given f(x)= |1-5x|, find f(9)

Answer:

a) f(t) = 30000 - 850t

b) 23,200 after 8 minutes

c) Lands in 35.29 minutes

Step-by-step explanation:

f(t) = 30000 - 850t

f(8) = 30000 - 850(8) = 23,200

0 = 30000 - 850t

850t = 30000

t = 35.29 minutes

The vertex is (-5 , 5) , y-intercept is (0 , -20) and reflection of y-intercept across symmetry is (-10 , -20).  

What is parabola ?
A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line.

a curve made when a cone's surface collides with a plane that is perpendicular to a straight line: a curve created when a point moves in such a way that its separation from a fixed point equals its separation from a fixed line something with a bowl-like form.

Parabola, also known as an open curve or conic section, is formed when a right circular cone and a plane perpendicular to one of the cone's elements cross.

In the equation you provided, the corresponding values are:

a = -1

b = -10

c = -20

Plugging in the values to find the vertex yields:

- (-10)/(2*-1)

= 10/-2

= -5

This is the x-coordinate of the vertex

-x²-10x - 20

= -(-5)² - 10×(-5) - 20

= -25 +  50 - 20

= 5

∴The vertex is located at the point (-5 , 5)

The y-intercept when x = 0

-x² - 10x - 20

= -20

The y-intercept of the vertex at the point (0 , -20)

Since you have 2 points, look at the y-intercept and imagine a point reflected across the line of symmetry.

That point will be your last point, and is located at: (-10 , -20)

To learn more about parabola from the given link  

https://brainly.com/question/4061870

#SPJ1

Answer:179 between 191

Step-by-step explanation:

The integral is  9/4 ln|x| - 1/2 ln|x-2| - 7/4 ln|x+2| + C

How to find integral?

First factor the denominator:

x^3 - 4x = x(x^2 - 4) = x(x-2)(x+2)

Now write the integrand as a sum of two fractions:

(x^2 + 36x - 36) / (x^3 - 4x) = A/x + B/(x-2) + C/(x+2)

To find A, we multiply both sides of the equation by x and then take the limit as x approaches 0:

(x^2 + 36x - 36) / (x^2 - 4x) = A + B/(x-2) + C/(x+2)

(x^2 + 36x - 36) = A(x^2 - 4x) + B(x+2) + C(x-2)

-36 = -4A + 2B - 2C

To find B and C, we multiply both sides of the original equation by (x-2) and (x+2), respectively, and then substitute x=2 and x=-2:

(x^2 + 36x - 36) = A(x(x-2)(x+2)) + B(x-2)(x+2) + C(x(x-2)(x+2))

(x^2 + 36x - 36) = A(x^3 - 4x) + B(x^2 - 4) + C(x^3 - 4x)

Let x = 2: 52 = 8A + 4B + 2C

Let x = -2: -100 = -8A + 4B - 2C

Solving the system of equations gives:

A = 9/4, B = -1/2, C = -7/4

Therefore, the integral becomes:

∫ (x^2 + 36x - 36) / (x^3 - 4x) dx = ∫ (9/4)/x dx + ∫ (-1/2)/(x-2) dx + ∫ (-7/4)/(x+2) dx

= 9/4 ln|x| - 1/2 ln|x-2| - 7/4 ln|x+2| + C

Learn more about integral

brainly.com/question/18125359

#SPJ11

The function equation represented by the graph is f(x)=1/4x-3.

An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=10x+4. Where:

m= the slope.

b= the constant term that represents the y-intercept.

For the given example: m=10 and b=4.

From the graph is possible to see the following coordinates points: (0,-3) and (4,-2). Applying the standard form for the linear equation, you can write:

-3=0*m+b (1)

-2=4*m+b (2)

-3=b        (1)

-2=4m+b (2)

If b=-3, you can find m from equation 2. Then,

-2=4m-3

-2+3=4m

1=4m

m=1/4

Therefore, the linear equation represented in the graph is y=1/4b -3

Read more about the linear equations here:

brainly.com/question/2030026

#SPJ1

The value of A has been illustrated, computed and proven based in the triangle given.

It should be noted that that a triangle is a shape that has three sides and the value of the addition of all the angles are equal to 180°.

