Mrs. Trout estimated her math class next year would include 28 students. The actual size of the class turned out to be 32 students. She calculated the percent error in the following way.

28 - 32 = -4

4
32
= 0.125%

Is Mrs. Trout correct? Explain why or why not.

Answer: x=10

Step-by-step explanation:

1

Subtract

5

from both sides

2

Simplify

3

Divide both sides by the same factor

4

Simplify

Answer:

2x + 5 = 25

25 - 5= 2x

20 = 2x

20 ÷ 2 = 2x ÷ 2

x = 2

Venn diagram:

The percentage of students that studied mathematics = 25%
The percentage of students that studied electronics = 20%
The percentage of students that studied Communications = 55%
The percentage of students that studied both electronics and Communications subjects = 10%

P(studied Communications or electronics or both subjects)
= P(studied Communications) + P(studied electronics) - P(studied both electronics and Communications subjects)
= 55% + 20% - 10%
= 65%

Therefore, the probability that a student studied Communications or electronics or both subjects is 65%.

P(studied mathematics and Communications subjects)
= P(studied mathematics) × P(studied Communications)
= 25% × 55%
= 13.75%

Therefore, the probability that a student studied mathematics and Communications subjects is 13.75%.

Drawing a Venn diagram, we have 25% studying Mathematics (M), 20% studying Electronics (E), and 55% studying Communications (C).10% studied both Electronics and Communications.

Therefore, the percentages become as follows: M = 25% - 10% = 15% E = 20% - 10% = 10% C = 55%.

Part 2 - To obtain the probability that a student studied Communications or Electronics or both subjects

P(Communication or Electronics) = P(Communication) + P(Electronics) - P(Communication and Electronics) = 55% + 20% - 10% = 65%.

The probability that a student studied Communications or Electronics or both subjects is 65%.

Part 3 -To obtain the probability that a student studied Mathematics and Communications subjects,

P(Mathematics and Communications) = P(Mathematics) * P(Communications) = 25% * 55% = 13.75%.

The probability that a student studied Mathematics and Communications subjects is 13.75%.

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Answer:

A. Side a is 1.5 inches long, side b is 2 inches long, and side c is 2.5 inches long.

Explanation:

Divide each side by the Scale Factor; 4.1. Then see to which side each one correlates to.

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The value of the given expression for x=-2 y=3 and z = -1/5 is 6/5.

The given expression is xyz.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Put x=-2 y=3 and z = -1/5 in the given expression is

-2 × 3 × (-1/5)

= 6/5

Hence, the value of the given expression for x=-2 y=3 and z = -1/5 is 6/5.

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"Your question is incomplete, probably the complete question/missing part is:"

Evaluate the expression when x=-2 y=3 and z = -1/5, xyz=

To calculate the duration of the shift, you need to subtract the clock-in time from the clock-out time.

In this case, the shift worker clocked in at 1730 hours (5:30 PM) and clocked out at 0330 hours (3:30 AM). However, since the clock is based on a 24-hour format, it's necessary to consider that the clock-out time of 0330 hours actually refers to the next day.

To calculate the duration of the shift, you can perform the following steps:

1. Calculate the duration until midnight (0000 hours) on the same day:

  - The time between 1730 hours and 0000 hours is 6 hours and 30 minutes (1730 - 0000 = 6:30 PM to 12:00 AM).

2. Calculate the duration from midnight (0000 hours) to the clock-out time:

  - The time between 0000 hours and 0330 hours is 3 hours and 30 minutes (12:00 AM to 3:30 AM).

3. Add the durations from step 1 and step 2 to find the total duration of the shift:

  - 6 hours and 30 minutes + 3 hours and 30 minutes = 10 hours.

Therefore, the duration of the shift was 10 hours.

The best statement that describes the function of the logic variable X is: A. X is a variable whose value is 1 or 0.

