A group of students collected old newspapers for a recycling project. The data shows the mass, in kilograms, of old newspapers collected by each student.



23, 35, 87, 64, 101, 90, 45, 76, 105, 60, 55


98, 122, 49, 15, 57, 75, 120, 56, 88, 45, 100.



What percent of students collected between 49 kilograms and 98 kilograms of newspapers? Explain how you got to your solution

[tex]\sf y =\dfrac{2}{5}x-4[/tex]

Step-by-step explanation:

        To find the equation of the required line, first we need to find the slope of the given line in the graph.

          Choose two points from the graph.

         (0 ,4)    x₁ = 0 & y₁ = 4

         (2,-1)     x₂ = 2 & y₂ = -1

[tex]\sf \boxed{\sf \bf Slope=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

           [tex]\sf = \dfrac{-1-4}{2-0}\\\\=\dfrac{-5}{2}[/tex]

       [tex]\sf m_1=\dfrac{-5}{2}[/tex]

[tex]\sf \text{Slope of the perpendicular line m = $\dfrac{-1}{m_1}$}[/tex]

                                                    [tex]\sf = -1 \div \dfrac{-5}{2}\\\\=-1 * \dfrac{-2}{5}\\\\=\dfrac{2}{5}[/tex]

[tex]\boxed{\sf slope \ intercept \ form \ : \ y = mx + b}[/tex]

Here, m is slope and b is y-intercept.

Substitute the m value in the above equation,

                    [tex]\sf y =\dfrac{2}{5}x + b[/tex]

    The line is passing through (5 , -2),

                     [tex]\sf -2 = \dfrac{2}{5}*5+b[/tex]

                     -2 =  2 + b

                -2 - 2 = b

                      b = -4

Slope-intercept form:

                [tex]\sf y = \dfrac{2}{5}x-4[/tex]

Answer:

x = 13

Step-by-step explanation:

We Know

The sum of angles of a triangle must add up to 180°

We know 2 angles, one is 60° and the other is 90°

Solve for x.

Let's solve

3x - 9 + 60 + 90 = 180

3x + 141 = 180

3x = 39

x = 13

Answer:

part a: The slope of the function represents the rate of change of the balance in the bank account per day. To find the slope, we can use the formula: slope = (change in y)/(change in x).

Using the values from the table, we have: slope = (720-600)/(3-0) = 120/3 = 40. Therefore, the slope of the function g(x) is 40.

part b: Using the point-slope form of the equation of a line, we can write: g(x) - 600 = 40(x-0). Simplifying, we get: g(x) = 40x + 600. This is the slope-intercept form of the equation, where the y-intercept is 600 and the slope is 40.

To write in standard form, we can rearrange the equation as: -40x + g(x) = 600.

part c: Using function notation, we can write the equation as: g(x) = 40x + 600.

part d: To find the balance in the bank account after 7 days, we can use the equation we found in part c and substitute x = 7: g(7) = 40(7) + 600 = 880. Therefore, the balance in the bank account after 7 days is $880.

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By compound interest, The initial amount in the account is $300.

What does compound interest mean ?

When you earn interest on your interest earnings as well as the money you have saved, this is known as compound interest. As an illustration, if you put $1,000 in an account that offers 1% yearly interest, you will receive $10 in interest after a year.

                             Compound interest allows you to earn 1 percent on $1,010 in Year Two, which equates to $10.10 in interest payments for the year. This is possible because interest is added to the principle in Year Two.

A = 300(1.035)t

As we know the formula "Compound Interest" :

A = P(1 + r/100)t

So, According to our question,

Rate of interest = 0.35 = 135%

So, equate the both the equations , we get that

Hence, The initial amount in the account = $300

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Part A:

The definition provided for a circle is actually correct. However, if we change the definition slightly to say that a circle is the set of all points in a plane that are the same distance from a given point, we can find an example that contradicts it.

For instance, consider a cone in three-dimensional space. If we take a cross-section of the cone that is parallel to the base, we get a circle. However, this circle is not the set of all points that are the same distance from one given point, but rather from the axis of the cone.

To make the definition more accurate, we need to specify that the circle exists in a plane.

