Write an expression that can be used to find 65% of 120.

To determine the maximum safe driving speed on the freeway, we can use the equation x - 55 = 4.2. This equation represents the upper limit of the safe driving speed range, where x is the driving speed in miles per hour.



The equation |x - 55| = 4.2 represents the range of safe driving speeds on the freeway near Allan's town. The absolute value notation indicates that the difference between x and 55 should be equal to 4.2. However, to determine the maximum safe driving speed, we need to consider the positive difference between x and 55.

By setting x - 55 = 4.2, we isolate the positive difference and find the upper limit of the safe driving speed range. Therefore, the equation x - 55 = 4.2 can be used to determine the maximum safe driving speed.

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The steps outline the process of obtaining the asymptotic stabilization control law for the given system.\(x = Ax + Bu, y = Cx + Du\):

1. Check system controllability. Choose desired eigenvalues for the closed-loop system.

2. Design the control law u = -Kx.

3. Substitute the control law into the system equation: x = (A - BK)x.

4. Check stability by analyzing the eigenvalues of (A - BK).

5. Solve for the control gain matrix K.

6. Verify that the eigenvalues of (A - BK) match the desired values.

To obtain the asymptotic stabilization control law for the system x\(x = Ax + Bu, y = Cx + Du\), we can follow the steps outlined below:

Step 1: Assess system controllability

Check if the pair (A, B) is controllable. If the system is not controllable, it may not be possible to find a control law that stabilizes it.

Step 2: Determine desired eigenvalues

Choose the desired eigenvalues for the closed-loop system. These eigenvalues should be stable and suitable for achieving the desired system response.

Step 3: Design the control law

Design the control law u = -Kx, where K is the control gain matrix to be determined. The control law should ensure that the closed-loop system has the desired eigenvalues and achieves asymptotic stability.

Step 4: Obtain the closed-loop system

Substitute the control law u = -Kx into the original system equation x = Ax + Bu. This results in the closed-loop system equation:

x = (A - BK)x

Step 5: Check the stability

Check the stability of the closed-loop system. If the eigenvalues of (A - BK) have negative real parts, the closed-loop system is stable.

Step 6: Solve for the control gain matrix

Solve the algebraic equation (A - BK)x = 0 to obtain the control gain matrix K. This can be done using various methods, such as pole placement or linear matrix inequalities (LMI) techniques.

Step 7: Verify the stabilization

Check that the eigenvalues of the closed-loop system (A - BK) have the desired values obtained in Step 2. If they match, the control law u = -Kx asymptotically stabilizes the system.

These steps outline the general procedure for obtaining the asymptotical stabilization control law for the given system. The specific details and techniques used in each step may vary depending on the characteristics of the system and the desired performance criteria.

Therefore, the steps outline the process of obtaining the asymptotic stabilization control law for the given system.\(x = Ax + Bu, y = Cx + Du\):

1. Check system controllability. Choose desired eigenvalues for the closed-loop system.

2. Design the control law u = -Kx.

3. Substitute the control law into the system equation: x = (A - BK)x.

4. Check stability by analyzing the eigenvalues of (A - BK).

5. Solve for the control gain matrix K.

6. Verify that the eigenvalues of (A - BK) match the desired values.

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Answer:

a

Step-by-step explanation:

  

The only part of the expression representing f(t) involving the variable t is the exponential e−0.08t. Since the coefficient of t in the exponent, −0.08, is negative, the values of f(t) decrease as time passes. Thus the temperature of the coffee decreases as time elapses. This is appropriate as we know from experience that over time the coffee will cool down to room temperature: In this case, the 75 in the expression representing f(t) is the ambient room temperature in degrees Fahrenheit.

The beginning of the experiment is when the time variable t takes the value zero: Since

f(0)=110e−0.08⋅0+75=110+75=185,

the initial temperature of the coffee is 185 degrees Fahrenheit, a little less than the boiling temperature of water.

To find when the coffee is 140 degrees we want to solve

f(t)=110e−0.08t+75=140.

Subtracting 75 from both sides and then dividing both sides by 110 gives

e−0.08t=65110.

By the definition of the natural logarithm, this gives

−0.08t=ln(65110).

Dividing both sides by −0.08 gives a value of about 6.6 minutes for the coffee to cool to 140 degrees.

The same reasoning gives, as an expression for the time when the coffee has cooled to 100 degrees,

ln(25110)−0.08.

This is about 18.5 minutes. sorry if i forgot to put "/" for fractions

Answer:

x= -2

Step-by-step explanation:

hope this helped <3

Answer:

Step-by-step explanation:

\(\text{The area of a circle is }\pi r^2\text{ so the area of half a circle is }\frac{\pi r^2}{2}\\ \\ A=\frac{\pi 11^2}{2}\\ \\ A=\frac{3.14(121)}{2}\\ \\ A\approx 189.97cm^2\)

Answer:

760.25

Step-by-step explanation:

The formula for the surface area of a sphere is A=4πr².

r=the radius, or half of the diameter, of the circle.

when you plug in the radius and answer the formula, you should get 1520.5.

You should then divide it by 2 since we are trying to find half of the circle.

Answer:

Step-by-step explanation:

To solve the given equation \(\sf x - y = 4 \\\), we can perform the following calculations:

a) To find the value of \(\sf 3(x - y) \\\):

\(\sf 3(x - y) = 3 \cdot 4 = 12 \\\)

b) To find the value of \(\sf 6x - 6y \\\):

\(\sf 6x - 6y = 6(x - y) = 6 \cdot 4 = 24 \\\)

c) To find the value of \(\sf y - x \\\):

\(\sf y - x = - (x - y) = -4 \\\)

Therefore:

a) The value of \(\sf 3(x - y) \\\) is 12.

b) The value of \(\sf 6x - 6y \\\) is 24.

c) The value of \(\sf y - x \\\) is -4.

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Answer:

  2. 26.2 m

  3. 117.2 cm

Step-by-step explanation:

You want the perimeters of two figures involving that are a composite of parts of circles and parts of rectangles.

The circumference of a circle is given by ...

  C = πd . . . . . where d is the diameter

The length of the semicircle of diameter 12.6 m will be ...

  1/2C = 1/2(π)(12.6 m) = 6.3π m ≈ 19.8 m

The two lighted sides of the rectangle have a total length of ...

  3.2 m + 3.2 m = 6.4 m

The length of the light string is the sum of these values:

  19.8 m + 6.4 m = 26.2 m

The length of the string of lights is about 26.2 meters.

The perimeter of the figure is the sum of four quarter-circles of radius 11.4 cm, and 4 straight edges of length 11.4 cm.

Four quarter-circles total one full circle in length, so we can use the formula for the circumference of a circle:

  C = 2πr

  C = 2π·(11.4 cm) = 22.8π cm ≈ 71.6 cm

The four straight sides total ...

  4 × 11.4 cm = 45.6 cm

The perimeter of the figure is the sum of the lengths of the curved sides and the straight sides:

  71.6 cm + 45.6 cm = 117.2 cm

The design has a perimeter of about 117.2 cm.

__

Additional comment

The bottom 12.6 m edge in the figure of problem 2 is part of the perimeter of the shape, but is not included in the length of the light string.

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Answer:

Number 6 are (6,1) (-4,0)(-1,3)

Step-by-step explanation:

The Taylor polynomials P1, P2, P3, and P4 centered at a0 for f(x) are given as:P1(x) = 1P2(x) = 1 - x²/2!P3(x) = 1 - x²/2! + x⁴/4!P4(x) = 1 - x²/2! + x⁴/4! - x⁶/6!

We will apply the Taylor's theorem formula, which is supplied as follows, to determine the Taylor polynomials P1, P2, P3, and P4 centred at a0 for f(x) in the given question:f'(a)(x-a)/1 = f(x) = f(a) + f'(a)! + f''(a)(x-a)²/2! + ... + fⁿ(a)(x-a)ⁿ/n!We have f(0) = 1f'(0) = 0f''(0) = -1f'''(0) = 0f4(0) = 1 for f(x) = cos(x) at x = 0.We can get the following polynomial expressions by using these values in the Taylor's theorem formula:P1(x) = 1P2(x) = 1 - x²/2!P3(x) = 1 - x²/2! + x⁴/4!P4(x) = 1 - x²/2! + x⁴/4! - x⁶/6!Consequently, the Taylor polynomials P1, P2, P3, and P4 for f(x) are provided as follows:P1(x) = 1P2(x) = 1 - x²/2!P3(x) = 1 - x²/2! + x⁴/4!P4(x) = 1 - x²/2! + x⁴/4! - x⁶/6!

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The problem entails calculating the probability for a scenario in which the IRS audits 30% of tax returns at random and a married pair has filed separate returns. Calculate the chances of both husband and wife being audited, just one of them being audited, neither of them being audited, and at least one of them being audited.

a) Probability that both the husband and the wife will be audited: (0.3)² = 0.09 or 9%

b) Probability that only one of them will be audited:

c) Probability that neither one of them will be audited: (0.7)² = 0.49 or 49%

d) Probability that at least one of them will be audited: This is the complement of the probability that neither one of them will be audited. So, the probability that at least one of them will be audited is 1 - 0.49 = 0.51 or 51%.

The relevant terms in this question are probability and statistics. To solve for the probability of each scenario, we used the formulas for independent probabilities and complements.

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Answer:

8 and 14 im 100% sure its 8 and 14

Step-by-step explanation:

The possible order pair for the point D is (0, 0.72)

Triangles with the same shape but different sizes are said to be similar triangles. Triangle resemblance is shown here by the symbol "≈"

Since triangle ABC is similar to triangle ADE, the corresponding sides of these triangles are proportional.

Let's denote the length of AB as x and the length of AD as y. Then, we can write:

AB/AD = BC/DE

Substituting the values from the figure, we get:

x/y = 5/3

Multiplying both sides by y, we get:

x = (5/3)

x = (5/3)y

Substituting x = 1.2 (the x-coordinate of point A) and solving for y, we get:

1.2 = (5/3)y

y = (3/5)(1.2)

y = 0.72

Therefore, a possible order pair for point D is (0, 0.72).

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Here the data is slightly right skewed which means there is no symmetry in the distribution of waiter tips. We, cannot determine the probability for this case.

Now, we will look into the details of distribution,

Mean of distribution = $9.60

The standard deviation of the skewed data = $5.40

Tip to the waiter = $20

Now, understand a few terms,

Normal distribution, also known as  Gaussian distribution, is very commonly used for randomly generated variables.

The graph of normal distribution has some parameters: the average or mean which is the maximum point of the graph and it is the point about which the graph is symmetrical, and the standard deviation which tells how much each data point is away from the mean.

As the data is skewed so we can,t use the normal distribution, and no other details about the model and distribution are given in the problem. So, we cannot determine the Probability for this case.

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Answer: He bought 20 ice cream bars and 14 popsicle

Step-by-step explanation:

To solve this I used the elimination method, you could use substitution as well

Here are our two equations

x+y=34 Because the total number of ice creams bought must be given to 34 children and no more

2x+5y=128 because that is the cost for each ice cream and the amount he spent

For the elimination method we have to cancel out one of the variables, I decided to cancel out the x, so I multiplied the top equation by -2. So i got -2x-2y=-68

2x+5y=128 Then we get

3y=60 so

y=20

Now we can go back to the first equation and plug in y.

x+20=34

  -20  -20

x=14

So he bought 14 popsicles and 20 ice cream bars.

Answer:

i looked up the whole question and this popped up

pay between $6 and $12 persquarw foot

sorry if its wrong. Good day

Answer:

8

Step-by-step explanation:

Based on the monthly maintenance fee and the check writing fee, the total fees paid would be $166.96

Alyssa will pay a total fee of:

= Yearly maintenance fee + Check writing fee

= (Monthly maintenance fee x Number of months) + (Number of checks x Check writing fee)

Solving gives:

= (12 x 12) + (287 x 0.08)

= 144 + 22.96

= $166.96

In conclusion, the total fees was $166.96.

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From this graph , it takes 0.75 seconds to reach the highest position.

A graph is a visual representation of the relationship between two sets of data or variables, typically via lines or curves. A diagram or pictorial representation of facts or values that is arranged might be referred to as a graph in mathematics. The relationship between two or more items is frequently represented by the points on the graph

The graph indicates that the peak is at (0.75, 9)

The x-axis displays the time in seconds, while the y-axis displays the height in feet.

Consequently, it takes 0.75 seconds to reach the highest position.

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Answer:

C. (3,15) and (4, 12)

Step-by-step explanation:

Given the system of linear equations

y = -x² + 4x + 12 and y=-3x + 24

Since both equations represents the variable y, we will equate both of the equations together.

Step 1: Equating both equations together we have;

-x² + 4x + 12 = -3x + 24

-x²+3x+4x+12-24 = 0

-x²+7x-12 = 0

x² -7x+12 = 0

x²-4x-3x+12 = 0

x(x-4)-3(x-4)= 0

x-3(x-4) = 0

x = 3 and 4

Step 2: substitute x = 3 and 4 into any of the equations to get the value of y. Using equation 2

when x = 3, y = -3(3)+24

y = -9+24

y = 15

when x = 4, y = -3(4)+24

y = -12+24

y = 12

The solutions yo the system of equations are (3,15) and (4, 12)

Answer:

c

Step-by-step explanation:

or (3, 15) and (4, 12)

Answer:

f(x) = (x - 7)² - 14

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

f(x) = x² - 14x + 63

Step 2: Rewrite

Answer:

-7 and 14 on khan

Answer: -4

Step-by-step explanation:

the slope is -4 because when x goes down by 2, y goes down by -8, so the y intercept is -4 because when x=-1 y=0 so if you go down 4 and over 1, you get the point x=0 and y=-4

The diagram shows a convex polygon. 57.67 degrees, is the value of b.

Any polygon whose inner angles are all less than 180 degrees and whose vertices all point outward is said to be convex. It has a minimum of three sides and angles and is closed.

Setting up an equation, we get:

b + 7 + 2b = 180 (sum of angles in a triangle)

3b + 7 = 180

3b = 173

b = 57.67 degrees (rounded to two decimal places).

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On average, we can expect approximately 1.8 people to be waiting in line at the grocery store based on the given probability distribution.

The expected number of people waiting in line, rounded to the nearest tenth, can be calculated using the probability distribution provided. Let's denote the number of people waiting in line as X and the corresponding probabilities as P(X).

X: 0 1 2 3 4

P(X): 0.1 0.3 0.4 0.15 0.05

To find the expected number of people waiting in line, we multiply each value of X by its corresponding probability and sum up the results:

Expected value = (0 * 0.1) + (1 * 0.3) + (2 * 0.4) + (3 * 0.15) + (4 * 0.05)

Calculating this expression, we get:

Expected value = 0 + 0.3 + 0.8 + 0.45 + 0.2 = 1.75

Rounded to the nearest tenth, the expected number of people waiting in line is 1.8. This means that, on average, we can expect approximately 1.8 people to be waiting in line at the grocery store based on the given probability distribution.

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Answer:

β = 110

Step-by-step explanation:

Here, we want to find the value of beta

From the diagram;

70 + β = 180

The reason for this is that the sum of angles on a straight line is 180

Thus, we have that

β = 180-70

β = 110

Answer: 20 weeks in 1 week

in 2 weeks 40

Step-by-step explanation:

This proves that the equation is true

Answer:

$19.95 per hour

Step-by-step explanation:

1. To find the cost per hour, we have to divide the total amount paid by the number of hours!

2. (Solving)

Therefore, the answer is $19.95 per hour.

A p-value for correlation which is statistically significant implies the correlation is due to random chance. The correct solution to this is False.

A p-value for correlation which is statistically significant implies that it is unlikely that the observed correlation is due to random chance alone. In other words, it suggests that there is evidence to support the presence of a true correlation between the two variables being studied. The p-value is a measure of the strength of evidence against the null hypothesis (i.e., that there is no correlation between the two variables), and a smaller p-value indicates stronger evidence against the null hypothesis.

Interpretation of the intercept: The intercept in a linear regression model represents the value of the dependent variable when all independent variables are equal to zero. It is the value of the dependent variable when there is no effect of the independent variable(s) on it. For example, in a regression model predicting height based on age, the intercept would represent the expected height of a person at age zero (which is not a realistic scenario).

Interpretation of a residual: A residual is the difference between the actual observed value of the dependent variable and the predicted value of the dependent variable based on the regression model. It represents the part of the dependent variable that the model was not able to explain. A positive residual means that the actual value is greater than the predicted value, while a negative residual means that the actual value is smaller than the predicted value.

Interpretation of r-squared: R-squared is a measure of how much of the variation in the dependent variable is explained by the independent variable(s) in the regression model. It ranges from 0 to 1, with higher values indicating a better fit of the model to the data. Specifically, it represents the proportion of the total variation in the dependent variable that is explained by the independent variable(s) in the model. For example, if r-squared is 0.75, it means that 75% of the variability in the dependent variable is explained by the independent variable(s) in the model.

Interpretation of the slope: The slope in a linear regression model represents the change in the dependent variable that is associated with a one-unit increase in the independent variable, holding all other variables constant. It reflects the average change in the dependent variable for each unit change in the independent variable. For example, in a regression model predicting height based on age, the slope would represent the average change in height for each additional year of age.

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