Based on the information that's given, it should be noted that the value of angle A, angle B, and angle C will be equal to 180°.

In this case, the following can be deduced:

A = 5x

B = 90°

C = x + 10°

Therefore, A + B + C = 180° (sum of angles in a triangle)

5x + 90 + x + 10 = 180°

6x = 180° - 90° - 10°

6x = 80°

x = 80/6

x = 13 1/3

Therefore, the value of A will be:

= 5x

= 5 × 13 1/3

= 66 2/3

Therefore, A is 66 2/3.

Learn more about triangles on:

brainly.com/question/1058720

#SPJ1

Answer:

n = 5

Step-by-step explanation:

Coordinate of P = (n,3)

R is on y-axis & the y-coordinate of P & R are equal. So coordinate of R = (3,0)

Coordinate of Q = (n,-2)

Using distance formula,

Distance between P & Q =

\( \sqrt{ {( n - n}) ^{2} + {( 3- ( - 2) })^{2} } \)

\( = > \sqrt{ {(3 + 2)}^{2} } = \sqrt{ {5}^{2} } = 5\)

Distance between P & R =

\( \sqrt{ {(n - 0)}^{2} + {(3 - 3)}^{2} } \)

\( = > \sqrt{ {n}^{2} } = n\)

But in question it is given that distance between P & Q is equal to the distance between P & R. So,

\(n = 5\)

Hypothesis testing is a statistical method in which an analyst conducts a hypothesis test on a sample of data to draw inferences about the entire population.
1. Hypothesis tests are one of Inferential statistics. True. Inferential statistics, which deals with generalizing sample data to the population from which the sample was taken, includes hypothesis testing.
2. Mean is a central tendency measurement it is necessary to be one of the raw data. False. The mean measures central tendency calculated by adding all the values and dividing by the number of observations. The mean value does not have to be one of the raw data values. It's just a mathematical calculation used to represent a typical value for a dataset.
3. Calculation of the mean considers all the data, while other measurements do not consider all raw data. True. The mean calculation considers all data points, whereas other measures of central tendency, such as the median and mode, do not. This property makes the mean more representative of the entire data set.
4. Mode, median, and mean are single when that data is normally distributed. False. The mode, median, and mean are distinct when the data is non-normal. The mode, median, and mean are identical when data is normally distributed.
5. Mutually exclusive events can contain common elements. False. If two events are mutually exclusive, they cannot occur simultaneously. They have no elements in common by definition.
6. In the standard normal distribution, μ=1 and σ=0. False. In the standard normal distribution, the mean (μ) is 0, and the standard deviation (σ) is 1.

To know more about the mutually exclusive events, visit:

brainly.com/question/29992365

#SPJ11

Answer:from least to greatest:

1) g (x)

2) f (x)

3) h (x)

Step-by-step explanation:

Answer:

For f (x):

f (x) = (x + 3) ^ 2 - 2

For x = -1

f (-1) = (-1 + 3) ^ 2 - 2

f (-1) = (2) ^ 2 - 2

f (-1) = 4 - 2

f (-1) = 2

For x = 3

f (3) = (3 + 3) ^ 2 - 2

f (3) = (6) ^ 2 - 2

f (3) = 36 - 2

f (3) = 34

AVR = ((34) - (2)) / ((3) - (- 1))

AVR = 8

For g (x):

linear graph with and intercept of negative 3 over 2 and x intercept of 3

y = mx + b

b = -3/2

For me we have:

0 = m (3) - 3/2

3m = 3/2

m = 1/2

The function g (x) is:

g (x) = (1/2) x - 3/2

For x = -1

g (-1) = (1/2) (- 1) - 3/2

g (-1) = -1/2 - 3/2

g (-1) = -4/2

g (-1) = -2

For x = 3

g (3) = (1/2) (3) - 3/2

g (3) = 3/2 - 3/2

g (3) = 0

AVR = ((0) - (- 2)) / ((3) - (- 1))

AVR = 1/2

For h (x):

Using the table we have:

AVR = ((62) - (14)) / ((3) - (- 1))

AVR = 12

Step-by-step explanation:

Answer:

400

Step-by-step explanation:

We have, 32% × x = 128

or, 32/100 × x = 128

Multiplying both sides by 100 and dividing both sides by 32,

we have x = 128 × 100/32

x = 400

please mark as brainliest!

The correct option A, "None of the associations listed are correct," is the appropriate response.To determine the association suggested by the two-way table, we need to calculate the relative frequency of the data.

The table provides information about whether individuals have a brother and a sister.

Based on the options given, let's calculate the relative frequencies to see which association is suggested:

Calculate the relative frequency for individuals who have a brother and a sister:Relative frequency = (Number of individuals with both a brother and a sister) / (Total number of individuals)

Calculate the relative frequency for individuals who have a brother but no sister:Relative frequency = (Number of individuals with a brother but no sister) / (Total number of individuals)

Calculate the relative frequency for individuals who have a sister but no brother:Relative frequency = (Number of individuals with a sister but no brother) / (Total number of individuals)

Calculate the relative frequency for individuals who have neither a brother nor a sister:Relative frequency = (Number of individuals with neither a brother nor a sister) / (Total number of individuals)

By comparing the relative frequencies, we can determine which association is suggested by the data.Unfortunately, the given two-way table is missing, so we cannot perform the necessary calculations to determine the association.

For such more questions on Association:

https://brainly.com/question/2511791

#SPJ11

Answer:  =-1/2x+-1/2y

Step-by-step explanation:

7 (5) + 1 = 35 + 1 = 36

So, f(5) = 36

Answer:

I think the answer is 8 inches

Answer:

There are a lot of advantages of using a chart or graph instead of a table:

- They can present data in a more precise way, and is able to simplify large data in a easier manner.

- They will pretty much show you an overall trend/pattern of the data, it's either be a positive, negative or no trend at all.

Answer:

True

Step-by-step explanation:

The requried, an equation allows you to find the x- and y-coordinates of any point on the xy- plane. The given statment is true.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

An equation in two variables (such as y = mx + b, where m and b are constants) allows you to find the x- and y-coordinates of any point on the xy-plane that satisfies the equation.

To find the x-coordinate of a point, you can plug in a value for y and solve for x. To find the y-coordinate of a point, you can plug in a value for x and solve for y.

Learn more about equations here:

brainly.com/question/10413253

#SPJ7

In multivariable calculus, the tangent plane is a plane that "touches" a surface at a given point and has the same slope or gradient as the surface at that point.

To find the equation for the tangent plane at the point P0(2, 1, 2) on the surface 2x^2 + 4y^2 +3z^2 = 24, we need to find the gradient vector of the surface at P0, which gives us the normal vector of the plane. Then, we can use the point-normal form of the equation for a plane to find the equation of the tangent plane.

The gradient vector of the surface is given by:

grad(2x^2 + 4y^2 +3z^2) = (4x, 8y, 6z)

At P0(2, 1, 2), the gradient vector is (8, 8, 12), which is the normal vector of the tangent plane.

Using the point-normal form of the equation for a plane, we have:

8(x - 2) + 8(y - 1) + 12(z - 2) = 0

Simplifying, we get:

4x + 4y + 3z = 20

Therefore, the correct equation for the tangent plane is D. 5x + 4y + 3z = 20.

To find the equations for the normal line, we need to use the direction vector of the line, which is the same as the normal vector of the tangent plane. Thus, the direction vector of the line is (8, 8, 12).

The equations for the normal line can be expressed as:

x = 2 + 8t

y = 1 + 8t

z = 2 + 12t

where t is a parameter that can take any real value.

To learn more about  equation visit:

brainly.com/question/10413253

#SPJ11

As described in statistics the mean standard deviation of the headway is 0.890

what is the statistics ?

The study of statistics is the field that deals with the gathering, structuring, analyzing, interpreting, and presenting of data. In order to apply statistics to a problem in science, business, or society, it is customary to start with a statistical population or a statistical model that will be investigated.

solution:

P(0.995 ≤ x ≤ 1.445) = F(1.445) - F is the given mean value (0.995).