Part B:

An example of an undefined term related to a circle is the term "point." A circle is defined as the set of all points that are the same distance from a given point, but the term "point" is not defined within this definition.

A point is typically defined as a location in space that has no size or shape. In the context of a circle, a point can be thought of as any location on the circumference of the circle. However, it is important to note that the definition of a point is not dependent on the definition of a circle, and vice versa.

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The vertex form of the equation of the parabola is:

r = (1/24)(y - 1)^2 + 3

Since the directrix is a horizontal line, the axis of the parabola is vertical. Therefore, the vertex form of the equation of the parabola is:

r = a(y - k)^2 + h

where (h, k) is the vertex of the parabola and "a" is a constant that determines the shape and orientation of the parabola.

Since the focus is (3,-5), the vertex of the parabola is halfway between the focus and the directrix. The directrix is 6 units above the vertex, so the vertex is (3,1).

We can use this information to write the vertex form of the equation:

r = a(y - 1)^2 + 3

To find the value of "a", we need to use the distance formula between the vertex and the focus:

distance = |y-coordinate of focus - y-coordinate of vertex| = 6

| -5 - 1 | = |-6| = 6

Using the definition of the parabola, the distance from the vertex to the focus is also equal to 1/(4a). Therefore:

1/(4a) = 6

a = 1/(4*6) = 1/24

Substituting this value of "a" into the vertex form equation, we get:

r = (1/24)(y - 1)^2 + 3

Therefore, the vertex form of the equation of the parabola is:

r = (1/24)(y - 1)^2 + 3

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The equation y = (4/5)x - 3 is in slope-intercept form, y = mx + b, where m is the slope of the line. Therefore, the slope of the line represented by the equation is:

m = 4/5

So the answer is C) 4/5.

The domain of the function f(x) is {x | 0 ≤ x ≤ 3650} and the range is {f(x) | 20 ≤ f(x) ≤ 9145}, where f(x) represents the amount Billy would spend to rent x films.

The domain D of the function f(x) is the collection of all possible values for x. In this scenario, because Billy is not permitted to rent more than ten films every day, the maximum number of films he may rent in a year is ten times the number of days in a year, or 10 x 365 = 3650 films.

Furthermore, because he must pay a membership fee of $20 regardless of how many movies he rents, the minimum number of movies he could rent in a year is zero. As a result, the domain of the function f(x) is as follows:

D = {x | 0 ≤ x ≤ 3650}

The range R of the function f(x) is the collection of all possible values for f(x). In this scenario, the function: returns the amount Billy would spend to rent x films.

f(x) = 2.5x + 20

where 2.5x is the rental charge for x films and 20 is the membership fee. Because x can be any value between 0 and 3650, the smallest value that f(x) can be is:

f(0) = 2.5(0) + 20 = 20

and f(x) has the following maximum value:

f(3650) = 2.5(3650) + 20 = 9145

As a result, the function f(x) has the following range:

R = {f(x) | 20 ≤ f(x) ≤ 9145}

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The closest amount to the total balance is option B, 695.00.

For Account A, the interest earned after 2 years is:

Interest = Principal * Rate * Time = 400 * 0.035 * 2 = 28

So the total balance in Account A after 2 years is:

Total A = Principal + Interest = 400 + 28 = 428

For Account B, the interest earned after 2 years is:

Interest = Principal * (1 + Rate/100)^Time - Principal = 250 * (1 + 3.25/100)^2 - 250 = 25.95

The total balance in Account B after 2 years is:

Total B = Principal + Interest = 250 + 25.95 = 275.95

The total balance in both accounts after 2 years is:

Total Balance = Total A + Total B = 428 + 275.95 = 703.95

The closest amount to the total balance is option B, 695.00.

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Answer:

6, 9, 10, 10, 11, 11, 12, 13, 15, 15, 18

Q1 (the first quartile) represents the data point that separates the lowest 25% of the data from the rest of the data. To find Q1, we can use the formula:

Q1 = (n + 1) / 4

where n is the total number of data points.

In this case, n = 11, so:

Q1 = (11 + 1) / 4 = 3rd data point

So, Q1 is 10.

Q3 (the third quartile) represents the data point that separates the highest 25% of the data from the rest of the data. To find Q3, we can use the formula:

Q3 = 3(n + 1) / 4

In this case:

Q3 = 3(11 + 1) / 4 = 9th data point

So, Q3 is 15.

D4 represents the fourth decile, which is the data point that separates the lowest 40% of the data from the rest of the data. To find D4, we can use the formula:

D4 = (n + 1) / 10 * 4

In this case:

D4 = (11 + 1) / 10 * 4 = 5th data point

So, D4 is 11.

D Assimilation represents the data point that is closest to the mean (average) of the data. To find D Assimilation, we first need to find the mean of the data:

Mean = (6 + 9 + 10 + 10 + 11 + 11 + 12 + 13 + 15 + 15 + 18) / 11 = 12

The data point closest to the mean is 12, so:

D Assimilation = 12

Pss (the range) represents the difference between the largest and smallest data points. In this case:

Pss = 18 - 6 = 12
6  9  10 10 11 11 12 13 15 15 18

                             Dss=12

   Q1=10       Q3=15

       D4=11

Step-by-step explanation:

The student from the first class performs better when comparing their scores using z-scores.

To compare the students' performances, we will calculate their z-scores, which show how many standard deviations away their scores are from the mean of their respective classes.

For the student from the first class:
z-score = (Score - Mean) / Standard Deviation
z-score = (62 - 56) / 9
z-score ≈ 0.67

For the student from the second class:
z-score = (83 - 75) / 15
z-score ≈ 0.53

The student from the first class has a higher z-score (0.67) compared to the student from the second class (0.53). This means the student from the first class performed better relative to their classmates.

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All interior angles are equal, so Angle ABE = 120°.
the exterior angle is equal to 60 degrees.

Angle BCE is equal to 180 degrees.

The polygon must have 18 sides because its exterior angles sum to 360°, and each exterior angle is 20°.

1) In a regular hexagon:
a) Angle ABE is an interior angle. To calculate the size of Angle ABE, we first find the sum of interior angles of a hexagon, which is (n-2)×180°, where n is the number of sides.

For a hexagon, n = 6, so the sum of interior angles is (6-2)×180° = 720°. Since it's a regular hexagon, all interior angles are equal, so Angle ABE = 720°/6 = 120°.

b) Angle DCE is an exterior angle. In a regular hexagon, the exterior angles are equal. To find the size of an exterior angle, we can use the formula: exterior angle = 360°/n, where n is the number of sides. For a hexagon, n = 6, so Angle DCE = 360°/6 = 60°.

c) Angle BEC is the sum of Angle ABE and Angle DCE. Therefore, Angle BEC = 120° + 60° = 180°.

2) For a regular polygon with an exterior angle of 20°:
a) The sum of the interior angle and exterior angle for any polygon is 180°. So, the size of its interior angle = 180° - 20° = 160°.

b) To find the number of sides in the polygon, we can use the formula for the exterior angle: exterior angle = 360°/n, where n is the number of sides. We know that the exterior angle is 20°, so 20° = 360°/n.

Solving for n, we get n = 360°/20° = 18 sides. The polygon must have 18 sides because its exterior angles sum to 360°, and each exterior angle is 20°.

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The exponential term (87^t)^(1.75) increases, leading to an exponential growth in the number of people who receive the email.

The relationship between the elapsed time t, in days, since Bharat sent the letter and the number of people P(t) who receive the email is modeled by the following function:

P(t) = 2401 * (87^t)^(1.75)

In this function, t represents the number of days that have passed since Bharat sent the letter, and P(t) represents the number of people who receive the email at that time.

The function is an exponential growth model where the base is 87, and the exponent is t raised to the power of 1.75. The constant 2401 is a scaling factor that determines the initial number of people who receive the email at t=0.

As time passes, the exponential term (87^t)^(1.75) increases, leading to an exponential growth in the number of people who receive the email.

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The finished table contains the following amount of cans per day:

To find out how many cans of food per day to give a cat, divide the cat's weight by 4. If the weight is not a multiple of 4, the result will be a fraction, which represents a fraction of a can of food.

A 5-pound cat needs 5/4 or 1.25 cans of food per day. Simplify this fraction to 1 ¹/₄ or 1.25.

Others include:

6/4 = 1.5

7/4 = 1.75

8/4 = 2

9/4 = 2.25

10/4 = 2.5

11/4 = 2.75

12/4 = 3

13/4 = 3.25

14/4 = 3.5

15/4 = 3.75

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Answer:

Mean=15.86

Median=18

Mode=18

A random sample that has 1000 college students in the United States is surveyed about how much money they spend on books per year, and the mean amount calculated is 1000 college students in the US. Option A is the correct answer.

The sample in this scenario refers to the group of college students who were surveyed about their book spending habits. In this case, the sample size is 1000 college students in the United States.

The purpose of this survey is to estimate the mean amount of money spent on books per year by college students in the US, using the sample mean as an estimate. It is important to note that the sample should be representative of the larger population of college students in the US.

Therefore, option A, "1000 college students in the US," is the correct answer. Option B, "all college students in the US," represents the population, not the sample. Options C and D are not relevant to the given scenario.

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The question is -

A random sample of 1000 college students in the United States is surveyed about how much money they spend on books per year, and the mean amount is calculated. What is the sample?

a. 1000 college students in the US

b. all college students in the US

c. 1000 college students in CA

d. all college students in CA

Dominick has earned $6,465.55 - $4,420.00 = $2,045.55 more interest than Ryan after 10 years.

To solve this problem, we can use the formulas for compound interest and simple interest.

Compound interest formula:

[tex]A = P(1 + r/n)^(^n^t^)[/tex]

Where:

A = the amount after time t

P = the principal

r = the annual interest rate

n = the number of times the interest is compounded per year

t = time in years

Simple interest formula:

I = Prt

Where:

I = the interest earned

P = the principal

r = the annual interest rate

t = time in years

Using the compound interest formula for Dominick's account:

[tex]A = P(1 + r/n)^(^n^t^)[/tex]

A = 6500(1 + 0.068/365)^(365*10)

A ≈ $12,965.55

Using the simple interest formula for Ryan's account:

I = Prt

I = 65000.06810

I = $4,420.00

Dominick's account has earned: $12,965.55 - $6,500 = $6,465.55 in interest.

Ryan's account has earned: $4,420.00 in interest.

Therefore, Dominick has earned $6,465.55 - $4,420.00 = $2,045.55 more interest than Ryan after 10 years.

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Answer:Blue one.71.82

Step-by-step explanation:

6.3*11.4=71.82

Answer:

71.82 I think

Step-by-step explanation:

The probability that four boys are given the first four seats on the first teacup is approximately equal to 0.004.

To determine the probability that four boys are given the first four seats on the first teacup.

The total number of ways to distribute 12 tickets among 12 seats is 12! (12 factorial), which is equal to 479,001,600.

We need to find the number of ways that four boys can be selected from the seven boys, multiplied by the number of ways that eight people (including the remaining three boys and five girls) can be selected from the ten remaining people,

multiplied by the number of ways that the selected people can be arranged on the teacup ride.

The number of ways to select four boys from seven boys is 7C4, which is equal to 35. The number of ways to select eight people from the remaining ten people is 10C8, which is equal to 45.

Finally, the number of ways to arrange the selected twelve people on the teacup ride is 4!, which is equal to 24.

Therefore, the probability that four boys are given the first four seats on the first teacup is (35 x 45 x 24) / 12!, which is approximately equal to 0.004.

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The unit rate of dirt is 2 metric tons per hour.

In order to determine the unit rate, divide the metric tons of dirt by the number of hours it take to remove the dirt.

Division is the process of grouping a number into equal groups using another number. The sign that represents division is ÷.

Unit rate = metric tons of dirt ÷ number of hours

1/2 ÷ 1/4

1/2 x 4 = 2 metric tons per hour

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The missing sides are given as;

1. x = 12. 9

2. a = 12. 4

3. n = 5. 2

4. k = 13. 5

5. n = 22. 5

To determine the missing sides, we have to use the different trigonometric identities. These identities are;

Using the cosine identity, we have;

cos 31 = x/15

cross multiply the values, we get;

x = 12. 9

2. Using the tangent identity, we have;

tan 44 = 12/a

cross multiply the values

a = 12. 4

3. Using the sine identity;

sin 48 = n/7

n = 5. 2

4. Using the cosine identity;

cos 42 = 10/k

cross multiply

k = 13. 5

5. cos 26 = n/25

n = 22. 5

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√6a + 3 < a + 2,  we have proven that √6a + 3 < a + 2 for all a > 1 using the Mean Value Theorem.

To use the Mean Value Theorem to prove √6a + 3 < a + 2 for all a > 1, we first note that the function f(x) = √6x + 3 is continuous on the interval [1,a].

Next, we need to find a point c in the interval (1,a) such that the slope of the line connecting (1,f(1)) and (a,f(a)) is equal to the slope of the tangent line to f(x) at c.

The slope of the line connecting (1,f(1)) and (a,f(a)) is given by:

(f(a) - f(1)) / (a - 1) = (√6a + 3 - √9) / (a - 1) = (√6a) / (a - 1)

To find the slope of the tangent line to f(x) at c, we first find the derivative of f(x):

f'(x) = (1/2) * (6x + 3)^(-1/2) * 6 = 3 / √(6x + 3)

Then, we evaluate f'(c) to get the slope of the tangent line at c:

f'(c) = 3 / √(6c + 3)

Now, by the Mean Value Theorem, there exists a point c in (1,a) such that:

f'(c) = (√6a) / (a - 1)

Setting these two expressions for f'(c) equal to each other, we get:

3 / √(6c + 3) = (√6a) / (a - 1)

Solving for c, we get:

c = (a + 2) / 6

(Note that c is indeed in (1,a) since a > 1.)

Now, we can evaluate f(a) and f(1) and use the Mean Value Theorem to show that:

√6a + 3 - √9 < (√6a) / (a - 1) * (a - 1)

Simplifying, we get:

√6a + 3 < a + 2

as desired.

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Answer:

Step-by-step explanation:

To find the percentage of Tara's monthly income spent on her car payment, we need to divide her car payment by her monthly income and then multiply by 100 to get the percentage:

$219 / $3,200 = 0.0684375

0.0684375 * 100 = 6.84375

So, Tara spends approximately 6.8% of her monthly income on her car payment.

The closest answer choice is C. 6.8%.

Answer:

C

Step-by-step explanation:

I got just did it and got it right

The area of the larger sheet is 180 times greater than the area of the smaller sheet.

To determine which sheet has a larger area, Let's assume that the length of the smaller sheet of paper is l and the width of the smaller sheet is w. Then, we can express the dimensions of the larger sheet in terms of l and w as follows:

Length of larger sheet = 12l

Width of larger sheet = 15w

The area of the smaller sheet can be calculated as:

Area of smaller sheet = length × width = lw

Similarly, the area of the larger sheet can be calculated as:

Area of larger sheet = length × width = (12l) × (15w) = 180lw

To find the factor by which the area of the larger sheet is greater than the area of the smaller sheet, we can divide the area of the larger sheet by the area of the smaller sheet:

Factor = Area of larger sheet / Area of smaller sheet

Factor = (180lw) / (lw)

Simplifying the expression, we get:

Factor = 180

Therefore, the area of the larger sheet is 180 times greater than the area of the smaller sheet.

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The conic section formed when a plane intersects the central axis of a double-napped cone at a 90° angle is circle.

The conic curve refers to the intersection of right circular cone via the plane. The shape of conic sections are determined by the location of the plane that intersects or divides the angle of intersection and cones.

These can be of four types, parabola, circle, ellipse and hyperbola. The conic curves find application in daily life such as mirrors, satellites, telescopes and other similar devices.

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Answer:circle A.

Step-by-step explanation:

The probability of getting to sleep in an interval is 0.0903.

The expected time the doctor spends awake in each interval is 1.8648 hours.

(a) To compute the long-run fraction of time the doctor spends sleeping, we can formulate a renewal reward process. In this process, each interval represents the time between consecutive emergencies.

Let T be the inter-arrival time between emergencies, which follows an exponential distribution with a rate of λ = 0.5 per hour. The average inter-arrival time is given by E(T) = 1/λ = 1/0.5 = 2 hours.

In each interval, the doctor can only get to sleep if it has been 36 minutes (6 hours) since the last emergency. Otherwise, she remains awake.

Let R be the reward obtained in each interval, which is the amount of time the doctor gets to sleep. If the doctor gets to sleep in an interval, the reward is (T - 0.6) since she has already waited for 0.6 hours (36 minutes). Otherwise, the reward is zero.

The long-run fraction of time spent sleeping, denoted by ρ, can be calculated as the expected reward per unit time:

ρ = E(R)/E(T)

To compute E(R), we need to consider the conditional probability that the doctor gets to sleep in an interval.

Given an interval length T, the probability that T > 0.1 (36 minutes) is given by P(T > 0.1) = 1 - P(T ≤ 0.1). This probability is equal to the cumulative distribution function (CDF) of the exponential distribution with rate λ evaluated at 0.1.

P(T > 0.1) = 1 - F(0.1) = 1 - (1 - exp(-λ * 0.1))

Substituting the value of λ = 0.5, we get:

P(T > 0.1) = 1 - (1 - exp(-0.5 * 0.1)) ≈ 0.0903

Therefore, the probability of getting to sleep in an interval is approximately 0.0903.

E(R) = (T - 0.6) * P(T > 0.1) + 0 * (1 - P(T > 0.1))

= (T - 0.6) * 0.0903

Substituting the average inter-arrival time E(T) = 2 hours:

E(R) = (2 - 0.6) * 0.0903 ≈ 0.1352 hours

Finally, we can compute ρ:

ρ = E(R)/E(T) = 0.1352/2 ≈ 0.0676

Therefore, the long-run fraction of time the doctor spends sleeping is approximately 0.0676.

(b) To compute E(ui), the expected time the doctor spends awake in each interval, we can use the fact that the total time spent in each interval is T, and the time spent sleeping is (T - R), where R is the reward obtained in each interval.

E(ui) = E(T - R)

= E(T) - E(R)

= 2 - 0.1352

≈ 1.8648 hours

Therefore, the expected time the doctor spends awake in each interval is approximately 1.8648 hours.

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The horizontal distance between the two cafes is approximately 19.36 meters.

To solve this problem, we can use the Pythagorean theorem which states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the atrium can be considered as the base of a right-angled triangle, with the difference in height between the two cafes as the vertical side and the distance between them as the hypotenuse.

Let's call the horizontal distance we are looking for "x". Using the Pythagorean theorem, we have:

[tex]x^2 = 20^2 - (15 - 10)^2\\x^2 = 400 - 25\\x^2 = 375[/tex]

x ≈ 19.36

Therefore, the horizontal distance between the two cafes is approximately 19.36 meters.

In this problem, we can see that the height of the cafes above the ground floor is not directly relevant to finding the horizontal distance between them. Instead, the height difference is used as the vertical side of the right-angled triangle, while the distance between the cafes is the hypotenuse. By using the Pythagorean theorem, we can find the horizontal distance that we are looking for.

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The cost of one hamburger is $2.50 and the cost of one order of fries is $1.50.

Let's use h to represent the cost of one hamburger and f to represent the cost of one order of fries.

The Smith family's order can be represented by the equation:

6h + 3f = 19.50

The Jansen family's order can be represented by the equation:

8h + 6f = 29.00

We now have a system of two linear equations with two variables:

6h + 3f = 19.50

8h + 6f = 29.00

To solve for h and f, we can use the elimination method. We can start by multiplying the first equation by 2 to eliminate the variable f:

12h + 6f = 39.00

8h + 6f = 29.00

Subtracting the second equation from the first, we get:

4h = 10.00

Solving for h, we get:

h = 2.50

Now that we know the cost of one hamburger, we can substitute this value back into one of the original equations to solve for f. Using the first equation:

6h + 3f = 19.50

6(2.50) + 3f = 19.50

15 + 3f = 19.50

3f = 4.50

f = 1.50

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Answer:

log base 4 (5x + 4) = 3

Step-by-step explanation:

a^b=c  is  loga(c)=b

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