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

(34) the sum of the series is 170. (33) The sum of the series is 341. (35) the sum of the series is 21844

To evaluate a geometric series, we use the formula:

Sn = a(1 - r^n) / (1 - r)

where:

Sn = the sum of the first n terms of the series
a = the first term of the series
r = the common ratio between consecutive terms
n = the number of terms we want to sum

Let's use this formula to evaluate the given geometric series:

34) a1 = -2, a8 = 256, r = -2

To find the sum of this series, we need to know the value of n. We can find it using the formula:

an = a1 * r^(n-1)

a8 = -2 * (-2)^(8-1) = -2 * (-2)^7 = -2 * (-128) = 256

Now we can solve for n:

an = a1 * r^(n-1)
256 = -2 * (-2)^(n-1)
-128 = (-2)^(n-1)
2^7 = 2^(1-n+1)
7 = n-1
n = 8

So this series has 8 terms. Now we can use the formula to find the sum:

Sn = a(1 - r^n) / (1 - r)
S8 = (-2)(1 - (-2)^8) / (1 - (-2))
S8 = (-2)(1 - 256) / 3
S8 = 510 / 3
S8 = 170

Therefore, the sum of the series is 170.

33) a1 = -1, a9 = 512, r = -2

We can use the same method as before to find n:

an = a1 * r^(n-1)
512 = -1 * (-2)^(9-1) = -1 * (-2)^8
512 = 256
This is a contradiction, so there must be an error in the problem statement. Perhaps a9 is meant to be a5, in which case we can find n as:

an = a1 * r^(n-1)
a5 = -1 * (-2)^(5-1) = -1 * (-2)^4
a5 = 16
512 = -1 * (-2)^(n-1)
-512 = (-2)^(n-1)
2^9 = 2^(1-n+1)
9 = n-1
n = 10

So this series has 10 terms. Now we can use the formula to find the sum:

Sn = a(1 - r^n) / (1 - r)
S10 = (-1)(1 - (-2)^10) / (1 - (-2))
S10 = (-1)(1 - 1024) / 3
S10 = 1023 / 3
S10 = 341

Therefore, the sum of the series is 341.

35) a1 = 4, a14 = 16384, r = 4

Again, we can find n using the formula:

an = a1 * r^(n-1)
16384 = 4 * 4^(14-1) = 4 * 4^13 = 4 * 8192 = 32768
This is a contradiction, so there must be an error in the problem statement. Perhaps a14 is meant to be a7, in which case we can find n as:

an = a1 * r^(n-1)
a7 = 4 * 4^(7-1) = 4 * 4^6 = 4 * 4096 = 16384
16384 = 4 * 4^(n-1)
4096 = 4^(n-1)
2^12 = 2^(2n-2)
12 = 2n-2
n = 7

So this series has 7 terms. Now we can use the formula to find the sum:

Sn = a(1 - r^n) / (1 - r)
S7 = (4)(1 - 4^7) / (1 - 4)
S7 = (4)(1 - 16384) / (-3)
S7 = 65532 / 3
S7 = 21844

Therefore, the sum of the series is 21844.

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John needs approximately 1,814.4 mm² of tape to cover the pepper shaker. Rounded to the hundredths, the answer is 1,814.40 mm².

To calculate the amount of tape needed to cover the pepper shaker, we need to find the lateral area of the cylinder. This is given by the formula L = 2πrh, where r is the radius and h is the height.

Substituting the values given, we get L = 2π(9 mm)(32 mm) = 1,814.4 mm².

Therefore, John needs approximately 1,814.40 mm² of tape to cover the pepper shaker.

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To solve the triangle, we have;

Angle Q = [tex]112^{o}[/tex]

QR = 30.0

PR = 40.2

A sine rule is a trigonometric function that can be applied to determined the unknown side, or angle of a none right triangle.

From the information given in the question, to solve the triangle;

P + R + Q = 180

42 + 26 + Q = 180

Q = 180 - 68

   = 112

Q = [tex]112^{o}[/tex]

Applying the sine rule,

QR/Sin P = PR/Sin Q = PQ/Sin R

PR/Sin Q = PQ/Sin R

PR/Sin 112 = 19/ Sin 26

PRSin 26 = 19*Sin 112

             = 17.6165

PR = 17.6165/ 0.4384

  = 40.1836

PR = 40.2

Also,

QR/Sin P = PQ/Sin R

QR/Sin 42 = 19/ Sin 26

QRSin 26 = 19*Sin 42

                = 12.7135

QR = 12.7135/ 0.4384

     = 28.9998

QR = 30

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(i) A Venn-diagram of this information is shown below.

(ii) The number of students who like picnic = 34

(iii) The number of students who like hiking only = 51

(iv) The percentage of students who like picnic only. = 45.33%

Let us assume that A represents the set of students who like picnic.

B represents the set of students who like the hiking.

The total number of students in a  class are: n(A U B) = 75

Out of 75 students, 10 like both the activities.

n(A ∩ B) = 10

The ratio of the number of students who like picnic to those who like hiking is 2 : 3

Let number of students like tea n(A) = 2x

and the number of students like coffee n(B) = 3x

n(A U B) = n(A) + n(B) - n(A ∩ B)

75 = 2x + 3x - 10

75 + 10 = 5x

85/5= x

x = 17

The number of students like picnic = 2x

                                                          = 2 × 17

                                                          = 34

The number of students like hiking = 3x

                                                           = 3 × 17

                                                           = 51

This informtaion in Venn diagram is shown below.

The percentage of students who like picnic only would be,

(34/75) × 100 = 45.33%

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Answer: 64$

Step-by-step explanation:

the equivalent integral with the order of integration reversed is: ∫0^1 ∫1^2 log(x) 9(y) dydx = (9/2) (2log(2) - 1)

To write an equivalent integral with the order of integration reversed, we need to integrate first with respect to y and then with respect to x. So, we have:

∫a^b ∫f(y)g(x) F(x,y) dxdy

Reversing the order of integration, we get:

∫f(y)g(x) ∫a^b F(x,y) dydx

Now, substituting the given values for f(y), g(x), and F(x,y), we get:

∫0^1 ∫1^2 log(x) 9(y) dydx

= ∫0^1 [9(y)∫1^2 log(x) dx] dy

= ∫0^1 [9(y) (xlog(x) - x) from x=1 to x=2] dy

= ∫0^1 [9(y) (2log(2) - 2 - log(1) + 1)] dy

= ∫0^1 [9(y) (2log(2) - 1)] dy

= (9/2) [(2log(2) - 1) y] from y=0 to y=1

= (9/2) (2log(2) - 1)

Therefore, the equivalent integral with the order of integration reversed is:

∫0^1 ∫1^2 log(x) 9(y) dydx = (9/2) (2log(2) - 1)

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For the sample size of 200 and sample data 96 there is no sufficient evidence to conclude that proportion of palay harvested is different from 0.50.

Sample size 'n' = 200

The proportion of palay harvested is different from 0.50

Use a hypothesis test.

Let us assume the null hypothesis H₀ is that the proportion of palay harvested is equal to 0.50,

and the alternative hypothesis Hₐ is that the proportion of palay harvested is different from 0.50.

H₀: p = 0.50 proportion of palay harvested is equal to 50%

Hₐ: p ≠ 0.50 proportion of palay harvested is not equal to 50%

where p is the population proportion of palay harvested.

To test this hypothesis, use the sample data of 96 out of 200 one-hectare farm lands that harvested palay.

The sample proportion of palay harvested is,

p₁= 96/200

  = 0.48

To determine if this sample proportion is significantly different from the hypothesized proportion of 0.50,

Use a two-tailed z-test with a significance level of α = 0.05.

The test statistic is calculated as,

z = (p₁ - p) / √(p(1-p)/n)

where n is the sample size.

Substituting the values, we get,

z = (0.48 - 0.50) / √(0.50(1-0.50)/200)

⇒ z = -0.5658

Using a z-table,

The probability of getting a z-value of -0.5658 or lower in the left tail of the distribution is approximately 0.7123.

Since this is a two-tailed test,

Probability of getting a z-value of 0.5658 or higher in the right tail of the distribution is also approximately 0.7123

p-value for this test is 0.7123+ 0.7123 = 1.4246

Since the p-value is greater than the significance level of α = 0.05,

Fail to reject the null hypothesis.

Therefore,  do not have sufficient evidence to conclude that the proportion of palay harvested is different from 0.50.

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The margin of error at the 99% confidence interval is 0.018 or 1.8%.

Interpretation: This means that if we were to repeat the survey many times, about 99% of the intervals calculated from the samples would contain the true proportion of viewers under 30 in the population, and the margin of error for each interval would be no more than 1.8%.

The margin of error is the amount by which the sample statistic (in this case, the proportion of viewers under 30) may differ from the true population parameter.