The distribution's cdf is

f(x) = { (1 - 1/x⁶ , x > 1) (0. x ≤ 1)

F(1.445) = 1 - (1/(1.445)⁶)

F(0.995) = 0

Now, using the values of F(1.445) and F(0.995) in P( 0.995 ≤ x ≤ 1.445) to get F(1.445) - F(0.995):

P( 0.995 ≤ x ≤ 1.445)

=1 - (1/(1.445)⁶) - 0

=0.890

Therefore the mean value of standard deviation is 0.890

To learn more about the statistics from the given link

https://brainly.com/question/15525560

#SPJ4

we have shown that the expression ρ(x,t) = [1/(1 + t^2)] ρ0 [(x/(1 + t^2)) - t] satisfies the advection equation ∂ρ/∂t + v ∂ρ/∂x = -ρ ∂v/∂x.

The density of radioactive material, denoted by ρ(x,t), evolves according to the equation:

∂ρ/∂t + v ∂ρ/∂x = -ρ ∂v/∂x

This equation describes the transport of a substance by a moving medium, where the rate of movement of the radioactive material is influenced by the velocity of the wind, determined by the function v(x,t).

To solve the equation, we use the method of characteristics. We define the characteristic equation as:

x = ξ(t)

and

ρ(x,t) = f(ξ)

where f is a function of ξ.

Using the method of characteristics, we find that:

∂ρ/∂t = (∂f/∂t)ξ'

∂ρ/∂x = (∂f/∂ξ)ξ'

where ξ' = dξ/dt.

Substituting these derivatives into the original equation, we have:

(∂f/∂t)ξ' + v(∂f/∂ξ)ξ' = -ρ ∂v/∂x

Dividing by ξ', we get:

(∂f/∂t)/(∂f/∂ξ) = -ρ ∂v/∂x / v

Letting k(x,t) = -ρ ∂v/∂x / v, we can integrate the above equation to obtain f(ξ,t). Since f(ξ,t) = ρ(x,t), we can express the solution ρ(x,t) in terms of the initial value of ρ and the function k(x,t).

Now, let's solve the advection equation using the method of characteristics. We define the characteristic equation as:

x = x(t)

Then, we have:

dx/dt = v(x,t)

ρ(x,t) = f(x,t)

We need to find the function k(x,t) such that:

(∂f/∂t)/(∂f/∂x) = k(x,t)

Differentiating dx/dt = v(x,t) with respect to t, we have:

dx/dt = (2xt)/(1 + t^2) + 1 + t^2

Integrating this equation with respect to t, we obtain:

x = (x(0) + 1)t + x(0)t^2 + (1/3)t^3

where x(0) is the initial value of x at t = 0.

To determine the function C(x), we use the initial condition ρ(x,0) = ρ0(x).

Then, we have:

ρ(x,0) = f(x,0) = F[x - C(x), 0]

where F(ξ,0) = ρ0(ξ).

Integrating dx/dt = (2xt)/(1 + t^2) + 1 + t^2 with respect to x, we get:

t = (2/3) ln|2xt + (1 + t^2)x| + C(x)

where C(x) is the constant of integration.

Using the initial condition, we can express the solution f(x,t) as:

f(x,t) = F[x - C(x),t] = ρ0 [(x - C(x))/(1 + t^2)]

To simplify this expression, we introduce A(x,t) = (2/3) ln|2xt + (1 + t^2)x|/(1 + t^2). Then, we have:

f(x,t) = [1/(1 +

t^2)] ρ0 [(x - C(x))/(1 + t^2)] = [1/(1 + t^2)] ρ0 [(x/(1 + t^2)) - A(x,t)]

Finally, we can write the solution to the advection equation as:

ρ(x,t) = [1/(1 + t^2)] ρ0 [(x/(1 + t^2)) - A(x,t)]

where A(x,t) = (2/3) ln|2xt + (1 + t^2)x|/(1 + t^2).

Learn more about advection equation here :-

https://brainly.com/question/32107552

#SPJ11

The probability that exactly 250 out of 413 adults will be in favor of abolishing the sales tax and increasing the income tax can be calculated using the binomial probability formula.

Find the probability of exactly 250 out of 413 adults being in favor of abolishing the sales tax and increasing the income tax, we can use the binomial probability formula.

