The data list shows the scores of ten students in Mr. Smith's math class. 61, 67, 81, 83, 87, 88, 89, 90, 98, 100 What is the standard deviation, to the nearest tenth, of the data if the scores represent a sample of Mr. Smith's students? a0 What is the standard deviation, to the nearest tenth, of the data if the scores represent the entire population of Mr. Smith's students? a1

Final answer:

To find the perimeter of the rectangle, first find the dimensions using the given information and the formula. Then, use the formula for perimeter to calculate the final result.

Explanation:

To find the perimeter of the rectangle, we need to first find the dimensions of the rectangle. Let the width of the rectangle be w. According to the given information, the length of the rectangle is 5 times its width, so the length can be represented as 5w. The area of the rectangle is given as 320 m², so we can set up the equation:

w * 5w = 320

Simplifying this equation, we have:

5w² = 320

Dividing both sides of the equation by 5, we get:

w² = 64

Taking the square root of both sides, we find:

w = 8

So, the width of the rectangle is 8 meters. The length can be found by multiplying the width by 5:

length = 5 * 8 = 40 meters

The perimeter of the rectangle is calculated using the formula: Perimeter = 2*length + 2*width. Substituting the values we found:

Perimeter = 2*40 + 2*8

Calculating this expression, we get:

Perimeter = 80 + 16 = 96 meters

The number of different ways you can arrange 3 out of 5 letters is 10.

To find the number of different ways you can arrange 3 out of 5 letters, you can use the formula for combinations. The formula for combinations is given by nCr = n! / (r!(n-r)!), where n is the total number of items and r is the number of items being chosen at a time.

In this case, n = 5 and r = 3. So the number of different ways to arrange 3 out of 5 letters is 5C3 = 5! / (3!(5-3)!) = 10.

Therefore, there are 10 different ways you can arrange 3 out of the 5 letters.

Answer:

33

Step-by-step explanation:

The original side of square is [tex]10\;\rm{in[/tex].

Given: the dimensions of a square are altered so that [tex]8[/tex] inches is added to one side while [tex]3[/tex] inches is subtracted from the other. The area of the resulting recatangle is [tex]126\;\rm{in^2}[/tex].

As per question,

Let the side of square be [tex]x[/tex].

According to the question,

Length of new rectangle be [tex]x+8[/tex].

Breadth of new rectangle be [tex]x-3[/tex]

Area of rectangle [tex]=l\times b[/tex]

     [tex](x+8)(x-3)=126[/tex]

[tex]x^2+8x-3x-24=126\\[/tex]

      [tex]x^2+5x-150=0[/tex]

[tex]x^2+15x-10x-150=0\\x(x+15)-10(x+15)=0\\[/tex]

        [tex](x+15)(x-10)=0\\[/tex]

So, [tex]x=10\;\rm{in[/tex] and neglecting [tex]x=-15\;\rm{in[/tex] as distance can't be negative.

Hence, original side of square is [tex]10\;\rm{in[/tex].

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Answer:

the dimensions of rectangle are length = 15 m and width = 6 m

Step-by-step explanation:

Given;  The width  of a rectangle is [tex]\frac{2}{5}[/tex] its length i.e, [tex]w=\frac{2}{5}l[/tex]

and perimeter of rectangle is 42 meters.

Perimeter(P)of a rectangle in meters is given by:

[tex]P = 2(l+w)[/tex] ;  where [tex]l[/tex] is the length of the rectangle and w is the width of the rectangle.

then, substitute the value of P =42 m and [tex]w=\frac{2}{5}l[/tex] in above formula we get;

[tex]42 = 2(l+\frac{2}{5}l) =2 \cdot (\frac{7}{5}l)[/tex]

divide both side by 2 we get;

[tex]21=\frac{7}{5}l[/tex]

On Simplify:

[tex]l = \frac{21 \cdot 5}{7} =3 \cdot 5 =15[/tex] m

Now, substitute the value of [tex]l = 15[/tex] m  in [tex]w=\frac{2}{5}l[/tex] to solve for w;

[tex]w= \frac{2}{5} \cdot 15 =2 \cdot 3 =6[/tex] m

Therefore, the dimensions length = 15 m and width = 6 m

There are six important properties of parallelograms to know:

Answer: check

Step-by-step explanation:

done

The standard equation of the circle based on the given options is (x - 3)2 + (y + 2)2 = 18, which suggests a circle with a center at (3, -2) and a radius of 3√2.

