suppose the data on quiz scores will be grouped into five classes. the width of the classes for a frequency distribution or histogram is the closest to .

Answer:

42.85 inches wide

Step-by-step explanation:

You must use the Pythagorean theorem

width^2+19^2=47^2

width^2=47^2-19^2

width=square root of (2209-361)

width=square root of (1848)

width= 42.85 inches

Answer:

Step-by-step explanation:

Given equation: f(x)=x^2+x-6

The roots of the equation, set the equation equal to zero.

[tex]x^2+x-6=0\\x^2+3x-2x-6=0\\x(x+3)-2(x+3)=0\\ (x+3)(x-2)=0\\ x=-3,2[/tex]

Therefore, the roots of the equation are x=-3 and x=2

The concentration of solution A after dilution by a factor of 10 would be 0.0300 M.

The dilution factor is defined as the ratio of the final volume to the initial volume of the solution.

If a solution is diluted by a factor of 10, it means that the final volume of the solution is ten times greater than the initial volume. As a result, the concentration of the solute in the final solution will decrease by a factor of 10.

Therefore, if the initial concentration of the stock solution is 0.300 M, then the concentration after dilution by a factor of 10 of solution A would be

= 0.300 M / 10

= 0.0300 M

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The tangent line to the curve y = ln(x) - 10 at the point (1, -9) is parametrized by x = t and y = t - 10

To find the tangent line to the curve y = ln(x) - 10 at the point (1, -9), we need to find a parametrization of the line. We can do this by finding the slope of the tangent line and the point at which the tangent line intersects the y-axis.

First, we find the slope of the tangent line by taking the derivative of the function y = ln(x) - 10 at x = 1:

dy/dx = d/dx ln(x) = 1/x

So, the slope of the tangent line at (1, -9) is m = 1/1 = 1.

Next, we find the y-intercept of the tangent line. This can be found by using the point-slope form of a line:

y - y1 = m(x - x1)

Substituting in the values for m, x1, and y1, we get:

y - (-9) = 1(x - 1)

Simplifying, we find:

y + 9 = x - 1

y = x - 10

So, the y-intercept of the tangent line is -10.

Putting everything together, we find that the parametrization of the tangent line to the curve y = ln(x) - 10 at the point (1, -9) is given by:

x = t

y = x - 10 = t - 10

So, the tangent line to the curve y = ln(x) - 10 at the point (1, -9) is parametrized by x = t and y = t - 10.

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The total perimeter will be 4x^+17 and length be 22.76 cm

As per the data given in the questions,

We have, the shape of the sandwich be rectangular.

We know that, perimeter of the rectangle can be determined by using formula: 2(l+b),

where, l = length of the rectangle

and, b = breadth of the rectangle

The expression for the perimeter of the sandwich would be:

2 (2x^2 + 9) + 2 (2x^2 + 8)

= 4x^2 + 26

Now for finding the length of the crust,

we will put the value of x=1.2,

So, the value of the approximate length of the crust would be:

=4x^2 + 26

= 4 * 1.2^2 + 26

= 22.76 centimetres.

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A.Researcher 1: Since increases for a higher level of confidence, the researcher 1 would need larger sample size.

The benefits of studying probability are very useful for making the right decisions, because there is no certainty in life in the world, so it is necessary to know what is the probability that an event will occur. Probability is expressed as a fractional number between 0 and 1 or as a percentage. Some important terms in probability are (a) trial, (b) outcome, and (c) event.

There are three approaches in determining probability namely (a) the classical approach which gives the same probability, (b) a relative approach that pays attention to events that have occurred and (c) a subjective approach based on individual judgment.

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I and II only are solutions to the differential equation y′′ − 5y′ + 6y = 0.

Let's assume y = e^2t is the solution of the given differential equation y′′ − 5y′ + 6y = 0.

Now, put y = e^2t in the given differential equation y′′ − 5y′ + 6y = 0

(e^2t)'' - 5(e^2t)' + 6(e^2t) = 0

Now differentiate it; we get

4e^2t - 10e^2t + 6e^2t = 0

0 = 0

So, here we can see that y = e^2t satisfies the equation y′′ − 5y′ + 6y = 0.