The binomial probability formula is:

P(X = k) = (n C k) * p^k * (1 - p)^(n - k)

Where:

- P(X = k) is the probability of getting exactly k successes,

- (n C k) represents the number of combinations,

- p is the probability of success for a single trial,

- k is the number of successes,

- n is the number of trials.

In this case, n = 413 (sample size), p = 0.59 (probability of success), and k = 250 (number of successes).

Plugging in these values, we can calculate the probability:

P(X = 250) = (413 C 250) * (0.59^250) * (1 - 0.59)^(413 - 250)

Calculating the binomial coefficient (413 C 250) may require a large number of calculations, but it can be simplified using the symmetry property of binomial coefficients:

(413 C 250) = (413 C 163)

Once simplified, you can evaluate the expression using a calculator or statistical software to find the probability.

To know more about probability refer here

https://brainly.com/question/31828911#

#SPJ11

The results of the study suggest that the 4-day meditation program had a significant effect in reducing the stress levels of the medical students compared to the group that did not participate in the meditation program.

To determine if the results support the hypothesis that meditation helps reduce stress levels, we need to perform the necessary statistical analysis. Here are the steps involved:

Step 1: Define the hypothesis:

The null hypothesis (H₀) is that there is no significant difference in stress levels between the two groups.

The alternative hypothesis (Hₐ) is that there is a significant difference in stress levels between the two groups, with meditation reducing stress.

Step 2: Identify the appropriate statistical test:

Since we are comparing the means of two independent groups and want to test if there is a significant difference, we can use an independent samples t-test.

Step 3: Set the significance level:

The significance level (α) is the probability of rejecting the null hypothesis when it is true. In this case, we will use a significance level of 0.05, corresponding to a 95% confidence level.

Step 4: Calculate the sample statistics:

Calculate the means, standard deviations, and sample sizes for both groups.

Group 1:

Mean (x1) = (267 + 245 + 263 + 316 + 246 + 282 + 379 + 300 + 291 + 306 + 425 + 190 + 346 + 150 + 344) / 15 = 290.2

Standard deviation (s1) = 70.764

Sample size (n1) = 15

Group 2:

Mean (x2) = (470 + 222 + 443 + 506 + 455 + 518 + 360 + 408 + 375 + 246 + 189 + 368) / 12 = 377.5

Standard deviation (s2) = 109.057

Sample size (n2) = 12

Step 5: Conduct the statistical test:

We can now perform an independent samples t-test using the sample statistics.

Step 5a: Test for equal variances:

Before conducting the t-test, we need to check if the variances of the two groups are equal. We can use a F-test to compare the variances.

Null hypothesis (H₀): The variances of the two groups are equal.

Alternative hypothesis (Hₐ): The variances of the two groups are not equal.

Using a significance level of 0.02 (98% confidence), we can calculate the F-statistic and compare it to the critical F-value from the F-distribution table.

F = s1² / s2² = 70.764² / 109.057² = 0.428 (approximately)

The critical F-value for a 98% confidence level with (n1-1) = 14 and (n2-1) = 11 degrees of freedom is 3.72.

Since our calculated F-value is smaller than the critical F-value, we fail to reject the null hypothesis. Thus, we can assume equal variances.

Step 5b: Conduct the t-test:

Since the variances are assumed to be equal, we can perform the independent samples t-test using the sample means and pooled standard deviation.

Pooled standard deviation (sp) = √(((n1 - 1) × s1² + (n2 - 1) × s2²) / (n1 + n2 - 2)) = √(((15 - 1) × 70.764² + (12 - 1) × 109.057²) / (15 + 12 - 2)) = 90.362

t = (x1 - x2) / (sp × √(1/n1 + 1/n2)) = (290.2 - 377.5) / (90.362 × √(1/15 + 1/12)) = -2.227

Degrees of freedom (df) = n1 + n2 - 2 = 15 + 12 - 2 = 25

Using the t-distribution table or a statistical software, we can find the critical t-value for a two-tailed test at a significance level of 0.05 with 25 degrees of freedom. The critical t-value is approximately ±2.060.

Since our calculated t-value (-2.227) is smaller than the critical t-value (-2.060), we reject the null hypothesis and accept the alternative hypothesis. Therefore, there is evidence to support the claim that mindfulness meditation helps reduce stress levels, with a 95% confidence level.