The student asks to write the standard equation of the circle in the graph. To do this, we need to identify the factors of the circle equation, which are the center coordinates
(h,k) and the radius r. The general form of a circle's equation is (x - h)2 + (y - k)2 = r2. Since the radius is the square root of the number on the right-hand side
of the equation and the center coordinates come from the values that x and y are subtracted by, we can determine the equation based on the options provided. One of the statements provided by the student, (x + 3)2 + (y - 2)2 = 18, fits the right form but it suggests the wrong center coordinates and radius. The correct standard equation of a circle based on the given options would be the one with center coordinates (3, -2) and a radius of √18, which can be simplified to 3√2. This information alongside the provided options leads us to select (x - 3)2 + (y + 2)2 = 18 as the correct standard equation of the circle in question.

Answer:

c) 27 percent, 36 percent, 37 percent

Step-by-step explanation:

Given,

Hot dogs sold by,

Vendor a = 456

Vendor b = 607

Vendor c = 637,

Total hot dogs = 1700,

Thus, the percentage of the hot dogs sold by a = [tex]\frac{\text{Hot dog sold by a}}{\text{Total hot dogs}}\times 100[/tex]

[tex]=\frac{456}{1700}\times 100[/tex]

[tex]=\frac{456}{17}[/tex]

= 26.82%

≈ 27%

Similarly,

Percentage of the hot dogs sold by a

[tex]=\frac{607}{1700}\times 100[/tex]

[tex]=\frac{607}{17}[/tex]

= 35.71%

≈ 36%

Percentage of the hot dogs sold by a

[tex]=\frac{637}{1700}\times 100[/tex]

[tex]=\frac{637}{17}[/tex]

= 37.47%

≈ 37%

Hence, OPTION c) is correct.

There are 24 permutations of the letters a, b, c, d taken four at a time, calculated using the formula 4!.

The question revolves around finding the number of permutations of the letters a, b, c, d taken four at a time. To solve this, we need to understand that a permutation represents the arrangement of all members of a set in every possible order.

In the case of the letters a, b, c, d, we want to arrange them in all possible ways where order matters and taking all four at a time. The formula to calculate permutations is P(n, r) = n! / (n-r)!, where n is the total number of items to choose from, and r is the number of items to choose. However, since we are taking all four letters each time, we are essentially looking for 4!, which simplifies to 4*3*2*1.

Therefore, 4! equates to 24. This means there are 24 possible ways to arrange the letters a, b, c, d when taking all four at a time. It's an excellent exercise to manually write out all of these permutations to get practical experience with the concept.

To begin, we need to find the slope of the equation x = 2y + 3. The easiest way to find the slope is to put this equation into slope-intercept form, y=mx+b, where the variable m represents the slope. To do this, we must get the variable y alone on the left side of the equation. First, we subtract 2y from both sides.

x = 2y + 3

-2y + x = 3

Next, we subtract x from both sides.

-2y = -x + 3

Finally, we divide both sides by -2 (there cannot be a coefficient on the variable y in this form).

y = 1/2x + 3

Therefore, the slope of this equation is 1/2. However, we are looking for the slope of a line that is perpendicular to this one. This means that it creates four 90 degree angles where the lines cross, and it has the opposite reciprocal slope.

The opposite reciprocal of 1/2 is -2 (you take the opposite in this case by changing the value from positive to negative, and take the reciprocal by switching the numerator and the denominator).

Thus, your answer is -2.

Hope this helps!

The slope of a line perpendicular to the line represented by the equation x = 2y + 3 is -2.

The equation given is x = 2y + 3. To find the slope of a line perpendicular to this line, we need to determine the slope of the given line. The given equation is not in slope-intercept form, which is y = mx + b, where m represents the slope. So, we can rewrite the equation in slope-intercept form by rearranging it as 2y = x - 3 and then dividing both sides by 2, giving us y = (1/2)x - (3/2).

The slope of the line represented by this equation is 1/2. To find the slope of a line perpendicular to this line, we take the negative reciprocal of the slope of the given line. The negative reciprocal of 1/2 is -2. So, the slope of a line perpendicular to the line represented by the equation x = 2y + 3 is -2.

A line with a slope of -2 will have a steepness that is twice as steep as the line represented by the equation x = 2y + 3.

