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. What percent of students collected between 49 kilograms and 98 kilograms of newspapers

Answer:

Janet uses less than 4 cups of flour because is less than 4.

Step-by-step explanation:

She is using 3/8 of 4 so less than. Then you use 4 not 1 because there is 4 cups.

Answer:

She uses less than four cups because 3/8 (1.5) is less than 4.

Step-by-step explanation:

Answer:

The correct option is;

0.28

Step-by-step explanation:

The given parameters are;

The mean score for Michael, \(\bar x _1\) = 150

The standard deviation, σ₁ = 30

The mean score for Alan,  \(\bar x _2\) = 165

The standard deviation, σ₂ = 15

Taking n₁ = n₂ = 1

\(z=\dfrac{(\bar{x}_{1}-\bar{x}_{2})-(\mu_{1}-\mu _{2} )}{\sqrt{\dfrac{\sigma_{1}^{2} }{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}}\)

Taking μ₁ - μ₂ = 0

\(z=\dfrac{(150-165)}{\sqrt{\dfrac{30^{2} }{1}-\dfrac{15^{2}}{1}}} \approx -0.577\)

The p-value for a z-score of -0.577 from the z-table is 0.28434

Therefore, the probability that Michael, with mean score, \(\bar x _1\) = 150 will have a greater score than Alan, with a mean score of \(\bar x _2\) = 165 is 0.28434 ≈ 0.28

Therefore, the correct option is 0.28

Answer:

y - intercept is (0,-4)

x intercept is (-2,0)

Step-by-step explanation:

y - intercept is b from y = mx + b

in this case it is -4

y intercept is (0,-4)

x intercept can be found by replacing y with 0

0 = -2x - 4

4 = -2x

x = -2

x intercept is (-2,0)

If my answer is incorrect, pls correct me!

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-Chetan K

The model is rewritten as y = X'B' + ε, where y represents the observed values, X' is the new design matrix, B' is a vector of the three parameters a, ₃, and ₄, and ε represents the errors.

In this given scenario, an experimenter is observing independent observations denoted as Y₁₁, Y₁₂, ..., Yᵢ₁, Y₂₁, Y₂₂, ..., Y₂ₙ. The expectations of Y₁ and Y₂ are expressed as linear combinations of parameters a₁, a₂, ₁, ₂, and z. The errors are denoted by ε and are assumed to follow a normal distribution with mean zero and common variance σ². The objective is to estimate σ² using the least squares method.

By deriving the estimate, it can be verified that it is equal to a certain expression involving the differences between observed and predicted values of Y₁ and Y₂. In this expression, the coefficients are determined by the given parameters. Finally, if the assumption is made that ₀₁ = ₀₂ and ₃₁ = ₃₂, the model can be rewritten with only three parameters. The new design matrix X is then determined based on this simplified model.

To estimate the variance σ², the least squares method is used. The estimate is derived by calculating the sum of squared differences between the observed values Y and the predicted values based on the linear combinations of the parameters. The resulting expression for the estimate is E[(Y - E(Y₁)) - B₁(₂ - ₁)²] + E[(Y₂ - E(Y₂)) - B₂(x - ₂) - 4(₂ - ₁)²] divided by 2n-5, where B₁ and B₂ are coefficients determined by the parameters. This expression provides an estimate for the common variance σ² based on the given data.

In order to simplify the model and estimate the parameters under the assumption that ₀₁ = ₀₂ and ₃₁ = ₃₂, a new representation is created. The model is rewritten as y = X'B' + ε, where y represents the observed values, X' is the new design matrix, B' is a vector of the three parameters a, ₃, and ₄, and ε represents the errors. The specific form of the new design matrix X' is not provided in the given information, so it would need to be determined based on the simplified model.

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the fraction that rounds to 5 is option B, 5 1/2.

What is a fraction?

If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.

Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.

To round a fraction to 5, we need to find the fraction that is closest to 5. Therefore, we need to look at the fractional parts of each option and find which one is closest to 1/2.