In conclusion, the results of the study suggest that the 4-day meditation program had a significant effect in reducing the stress levels of the medical students compared to the group that did not participate in the meditation program.

Learn more about Statistics click;

https://brainly.com/question/31538429

#SPJ4

Assume a businessman has 7 suits and 8 ties. He is planning to take 4 suits and 3 ties with him on his next business trip. Possibilities of selection he have 1960.

A businessman has 7 suits

A businessman has 8 ties.

He is planning to take 4 suits and 3 ties with him on his next business trip.

We have to determining possibilities of selection he have.

Number of possible selections = \(^{7}C_{4}\times ^{8}C_{3}\)

Simplify

Number of possible selections = \(\frac{7!}{4!(7-4)!}\times\frac{8!}{3!(8-3)!}\)

Number of possible selections = \(\frac{7!}{4!3!}\times\frac{8!}{3!5!}\)

Number of possible selections = \(\frac{7\times6\times5\times4!}{4!\times3\times2\times1}\times\frac{8\times7\times6\times5!}{3\times2\times1\times5!}\)

After simplification we get

Number of possible selections = 7 × 5 × 8 × 7

Number of possible selections = 1,960

To learn more about possibilities of selection link is here

brainly.com/question/13718660

#SPJ4

Answer:

first blank= 2

second blank= 3

Step-by-step explanation:

No, enough information is not given to prove that triangles are congruent using the SSS congruence theorem.

The SSS congruence theorem  expresses that assuming in two triangles, three sides of one are consistent to three sides of the other, then, at that point, the two triangles are said to be congruent.

Now, we are given that triangle ACB and triangle DEB that share a common vertex b. So, both triangles share a common side. So, one side is same for both of triangles.

From the diagram, we can see that both triangles opposite side are equal. So, second side is equal for both of triangles.

Now, from the diagram, we can see that both triangles vertically opposite angles are equal. So, we have two sides equal and one angle is equal.

So, given triangle is proved to congruent by SAS congruency not by SSS congruency.

Hence, enough information is not given.

To know more about congruency, visit here:

https://brainly.com/question/6108628

#SPJ4  

Answer:

B) 3:24

D) 5:40

E) 7:56

Step-by-step explanation:

3x8= 24

3:24= 1:8

5x8= 40

5:40= 1:8

7x8= 56

7:56= 1:8

Answer:

60/8 = 7.5 mins per mile

Step-by-step explanation:

Approximate normal distribution in  the 97.8% confidence interval is given by (15.23;15.77)

Approximate normal distribution can be calculated as follows:

First we should compute the mean and standard deviation of the given data.

Using Excel,

=AVERAGE(number1, number2,....)

The mean is found to be \(\frac{}{X}\) = 15.5

and,

=STDEV(number1, number2,....)

The standard deviation is found to be \(s = 0.31\)

the confidence interval for mean amount juice in all bottle is given by

\(t_{\alpha/2\frac{s}{\sqrt[]{n}}\)

in order to calculate \(t_{\alpha/2}\) we need to find the deggre of freedom first

\(df = n -1 = 8-1 =7\)

the t-score corresponding to 97.8% confidence level so the value of \(\alpha =\) 0.022 and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.022,7)".And we see that  \(t_{\alpha/2} = 2.452\)

So the required 97.5% confidence interval is

CI = \(\frac{}{x}\) ±\(t_{\alpha/2\frac{s}{\sqrt[]{n}}\)

CI = \(15.5\) ±\(2.452\frac{0.31}{\sqrt[]{8}}\)

CI =  \(15.5\) ±2.453·0.1096

CI = 15.5 ± 0.2688

CI = 15.5 -  0.2688 , 15.5 +  0.2688

CI = ( 15.23, 15.77)

Therefore, we are 97.5% confident that the normal distribution of juice in all such bottles is within the range of 15.23 to 15.77 ounces.

Learn more on normal distribution here :  https://brainly.com/question/9561532

#SPJ4

We will solve as follows:

*525 is the 75% of:

So, 525 is 75% of 700.

*The percent equation is:

*The value of x is: