1, s0}" means that every symmetry of the n-sided polygon can be obtained by composing rotations and reflections using r1 and s0. That is, r1 and s0 generate all possible symmetries of the polygon.

In group theory, the dihedral group Dn is a group of symmetries of an n-sided polygon. It consists of rotations and reflections that preserve the shape of the polygon.

The generators of the dihedral group Dn are the elements that can be used to construct all other elements of the group. In the case of a polygon, the two generators are a rotation r1, which rotates the polygon counterclockwise by an angle of 360/n degrees, and a reflection s0, which reflects the polygon over a line passing through two opposite vertices.

Therefore, the statement "the dihedral group Dn of a polygon is generated by {r1, s0}" means that every symmetry of the n-sided polygon can be obtained by composing rotations and reflections using r1 and s0. That is, r1 and s0 generate all possible symmetries of the polygon.

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It should be noted that the composite function for hg(x) = -1 + (3/2)x^4.

A function is a relationship or expression involving one or more variables.  It has a set of input and outputs.  Each input has only one output.  The function is the description of how the inputs relate to the output.

(a) (i) To find g(-2), we substitute -2 for x in the expression for g(x):

g(-2) = 2 - 3(-2)^4 = 2 - 3(16) = 2 - 48 = -46

(ii) To express the composite function hg in the form hg(x), we need to find h(g(x)) and simplify the expression.

h(g(x)) = h(2 - 3x^4) = 3(2 - 3x^4)/2 - (2 - 3x^4) = 3 - 9x^4/2 - 2 + 3x^4 = -1 + (3/2)x^4

Therefore, hg(x) = -1 + (3/2)x^4.

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Answer: 5.3

Step-by-step explanation: (4/15)x20=5.3

Answer: 6/13

Step-by-step explanation:

Let the equation be represented as ANow , the value of A is Let the first number be p = 4 / 15Let the second number be q = 20And , A = p x qSubstituting the values in the equation , we getA = ( 4/15 ) x 20On simplifying the equation , we getA = ( 4/3 ) x 4A = 16/3

Answer:

Step-by-step explanation:

The standard deviation of the sampling distribution of sample means is given by the formula:

standard deviation = population standard deviation / sqrt(sample size)

Here, the population standard deviation is 0.8 years, and the sample size is 38. Substituting these values into the formula, we get:

standard deviation = 0.8 / sqrt(38)

standard deviation ≈ 0.13

Rounding to two decimal places, the standard deviation of the sampling distribution of sample means is approximately 0.13 years.

Answer: Sussy initially deposited $31.61.

Step-by-step explanation: 5% interest rate for 6 months with $32.45 earned, we can use the compound interest formula A=P(1 + r/n)^nt where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year and t is the time in years.

In this case, we know that P is what we are looking for, r=5%, n=2 (since it’s compounded twice a year), t=6/12=0.5 years and A=P+$32.45.

Substituting these values into the formula gives us:

A=P(1 + r/n)^nt + $32.45

$32.45=P(1 + 0.05/2)^(2*0.5)

$32.45=P(1 + 0.025)^1

$32.45=P(1.025)

P=$31.61

The expansion of (2t_3x)⁴ using Pascal's Triangle method is (2t_3x)⁴ = 16t_[tex]3^{4x^{4} }[/tex] + 96t_[tex]3^{3x^{3} }[/tex] + 216t_[tex]3^{2x^{2} }[/tex] + 192t_3x + 16.

A binomial expression is a mathematical expression that consists of two terms, which are typically separated by a plus or minus sign. The two terms can be constants, variables, or combinations of both, and they are raised to a certain power, called the degree of the binomial.

For example, (x + y) and (2a - b) are both binomial expressions. The first expression consists of the two terms x and y, which are both raised to the first power, so the degree of the binomial is 1. The second expression consists of the two terms 2a and b, which are both raised to the first power, so the degree of the binomial is also 1.

To expand the binomial (2t_3x)⁴ using Pascal's Triangle method, we need to write the fourth row of Pascal's Triangle, which is:

1 4 6 4 1

These numbers represent the coefficients of the terms in the expansion of (a+b)⁴, where a=2t_3x and b=1. Using this row, we can write the expansion of (2t_3x)⁴ as:

(2t_3x)⁴ = 1*(2t_3x)⁴ + 4*(2t_3x)³*(1)¹ + 6*(2t_3x)²*(1)² + 4*(2t_3x)¹*(1)³ + 1*(2t_3x)⁰*(1)⁴

Simplifying this expression gives:

(2t_3x)⁴ = 16t_[tex]3^{4x^{4} }[/tex] + 96t_[tex]3^{3x^{3} }[/tex] + 216t_[tex]3^{2x^{2} }[/tex] + 192t_3x + 16

Therefore, the expansion of (2t_3x)⁴ using Pascal's Triangle method is:

(2t_3x)⁴ = 16t_[tex]3^{4x^{4} }[/tex] + 96t_[tex]3^{3x^{3} }[/tex] + 216t_[tex]3^{2x^{2} }[/tex] + 192t_3x + 16

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Which involves calculating the square root of the sum of the squares of the differences between the coordinates of its endpoints.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.

The concept you are describing is that of a line segment, which is a part of a straight line that is defined by two endpoints and includes all the points between those endpoints. A line segment has a finite length, which is the distance between its endpoints, but it contains an infinite number of points in one dimension, which means that it can be divided into an infinite number of smaller segments or points.

The length of a line segment can be measured using various methods, including the Pythagorean theorem, which involves calculating the square root of the sum of the squares of the differences between the coordinates of its endpoints.

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The value of x in the solution to this system of equations is,

⇒ x = - 8

We have to given that;

A system of linear equations is shown are,

x - 3y = 7   ... (i)

x - 2y = 2  ... (ii)

Now, We can simplify as;

From (i);

x = 7 + 3y

Put in (ii);

7 + 3y - 2y = 2

7 + y = 2

y = - 7 + 2

y = - 5

Hence, From (i);

x - 3 x - 5 = 7

x + 15 = 7

x = - 15 + 7

x = - 8

Thus, The value of x in the solution to this system of equations is,

⇒ x = - 8

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Answer:

c. 4

Step-by-step explanation:

for this problem, you would have to set up a division equation, which would be

total number of cups

———————————————

unit rate amount for one dumpling

in this case, your equation would be

2

—

.5

when you solve 2/.5 you get 4 total dumplings

The term formula for a geometric progression where the second term is 54, the fourth term is 6, and the common ratio is 0.5 is Un = 108 * (0.5)n-1.

In a Geometric Progression (G.P.), each term is the product of the previous term and a constant multiplier (known as the common ratio). To begin, identify the common ratio (r) by using the formula r = Un / Un-1. If the second term is 54 and the fourth term is 6, then the common ratio (r) is √(6/54) = 0.5.

Once we have established the common ratio, we can find an arbitrary term of the progression using the formula Un = U1 * r(n-1). However, since we don't know the first term, we can derive it from U1 = U2 / r, substituting our given values, we find U1 = 54 / 0.5 = 108.

Now, we can substitute U1 and r into our term formula to find any term (n) in the series: Un = 108 * (0.5)n-1.

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Answer:

4 hours

Step-by-step explanation:

Let's call the distance between point A and point B "d", and let's call the speed of the bicycle "v" and the speed of the motorcycle "m".

When the bicycle left point A towards point B, it traveled for some time t at a speed v, so it covered a distance of d/2. We know that the motorcycle left two hours later and arrived at point B at the same time as the bicycle. This means that the motorcycle traveled for a time of t - 2 hours at a speed of m, so it also covered a distance of d/2.