A. 5 2/3 = 17/3, which is closer to 6 than to 5.

B. 5 1/2 = 11/2, which is exactly halfway between 5 and 6, so it rounds to 5.

C. 5 9/20 = 259/20, which is closer to 6 than to 5.

D. 4 9/20 = 209/50, which is closer to 4 than to 5.

Therefore, the fraction that rounds to 5 is option B, 5 1/2.

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Answer:

12.5

Step-by-step explanation:

x = 2.5, 5x = ?

5(2.5) = 5 x 2.5 = 12.5

Answer:

linear pairs are always 180 degree.

Step-by-step explanation:

sample: x + 30° + 20° = 180°

x = 180° - 50°

x = 130°

Answer: (24 + 60) = (6 × 4 + 6 × 10) = 6 × (4 + 10)

To find the height of the plant when p = 90 years, we can substitute p = 90 into the polynomial function \(R(p) = -2p^2 + 270p\)and evaluate it.

\(R(p) = -2p^2 + 270p\)

Substituting p = 90:

\(R(90) = -2(90)^2 + 270(90)\)

= -2(8100) + 24300

= -16200 + 24300

= 8100

Therefore, when p = 90 years, the height of the plant is 8100 inches.

Let's break down the problem step by step to provide a more detailed explanation.

The given polynomial function for the height of the plant is:

\(R(p) = -2p^2 + 270p\)

To find the height of the plant when p = 90 years, we substitute p = 90 into the function:

\(R(90) = -2(90)^2 + 270(90)\)

First, we evaluate the exponentiation:

R(90) = -2(8100) + 270(90)

Then, we perform the multiplications:

R(90) = -16200 + 24300

Finally, we add the two terms:

R(90) = 8100

Therefore, when the plant is 90 years old, the height of the plant is 8100 inches.

The polynomial function \(-2p^2 + 270p\) represents a quadratic relationship between the age of the plant (p) and its height (R(p)). By substituting the specific value of p into the function, we can determine the corresponding height of the plant. In this case, when p = 90 years, the height of the plant is calculated to be 8100 inches.

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The equation that can be used to determine the radius of the can isr = √(v/πh)

For example, Y is the subject of the following equations. Y = x + 1, Y = 4 + 2x, Y = 2(2x – 3). In the relation v=u + at, v is said to be the subject. When a formula is rearranged so that a different letter becomes the subject, this process is referred to as changing the subject of the relation.

Similar making r the subject in V= π r^2 h

divide both sides by πh

V/πh = r²

r² = V/πh

r = √(V/πh)

therefore the radius of the can be obtained from

r = √(V/πh)

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Answer:

x + 8

Step-by-step explanation:

Expand the brackets.

-4(x-2) + 5x

-4x + 8 + 5x

x + 8

Answer:

Option (C)

Step-by-step explanation:

Equation of the quadratic function having vertex at (3, 4) and opening upwards,

So the the minimum point of the function is (3, 4).

Therefore, minimum value of the function is 4 at x = 3.

y = (x - h)² + k [Here, (h, k) is the vertex]

g(x) = 2(x - 4)² + 3

Vertex of the parabola is (4, 3).

Since, leading coefficient is positive, parabola will open upwards.

Therefore, vertex will be the minimum point.

Minimum value of the function will be 3 at x = 4.

Minimum value of the function 'f' is greater than the minimum value of the function 'g'.

Option (C) will be the answer.

Answer:

C. The minimum value of f is greater than the minimum value of g.

Step-by-step explanation:

I got a 100% on my test

Answer:

Step-by-step explanation:

We can defined the amplitude of a wave as the height of it, because it's the distance from the maxium point to the minimum point. In other words, it's the longest vertical displacement along the wave.

Additionally, amplitude represents power, when we apply waves to real phenomenons like the sound. So, greater grade of amplitude would represent louder sounds.

Therefore, the increase of amplitude would increase distance between the maximum and minimun point of the wave.

Answer:

X= 48

Step-by-step explanation:

math

Way

- It’s a calculator for algebra and stuff

Answer:

The answer is 16 units.