Therefore y = e^2t is the solution of the given differential equation.

Now let's assume y = 3e^3t is the solution of the given differential equation y′′ − 5y′ + 6y = 0.

Put y = 3e^3t in the given differential equation y′′ − 5y′ + 6y = 0

(3e^3t)'' - 5(3e^3t)' + 6(3e^3t) = 0

Now differentiate it; we get

27e^3t - 45e^3t + 18e^3t = 0

0 = 0

So, here we can see that y = 3e^3t satisfies the equation y′′ − 5y′ + 6y = 0.

Therefore y = 3e^3t is the solution of the given differential equation.

Similarly, let's assume y = 3sin(2t) is the solution of the given differential equation y′′ − 5y′ + 6y = 0.

Put y = 3sin(2t) in the given differential equation y′′ − 5y′ + 6y = 0

(3sin(2t)'' - 5(3sin(2t))' + 6(3sin(2t)) = 0

Now differentiate it; we get

-24cos(2t) + 30cos(2t) + 18sin(2t) = 0

-24cos(2t) + 30cos(2t) + 18sin(2t) ≠ 0

So, here we can see that y = 3sin(2t) does not satisfies the equation y′′ − 5y′ + 6y = 0.

Therefore y = 3sin(2t) is not the solution of the given differential equation.

Hence, I and II only are solutions to the differential equation y′′−5y′+6y=0.

--The given question is incorrect; the correct question is

"Of the following, which are solutions to the differential equation y′′−5y′+6y=0?

I. y = e^2t

II. y = 3e^3t

III. y = 3sin(2t)

I only

II only

III only

I and II only"--

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The distance from point P = (1, -1) to the line through points A = (-2, 2) and B = (0, -4) is 2.23.

What is distance ?

Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria.

The slope of the line can be found using the coordinates of points A and B:

m = (y2 - y1) / (x2 - x1) = (-4 - 2) / (0 - (-2)) = -3

Next, we can use the coordinates of point A to find the y-intercept:

b = y - mx = 2 - (-3)(-2) = 2 + 6 = 8

m_perpendicular = -1 / -3 = 1/3

Using the coordinates of point P, we can find the equation of the perpendicular line:

y = m_perpendicular x + b_perpendicular

y = 1/3 x - 1/3

Setting the y-coordinates equal, we can find the x-coordinate of the intersection point:

-3x + 8 = 1/3 x - 1/3

-9x + 24 = x - 1/3

-10x + 24.33 = x

x = 24.33 + 10x

11x = 25.66

x = 2.33

Finally, we can find the y-coordinate of the intersection point using the equation of the perpendicular line:

y = 1/3 x - 1/3

y = 1/3 (2.33) - 1/3 = 0.77

The intersection point is (2.33, 0.77), and the distance from point P to the line is the distance between the two points:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((2.33 - 1)^2 + (0.77 + 1)^2) = sqrt(1.33^2 + 1.77^2) = sqrt(1.7769 + 3.1369) = sqrt(4.9138) = 2.23.

So, the distance from points P = (1, -1) to the line through points A = (-2, 2) and B = (0, -4) is 2.23.

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The simple interest rate for his loan could be 6%

If the initial amount (also called as principal amount) is P, and the interest rate is R% annually, and it is left for T years for that simple interest, then the interest amount earned is given by:

[tex]I = \dfrac{P \times R \times T}{100}[/tex]

Given that Mr. Gabel borrowed $1860 to buy a computer. He will pay $71Mr. Gabel borrowed $1860 to buy a computer. He will pay $71.30 per month for 30 months.

To Find the simple interest rate for his loan.

P= 1860R= x

T= 30 months = 2.5 years

I = $279

Therefore, I= prt

279 = 1860 (r)(2.5)

279 = 4650r

0.06 = r

r = 6%

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They will lift the same weight (which is 26 kilograms) after one set.

Mason starts at 19kg bar and adds 7kg after each set, so after x sets, he will be lifting:

M(x) = 19 + 7*x

And Jack starts at 18kg, and after each set adds 8kg, then in this case the linear equation is:

J(x) = 18 + 8*x

They will lift the same weight when:

M(x) = J(x)

19 + 7*x =  18 + 8*x

19 - 18 = 8x - 7x

1 = x

So they will be lifting the same weight after one set, and that is:

J(1) = 18 + 8*1 = 26

26 kilograms.

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1. The measure of AC = 8.4

2. The measure of AC' = 6

3. The measure of C'B' = 12.6

Lines in a plane that are consistently spaced apart are known as parallel lines. Parallel lines don't cross each other.

Given:

Segment B'C' is parallel to segment BC.

A line splits a triangle's sides in the same proportion if it runs parallel to one side and crosses the other sides at two different spots.

Then,

10/4 = 6/x

x = 2.4

The measure of AC = 2.4

And,

14/8.4 = 21/y

y = 12.6

The measure of C'B' = 12.6

Therefore, all the required values are given above.

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Answer:

32/85=26/100

Step-by-step explanation:

The required Angle in radian in simplest form is 2π.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.

The centre angle of one radian (s = r) subtends an arc length of one radius. One radian has the same value for all circles because they are all alike. The central angle of a circle is measured by its arc, which is 360 degrees, and its radian measure, which is 2 radians.

Radius = 4 unit, arc = 8π

We know that

angle = arc/radius

angle = 8π/4

angle = 2π radian.

Thus, required angle in radian is 2π.

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Answer: A: 50,000

Answer: B: 55

Step-by-step explanation:

You can use ratio proportions to answer this problem

10/10,000 = 50/x

Cross multiply: 10x/10 = 500,000/10

x = 50,000

You can use ratio proportions to answer this problem

10/10,000 =  x/55,000

Cross mupltipy: 10,000x/10,000 = 550,000/10,000

x = 55

May or may not be correct

The distinction in cost between the two sellers is $1.44, with Store-Ur-Stuff being savvier.

Expect you to take care of the two bills preceding the first of the month, the distinction in cost between leasing from Lease A-Space and Store-Ur-Stuff is $10. Lease A-Space would cost $88 (400 cubic feet x 22 pennies/cubic foot + 5.5% deals charge) while Store-Ur-Stuff would cost $78 (400 cubic feet x quarter/cubic foot + 4% markdown + 5.5% deals charge).

The distinction in cost between Lease A-Space and Store-Ur-Stuff can be determined as follows:

Lease A-Space: 400 cubic feet x $0.22/cubic foot = $88 in addition to burden = $92.64

Store-Ur-Stuff: 400 cubic feet x $0.25/cubic foot = $100 in addition to 4% markdown = $96 less expense = $91.20

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W = 12

L = 8

so multiply 8 and 12

The four-sided geometric object known as a tetrahedron (WXYZ) has four triangle faces that are joined to one another at their edges. Its vertices are all linked, and its faces are all equilateral triangles.

The three-dimensional geometric structure known as a tetrahedron (WXYZ) has four triangle-shaped faces. The edges of each of the tetrahedron's faces are joined to one another. All of the faces are triangular shapes with equal sides, or equilateral triangles. The tetrahedron is a solid shape because all of its vertices are joined together. The tetrahedron's four vertices are joined to one another, forming a pyramid-like shape. The tetrahedron's four vertices are the only points that do not form the triangle faces. The tetrahedron's four faces come together to produce a point in the middle of the shape. The apex of the tetrahedron is where this point is located. The faces of the tetrahedron are all congruent, or identical, as they are a regular polyhedron.

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Answer:Let x be the cost of a hard-cover book and y be the cost of a paperback book.

We know that Steve spent 2 hard-cover books and 3 paperback books. So we can write the equation as:

2x + 3y = 50 - 15.5

2x + 3y = 34.5

We also know that he was planning to buy 3 hard-cover books and 4 paperbacks, so we can write another equation as:

3x + 4y = 50

Now we have a system of two equations with two unknowns:

2x + 3y = 34.5

3x + 4y = 50

We can use the first equation to eliminate one variable by multiplying both sides by 2 and then subtracting 3y:

4x + 6y = 69

3x + 4y = 50

x = 19.5

Now we can substitute this value of x into the second equation and find the value of y:

3(19.5) + 4y = 50

58.5 + 4y = 50

4y = -8.5

y = -2.125

Therefore, the cost of a hard-cover book is $19.5 and the cost of a paperback book is $-2.125.

Note that the cost of a paperback book is a negative value which is not possible in this case. It means that the given information does not have a solution.

Step-by-step explanation:

The unit rate of the coffee is found as $0.483.

For the given question:

cost of 12.4 ounce of coffee  = $5.99.

For the unit rate, divide both sides by 12.4.

cost of 1 ounce of coffee  = $5.99/12.4

cost of 1 ounce of coffee  = $0.483

Thus, the unit rate of the coffee is found as $0.483.

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The area of the region bounded between the given curves is =0.640675 unit square.

The center point of a straight line can be located using the midpoint formula. You may occasionally need to determine the difference between two specific numbers. The average of the two numbers is what you find there. In a similar way, we obtain the halfway number (or point) between two coordinates using the midpoint formula in coordinate geometry.

The midpoint rule states that you can calculate the area under a curve by using the formula:

[tex]M_n=\frac{b-a}{2}[f(\frac{(x_0+x_1)}{2})+f(\frac{x_1+x_2}{2})+....+f(\frac{x_{n-1}+x_n}{2})][/tex]

In our case a=0 ,b=1 ,n=4

[tex]x_0=0 ,x_1=1/4,x_2=1/2, x_3=3/4\ and \ x_4=1[/tex]

Therefore, we have-

[tex]M_4=\frac{1}{4}[f(\frac{1}{8})+f(\frac{3}{8})+f(\frac{5}{8})+f(\frac{7}{8}][/tex]

now to evalute f(x),

[tex]f(x)=cos^{2}(\frac{\pi x}{4})-sin^{2}(\frac{\pi x}{4})\\ \\f(x)= cos(\frac{\pi x}{2})\\\\f(1/8)=cos(\frac{\pi}{16})=0.9807\\\\f(3/8)=0.8314\\\\f(5/8)=0.5555\\\\f(7/8)=0.19509[/tex]

hence the value of integral is equal to -

M4= 2.56279÷4=0.640675

The area of the region bounded between the given curves is =0.640675 unit square.

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From the figure , and by using congruent complements theorem, the angle that is congruent to angle4 is (a) angle1  .

The "Congruent Complements Theorem" states that if two angles are complementary to same angle, then they are congruent. In other words, if two angles add up to 90 degrees, and they both complement the same third angle, then they are equal in measure.

The ∠4 and ∠5 are the complements and ∠1 and ∠5 are complements.

Which proves that :  ∠1 and ∠4 are complimentary to the same angle that is ∠5.

Therefore, the ∠ 1 is congruent to angle 4 .

The given question is incomplete , the complete question is

From the figure below , the angle 4 and angle 5 are complements and angle 1 and angle 5 are complements , By using the congruent complements theorem, which angle is congruent to angle4 ?

(a) angle1

(b) angle2

(c) angle3

(d) angle5

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Answer:

A. True

Making an inference is the first part of the process of investigating a question using data. Making an inference is the process of drawing a conclusion based on evidence and reasoning. It is the first step in the process of data analysis, as it allows us to make a prediction or understand the relationship between variables, before any analysis is done.

Step-by-step explanation:

The dimensions of the outdoor enclosure with the most area is 250 feet and 125 feet.

One side of the store is 270 feet long

There are 500 feet of fencing available for the other three sides of the enclosure.

