Solve the following.

Step-by-step explanation:

b^2-4b+3=0

b²-3x-b+3=0

b(b-3)-1(b-3)=0

(b-3)(b-1)=0

either

b=3 or b=1

.

2n^2 + 7 = -4n + 5

2n²+4n+7-5=0

2n²+4n+2=0

2(n²+2n+1)=0

(n+1)²=0/2

:.n=-1

.

x - 3x^2 = 5+ 2x - x^2

0=5+ 2x - x^2-x +3x^2

0=5+x+2x²

2x²+x+5=0

comparing above equation with ax²+bx +c we get

a=2

b=1

c=5

x={-b±√(b²-4ac)}/2a ={-1±√(1²-4×2×5)}/2×1

={-1±√-39}/2

The correct answers are a) true, b) true, c) false, d) true, and e) false.

a) True
Let f(x) be differentiable on an open interval (a, b), then the following holds that if f'(x) = 0 at each x in (a,b), then f(x) = C is a constant for all x in (a,b). b) True
Suppose that f is twice differentiable on an open interval I, then the graph of f is concave up if f' increases on I. c) False
Suppose that f is twice differentiable on an open interval I. If f' decreasing on I, then the graph of f is not necessarily concave down. d) True
Let c be in I, if f'(c) = 0 and f''(c) < 0 then f has a local min at x = c. e) False
If the point (c,f(c)) is a point of inflection, then f''(c) can be equal to 0 or not.

The point of inflection refers to the change in the concavity of a function from upward to downward or vice versa. It's also the point on the curve where the second derivative changes its sign.

Hence, the correct answers are a) true, b) true, c) false, d) true, and e) false.

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The necessary and sufficient conditions for a given random process X(t) to be a wide-sense stationary (WSS) process are as follows:

Mean and variance are constant over time:

For all t1 and t2 (where t1 ≠ t2), μX(t1) = μX(t2) and σ²X(t1) = σ²X(t2).

Autocorrelation function (ACF) depends only on the time difference: The autocorrelation function of X(t) depends only on the difference between the two times t1 and t2, not on the specific values of t1 and t2.

That is,

R(τ) = R(t2 – t1) for all t1 and t2.

The process X(t) is a sum of two random variables A cos(wt) and B sin(wt). Therefore, using the linearity of mean and variance,

we get the following:

μX(t) = E[X(t)] = E[A cos(wt)] + E[B sin(wt)] = 0σ²X(t) = Var[X(t)] = Var[A cos(wt)] + Var[B sin(wt)] = E[A²] E[cos²(wt)] + E[B²] E[sin²(wt)]

Since cos²(wt) and sin²(wt) both have an average value of 1/2 over one period, the variance is given by:

σ²X(t) = 1/2(E[A²] + E[B²])

Using the cosine addition formula,

we obtain the following expression for the ACF:R(τ) = E[X(t)X(t + τ)] = E[(A cos(wt) + B sin(wt))(A cos(w(t + τ)) + B sin(w(t + τ)))] = E[A² cos(wt) cos(w(t + τ))] + E[B² sin(wt) sin(w(t + τ))] + E[AB cos(wt) sin(w(t + τ))] + E[AB sin(wt) cos(w(t + τ))] = E[A² cos(wt) cos(wt) cos(wτ) – A² sin(wt) sin(wt) cos(wτ)] + E[B² sin(wt) sin(wt) cos(wτ) – B² cos(wt) cos(wt) cos(wτ)] + E[AB cos(wt) sin(wt) cos(wτ) – AB cos(wt) sin(wt) cos(wτ)] + E[AB sin(wt) cos(wt) cos(wτ) – AB sin(wt) cos(wt) cos(wτ)]R(τ) = E[(A² – B²) cos(wτ)]If A and B are identically distributed, then E[(A² – B²)] = 0.

Therefore, the ACF depends only on the time difference and X(t) is a WSS process.

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Answer: 824 Miles

Step-by-step explanation:435 + 389

As angle OAB =40-degree, angle AOB is 100 degrees according to the properties of circle and triangle.

Some Properties of circle are distance from center of the circle to each point on the circumstances are equal. hence, OA=OB

Diameter is twice of radius.

The triangle having two equal side length is called isosceles triangle. In the figure, triangle OAB is an isosceles as OA=OB=radius

According to the criteria of isosceles triangle angle OAB =OBA =40°

hence, angle AOB= 180 degrees - (40°+40°) [angle sum of triangle =180°]

                  angle AOB= 100 degrees.

We get, AOB = 100 degrees

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Answer:

Number 1 will be 95

Number 2 will be 130

Am I right

Answer:

\(y = 1/3x-2\)

Step-by-step explanation:

General line equation:

\(\frac{y-y_{1}}{x-x_{1}} = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\)

Or

\(y = a.x + b\\a = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\b = y_{1} - a.x_{1}\)

where a is the slope and b is vertical displacement.

For a line to be parallel to another, they both have to have the same slope, therefor, the parallel line's slope is 1/3.

By substituting the given point and a = 1/3 in above equation for b, b is equal to -2. Therefore,

\(y = 1/3x - 2\)

The length of the garden is 3x - 4 feet.

Because the garden is square, we must take the square root of the area to determine its length.

The square garden's area is given by: 9x2 - 24x + 16

This expression can be factored as (3x - 4)(3x - 4)

We get 3x - 4 by taking the square root of this expression.

Hence, the garden's length is 3x - 4 ft.

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Since the tallest man is a lone individual, he can only take a seat in the center. The four other men can sit in 4! = 24 different positions.

We'll take pictures of five people standing in a row, all of varying heights. The tallest individual must be in the middle, so. A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

The likelihood that an event will take place. the proportion between the total number of conceivable outcomes and the number of outcomes in a comprehensive collection of equally likely alternatives that result in a given occurrence. Probability is a measure of the likelihood that an event will occur or the likelihood that something will happen. If we throw a coin into the air,

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Answer:

Solution,

\(f(x) = - 4 {x}^{2} + 5x \\ f(6) = - 4 \times {6}^{2} + 5 \times 6 \\ \: \: \: \: \: \: = - 4 \times 36 + 30 \\ \: \: \: = - 144 + 30 \\ \: \: \: - 114\)

hope this helps.

Good luck on your assignment..

Answer:

-114

Step-by-step explanation:

To find f(6), you need to plug in the value in parentheses wherever there is an x in the equation.

f(x) = -4x + 5x

f(6) = -4(6) + 5(6)

f(6) = -4(36) + 30

f(6) = -144 + 30

f(6) = -114

The answer is -114.

Hello!

If Brad had a small gathering at a local steakhouse where they ordered 4 of the 6-ounce platters, 3 of the 8-ounce platters, and 2 of the 11-ounce platters. After adding an 18% gratuity their total before sales tax should have been $130.45

Step-by-step explanation:

\(4\) x \(9.95=39.80\)

\(3\) x \(12.95=38.85\)

\(2\) x \(15.95=31.90\)

\(31.90+\)\(38.85+\)\(39.80=\)\(110.55\)

\(110.55\) x \(0.18\) \(=19.899\)

\(110.55+19.90\)\(=130.45\)

There are 30 cubic feet of water in the pipe at time t = 0. 76.570 cubic feet of rainwater flow into the pipe during the 8-hour time interval 0 ≤ t ≤ 8.

\(\int\limits^8_0\)   [R(t) dt = \(\int\limits^8_0\) 20 sin \(\frac{t^2}{35}\) dt = 76.570

What Is Time Interval?

The amount of time between two given times is known as time interval. In other words, it is the amount of time that has passed between the beginning and end of the event. It is also known as elapsed time.

INTERVAL types are divided into two classes: year-month intervals and day-time intervals. A year-month interval can represent a span of years and months, and a day-time interval can represent a span of days, hours, minutes, seconds, and fractions of a second.

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Step-by-step explanation:

f (x)= x-7

= -1-7

= -6

g (x)= x^2

= (-1)^2

=1

Answer:

25/24

Step-by-step explanation:

multiply first then add

Overall fraction of sold seats is 0.63333...

First we use the fact that 2/3 of the seats are located on the main floor and the number of seats on the main floor is 600, so the total number of seats can be calculated as follows:

Total number of seats = 600 / (2/3) = 900 seats

Next, we can find the number of seats in the balcony:

Balcony seats = Total number of seats - Main floor seats = 900 - 600 = 300 seats

Next, we can find the number of sold floor seats:

Sold floor seats = 4/5 * 600 = 480 seats

And the number of sold balcony seats:

Sold balcony seats = 1/2 * 300 = 150 seats

Finally, to find the overall fraction of sold seats in the theater, we add the number of sold floor seats and the number of sold balcony seats and divide by the total number of seats:

Overall fraction of sold seats = (480 + 150) / 900 = 0.63333... (rounded to the nearest hundredth)

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Answer:

107

Step-by-step explanation:

Sum of all angles is 180

12+BC+61 = 180

73+ BC = 180

73 - 73 + BC = 180 - 73

BC = 107

we can conclude that there is sufficient evidence to suggest that the mean speed of cars driven by all men drivers on this highway is higher than that of cars driven by all women drivers.

a. Confidence interval for the difference between the mean speeds of cars driven by all men and all women on this highway is given by:

Confidence Interval = \(\bar x_m - \bar x_w ± z*(\frac{{s_m}^2}{m}+\frac{{s_w}^2}{n})^{1/2}\)

Here, \(\bar x_m\) = 72 miles per hour,\(s_m\)= 2.2 miles per hour, m = 27, \(\bar x_w\)= 68 miles per hour, \(s_w\)= 2.5 miles per hour and n = 18.

Using the formula for a 98% confidence interval, the values of z = 2.33.

Thus, the confidence interval is calculated below:

Confidence Interval = 72 - 68 ± 2.33 * \((\frac{{2.2}^2}{27} + \frac{{2.5}^2}{18})^{1/2}\)

= 4 ± 2.37

= [1.63, 6.37]

Thus, the 98% confidence interval for the difference between the mean speeds of cars driven by all men and all women on this highway is (1.63, 6.37).

b. The null and alternative hypotheses are:

Null Hypothesis:

\(H0: \bar x_m - \bar x_w ≤ 0\) (Mean speed of cars driven by men is less than or equal to that of cars driven by women)

Alternative Hypothesis:

H1: \(\bar x_m - \bar x_w\) > 0 (Mean speed of cars driven by men is greater than that of cars driven by women)

Test Statistic: Under the null hypothesis, the test statistic t is given by:

t =\((\bar x_m - \bar x_w - D)/S_p\)

(D is the hypothesized difference in population means,

\(S_p\) is the pooled standard error).

\(S_p = ((s_m^2 / m) + (s_w^2 / n))^0.5\)

= \(((2.2^2 / 27) + (2.5^2 / 18))^0.5\)

= 0.7106

t = (72 - 68 - 0)/0.7106

= 5.65

Using a significance level of 1%, the critical value of t is 2.60, since we have degrees of freedom (df) = 41

(calculated using the formula df = \(\frac{(s_m^2 / m + s_w^2 / n)^2}{\frac{(s_m^2 / m)^2}{m - 1} + \frac{(s_w^2 / n)^2}{n - 1}}\), which is rounded down to the nearest whole number).

Thus, since the calculated value of t (5.65) is greater than the critical value of t (2.60), we can reject the null hypothesis at the 1% level of significance.

Hence, we can conclude that there is sufficient evidence to suggest that the mean speed of cars driven by all men drivers on this highway is higher than that of cars driven by all women drivers.

c. For this part, the only change is in the sample standard deviation for women drivers.

The new values are \(\bar x_m\) = 72 miles per hour, \(s_m\) = 1.9 miles per hour, m = 27, \(\bar x_w\) = 68 miles per hour, \(s_w\) = 3.4 miles per hour, and n = 18.

Using the same formula for the 98% confidence interval, the confidence interval becomes:

Confidence Interval = \(72 - 68 ± 2.33 * (\frac{{1.9}^2}{27} + \frac{{3.4}^2}{18})^{1/2}\)

= 4 ± 2.83

= [1.17, 6.83]

Thus, the 98% confidence interval for the difference between the mean speeds of cars driven by all men and all women on this highway is (1.17, 6.83).

The null and alternative hypotheses for part b remain the same as in part a.

The test statistic t is given by:

t = \((\bar x_m - \bar x_w - D)/S_pS_p\)

= \(((s_m^2 / m) + (s_w^2 / n))^0.5\)

= \(((1.9^2 / 27) + (3.4^2 / 18))^0.5\)

= 1.2565

t = (72 - 68 - 0)/1.2565

= 3.18

Using a significance level of 1%, the critical value of t is 2.60 (df = 41).

Since the calculated value of t (3.18) is greater than the critical value of t (2.60), we can reject the null hypothesis at the 1% level of significance.

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The probability that the Texas Sharpshooters score exactly 1 goal next hockey game is 0.5

The following figure accurately depicts the table.

Experimental probability is the likelihood of a future event based on past happenings.

Experimental probability is equal to the ratio of good results to all possible results.

To calculate the likelihood that the Texas Sharpshooters will score precisely

Next hockey game: 1 goal

As displayed in the table:

a successful outcome is repeated four times.

So, positive results equal 4

8 total results

likelihood = 4/8 = 0.5

So, The probability that the Texas Sharpshooters score exactly 1 goal next hockey game is 0.5

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Answer:

0.50 (Choice C)

Step-by-step explanation:

Khan Academy told me.

the interval of time between when a vector takes an infectious meal, and when it begins to transmit the pathogen, is referred to as the extrinsic incubation period.

The incubation period refers to the duration of time between the invasion by an infectious pathogen and the start (first appearance) of symptoms of the disease in question. The host enters the symptomatic phase after the incubation period is over. Additionally, after infection, the host develops the ability to spread infections to other people, or they become infectious or communicable. The host person may or may not be contagious throughout the incubation phase, depending on the disease. The dynamics of disease transmission depend on the incubation period since it establishes the timing of case detection in relation to infection. This aids in assessing the success of symptomatic surveillance-based control methods.

the interval of time between when a vector takes an infectious meal, and when it begins to transmit the pathogen, is referred to as the extrinsic incubation period.

The complete question is-

The interval of time between when a vector takes an infectious meal, and when it begins to transmit the pathogen, is referred to as the: (a) vectorial capacity; (b) intrinsic incubation period; (c) vectorial competence; (d) extrinsic incubation period.

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Answer:

The recipe will make 7.2 quarts of punch.

Step-by-step explanation:

A punch recipe calls for 3 liters of ginger ale and 1.5 liters of tropical fruit juice.

Then the recipe will make 4.5 liters of punch, obtained by the sum of ginger ale and tropical fruit juice.

The ration is the comparison of two quantities and is measured from the division of two values, then: \(\frac{a}{b}\).

The proportion is the equality between two or more ratios. That is, \(\frac{a}{b}=\frac{c}{d}\) equals a proportion.

In this case, being 1 L= 1.6 quarts, you have:

\(\frac{1.6 quarts}{1 L}=\frac{x}{4.5 L}\)

Solving:

\(x=4.5 L*\frac{1.6 quarts}{1 L}\)

x= 7.2 quarts

So, the recipe will make 7.2 quarts of punch.

Answer: No solution

Step-by-step explanation:

No solution.   If the graph only has one line then there's no solution. Since system of equation need two equations or two lines.

Answer:

The answer is: the equation of the line.

Step-by-step explanation:

Since there is only one line, then all points of the line are the solution.

The answer is: the equation of the line.

Answer:

$283

Step-by-step explanation:

Let,

   x - for $2 notes

   x + 16 - for $5 notes

EQUATION:

  (x) + (x + 16) = 74

  2x = 74 - 16

  2x = 58

  x = 29

SUBSTITUTE

  x = 29 pieces of $2 notes

  x + 16 = 29 + 16 = 45 pieces of $5 notes

TOTAL VALUE IS:

   (29 x $2) + (45 x $5) = $283

We have shown that the minimum of two independent exponential random variables with parameters λ and μ is an exponential random variable with parameter λ+μ.

To show that the minimum of two independent exponential random variables with parameters λ and μ is an exponential random variable with parameter λ+μ, we can use the concept of the cumulative distribution function (CDF).
Let X and Y be two independent exponential random variables with parameters λ and μ, respectively. The CDF of an exponential random variable with parameter θ is given by F(t) = 1 - e^(-θt), for t ≥ 0.

To find the CDF of the minimum, Z = min(X, Y), we can use the fact that Z > t if and only if both X > t and Y > t. Since X and Y are independent, we can multiply their probabilities:
P(Z > t) = P(X > t and Y > t) = P(X > t)P(Y > t)
Using the exponential CDFs, we have:
P(Z > t) = (1 - e^(-λt))(1 - e^(-μt))
The complement of the CDF, P(Z ≤ t), is equal to 1 - P(Z > t):
P(Z ≤ t) = 1 - (1 - e^(-λt))(1 - e^(-μt))
Simplifying this expression, we get:
P(Z ≤ t) = 1 - (1 - e^(-λt) - e^(-μt) + e^(-(λ+μ)t))

This is the CDF of an exponential random variable with parameter λ+μ. Hence, we have shown that the minimum of two independent exponential random variables with parameters λ and μ is an exponential random variable with parameter λ+μ.

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Answer: what the question

Step-by-step explanation:

Based on the given side lengths of 8, 11, and 12, none of them are equal. Therefore, we can classify the triangle as a Scalene Triangle.

To classify a triangle by its angles and sides, we can use the properties and definitions of different types of triangles. Let's analyze the given triangle with sides measuring 8, 11, and 12 and angles measuring 45 degrees, 65 degrees, and 70 degrees.

Classification by angles:

Acute Triangle: An acute triangle has all three angles less than 90 degrees.

Obtuse Triangle: An obtuse triangle has one angle greater than 90 degrees.

Right Triangle: A right triangle has one angle exactly 90 degrees.

Based on the given angles of 45 degrees, 65 degrees, and 70 degrees, none of them are greater than 90 degrees, so we can classify the triangle as an Acute Triangle.

Classification by sides:

Equilateral Triangle: An equilateral triangle has all three sides of equal length.

Isosceles Triangle: An isosceles triangle has two sides of equal length.

Scalene Triangle: A scalene triangle has all three sides of different lengths.

Based on the given side lengths of 8, 11, and 12, none of them are equal. Therefore, we can classify the triangle as a Scalene Triangle.

In summary, based on the given measurements, the triangle can be classified as an Acute Scalene Triangle. We determined this by comparing the angles to the definitions of acute, obtuse, and right triangles, and comparing the side lengths to the definitions of equilateral, isosceles, and scalene triangles.

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A correlation coefficient is a numerical index that reflects the relationship between two variables.

A correlation coefficient is a statistical measure that quantifies the strength and direction of the linear relationship between two variables.

The correlation coefficient ranges from -1 to +1, where -1 indicates a perfectly negative linear relationship, 0 indicates no linear relationship, and +1 indicates a perfectly positive linear relationship of two variables.

The correlation coefficient is calculated using a formula that takes into account the covariance and standard deviations of the two variables.

It is commonly used in many fields, such as psychology, economics, and biology, to explore and understand the association between two variables.

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They have traveled 234 miles when they completed 72 percent of the trips distance ​

from the question, we have the following parameters that can be used in our computation:

Distance = 325 miles

Distance completed = 72%

Using the above as a guide, we have the following:

Distance completed = 72% * Total distance

Substitute the known values in the above equation, so, we have the following representation

Distance completed = 72% * 325 miles

Evaluate

Distance completed = 234 miles

Hence, the distance completed = 234 miles

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