Step-by-step explanation:

Now we have to use the distance formula i.e distance between two points =root under (x2-x1)^2+(y2-y1)^2

Answer:

22 is the distance between the points

There are several possible reasons why per capita per day water consumption could be higher than the wastewater generated:

Non-domestic water use: Per capita water usage includes not only water used in households but also water used for commercial, industrial, and agricultural purposes. Wastewater, on the other hand, only includes water that has been used in households and is discharged into the sewer system. Therefore, if there is significant non-domestic water use in the area, per capita water usage could be higher than wastewater generated.

Inefficient water use: Even though per capita water usage is high, some of the water used may not end up in the wastewater stream. For example, water may be used for landscaping or irrigation, and much of it could evaporate or soak into the ground before it reaches the sewer system. This would result in higher water usage than wastewater generated.

Water loss: The water distribution system may experience leaks or other losses, resulting in some of the water being lost before it reaches households or other water users. This would result in higher water usage than wastewater generated.

Infiltration and inflow: In some cases, rainwater or groundwater can infiltrate into the sewer system or inflow into wastewater treatment plants, increasing the volume of wastewater generated. This could result in lower wastewater generated than per capita water usage.

Time lag: There may be a time lag between water usage and wastewater generated, especially in areas with septic systems. It is possible that some of the water used today may not be discharged into the sewer system for several days or even weeks, resulting in higher per capita water usage than wastewater generated on any given day.

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1.  x² - 5x - 16 can be written as (x - 8)(x + 2).

2. 6an² - 3b²n² = n²(6a - 3b²).

3. This expression represents a perfect square trinomial, which can be factored as (2x - y)².

4. Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

5. 17x³y⁴z⁶ = (x²y²z³)².

6. 12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

Let's simplify the given expressions:

Simplifying x² - 5x - 16:

To factorize this quadratic expression, we look for two numbers whose product is equal to -16 and whose sum is equal to -5. The numbers are -8 and 2.

Therefore, x² - 5x - 16 can be written as (x - 8)(x + 2).

Simplifying 6an² - 3b²n²:

To simplify this expression, we can factor out the common term n² from both terms:

6an² - 3b²n² = n²(6a - 3b²).

Simplifying 4x² - 4xy + y²:

This expression represents a perfect square trinomial, which can be factored as (2x - y)².

Simplifying n + 1 - n³ - n²:

Rearranging the terms, we have -n³ - n² + n + 1.

Combining like terms, we get -n³ - n² + n + 1 = -(n³ + n² - n - 1).

Simplifying 17x³y⁴z⁶:

To simplify this expression, we can divide each exponent by 2 to simplify it as much as possible:

17x³y⁴z⁶ = (x²y²z³)².

Simplifying 12a²b³:

To simplify this expression, we can multiply the exponents of a and b with the given expression:

12a²b³ = (2a)(6b³) = 12a6b³ = 12a⁷b³x⁶.

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To hypothesize that autism is a quantitative trait normally distributed in the population.

Hypothesis that autism is a quantitative trait normally distributed in the population is actually showing the assumption that we can calculate the level of autism in the population in numbers as well as it is present in everyone at some level just like weight.

There are two types of data:

• Quantitative: Any information that can be counted is referred to as quantitative data and is given a numerical value. You can find out “how many,” “how much,” or “how often” using quantitative variables.

• Qualitative: Qualitative information is descriptive in character and communicated verbally as opposed to numerically.

Hence, here they are assuming that we can measure the level of autism in the population.

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There are 402.28 in2 of pasta in the container.

The mathematical branch is known as algebra deals with symbols and the rules governing their manipulation. These characters, which are now expressed as Latin and Greek letters, stand for variables, or quantities without set values, in elementary mathematics.

Mathematical expressions can be used to depict situations or issues, and algebra is the field of mathematics that does this. For a mathematical expression to have meaning, it needs to include variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division.

The radius of cylinder (r) = 3.2 inches

Height of cylinder (h) = 14 inches

Height of pasta = 14 – 1.4 = 12.5 inches

Pasta in container = 22/7*(3.2)2*12.5

=402.8 in2

Hence, the container carries 402.8 in2 of pasta in it.

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Answer: -5/7

Step-by-step explanation:

-11/28 = -0.39

-5/7 = -0.71

9/-14 = -0.64

29/-42 = -0.69

Out of these, -5/7 is the greatest rational number, even if they are all negative.

Hope this helps!

Answer:

No, this is not a solution.

Step-by-step explanation:

To solve this you have to substitute 16 into the inequality w - 12 < 4.

Subtracting 12 from 16 gives you 4 which is equal to 4 not less than. So 16 is not a solution to this problem.

After simplifying i^61 we get the answer is i

Define Complex number

Every complex number may be represented in the form a + bi, where a and b are real numbers. A complex number is an element of a number system that extends the real numbers with a specific element labelled i sometimes known as the imaginary unit, and satisfying the equation i² = 1.

We have the given expression : i ^ 61

Rewrite it,

i ^ 61 as (i^4)^15 * i

we know, i² = -1

so, i ^ 4 = i² * i² = -1 * -1 = 1

so, put i ^ 4 value,

⇒1^15 * i

power 1 to the 15 is 1,

⇒1 * i

⇒ i

Hence, the answer is ' i '

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Answer:

The biggest common factor number is the GCF number. So the greatest common factor 32 and 48 is 16.

Step-by-step explanation:

Answer:

16

Step-by-step explanation

32 =2^5

48 =2^4×3

Prime factor is 2 ^4 =16

Answer:

1. Profit =  Revenue - Cost

2.  For the Alcone Company Revenue = $45 × x

For the Besame Beauty Revenue = $55 × x

3.  Alcone Company; Cost = $1,500 + $36×x

Besame Beauty; Cost = $2,200 + $44×x

4)  For Alcone Company, we have;

Profit = $9 × x - $1,500

For  Besame Beauty, we have;

Profit = $11 × x - $2,200

5) For Alcone Company;

Profit= $525

For Besame Beauty;

Profit = $275

6) For Alcone Company;

Profit = -$150

For Besame Beauty;

Profit  -$550

7) Order of operations is used to ensure that the revenue is first calculated before the cost is subtracted to find the costs

8) In order to find the number of tubes that the company would need to manufacture in order to have a profit of greater than 0, we equate the expression using the inequality of greater than 0 to find the value of x that must be surpassed to have a profit greater than 0

9) For Alcone Company;

The profit will be > 0 at x = 167 tubes

For Besame Beauty;

The profit will be > 0 at x = 201 tubes

Step-by-step explanation:

The given parameters are;

The Alcone Company

The price at which the shade of lip color is sold = $45 per tube

The cost incurred to make  the lip color = $36 per tube

The monthly manufacturing cost of manufacturing the lip color = $1,500

For Besame Beauty

The price at which the shade of lip color is sold = $55 per tube

The cost incurred to make  the lip color = $44 per tube

The monthly manufacturing cost of manufacturing the lip color = $2,200

1. The formula for finding the profit is given as follows;

Profit =  Revenue - Cost

Revenue = Sale price × Number of tubes sold

Cost = The monthly manufacturing cost + The cost incurred to make the lip color × Number of tubes

2. The expression for revenue for the Alcone Company is given as follows;

Revenue = $45 × x

The expression for revenue for the Besame Beauty is given as follows;

Revenue = $55 × x

3. The expression for the cost for the manufacture of the lip color by the Alcone Company per month is given as follows;

Cost = $1,500 + $36×x

The expression for the cost for the manufacture of the lip color by the Besame Beauty per month is given as follows;

Cost = $2,200 + $44×x

4)  For Alcone Company, we have;

Revenue = $45 × x

Cost = $1,500 + $36×x

By transitive property and distributive property, we have

Profit =  Revenue - Cost = $45 × x - ($1,500 + $36×x) = $9 × x - $1,500

Profit = $9 × x - $1,500

For  Besame Beauty, we have;

Revenue = $55 × x

Cost = $2,200 + $44×x

By transitive property and distributive property, we have;

Profit =  Revenue - Cost = $55 × x - ($2,200 + $44×x) = $11 × x - $2,200

Profit = $11 × x - $2,200

5) With the number of tubes produced = 225 tubes, we have;

For Alcone Company;

Profit = $9 × x - $1,500 = $9 × 225 - $1,500 = $525

ForBesame Beauty;

Profit = $11 × x - $1,500 = $11 × 225 - $2,200 = $275

6) With the number of tubes produced = 150 tubes, we have;

For Alcone Company;

Profit = $9 × x - $1,500 = $9 × 150 - $1,500 = -$150

For Besame Beauty;

Profit = $11 × x - $2,200 = $11 × 150 - $2,200 = -$550

7) Order of operations is used to ensure that the revenue is first calculated before the cost is subtracted to find the costs

8) In order to find the number of tubes that the company would need to manufacture in order to have a profit of greater than 0, we equate the expression using the inequality of greater than 0 to find the value of x that must be surpassed to have a profit greater than 0

9) For Alcone Company;

Profit = $9 × x - $1,500 >0

$9 × x  >0 + $1,500

$9 × x  > $1,500

x > $1,500/$9

x > 500/3

x > \(166\frac{2}{3}\)

Therefore, the profit will be > 0 at x = 167 tubes

For Besame Beauty;

Profit = $11 × x - $2,200 > 0

$11 × x  > 0 + $2,200

$11 × x  > $2,200

x > $2,200/$11

x > 200

Therefore, the profit will be > 0 at x = 201 tubes

Answer:

3.2 x 4.1= 13.12

Step-by-step explanation:

3.2

4.1

____

3.2

+ 12.0=. 13.12

As the interest rate increases from 10 percent to 11 percent, the present value of the bond decreases from $1,074.47 to $1,058.31. Conversely, when the interest rate decreases to 9 percent, the present value increases to $1,091.19. This is because the discount rate used to calculate the present value is inversely related to the interest rate, meaning that as the interest rate increases, the present value decreases, and vice versa.

To compute the present value of a five-year, 10 percent coupon bond with a face value of $1,000, we need to discount the future cash flows (coupon payments and face value) by the appropriate interest rate.

Step 1: Calculate the present value of each coupon payment.
Since the bond has a 10 percent coupon rate, it pays $100 (10% of $1,000) annually. To calculate the present value of each coupon payment, we need to discount it by the interest rate.

Using the formula: PV = C / (1+r)^n
Where PV is the present value,

C is the cash flow,

r is the interest rate, and

n is the number of periods.

At an interest rate of 10 percent, the present value of each coupon payment is:
PV1 = $100 / (1+0.10)^1 = $90.91

Step 2: Calculate the present value of the face value.
The face value of the bond is $1,000, which will be received at the end of the fifth year. We need to discount it to its present value using the interest rate.

At an interest rate of 10 percent, the present value of the face value is:
PV2 = $1,000 / (1+0.10)^5 = $620.92

Step 3: Calculate the total present value.
To find the present value of the bond, we need to sum up the present values of each coupon payment and the present value of the face value.
Total present value at an interest rate of 10 percent:
PV = PV1 + PV1 + PV1 + PV1 + PV1 + PV2
PV = $90.91 + $90.91 + $90.91 + $90.91 + $90.91 + $620.92
PV = $1,074.47

When the interest rate goes to 11 percent, we would repeat the above steps using the new interest rate.
Total present value at an interest rate of 11 percent:
PV = PV1 + PV1 + PV1 + PV1 + PV1 + PV2
PV = $90.91 + $90.91 + $90.91 + $90.91 + $90.91 + $620.92
PV = $1,058.31

When the interest rate goes to 9 percent, we would repeat the above steps using the new interest rate.
Total present value at an interest rate of 9 percent:
PV = PV1 + PV1 + PV1 + PV1 + PV1 + PV2
PV = $90.91 + $90.91 + $90.91 + $90.91 + $90.91 + $620.92
PV = $1,091.19

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Given:

Factor of (x-7) is:

so factor of (x-7) is: