3. (10 points) Prove or disprove: If G is an n-vertex disconnected graph of size n - two components, then G is a forest. 2 having

Answer:

i think it is A

Step-by-step explanation:

The inequality for "number t​ divided by 32 is at most 4. 25" is t/32 ≤ 4.25 and the solution is t ≤ 136

To write the word sentence as an inequality, we need to translate the words into mathematical symbols.

The phrase "a number t divided by 32" can be written as t/32. The word "is" can be translated as an equals sign, and "at most" can be translated as less than or equal to. Therefore, the word sentence "A number t divided by 32 is at most 4.25" can be written as:

t/32 ≤ 4.25

To solve the inequality, we can isolate the variable t by multiplying both sides by 32:

t ≤ 4.25 * 32

t ≤ 136

Therefore, the solution to the inequality is t is less than or equal to 136. This means that any value of t that is less than or equal to 136 will make the original inequality true. If t is greater than 136, then the inequality will be false.

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Answer:

zero

Step-by-step explanation:

y = 0

x = negative

0 / negative = 0

With a 95% probability, 62 students should be sampled to be within 0.25 drinks of the population mean.

\(\alpha\) is the level obtained by subtracting 1 from the confidence interval and dividing by 2.

So,

\(\alpha\) = (1 - 0.95) ÷ 2 = 0.25

Now, find z in the Z-table, as z has a p-value of 1 - \(\alpha\).

As a result, z has a p-value of (1 - 0.025) = 0.975

so, z  = 1.96

Now, infer M as follows:

M = z × (σ ÷ √n) where n is the sample size and is σ the population standard deviation.

When M = 1, this is n.

According to the question, the standard deviation is roughly 1.

σ = 1

M = z × (σ ÷ √n)

0. 25 = 1.96 × (1 ÷ √n)

√n = 1.96 × (1 ÷ √n)

Square both sides,

(√n)² = ((1.96 × 1) ÷ 0.25)²

n = (7.84)²

n = 61.4656

n ≈ 62

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The area of the rectangle is multiplied by 1/25 when the dimensions are multiplied by 1/5.

The length and width of a square shape are decreased to one-fifth of their unique sizes when the aspects are duplicated by 1/5.

The district of a square not set in stone by copying its length by its width. Let's say we refer to the initial length as L and the initial width as W. After duplicating the two aspects by one fifth, the new length becomes L/5 and the new width becomes W/5.

We calculate the new area of rectangle (A') with the updated dimensions to determine how the area is affected:

A' = (L/5) * (W/5) As these parts are increased, we get:

Adding more simplicity: A' = (L * W)/(5 * 5)

At the point when the aspects are increased by 1/5, the region of the square shape is duplicated by 1/25 (L * W/25).

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Answer:

Step-by-step explanation:

One winter day, the temperature at noon was -9°F.

The temperature then rose by ​1/2 degree each hour for 3 hours:

The temperature then dropped by 2 1/4 degrees each hour for 2 hours:

Now add up all three values to find the final value:

Answer:

\(Rate = 0.125\)

Step-by-step explanation:

Given

\(Daily\ Cups = 500\)

\(Weekly\ Cups =4000\)

Required

Determine the day to week rate

This can be calculated by dividing the daily medicine cups by the weekly cups;

\(Rate = \frac{Daily}{Weekly}\)

Substitute 500 for Daily and 4000 for Weekly

\(Rate = \frac{500}{4000}\)

\(Rate = 0.125\)

Hence, the rate of the daily to weekly medicine cup is 0.125

To construct a confidence interval for the population variance, we use the chi-square distribution. The 98% confidence interval for the population variance is obtained by finding the lower and upper bounds using the chi-square distribution with the degrees of freedom equal to the sample size minus 1.

To construct a confidence interval for the population variance (σ²), we use the chi-square distribution.

The chi-square distribution is a probability distribution that arises when dealing with the variability of a sample from a normally distributed population.

For a 98% confidence interval, we divide the significance level (α) by 2, resulting in α/2 = 0.01.

This means we need to find the chi-square values that correspond to a cumulative probability of 0.01 in the lower tail and 0.99 in the upper tail. The degrees of freedom for the chi-square distribution are equal to the sample size minus 1.