Answer:

It's A 3x

Step-by-step explanation:

I just did the test it's 3x hope this helped. :)

El cambio climático ha empeorado en los últimos años, la razón principal es la contaminación excesiva tanto del aire, del agua, del suelo y muchas otras cosas.

Todos debemos tomar conciencia del daño que estamos ocasionando con la contaminación excesiva. El cambio climático nos ha traído grandes problemas por no actuar con responsabilidad en el cuidado del medio ambiente. Si no tomamos conciencia de lo que estamos perjudicando, en un tiempo más adelante habrá consecuencias negativas peores de las que ya hay.

El cambio climático no se da de forma negativa por sí solo, somos nosotros los que estamos perjudicándolo con la contaminación.

deberiamos de Cuidar  la planeta para que no haya tanto exceso de contaminación y así evitar cambios drásticos en el clima

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To translate point B(−4, 1) 3 units to the right and 2 units down, you add 3 to the x-coordinate and subtract 2 from the y-coordinate, resulting in the new coordinates B' = (−1, −1).

The coordinates that represent a translation of B(−4, 1) 3 units to the right and 2 units down can be found by adding 3 to the x-coordinate and subtracting 2 from the y-coordinate of point B. The new coordinates will be:

B' = (−4 + 3, 1 − 2)

So, the new coordinates would be B' = (−1, −1).

To calculate the tax on $42 at a 3.9% rate, first convert the percentage to a decimal (0.039) then multiply the amount by the tax rate. The result is approximately $1.64.

The problem involves calculating the tax on a certain amount using a specified tax rate. In this case, the tax rate is given as 3.9% and the amount is $42.

You calculate the tax by multiplying the tax rate by the amount.

First, convert the percentage into a decimal by dividing by 100: 3.9 ÷ 100 = 0.039.

Next, multiply the amount by the tax rate: $42 x 0.039 = $1.638.

Therefore, the tax on $42 at a rate of 3.9% is approximately $1.64, when rounded to the nearest hundredth.

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The tax on $42 with a 3.9% tax rate is approximately $1.64 when rounded to the nearest hundredth.

To find the tax on $42 with a tax rate of 3.9%, we need to multiply the total amount by the tax rate. First, turn the percentage into a decimal by dividing 3.9 by 100, which gives us 0.039. After that, you multiply $42 by 0.039. This results in approximately $1.64, which we round to the nearest hundredth as per the instructions, thus our answer is $1.64.

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Answer:

D. 12 on edge

Step-by-step explanation:

To find the fraction of a mile represented by 1100 yards, divide 1100 yards by 1760 yards (the total number of yards in a mile). The fraction is 0.625.

To find the fraction of a mile represented by 1100 yards, we need to divide 1100 yards by the total number of yards in a mile, which is 1760 yards. We can set up a proportion with the fraction we're looking for, x, in the numerator and 1760 in the denominator:

1100 yards / 1760 yards = x / 1 mile

Since the denominator on the left side is the same as the denominator on the right side, we can cross-multiply and solve for x:

x = 1100 / 1760

x = 0.625

Therefore, the fraction of a mile represented by 1100 yards is 0.625.

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Answer:

he`s right its a or b

i'm going with b

Step-by-step explanation:

Answer:

Option A is correct that is x° = 56°

Step-by-step explanation:

Let Given Lines are tangents.

So we use a result which states that Tangents are perpendicular with radius at point of contacts.

⇒ ∠ B = ∠ D = 90°

Angle sum property of Quadrilateral = 360°

⇒ ∠A + ∠B + ∠O + ∠D = 360

x + 90 + 124 + 90 = 360

x + 304 = 360

x = 360 - 304

x = 56

Therefore, Option A is correct that is x° = 56°

-5/0 is undefined.

The reason why division by zero is undefined is because there is no real number that can be multiplied by 0 to get -5.

In essence, the division operation asks how many times the denominator can be contained within the numerator. Since nothing times zero gives any number other than zero, this question has no answer.

Moreover, division by zero is not allowed in the real number system because it can lead to logical contradictions and undefined behavior.

Answer- 31.11 minutes

Let 'T' be the total number of newspapers.

Newspapers distributed by girl alone in 55 minutes = T

Newspapers distributed by girl alone in 1 minute = T/55

Newspapers distributed by girl and boy in 20 minutes = T

Newspapers distributed by girl and boy in 1 minutes = T/20

Newspapers distributed by boy alone in 1 minute = T/20 - T/55 = 7T/220

On solving, total time taken by boy to distribute newspapers = 31.11 minutes