Using the given formula for margin of error:

Margin of error = z* * sqrt(p*(1-p)/n)

Where:

- z* is the z-score corresponding to the confidence level (99% in this case), which is 2.576

- p is the proportion of viewers under 30, which is 0.3

- n is the sample size, which is 5000

Substituting these values, we get:

Margin of error = 2.576 * sqrt(0.3*(1-0.3)/5000) = 0.018

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Answer:

Step-by-step explanation:

60 x 3 = 180

180 miles

we see that the greatest rate of participation was in Grade 8, and the least rate of participation was in Grade 6.

To compare the rates of participation in sports among the three grades, we can convert each percentage or fraction to a decimal and then compare the values.

Grade 6: 0.872

Grade 7: 0.87 (87% converted to decimal)

Grade 8: 0.875 (7/8 converted to decimal)

Therefore, we see that the greatest rate of participation was in Grade 8, and the least rate of participation was in Grade 6.

Answer:

Grade 8 had the greatest rate of participation.

Grade 6 had the least rate of participation.

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The measure of the angle is 50.7° and the measure of its complementary angle is 39.3°.

Let x be the measure of the angle and y be the measure of its complementary angle.

Then we have:

x = y + 11.4 (since the angle measures 11.4° more than its complementary angle)

x + y = 90 (since the two angles are complementary)

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

(y + 11.4) + y = 90

2y + 11.4 = 90

2y = 78.6

y = 39.3

Substituting y = 39.3 into the first equation, we get:

x = y + 11.4 = 50.7

So, we have

x = 50.7

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The probability of a randomly selected family from the United States having at least 2 children is 0.2734. The probability that if 40 families from the United States are randomly selected, the mean number of children per family is at least 2 children is 0.1884. Analyst 1 plans to use a sample size of 1 and analyst 2 plans to use a sample size of 40.

Analyst 1 wants to calculate the probability that a randomly selected family from the United States has at least 2 children. Since the number of children under age 18 per family is skewed right with a mean of 1.9 children and a standard deviation of 1.1 children, we can use the normal distribution to solve this problem.

To calculate the probability of a randomly selected family having at least 2 children, we need to find the area under the normal curve to the right of 2.

Using a standard normal distribution table or calculator, we can find that the area to the right of 2 is approximately 0.2734. Therefore, the probability of a randomly selected family from the United States having at least 2 children is 0.2734.

Analyst 2 wants to calculate the probability that if 40 families from the United States are randomly selected, the mean number of children per family is at least 2 children. Since we know that the mean number of children per family in the population is 1.9 children and the standard deviation is 1.1 children, we can use the central limit theorem to approximate the sampling distribution of the sample means.

The central limit theorem tells us that the sampling distribution of the sample means will be approximately normal with a mean of 1.9 children and a standard error of the mean equal to the population standard deviation divided by the square root of the sample size.

We want to find the probability that the mean number of children per family is at least 2, so we need to standardize the sample mean using the formula:

z = (sample mean - population mean) / (standard error of the mean)

Plugging in the values, we get:

z = (2 - 1.9) / (1.1 / sqrt(40)) = 0.889

Using a standard normal distribution table or calculator, we can find that the area to the right of 0.889 is approximately 0.1884. Therefore, the probability that if 40 families from the United States are randomly selected, the mean number of children per family is at least 2 children is 0.1884.

So, analyst 1 plans to use a sample size of 1 and analyst 2 plans to use a sample size of 40.

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The first order partial derivatives of f(x, y) =  ex cos y and the second order partial derivatives are ex sin y = ex cos y.

The given function is f(x, y) = ex sin y. We need to find the first and second order partial derivatives of this function with respect to x and y.
First order partial derivatives:
To find the partial derivative of f(x, y) with respect to x, we treat y as a constant and differentiate ex with respect to x. This gives:
∂f/∂x = ex sin y
To find the partial derivative of f(x, y) with respect to y, we treat x as a constant and differentiate sin y with respect to y. This gives:
∂f/∂y = ex cos y
Second order partial derivatives:
To find the second order partial derivatives, we differentiate the first order partial derivatives we found above. That is, we differentiate ∂f/∂x and ∂f/∂y with respect to x and y, respectively.
∂/∂x (ex sin y) = ex sin y
∂/∂y (ex cos y) = -ex sin y
To find the mixed partial derivatives, we differentiate one of the first order partial derivatives with respect to the other variable. That is,
∂/∂y (ex sin y) = ex cos y
We can also find the mixed partial derivative  by differentiating ∂f/∂y with respect to x, which gives the same result:
∂/∂x (ex cos y) = ex cos y
The first order partial derivatives of f(x, y) = ex sin y are ∂f/∂x = ex sin y and ∂f/∂y = ex cos y and the second order partial derivatives are ex sin y, ∂f/∂[tex]y^2[/tex] = -ex sin y, and ∂f/∂x∂y = ∂f/∂y∂x = ex cos y.

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Answer:

16 peaches

Step-by-step explanation:

Let's break this down:

Total: 144 peaches

Number of boxes she has to fill evenly: 9

Question: How many peaches are able to fit into each box evenly?

144 peaches/9 boxes = 16 peaches

So, Ariana should pack 16 peaches into each box

Hope this helps :)

The gardener used 36.9 gallons of gasoline in the lawnmowers in that month.

In mathematics, a proportion is a statement that two ratios are equal. It expresses the relationship between two or more quantities that are directly proportional to each other. A proportion can be represented as an equation of the form:

a/b = c/d

We know that the gardener used a total of 61.5 gallons of gasoline in a month and that 3/5 of that total was used in the lawnmowers.

To find out how much gasoline the gardener used in the lawnmowers, we need to multiply the total amount of gasoline by 3/5:

61.5 gallons x 3/5 = 36.9 gallons

Therefore, the gardener used 36.9 gallons of gasoline in the lawnmowers in that month.

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The probability of choosing a king or queen from a standard 52-card deck is 2/13 or approximately 15.4%.

The probability of choosing a king or a queen from a standard 52-card deck can be calculated by first determining the number of kings and queens in the deck. There are four kings (hearts, diamonds, clubs, and spades) and four queens (hearts, diamonds, clubs, and spades) in the deck, for a total of eight cards.

To find the probability of choosing a king or a queen, you need to divide the number of desired outcomes (eight) by the total number of possible outcomes (52).

Probability = Number of desired outcomes / Total number of possible outcomes

Probability = 8 / 52

This simplifies to:

Probability = 2 / 13

Therefore, the probability of choosing a king or a queen from a standard 52-card deck is approximately 0.154 or 15.4%.

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The area of the circle is approximately 202.03 square feet

If the circumference of a circle is 50.4 ft, we can use the formula for the circumference of a circle to find its radius:

C = 2πr

C = circumference

r = radius

r = C / (2π)

Substituting C = 50.4 ft, we get:

r = 50.4 / (2π)

Using a calculator, we can approximate this value to be:

r =25.2/π ft

A circle's area can be calculated using the following formula:

A = πr²

Substituting r = 25.2/π ft, we get:

A = π(25.2/π)²

= 635.04/3.14

= 202.03

Therefore, the area of the circle is approximately 202.03 square feet.

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Answer:

[tex] \: \frac{11}{1620} \: \pi^{2} [/tex]

Step-by-step explanation:

I think this is it. But if you find a mistake somewhere let me know? I'm confused because the answer seems a little weird. Like 11/1620 pi² really?

Also at the bottom I wrote "area of sector =" but the area got cut off

Answer:

Step-by-step explanation:

An obtuse angle has a measure between 90 and 180 degrees. Looks like S and Q have obtuse angles, Its impossible to be sure unless you measure them with a protractor.

For the expression (3m⁴n)³(2m²n⁵p)/6m⁴n⁹p⁸, the simplified-value is 9m¹⁰n⁻¹p⁻⁷.

To simplify the expression (3m⁴n)³(2m²n⁵p)/6m⁴n⁹p⁸, we first use the exponent-rule that states (qᵃ)ᵇ = qᵃᵇ to simplify the first part of the expression:

⇒ (3m⁴n)³ = 3³(m⁴)³n³ = 27m¹²n³;

Next, we can simplify the denominator by using the rules of exponents to combine the like terms:

⇒ 6m⁴n⁹p⁸ = 2×3m⁴n⁹p⁸;

Substituting the values,

We get;

⇒ (27m¹²n³)×(2m²n⁵p)/(2*3m⁴n⁹p⁸);

Simplifying the expression by cancelling out the common factors, we get:

⇒ 9m¹⁰n⁻¹p⁻⁷;

Therefore, the simplified-value is : 9m¹⁰n⁻¹p⁻⁷.

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The given question is incomplete, the complete question is

What is the simplified form of the expression below (3m⁴n)³(2m²n⁵p)/6m⁴n⁹p⁸;

To enclose his garden, Jayden needs 24 feet of wood assuming his rectangular-shaped garden has sides of 6 feet each.

Jayden needs wood to enclose his garden. He measured one side of his garden and found that it is 6 feet long.

To calculate how many feet of wood Jayden needs to enclose his garden, we need to know the length of all sides of the garden.

Assuming that the garden is rectangular in shape, we need to know the length of the other side as well.

Let's say the other side is also 6 feet long. In this case, we can calculate the total length of wood required by using the formula for the perimeter of a rectangle, which is:

                   Perimeter = 2 x (Length + Width)

Here, the length and width of the garden are both 6 feet.

So, we can substitute these values in the formula and get:

                   Perimeter = 2 x (6 + 6) = 2 x 12 = 24 feet

Therefore, Jayden needs 24 feet of wood to enclose his garden.

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Answer:

x-intercepts (4,0) (2,0)

y-intercepts (0,8)

Step-by-step explanation:

have a good day :)

The values of a and b that satisfy the equation of the line and pass through points A(2,5) and B(3,7) are a = 3 and b = 2.

To find the values of a and b, we need to use the coordinates of points A and B and the equation of the line ax+by=16.

First, we substitute point A(2,5) into the equation to get:

a(2) + b(5) = 16

Next, we substitute point B(3,7) into the equation to get:

a(3) + b(7) = 16

We now have two equations with two unknowns, which we can solve simultaneously.

Multiplying the first equation by 3 and the second equation by -2, we get:

6a + 15b = 48

-6a - 14b = -32

Adding the two equations, we eliminate the a variable and get:

b = 2

Substituting b = 2 into one of the original equations, we get:

2a + 10 = 16

Solving for a, we get:

a = 3

Therefore, the values of a and b that satisfy the equation of the line and pass through points A(2,5) and B(3,7) are a = 3 and b = 2.

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Mary's average monthly expense for housing is $2,129.93.

We need to add up all her annual housing expenses and divide the total by 12 (the number of months in a year):

Total annual housing expenses = mortgage payments + real estate taxes + annual insurance premium + maintenance + utilities

Total annual housing expenses = $14,169.20 + $3,960.00 + $840.00 + $1,410.00 + $5,180.00

Total annual housing expenses = $25,559.20

Average monthly expense = Total annual housing expenses ÷ 12

Average monthly expense = $25,559.20 ÷ 12

Average monthly expense = $2,129.93

Therefore, Mary's average monthly expense for housing is $2,129.93.

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-5 and 7

Step-by-step explanation

lets try putting -5 and 7

-5 +7=2

and the difference is 8

i am not smart sorry

Step-by-step explanation:

C= 2πr

Given,

Diameter= 9

so, radius = 9÷2 = 4.5

C= 2 x π x 4.5

= 28.3 (3.s.f)

1. The probability that the point chosen is in the triangle is 0.1 (nearest tenth)

2. The probability that the point is in the square is 0.2( nearest tenth)

A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty for an event is 1 which is equivalent to 100%.

Probability = sample space / total outcome

total outcome is the area of rectangle , which is

A = l× w

= 12 × 8

= 96

area of the rectangle = 1/2 bh

= 1/2 × 4 × 5

= 2 × 5

= 10

Area of the square = 4×4

= 16

1. Probability the the point will be in the triangle= 10/96 = 5/48

= 0.1( nearest tenth)

2. probability the the point will be in the square =

16/96 = 1/6

= 0.2 ( nearest tenth)

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the area of the circle is 615. 4 m²

The formula that is used to calculate the area of a circle is expressed with the equation.

We have the equation as;

A = πr²

Such that the parameters are given as;

From the diagram shown, we have that;

A = unknown

r = 14m

Now, substitute the values, we get;

Area = 3.14 ×14²

Find the square value

Area = 3.14(196)

Multiply the values

Area = 615. 4 m²

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1.  The proportion of students at the school who write with their left hand is 2/15 OR 13.3%

2. The estimated number of students who write with their left hand is 77 students

3. The estimated number of students in the different class of 18 students who write with their left hand is 2

From the question, we are to estimate the proportion of students who write with their left hand

To estimate the proportion of students at the school who write with their left hand, we need to count the number of students in the sample who write with their left hand and divide by the total number of students in the sample.

From the given sample, there are 2 students who write with their left hand and 13 students who write with their right hand. So the estimated proportion of students who write with their left hand is:

2/15 = 0.133

OR

13.3%

2.

To estimate the number of students at the school who write with their left hand, we can multiply the proportion by the total number of students in the school

That is,

2/15 x 580 = 77.33

Thus, about 77 students write with their left hand

3.

To estimate how many students in a different class of 18 students write with their left hand, we can apply the proportion to the new sample:

2/15x 18 = 2.4

Hence, about 2 students in the different class write with their left hand.

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