Once we have the chi-square values, we use the formula for the confidence interval:

Lower Bound = (n - 1) * s² / Chi-square Upper

Upper Bound = (n - 1) * s² / Chi-square Lower

where n is the sample size and s² is the sample variance.

By plugging in the appropriate values into the formula, we can calculate the lower and upper bounds for the confidence interval for the population variance (σ²).

The result is rounded to three decimal places as requested.

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The differential of the function, dt, can be represented as: dt = (∂t/∂v) dv + (∂t/∂u) du + (∂t/∂w) dw = (6v^5 + uw) dv + (vw) du + (uv) dw, Therefore, the differential of the function t = v6 + uvw is (6v5 + uw) dv + uv dw.

To find the differential of the function t = v6 + uvw, we can use the rules of calculus.

First, we can take the derivative of each term separately. The derivative of v6 is 6v5, and the derivative of uvw with respect to v is uw.

Then, we can multiply each derivative by the differential of the corresponding variable. So the differential of v is dv, the differential of u is du, and the differential of w is dw.

Putting it all together, we get:

dt = 6v5 dv + uw dv + uv dw + uv dv

Simplifying this expression, we get:

dt = (6v5 + uw) dv + uv dw

Therefore, the differential of the function t = v6 + uvw is (6v5 + uw) dv + uv dw.

To find the differential of the function t = v^6 + uvw with respect to a variable, say x, we'll use partial derivatives.

The partial derivative with respect to v: ∂t/∂v = 6v^5 + uw
The partial derivative with respect to u: ∂t/∂u = vw
The partial derivative with respect to w: ∂t/∂w = uv

The differential of the function, dt, can be represented as:

dt = (∂t/∂v) dv + (∂t/∂u) du + (∂t/∂w) dw = (6v^5 + uw) dv + (vw) du + (uv) dw

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Answer:

Step-by-step explanation:

You want values of ∆y and dy for y = x² -6x and x = 5, ∆x = dx = 0.5.

The value of dy is found by differentiating the function.

  y = x² -6x

  dy = (2x -6)dx

For x=5, dx=0.5, this is ...

  dy = (2·5 -6)(0.5) = (4)(0.5)

  dy = 2

The value of ∆y is the function difference ...

  ∆y = f(x +∆x) -f(x) . . . . . . . where y = f(x) = x² -6x

  ∆y = (5.5² -6(5.5)) -(5² -6·5)

  ∆y = (30.25 -33) -(25 -30) = -2.75 +5

  ∆y = 2.25

__

Additional comment

On the attached graph, ∆y is the difference between function values:

  ∆y = -2.75 -(-5) = 2.25

and dy is the difference between the linearized function value and the function value:

  dy = -3 -(-5) = 2.00

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Answer:

a) y + 1...etc

The circumference of the circle in terms of π whose radius is given would be = 63π. That is option D.

To calculate the circumference of a circle, the formula that should be used would be given below.

That is;

circumference of circle= 2πr

The radius = 31½

circumference = 2×π × 31½

= 2×π× 63/2

= 63π

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The distance of the jot air balloon to ground is 21.62 ft.

Here, we have,

In triangle ACB:

tan36° = x/y

x  = y tan36°

In triangle ADB:

tan25° = x/y + 12

x  = y+12 * tan25°

Therefore equating both equations gives:

y tan36°  =  y+12 * tan25°

y tan36°  =  y tan25° + 12tan25°

so, we get,

y = 21.50 ft

Therefore x = 21.50*tan(36) = 15.62 ft

The distance of the jot air balloon to ground = 15.62 + 6 = 21.62 ft

Hence, The distance of the jot air balloon to ground is 21.62 ft.

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Answer:

( 0, -10 )

Step-by-step explanation:

the y intercepts is ( 0, -10 ) as u can see in this pic

Answer:

Step-by-step explanation:

We need to convert the equation to slope-intrcept form y=mx+b, where b is the y-coordinate of Y-intercept point

2x - y = 10​           {subtract 2x from both sides}

- y = -2x + 10                    {divide both sides by (-1)}

y = 2x - 10     ⇒    b = -10

Therefore y-intercept of the line is (0, -10)

a. The equation in slope-intercept form is y = -2x + 2.

b. A table for the equation is shown below.

c. A graph of the points with a line for the inequality is shown below.

d. The solution area for the inequality has been shaded.

e. Yes, the test point (0, 0) satisfy the conditions of the original inequality.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + b

Where:

Part a.