The Perimeter of rectangular outdoor storage = 2x + y

2x + y = 500

To maximize the area

y = 500 - 2x...............(1)

Area of rectangle;

A = xy

Now putting the value of y

A = x(500 - 2x)

Solve

A = 500x - 2x^2...................(2)

To finding the value of x differentiating on both side with respect to x.

dA/dx = 500 - 4x...................(3)

Equating dA/dx = 0

500 - 4x = 0

Subtract 4x on both side, we get

4x = 500

Divide by 4 on both side, we get

x = 125

Now putting the value of x in equation 1

y = 500 - 2(125)

y = 500 - 250

y = 250

Differentiating equation 3 again with respect to x

d^2A/dx^2 = -4 < 0 (Maximum)

Hence, for the maximum storage area

Length parallel to the store wall = 250 feet

Length perpendicular to the store wall = 125 feet

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Answer:

2s

Step-by-step explanation:

sq pool so total length = 4s

so need 4s/2 = 2s tiles

Answer: B. No, the adjacent sides are not perpendicular.

Step-by-step explanation:

B(2,4), A(4, -1), C(-2, 2), D(0, -3)

Slope of BA = [tex]\frac{4-(-1)}{2-4} = \frac{5}{-2}[/tex]

Slope of CD = [tex]\frac{2-(-3)}{-2-0} =\frac{5}{-2}[/tex]

BA║CD

Slope of BC = [tex]\frac{4-2}{2-(-2)} =\frac{2}{4} =\frac{1}{2}[/tex]

Slope of AD = [tex]\frac{-1-(-3)}{4-0} =\frac{2}{4} =\frac{1}{2}[/tex]

BC║AD

Slope of BA [tex]=\frac{5}{-2}[/tex]

Slope of BC [tex]=\frac{1}{2}[/tex]

BA is not perpendicular to BC

Option D is correct. Around 15% of health care workers (including physicians) that do not wash their hands before examining patients.

According to a study published in the Journal of Hospital Infection, an estimated 15% of healthcare workers do not consistently wash their hands before examining patients. This is a concerning statistic, as hand hygiene is one of the most important ways to prevent the spread of healthcare-associated infections.

Handwashing helps to remove dirt, bacteria, and viruses from the skin, reducing the risk of transmitting these harmful organisms to patients. Improving hand hygiene among healthcare workers is a critical component of patient safety, and many hospitals and healthcare organizations have implemented programs to increase handwashing rates and prevent the spread of infections.

Despite these efforts, the 15% figure highlights the continued need for education and training to promote hand hygiene among healthcare workers, and to ensure that all healthcare workers understand the importance of washing their hands before and after patient interactions.

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The x- intercepts in parabola is (1,0) and (5,0).

A parabola is a type of symmetrical, U-shaped curve that is a graph of a quadratic function. It is defined by the equation y = ax² + bx + c, where a, b, and c are constants. The shape of the parabola is determined by the value of the coefficient "a". If a > 0, the parabola opens upwards, and if a < 0, the parabola opens downwards.

Parabolas are used in many areas of mathematics and science, including physics, engineering, and economics. For example, they are used to model the trajectory of objects under the influence of gravity, to describe the motion of objects in space, and to analyze the behavior of systems that exhibit parabolic patterns.

The vertex of a parabola is the point that represents the highest or lowest point on the curve, and the axis of symmetry is a line that separates the curve into two congruent halves.

The x-intercepts of a parabola can be found by setting the y-value to 0 and solving for x. In this case, the y-coordinate of the x-intercepts will be 0, so we have:

y = 0

To find the x-intercepts, we can use the information given in the coordinates of the parabola: (1,0), (5,0), and (0,6).

From the coordinates (1,0) and (5,0), we can see that the x-intercepts are at 1 and 5.

From the coordinate (0,6), we can see that the y-intercept is at (0,6).

So, the x-intercepts of the parabola are (1,0) and (5,0).

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The decimal equivalent of 1101.101 in base 9 is 729.1184.

The decimal equivalent of an unsigned base 9 value is simply the number represented in the decimal system.

To find the decimal equivalent of 1101.101 in base 9, we need to convert each digit to its decimal equivalent.

First, we'll convert the whole number portion of 1101.101.

1101 in base 9 is equivalent to

=> 9³ + 1 = 729

Now, we'll convert the fractional portion.

The first digit after the decimal point, 1, represents 1/9.

The next digit, 0, represents 0/9².

The last digit, 1, represents 1/9³.

Adding these values together, we get

=> 729 + 1/9 + 1/729 = 729.1184

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