Elisa bought some boxes of pencils for $3.99 each and some boxes of pens at $4.99 each. If p represents the number of boxes of pencils and b represents the number of boxes of pens, which equation describes the relationship between these two variables if she spent a total of $39.91 on these items?

A. 4.99p + 3.99b = 39.91
B. 4.99p - 3.99b = 39.91
C. 3.99p + 4.99b = 39.91
D. 3.99p - 4.99b = 39.91

To make a boxplot of the six measurements, first arrange them in order from smallest to largest: 1.303, 1.308, 1.310, 1.311, 1.316, 1.321. Then, draw a number line and plot a box that spans the range from the first quartile (Q1) to the third quartile (Q3), with a line inside the box representing the median.

The whiskers should extend to the smallest and largest observations that fall within 1.5 times the interquartile range (IQR) from the box. Any observations that fall outside of this range are considered outliers and should be plotted as individual points.

In this case, Q1 is 1.308, Q3 is 1.316, the median is 1.311, and there are no outliers. Therefore, the boxplot would show a box from 1.308 to 1.316, with a line at 1.311 in the middle.

As for whether the t distribution should be used to find a 99% confidence interval for the thickness, it depends on whether we know the population standard deviation or not. If we know it, we could use a z-score instead of a t-score to calculate the confidence interval. However, if we do not know the population standard deviation, we would need to use the t distribution to account for the extra uncertainty in our sample estimate of the standard deviation. In either case, a 99% confidence interval would be wider than a 95% confidence interval, since we are more certain that the true population mean falls within the wider range.

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The reflection of the point (8,0) across the x-axis is (8, 0)

From the question, the point is given as:

Point = (8, 0)

Rewrite this point as

(x, y) = (8, 0)

The transformation is given as

Reflection across the x-axis

Mathematically, we have

(x, y) = (x, -y)

So,we have

Image = (8, 0)

Hence, the image of the reflection is (8, 0)

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An equation of the line passing through the pair of points (-5,2) and (-6,-8) in the form Ax + By = C is 5x + 7y = -36.

We can find the equation of the line passing through the pair of points (-5,2) and (-6,-8) using the point-slope form of the equation:

y - y1 = m(x - x1)

where (x1,y1) and (x,y) are points on the line, and m is the slope of the line. To find the slope, we use the formula:

m = (y2 - y1)/(x2 - x1)

where (x1,y1) and (x2,y2) are the given points.

Substituting the values:

m = (-8 - 2)/(-6 - (-5)) = -10/-1 = 10

Now, we can use either point and the slope to find the equation of the line in point-slope form:

y - 2 = 10(x + 5)

Simplifying:

y - 2 = 10x + 50

y = 10x + 52

To write the equation in the form Ax + By = C, we rearrange the terms:

-10x + y = 52

Multiplying both sides by -1:

10x - y = -52

Multiplying both sides by -1 again to make the coefficient of x positive, we get:

-10x + y = 52

Thus, the equation of the line passing through (-5,2) and (-6,-8) in the form Ax + By = C is 5x + 7y = -36.

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Answer:

16 ft.

Step-by-step explanation:

Distance Formula:

A = (2,2)

B = (12,14)

So, sqrt(12^2 + 10^2) = 16 ft.

This is the same for B to C.

So, 16 ft.

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To find the integral representing the volume of the solid that the cylinder with base r, we can use cylindrical coordinates. The volume of the cylinder is given by the formula V = πr^2h, where r is the radius of the base and h is the height.

Using cylindrical coordinates, the solid can be represented as the region bounded by the planes z=0, z=h, and the cylinder \(x^2+y^2=r^2\). The integral to find the volume of this solid is then given by the triple integral over the region in cylindrical coordinates, i.e., ∭E r dr dθ dz

where E is the region bounded by the planes z=0, z=h, and the cylinder \(x^2+y^2=r^2\), and the limits of integration are r=0 to r=r, θ=0 to 2π, and z=0 to h. In this integral, the integrand is simply r, which represents the infinitesimal volume of the solid element at each point in the region E. Integrating this over the entire region E gives the total volume of the solid.

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The solution to the given initial value problem is y = (1/7)t³ - (1/6)t² + t + (29/42)t⁻⁴, obtained using the method of integrating factors.

To find the solution of the given initial value problem, we can use the method of integrating factors.

First, let's rearrange the equation to put it in standard form: y' + (4/t)y = t² - t + 5.

The integrating factor is given by the exponential of the integral of the coefficient of y, which in this case is 4/t. So, the integrating factor is e^(∫(4/t)dt).

To integrate 4/t, we can rewrite it as 4t⁻¹ and apply the power rule of integration. The integral becomes ∫(4/t)dt = 4∫(t⁻¹)dt = 4ln|t|.

Therefore, the integrating factor is e^(4ln|t|) = e^(ln(t⁴)) = t⁴.

Next, we multiply both sides of the equation by the integrating factor: t⁴ * (y' + (4/t)y) = t⁴ * (t² - t + 5).

This simplifies to t⁴ * y' + 4t³ * y = t⁶ - t⁵ + 5t⁴.

Now, we can rewrite the left side of the equation using the product rule of differentiation: (t⁴ * y)' = t⁶ - t⁵ + 5t⁴.

Integrating both sides with respect to t gives us t⁴ * y = (1/7)t⁷ - (1/6)t⁶ + (5/5)t⁵ + C, where C is the constant of integration.

Finally, we solve for y by dividing both sides by t⁴: y = (1/7)t³ - (1/6)t² + t + C/t⁴.

To find the particular solution that satisfies the initial condition y(1) = 2, we substitute t = 1 and y = 2 into the equation.

2 = (1/7)(1³) - (1/6)(1²) + 1 + C/(1⁴).

Simplifying this equation gives us 2 = 1/7 - 1/6 + 1 + C.

By solving for C, we find that C = 29/42.

Therefore, the solution to the initial value problem is y = (1/7)t³ - (1/6)t² + t + (29/42)t⁻⁴.

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Answer:

59

Step-by-step explanation:

Answer:

The mean of this data set is 10.6

Step-by-step explanation:

To find the Mean of a data set, you add up all the values and then divide by the number of values.

3 + 4 + 6 + 7 + 10 + 15 + 19 + 21 = 85

This data set has 8 values.

85 ÷ 8 = 10.6

Answer:

5.3

Step-by-step explanation:

The scale of the drawing is 6 feet = 17 inches

Scaling is the process of increasing or reducing the size of a figure by a factor k.

In the given statement is:

Shane made a scale drawing of a hotel. a room in the hotel, which is 18 feet wide in real life, is 51 inches wide in the drawing.

A figure which is 18 feet wide in real life, is 51 inches wide in the drawing, hence the scale is:

Now, According to the question is

18 feet = 51 inches

Divide both sides by 3:

6 feet = 17 inches

Therefore, the scale of the drawing is 6 feet = 17 inches

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Answer: 150 hours each month and 37.5 hours each week

Step-by-step explanation:

Answer: IN week he need to work - 14.56 hr = 14hr 33 min

In month he need to do 62.4 hr= 62 hr 24 min

Step-by-step explanation:

The component form of a vector refers to breaking the vector into components with unit vectors denoting the direction of each component. The general component form angled vectors in a two-dimensional space is given by:

\(\vec v=|v|cos\theta\hat{x}+|v|sin\theta\hat{y}\)

where |v| is the magnitude of the vector component and theta is the angle of the vector.

Using the magnitude and angle given for vector u we can write its component form :

\(\vec u=|u|cos\theta_u \hat{x}+|u|sin\theta_u \hat{y}\\\vec u=|5|cos(9)\hat{x}+|5|sin\(9) \hat{y}\\\vec v=5cos9_u\hat{x}+5sin9_u\hat{y}\)

Doing the same for v

\(\vec v=|v|cos\theta_u \hat{x}+|v|sin\theta_u \hat{y}\\\vec v=|1|cos5_u \hat{x}+|1|sin5_u \hat{y}\\\vec v=1cos5_u\hat{x}+sin5_u\hat{y}\)

Now adding both vector together

\(\vec u+\vec v=(5cos9_u\hat{x}+5sin9_u\hat{y})+(cos5_u\hat{x}+sin5_u\hat{x})\\\vec u+\vec v=(5cos9_u\hat{x}+cos5_u\hat{x})+(5sin9_u\hat{y}+sin5_u\hat{y})\)

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Answer:

6 hours

Step-by-step explanation:

They meet at distance d from their starting point.

Juan walks at 4 mph for time t.

Cathy jogs at 5 mph for time t - 1.5 since she starts 1.5 hour later.

speed = distance/time

distance = speed × time

Juan

d = 4t

Cathy

d = 5(t - 1.5)

4t = 5t - 7.5

t = 7.5

They meet 6.5 hours after Juan started walking.

Cathy jogged for 1.5 hours less than Juan walked.

7.5 hours - 1.5 hours = 6 hours

Answer: 6 hours

Answer:

-1, -7

1, 3

3, -1

5, -5

Step-by-step explanation:

Answer:

8.1-5.6n

Step-by-step explanation:

So first combine like terms

3.1+5=8.1

-3.6n-2n= -5.6n

Now just combine them

8.1-5.6n

First find the center, then graph all the points that are at a distance of R units from that center.

A circle of radius R is the set of all points that are at a distance R from a given point (the center of the circle).

So to graph it, we need to know these two things, radius and center.

Once we do, first we graph the center on the coordinate plane.

Once we find the center, we can find all the poiints that are at a distance of R units from our center, so we need to graph these. Once we do, we will have the graph of our circle on the coordinate plane.

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The total number of ways to distribute all the fruits to the 30 children, ensuring each child who prefers apples gets at least 2 apples and each child who prefers oranges gets at least 2 oranges, is given by the product of C(29, 9) and C(59, 19).

To find the total number of ways, we can consider the distribution of apples and oranges separately. For the children who prefer apples, we need to distribute 20 apples among 10 children, with each child receiving at least 2 apples. This can be calculated using the stars and bars combinatorial technique. Similarly, for the children who prefer oranges, we need to distribute 40 oranges among 20 children, with each child receiving at least 2 oranges.

The number of ways to distribute the apples can be calculated as C(20+10-1, 10-1) = C(29, 9). Likewise, the number of ways to distribute the oranges can be calculated as C(40+20-1, 20-1) = C(59, 19). To find the total number of ways to distribute both fruits, we multiply these two values together.

Therefore, the total number of ways to distribute all the fruits to the 30 children while satisfying the given conditions is C(29, 9) x C(59, 19).

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Answer:

To find the length of q, we can use the Law of Cosines formula:

q = sqrt(p^2 + o^2 - 2 * p * o * cos(Q))

where p and o are the lengths of sides PQ and PO, and Q is the measure of the included angle between them.

Since we know that p = 9.7 inches and ∠Q = 93°, we can use the Law of Sines to find o:

sin(Q) = o/q

=> o = q * sin(Q)

=> o = 9.7 * sin(93)

Using this formula and rounding to the nearest tenth, we can find that o = 11.7 inches.

Now we can use the Law of Cosines to find q:

q = sqrt(p^2 + o^2 - 2 * p * o * cos(Q))

=> q = sqrt(9.7^2 + 11.7^2 - 2 * 9.7 * 11.7 * cos(93))

Rounding to the nearest tenth, we get that q = 17.2 inches.

Answer:

111.1

Step-by-step explanation:

The smallest unit of matter is an atom. The fundamental building block of an element is an atom, which is made up of protons, neutrons, and electrons. This statement is true.

An atom is made up of a nucleus and one or more electrons that are bound to the nucleus. The nucleus is made up of one or more protons, a significant number of neutrons, and other particles. Only the most common form of hydrogen lacks neutrons.

An atom, which is the smallest part of a material, retains all of its properties. A molecule is made up of protons, neutrons, and electrons, which are the building components of matter. Protons and neutrons, which are the only particles in an atom that contribute to its atomic mass, are found in the nucleus of each atom. These early 20th-century discoveries of particles that  a nuclide itself and chemical components are explained by contemporary atomic theory.

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Answer:

$50.40

Step-by-step explanation:

To find how much Lana will pay in total follow these steps.

First, multiply 40 by 1.05.

40×1.05=42.

This is how much she will pay for the food plus tax.

Now, multiply 42 by 1.2.

42×1.2=50.40

This is how much she will pay for the food, tax, and tip.

Lana will pay a total of $50.40.

Hope this helps!

Answer:

Jordon's brother got $40

Step-by-step explanation:

We can set up a system of equations to solve this.

Let's say that Jordon got x dollars.

His brother got y dollars.

x+y=100 since they are dividing the 100 dollars

1/3x=1/2y (the same indicates that they are equal)

Multiply the entire second equation by 3.

x=1.5y

Now we can substitute 1.5y in for x in the first equation.

x+y=100

1.5y+y=100

2.5y=100

Divide both sides by 2.5

y=40

Jordon's brother got $40.

Plug that in to find how much Jordon got.

x+y=100

x+40=100

Subtract 40 from both sides

x=60

Jordon got 60.

Answer:

Perimeter = 8w

Step-by-step explanation:

Let the width of the rectangular framework be w.

Length = 3w

We know that the perimeter of a rectangular shaped object is given by :

P = 2(l+w)

Substitute all the values in the above formula,

Perimeter = 2(3w+w)

= 2(4w)

= 8w

So, the perimeter of the art be 8w.

Answer:

(x+1) (x-1)

Step-by-step explanation:

rewrite 1 as 1^2

Apply diffrence of two squares formula

x^2-y^2= (x+y)(x-y)

x^2-1^2= (x+1) (x-1)

Answer:  2 distinct complex solutions (ie non real solutions).

Work Shown:

The given equation is in the form ax^2+bx+c = 0, so

a = 1, b = 3, c = 8

Plug those into the formula below to find the discriminant

D = b^2 - 4ac

D = 3^2 - 4(1)(8)

D = -23

The discriminant is negative, so we get two nonreal solutions. The two solutions are complex numbers in the form a+bi, where a & b are real numbers and \(i = \sqrt{-1}\). The two solutions are different from one another.

Answer:

Discriminant: -23

Number of real roots: 0

Step-by-step explanation:

For a quadratic in standard form \(ax^2+bx+c\), the discriminant is given by \(b^2-4ac\).

In \(x^2+3x+8\), assign:

The discriminant is therefore:

\(3^2-4(1)(8)=9-32=\boxed{-23}\)

For any quadratic:

Since the quadratic in the question has a discriminant less than 0, there are no real solutions to this quadratic.

Answer:

C

Step-by-step explanation:

tan S = opposite / adjacent

S = tan -1 ( 120 / 52) = 66.57 degree ≅ 67

The area of the quadrilateral ABCD is 4 square units

From the question, we have the following parameters that can be used in our computation:

The figure

The quadrilateral ABCD is a polygon that is formed from two congruent triangles with the following dimensions

Base = 2

Height = 2

So, we have

Area = 2 * 1/2 * Base * Height

Substitute the known values in the above equation, so, we have the following representation

Area = 2 * 1/2 * 2 * 2

Evaluate

Area = 4

Hence, the area is 4 square units

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Answer:

3

Step-by-step explanation:

Vol = length x width x height

Vol = 3 x 3 x3

Vol = 27

Answer:

2(29D-28adn-29)

Step-by-step explanation:

The sine and the cosine of the acute angle are the same for θ = π / 4. (Correct choice: 2)

Acute angles are angles whose measures are greater than 0° and less than 90°. According to the statement, we must find at least a value such that sin θ = cos θ:

sin θ = cos θ                     Given

sin θ / cos θ = 1                 Compatibility with multiplication / Existence of multiplicative inverse / Modulative property

tan θ = 1                            Definition of tangent

θ = π / 4                            Inverse trigonometric function / Result

In a nutshell, the sine and the cosine of the acute angle are the same for θ = π / 4. (Correct choice: 2)

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The probability that a student will get exactly 13 questions right is 0.003.

Let E be an event that student gives 13 right answers.

According to the given question.

An exam contain total number of questions is 15.

Now,

The probability that a student gives a right answer, p = 1/2 = 0.5

And, the probability that a student gives a wrong answer, q = 1 - 1/2 = 1/2 = 0.5

Therefore,

The probability that a student will get exactly 13 questions right is given by

⇒ P(E) = C(15, 13) p^(13)q^(15 - 13)

⇒ P(E) = (15!/13!2!)(0.5)^13(0.5)^2

⇒ P(E) = (15(14)/2 ) ×  ( 0.00012) × 0.25

⇒ P(E) = 105 × 0.00012 × 0.25

⇒ P(E) = 0.00315

Hence, the probability that a student will get exactly 13 questions right is 0.003.

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