If the bicycle and motorcycle left point A simultaneously and traveled towards each other, they would meet after 1 and 1/3 hours. During this time, the bicycle traveled for t + 1 and 1/3 hours at a combined speed of v + m, so it covered a distance of (v + m)*(4/3). The motorcycle also traveled for 1 and 1/3 hours at a combined speed of v + m, so it covered the same distance.

We can set up two equations based on these distances:

d/2 = vt

d/2 = m(t - 2)

(v + m)*(4/3) = d

We can use the first two equations to solve for v and m:

d = 2vt

d = 2mt - 4m

2(v + m)*(4/3) = d

Substituting the first equation into the third equation, we get:

2(v + m)*(4/3) = 2vt + 2mt - 4m

8/3(v + m) = 2v + 2m - 4m/3

8v/3 + 8m/3 = 2v + 2m - 4m/3

2v/3 = 4m/3

v = 2m

Substituting this into the first two equations, we get:

d = 4mt

d = 2mt - 4m

Solving for t, we get:

t = 4 hours

Therefore, the bicycle traveled for 4 hours to cover the distance between point A and point B.

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The fraction written in 3 different forms is:

6/8 = 3/4 = 0.75

We want a fraction that is greater than five-eighths and less than thirteen-eighths. Then if our fraction is x:

5/8 < x < 13/8

So we can write the fraction such that the denominator is also 8, but the numerator is between 5 and 13, then we could use 6/8

5/8 < 6/8 < 13/8

To write the fraction in other forms we can simplify it:

6/8 = 3/4 = 0.75

There are 3 ways.

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Answer: 594 Rabbits

Step-by-step explanation:

To solve this problem, we can use the formula for exponential growth:

A = P(1 + r)^t

where A is the final amount, P is the initial amount, r is the monthly growth rate (as a decimal), and t is the number of months.

In this case, we know that the initial amount (in July) is 260, the monthly growth rate is 9% or 0.09, and we want to find the final amount after 12 months (from July to next July).

So we have:

A = 260(1 + 0.09)^12

A ≈ 593.87

Rounding to the nearest whole number, we get:

A ≈ 594

Therefore, we can expect about 594 rabbits by next July.

The dimensions that minimize the cost are a square base and top with a side length of 3.11 ft, and a height of 41.2 ft.

We have,

Let the side length of the square base and top be x, and the height of the rectangular box be y.

Then we know that the volume of the box is 400 ft³, so we can write:

x² y = 400

We want to minimize the cost of constructing the box, which is given by the cost of the bottom plus the cost of the top plus the cost of the sides.

The cost of the bottom and top is given by the area of a square with side length x, multiplied by the cost per square foot:

Cost of bottom and top = 2x² (0.20) = 0.4x²

The cost of the sides is given by the area of the four rectangles that make up the sides of the box, which have dimensions x by y:

Cost of sides

= 4xy (0.015)

= 0.06xy

Total cost = Cost of bottom and top + Cost of sides

Total cost = 0.4x² + 0.06xy

We want to find the dimensions that minimize this cost, subject to the constraint that the volume of the box is 400 ft³.

We can use the volume equation to eliminate y, and obtain a function of x alone:

x² y = 400

y = 400 / x²

Substituting this expression for y into the cost equation, we get:

Total cost = 0.4x² + 0.06x(400 / x²)

Total cost = 0.4x² + 24 / x

To minimize this function, we take its derivative with respect to x, set it equal to zero, and solve for x:

d(Total cost)/dx = 0.8x - 24/x² = 0

0.8x³ - 24 = 0

x³ = 30

x = (30)^(1/3) = 3.11 ft (rounded to two decimal places)

Using the equation for y in terms of x, we can find the corresponding value of y:

y = 400 / x²

y = 400 / (3.11)² = 41.2 ft² (rounded to one decimal place)

Therefore,

The dimensions that minimize the cost are a square base and top with a side length of 3.11 ft, and a height of 41.2 ft.

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The mean of the sampling distribution of sample means is 5.3, and its standard deviation is 0.186.

By dividing the sum of the provided numbers by the total number of numbers, the mean—the average of the given numbers—is determined.

The mean of the sampling distribution of sample means is equal to the population mean, which is 5.3, regardless of the sample size. This is a fundamental property of the sampling distribution of the mean.

However, if we want to be more precise, we can use the formula for the standard error of the mean (SEM) to calculate the standard deviation of the sampling distribution of sample means:

SEM = σ / √(n)

where σ is the population standard deviation, n is the sample size, and sqrt represents the square root.

In this case, σ = 1.1 and n = 35, so:

SEM = 1.1 / √(35) = 0.186

Therefore, the mean of the sampling distribution of sample means is 5.3, and its standard deviation is 0.186.

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Jack is 15 miles from the airport.

The Pythagorean theorem is a fundamental principle in geometry that states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In mathematical terms, it can be expressed as:

c² = a² + b²

Let's denote the distance between Jack and the airport as x, and the distance between Jack and Tom as y. Then, we can see that we have a right triangle JAX with sides x, y, and hypotenuse JA = 17 miles. We also know that AT = 12 miles.

Using the Pythagorean theorem, we can write:

x² + y² = JA²

Squaring both sides, we get:

x² + y² = 17²

We also know that the distance between Tom and the airport is 12 miles, so the length of TX is also 12 miles. Therefore, we can write:

y = TX = 12 miles

Substituting this value into the equation above, we get:

x² + 12² = 17²

Simplifying this equation, we get:

x² = 17² - 12² = 225

Taking the square root of both sides, we get:

x = 15

Therefore, Jack is 15 miles from the airport.

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The mean for the given data items in the given frequency distribution is 2.818

From the question, we are to determine the mean for the given data items

The given frequency distribution is:

Score, x           : 1, 2, 3, 4, 5, 6, 7, 8

Frequency, f   : 3, 6, 5, 5, 4, 5, 3, 2

To find the mean, we need to first calculate the sum of the products of each score and its frequency, and then divide by the total frequency.

(1 x 3) + (2 x 6) + (3 x 5) + (4 x 5) + (5 x 4) + (6 x 5) + (7 x 3) + (8 x 2) = 93

Total frequency = 3 + 6 + 5 + 5 + 4 + 5 + 3 + 2 = 33

Thus,

Mean = Sum of (x * f) / Total frequency

= 93 / 33

= 2.818

Hence, the mean of the scores is 2.818

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Answer:

The mean of the sampling distribution of sample means is equal to the population mean, which is 5.3 years.

give thanks for more! your welcome!

Step-by-step explanation:

The measure of the two interior angles on the same side of the transversal are 78 degrees and 102 degrees, respectively, when the lines are parallel.

When two parallel lines are intersected by a transversal, the interior angles on the same side of the transversal are supplementary, which means they add up to 180 degrees. So, we can set up the following equation:

(5x + 3) + (6x + 12) = 180

Simplifying and solving for x, we have:

11x + 15 = 180

11x = 165

x = 15

Now that we know x, we can find the measure of each angle:

The first angle measures 5x + 3 = 5(15) + 3 = 78 degrees.

The second angle measures 6x + 12 = 6(15) + 12 = 102 degrees.

Therefore, the measure of the two interior angles on the same side of the transversal are 78 degrees and 102 degrees, respectively, when the lines are parallel.

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Complete question

Two interior angles on the same side of the transversal measure 5x+3 and 6x + 12°. Find x and  the measure of each angle if the lines are parallel

The growth factor of the credit card balance is 1.0142. The Option B is correct.

The growth factor is equal to the slope of the line representing a linear relationship. To calculate the growth factor of the credit card balance, we need to add the monthly interest rate to 1.

Monthly interest rate = 1.42% = 0.0142

The Growth factor will be:

= 1 + monthly interest rate

= 1 + 0.0142

= 1.0142.

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