In this exercise, we would change each of the inequality to an equation in slope-intercept form by replacing the inequality symbols with an equal sign as follows;

2x + y ≤ 2

y = -2x + 2

Part b.

Next, we would complete the table for each equation based on the given x-values as follows;

x       -1        0        1

y        4        2       0

Part c.

In this scenario, we would use an online graphing tool to plot the inequality as shown in the graph attached below.

Part d.

The solution area for this inequality y ≤ -2x + 2 has been shaded and a possible solution is (-1, 1).

Part e.

In conclusion, we would use the test point (0, 0) to evaluate the original inequality.

2x + y ≤ 2

2(0) + 0 ≤ 2

0 ≤ 2 (True).

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Answer:

5: 4

7: -8

6: 15

8: 7

I hope this helps you <3

Step-by-step explanation:

The factor form of the quadratic equations are listed below:

Case 13: (b - 4) · (b - 2)

Case 14: (n + 4) · (n + 2)

Case 15: 2 · (n + 9) · (n - 6)

Case 16: 5 · (n + 2)²

Case 17: 2 · (k + 5) · (k + 6)

Case 18: (a - 10) · (a + 9)

Case 19: (p + 10) · (p + 1)

Case 20: 5 · (v - 2) · (v - 4)

Case 21: 2 · (p + 2) · (p - 1)

Case 22: 4 · (v - 2) · (v + 1)

Case 23: (x - 10) · (x - 15)

Case 24: (v - 5) · (v - 2)

Case 25: (p + 6) · (p - 3)

Case 26: 6 · (v + 10) · (v + 1)

In this problem we find quadratic equations of the form a · x² + b · x + c, whose factor form is introduced below:

a · x² + b · x + c = a · x² + a · (- r₁ - r₂) · x + a · r₁ · r₂ = a · (x - r₁) · (x - r₂)

Where r₁, r₂ are real roots.

Now we proceed to present the factor form of each quadratic equation:

Case 13

b² - 6 · b + 8 = (b - 4) · (b - 2)

Case 14

n² + 6 · n + 8 = (n + 4) · (n + 2)

Case 15

2 · n² + 6 · n - 108 = 2 · (n² + 3 · n - 54) = 2 · (n + 9) · (n - 6)

Case 16

5 · n² + 10 · n + 20 = 5 · (n² + 2 · n + 4) = 5 · (n + 2)²

Case 17

2 · k² + 22 · k + 60 = 2 · (k² + 11 · k + 30) = 2 · (k + 5) · (k + 6)

Case 18

a² - a - 90 = (a - 10) · (a + 9)

Case 19

p² + 11 · p + 10 = (p + 10) · (p + 1)

Case 20

5 · v² - 30 · v + 40 = 5 · (v² - 6 · v + 8) = 5 · (v - 2) · (v - 4)

Case 21

2 · p² + 2 · p - 4 = 2 · (p² + p - 2) = 2 · (p + 2) · (p - 1)

Case 22

4 · v² - 4 · v - 8 = 4 · (v² - v - 2) = 4 · (v - 2) · (v + 1)

Case 23

x² - 15 · x + 50 = (x - 10) · (x - 15)

Case 24

v² - 7 · v + 10 = (v - 5) · (v - 2)

Case 25

p² + 3 · p - 18 = (p + 6) · (p - 3)

Case 26

6 · v² + 66 · v + 60 = 6 · (v² + 11 · v + 10) = 6 · (v + 10) · (v + 1)

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Answer:

2 times as much

Step-by-step explanation:

1 hour 2/3 = 60 + (2/3) 40 mins = 100 minutes

3 hours 1/3 = (60 ×3 ) + 20 mins = 200 mins

200 is twice as much as 100

Answer:

2

Step-by-step explanation:

just did it on khan acadmey.

Answer:

408

Step-by-step explanation:

To find the volume of a rectangular prism, we multiply the length of the prism by the width of the prism by the height of the prism

tell me if I’m right

The quantitative variables that can be identified from the problem are Median age of town, Average weekly sales, and Median income of town.

The units for Median age of town is years, Average weekly sales is dollars, and Median income of town is dollars.The remaining options City, Whether or not the store sells liquor, Type of food, and Town area have not specified the units and therefore are not quantitative variables. Quantitative variables are variables that are measured on a numerical scale. The problem in this question provides a list of options and asks to select the options that identify quantitative variables and specify their units. The following quantitative variables can be identified from the problem:Median age of town: Median age of town is a quantitative variable since it is measured in years. The median age of the town is the middle value of the ages of the population of the town. The unit for median age is years since it is a numerical scale that represents the age of the population in years.Average weekly sales: Average weekly sales is a quantitative variable since it is measured in dollars. The average weekly sales represent the mean sales of a store over a week, which can be calculated by dividing the total sales by seven. The unit for average weekly sales is dollars since it is a numerical scale that represents the currency value of sales.Median income of town: Median income of town is a quantitative variable since it is measured in dollars. The median income of the town is the middle value of the income of the population of the town. The unit for median income is dollars since it is a numerical scale that represents the income value of the population.

The units of quantitative variables are essential as they provide a measure of the scale of the variable. In this problem, the quantitative variables identified were Median age of town, Average weekly sales, and Median income of town. The units of these variables are years, dollars, and dollars, respectively. The remaining options do not specify the units and hence cannot be classified as quantitative variables.

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Answer:

Step-by-step explanation:

Let burger = b and fries = f

Alica:

Jack:

Simplify the second equation and subtract from the first one:

Find the value of b:

The scale factor and the perimeters are = 1/2 and 34 and 17 units.

Given that are two polygons are similar MNPQ ~ XYZW, we need to find the scale factor and the perimeter of each polygon.

Scale factor = ratio of the lengths of the sides of the similar polygons.

Scale factor = MQ / WX = 8/4 = 2

Now,

The perimeter of the polygon XYZW = 10 + 9 + 8 + 7 = 34 units.

We know that the ratio of the perimeters of the similar polygons is equal to the scale factor,

So,

The perimeter of the polygon MNPQ = 34 / 2 = 17 units.

Hence the scale factor and the perimeters are = 1/2 and 34 and 17 units.

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Answer:

1/5

Step-by-step explanation:

y = kx

k is the constant of proportionality

Pick any of the indicated points.

Using point (20, 4)

4 = k(20)

Divide both sides by 20

4/20 = k

reduce

1/5 = k

Answer:

try 30 1/4

Step-by-step explanation:

The Fibonacci series in which 0 does not consider is 1,2,3,5,8,13,21,34,…

A series of numbers known as the Fibonacci sequence is one in which each succeeding number is created by adding the two numbers that came before it. The Fibonacci sequence is named for the Italian mathematician who created it.

The standard Fibonacci series

0,1,1,2,3,5,8,13,21,34,…

When 0 is not considered as Fibonacci number, the series can be rewritten as,

1,2,3,5,8,13,21,34,…

The Fibonacci series where number 0 is excluded is 1,2,3,5,8,13,21,34,…

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Answer:

Hsvdbdbdb

Step-by-step explanation:

Evdghdbdbs

The exponential growth rate is obtained as 0.1099.

Now we know that an exponential function has to do with an exponential increase or decrease. An exponential function could increase or decrease and this means that the constant of the function could be a decay constant or a growth constant.

When we have an exponential function, we have to apply the general formula; P(t) = P(o)e^rt

Po = initial number

P(t) = number at time t

r = rate of growth

t = time taken

Thus;

270=90e^10r

270/90 = e^10r

3 = e^10r

ln3 = 10r

r = ln3/10

r = 0.1099

After 13 hours;

P(t) = 90e^(0.1099 * 13)

P(t) = 376

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Answer:

x1= \(\frac{5-2\sqrt{5} }{4} \\\)  x2=\(\frac{5+2\sqrt{5} }{4}\)

It is given that 339 calories in 3 ounce serving.

So in one ounce serving there will be:

So the unit rate is 113 calories/ounce.