Logic variables typically represent binary states or conditions, where 1 represents "true" or "on" and 0 represents "false" or "off". Therefore, option A accurately describes the function of the logic variable X as having a value of either 1 or 0. Logic variables are often used in the field of logic and computer science to represent binary states or conditions. The value of a logic variable can only be one of two possibilities: 1 or 0.

In this context, 1 typically represents "true" or "on," indicating that a certain condition is satisfied or a certain state is active. On the other hand, 0 represents "false" or "off," indicating that the condition is not satisfied or the state is inactive.

By using logic variables, we can model and manipulate binary logic in a precise and systematic manner. The values of logic variables are fundamental in logical operations, such as AND, OR, and NOT, which are essential in designing and analyzing digital circuits, programming, and logical reasoning.

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Answer: -684 i used a number line but then again im in 7th grade

The sequence yn = √(n+1) - √n converges, and its limit can be found by simplifying the expression and applying the limit rules. The limit of yn as n approaches infinity is 0.

To find the limit of yn as n approaches infinity, we can simplify the expression. Let's start by rationalizing the numerator:

yn = (√(n+1) - √n) (√(n+1) + √n) / (√(n+1) + √n)

Simplifying the numerator, we get:

yn = [(n+1) - n] / (√(n+1) + √n)

= 1 / (√(n+1) + √n)

As n approaches infinity, both √(n+1) and √n also approach infinity. Therefore, the denominator (√(n+1) + √n) also approaches infinity. In the numerator, the constant 1 remains constant.

Using the limit rules, we can simplify the expression further:

lim(n→∞) yn = lim(n→∞) [1 / (√(n+1) + √n)]

= 1 / (∞ + ∞)

= 1 / ∞

= 0

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Answer:

The Great Western Trail = 4,455 miles

Step-by-step explanation:

The Iditarod Trail = 1,025 miles long

The Great Western Trail is 355 miles longer than 4 times the length of the Iditarod Trail.

The Great Western Trail = (4 × 1,025) miles + 355 miles

= 4,100 miles + 355 miles

= 4,455 miles

The Great Western Trail = 4,455 miles

Answer: A.

A weak positive correlation

Step-by-step explanation:

The total price of 2 bags of apples and 3 bags of oranges can be calculated by adding 2 times the price of a bag of apples to 3 times the price of a bag of oranges.

To determine the total price of 2 bags of apples and 3 bags of oranges, you need to know the price per bag of apples and the price per bag of oranges. Let's assume the price per bag of apples is $A and the price per bag of oranges is $O.

The total price of 2 bags of apples would be 2 * A, and the total price of 3 bags of oranges would be 3 * O. To find the overall total price, you can simply add these two amounts together:

Total price = (2 * A) + (3 * O)

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Yes, the rhombus is also a parallelogram

The area of the rhombus is 77 ft²

The formula for calculating the area of a rhombus is expressed as;

A = bh

Such that the parameters of the equation are verbally as;

From the information given, we have that;

base = 7ft

Height = 11 ft

Substitute the values, we get;

Area = 7(11)

Multiply the values, we have;

Area = 77 ft²

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Answer:8% started saving at or before 21

30% believe their children or grandchildren should start saving at or before 21

Step-by-step explanation: on the graph, the ones in lighter color start saving for requirements

That is 3%+5%=8%

The second solution goes thus

13%+17%= 30%

the ones in dark colors believe their children or grandchildren should start saving before 21

Graphing the two parabolas y=x² and y=-x² in the same coordinate plane can be done in a few steps.

Step 1: Plotting the Points To plot the points, you can take values of x and then find the corresponding value of y. You can use a table to list down the values of x and y. For example, For x = -2, y = 4 (y=x²) For x = -2, y = -4 (y=-x²) Similarly, you can calculate more values of x and y and plot them. The plotted points should look like this: Step 2: Drawing the Parabolas can be drawn by connecting the plotted points with a smooth curve. You can use a ruler or freehand drawing to draw the curves. Once you have drawn the parabolas, it should look like this: Step 3: Finding the Equations of the Two Lines Simultaneously Tangent to Both Parabolas.

To find the equations of the two lines simultaneously tangent to both parabolas, you can use the following steps: Step 3a: Differentiating the Parabolas To find the equations of the tangent lines, you need to differentiate the parabolas. y = x²  dy/dx = 2x y = -x²+2x-5  dy/dx = -2x+2 Step 3b: Equating the Slopes Equate the slopes of the tangent lines to the slopes of the parabolas. 2m = 2x - 0 (for y = x²) 2m = -2x + 2 (for y = -x²+2x-5) Solve for x by equating the two equations. 2x = -2x + 2 4x = 2 x = 0.5Step 3c: Finding the y-Coordinate of the Points of Tangency Substitute x = 0.5 in the equation of the parabolas to find the y-coordinate of the points of tangency. y = x² y = 0.25 y = -x²+2x-5 y = -5.25Step 3d: Finding the Equations of the Lines Use the point-slope formula to find the equations of the lines. y - y₁ = m(x - x₁) y - 0.25 = 1(x - 0.5) y = x - 0.25 y - (-5.25) = -1(x - 0.5) y = -x - 4.75 The equations of the two lines simultaneously tangent to both parabolas are y = x - 0.25 and y = -x - 4.75.

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Answer:

x° = 145°

Step-by-step explanation:

x° + (2x - 255)° = 180°

3x = 180 + 255

3x = 435

x° = 145°

By evaluating an exponential function we can see that after 90 days there willbe 340 rabbits.

We know that the rabbit population can increase by 45% every 10 days, then the population can be modeled by the exponential function:

P(x) = A*(1 + 0.45)^(x/10)

Where x is the time in days and A is the initial population.

Here we know that the initial populationis 12 rabbits, then the function is:

P(x) = 12*(1.45)^(x/10)

And the population after 90 days is:

P(90) = 12*(1.45)^(90/10)

P(90) = 340

There will be 340 rabits in 90 days.

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The length of the common radius in the reversed curve can be calculated using the formula: radius = (chord length)² / (8 * perpendicular distance between the tangents)

Plugging in the given values: radius = (150m)² / (8 * 12m) = 1875m.

2) The distance from the Vito V2 (vertex of the reversed curve) can be calculated using the formula: distance from V2 = (chord length)² / (24 * perpendicular distance between the tangents) Substituting the values: distance from V2 = (150m)² / (24 * 12m) = 312.5m.

3) To calculate the station at PT, add the length of the reversed curve (chord length) to the station at PC: station at PT = station at PC + chord length = 20+348 + 150 = 20+498.

4) The length of the common radius can be calculated using the formula: radius = distance from PC to the 2nd tangent / (2 * sin(angle of convergence)) Substituting the given values: radius = 106m / (2 * sin(24°)) ≈ 246.74m.

5) The stationing at PCC can be found by subtracting the distance of the PC from the 2nd tangent from the station at PC: station at PCC = station at PC - distance from PC to the 2nd tangent = 32+460 - 106 = 32+354.

6) The stationing at PT can be calculated by adding the length of the reversed curve (chord length) to the station at PCC: station at PT = station at PCC + chord length = 32+354 + 150 = 32+504.

Note: The stations are written in the format "xx+xxx" where "xx" represents the whole stations and "xxx" represents the hundredths of a station.

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y₁ =  [1  -4  0  1] and y₂ = [5  1  -6  -1] is the orthogonal basis for w using Gram-Schmidt process.

Given,

The set;

x₁ = [1  -4  0  1]

x₂ = [7  -7  -6  1]

We have to produce the orthogonal basis for w using the Gram-Schmidt process;

Here,

y₁ = x₁ =  [1  -4  0  1]

Now,

Solve for y₂

y₂ = x₂ - [x₂y₁ / y₁y₁] y₁

That is,

y₂ = [7  -7  -6  1] - ( [7  -7  -6  1] [1  -4  0  1] / [1  -4  0  1] [1  -4  0  1] ) × [1  -4  0  1]

y₂ =  [7  -7  -6  1] - (7 + 28 - 0 + 1) / (1 + 16 + 0 + 1) × [1  -4  0  1]

y₂ = [7  -7  -6  1]  - 36/18 × [1  -4  0  1]

y₂ =  [7  -7  -6  1] - 2  × [1  -4  0  1]

y₂ =  [7  -7  -6  1] - [2  8  0  2]

y₂ = [5  1  -6  -1]

That is,

The orthogonal basis for w using Gram-Schmidt process is,

y₁ =  [1  -4  0  1] and y₂ = [5  1  -6  -1]

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To estimate the mean amount of detergent in 64-ounce jugs at a 98% confidence level, and the sample should be taken so that the estimate is within 0.05 ounce of the population mean. Let us find the sample size required. Sample size, n = (Z² * σ²) / E².

Where; Z is the Z-value at the given level of confidenceσ is the standard deviation of the population E is the maximum error allowed Z-value at the 98% confidence level is 2.33σ = 0.23E = 0.05Therefore, the sample size required is: n = (2.33² * 0.23²) / 0.05²= 25.6 or 26 (rounded to the nearest integer)Hence, the company should take a sample of 26 64-ounce jugs to estimate the mean amount of detergent at a 98% confidence level.

Let the areas of the three rugs be a, b, and c. Then according to the given information, a + b + c = 2200Also, area of overlap of the rugs (covered by exactly two layers of rug) = 24m²Hence, (a + b + c) – 2(area covered by two layers of rug) = area covered by three layers of rug (2200 – 2 × 24)m² = 2152m².

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Answer:

Step-by-step explanation:

The solution to the differential equation with the given initial conditions is: y = 2 e^(4t) - (1/2) t e^(4t)

To solve this differential equation, we first find the characteristic equation by assuming a solution of the form y = e^(rt). Plugging this into the differential equation, we get:

r^2 e^(rt) - 8re^(rt) + 16e^(rt) = 0

Factoring out the e^(rt) term, we get:

e^(rt) (r^2 - 8r + 16) = 0

The quadratic equation r^2 - 8r + 16 = 0 has a double root of r = 4. Therefore, the general solution to the differential equation is:

y = c1 e^(4t) + c2 t e^(4t)

To solve for the constants, we use the initial conditions. First, we have y(0) = 2, which gives us:

c1 = 2

Next, we have y'(0) = 0, which gives us:

c1 (4) + c2 (0) = 0

Solving for c2, we get:

c2 = -c1/4 = -1/2

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Answer:

$40

Step-by-step explanation:

use y = mx + b  

y = amount saved = ?

m = amount saved per week = $10

x = time (in  months) saving = 2.5

b = money jerry started with = $15

plug in:

y = (10)(2.5)+15

y = $40

Answer:

70

Step-by-step explanation:

as the discount is 20 thus the original price would be 70

Domain is all the values that go into a function, and the range is all the values that come out.

The complete table of values is

Edge length (ft)    3    8     ∛85  ∛100    5    ∛147

Volume                27   64    85    100   125    147

The area of the square is 82 square cm

From the question, we have:

Edge length and volume of several different cubes

The relationship between the edge length and the volume of cubes is

Volume = Edge length³

Using the above as a guide, we have

3³ = 27

8³ = 64 and so on

Here, we have

Length = √82

The area is

Area = Length²

So, we have

Area =√82² = 82

hence, the area is 82

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Answer:

Step-by-step explanation:

The slope of a line can be calculated:

\(m = \frac{y_2-y_1}{x_2-x_1}\\\)

We know that the slope is 7, so we want to solve for \(y_2\)

\(\frac{n-(-4)}{5-4} = 7\\\frac{n+4}{1} = 7\\n+4 = 7\\n = 3\)

Answer:

The lenght of AB is (4.45)

Step-by-step explanation:

Thanks and, Is that right??