The histogram displays the ages of 50 randomly selected users of an online music service. Based on the data, is advertising on the service more likely to reach people who are younger than 30 or people who are 30 and older?

For the following  equation, L.H.S = R.H.S is proved by solving the left-hand side and equating with it with the right-hand side equation :

[tex]\frac{tan x}{1-cot x} + \frac{cot x }{1-tan x} = 1+ tan x+ cot x[/tex]

L.H.S =  [tex]\frac{tan x}{1- cot x} + \frac{cot x }{1 - tan x}[/tex]

[tex]\frac{- tan^{2}x }{1- tan x} + \frac{cot x }{1 - tan x}[/tex]

[tex]\frac{-tan^{2} x + cot x}{1 - tan x}[/tex]

Multiply [tex]\frac{tan x}{tan x}[/tex] we get,

[tex]\frac{1- tan^{3} x}{tan x (1- tan x)}[/tex]

[tex]\frac{(1 - tan x ) (1 + tan x + tan ^{2}x) }{tan x (1 - tan x )}[/tex]

[tex]\frac{( 1- tan x + tan^{2}x) }{tan x}[/tex]

Divide each term separately,

[tex]\frac{1}{tan x} + \frac{tan x}{tan x} + \frac{tan^{2}x }{tan x}[/tex]

cot x + 1 + tan x

therefore, 1+ tan x + cot x = R.H.S

L.H.S = R.H.S, hence the theory is proved.

To know more about Trigonometry: https://brainly.com/question/29478746

If the French club is sponsoring a bake sale to raise at least $395. The number of  pastries they must they sell at $2.35 each in order to reach their goal  is: D. at least 168.

Set up an equation:

Total amount raised =Number of pastries x Price per pastry

Let x represent the number of pastries:

x × $2.35 = $395

To solve for x we need to isolate it on one side of the equation

x = $395 / $2.35

x = 168

Based on the above calculation the French club must sell at least 168 pastries to raise at least $395.

Therefore the correct option is D.

Learn more about  number of pastries here:https://brainly.com/question/27785191

#SPJ1

The statements that are true about the triangle are

a) m∠5 + m∠6 = 180°

b) ∠ 2+ ∠ 3 = ∠ 6

c) m∠2 + m∠3 + m∠5 = 180°

Given data ,

Let the triangle be represented as ΔABC

Now , An exterior angle of a triangle is equal to the sum of the opposite interior angles.

For Exterior ∠ 1 we have

∠ 1 = ∠ 5 + ∠ 3 ( Exterior angle Property of Triangle )

Similarly,

For Exterior ∠ 4 we have

∠ 4 = ∠ 5 + ∠ 2 ( Exterior angle Property of Triangle )

Similarly,

For Exterior ∠ 6 we have

∠ 6 = ∠ 2 + ∠ 3 ( Exterior angle Property of Triangle )

From the triangle sum property , we get

Ina triangle sum of the measures of angles is equal to 180°

m∠2 + m∠3 + m∠5 = 180°

Hence , the triangle is solved

To learn more about triangles click :

https://brainly.com/question/16739377

#SPJ1

The complete question is attached below :

A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options.
m∠5 + m∠3 = m∠4
m∠3 + m∠4 + m∠5 = 180°
m∠5 + m∠6 =180°
m∠2 + m∠3 = m∠6
m∠2 + m∠3 + m∠5 = 180°

Answer:

9(6+11)=(9/6)*(9/11)

Step-by-step explanation:

The left side of the equation can be simplified as follows:

9(6+11) = 9(17) = 153

On the right side, we use the fact that the product of two fractions is the product of their numerators over the product of their denominators. So:

(9/6)[6/(9/11)] = (9/6) * (611/9) = 11

Therefore, the equation becomes:

153 = 11

which is not true for any value of the missing numbers in the equation. So there is no solution for the missing numbers.

you have a good day too and you're welcome!

For problem 1, the solution is an = n.

For problem 2, the solution is an = 3n - 1.

For problem 3 (the hard problem), we can solve for the values of a, b, and c in the quadratic equation: [tex]an^2 + bn + c = 0[/tex], where a = 5, b = 6n - 1, and c = -2.

Using the quadratic formula, we get:

[tex]n= \frac{-b±\sqrt{b^{2}-4ac }  }{2a}[/tex]

Substituting the values of a, b, and c, we get:

[tex]n= \frac{-(6n-1)±\sqrt{(6n-1)^{2}-4(5)(-2) }  }{2(5)}[/tex]

Simplifying, we get:

[tex]n = \frac{(-6n+1 ± \sqrt{36n^{2}-48n+49 } ) }{10}[/tex]

Therefore, the solution for problem 3 is:

[tex]an= 5n^{2} + \frac{-6n+1 + \sqrt{36n^{2}-48n+49 } }{10}[/tex]

or

[tex]an= 5n^{2} + \frac{-6n+1 - \sqrt{36n^{2}-48n+49 } }{10}[/tex]

To know more about "Quadratic formula" refer here:

https://brainly.com/question/2615966#

#SPJ11

Answer: (1, 5)

Step-by-step explanation:

Hope this helps! :)

The distance from the ceiling to the reflection of the light bulb in the mirror is 6ft.

The tangent of the angle of incidence is equal to the tangent of the angle of reflection.

We have,

To find the distance from the ceiling to the reflection of the light bulb in the mirror we can use similar triangles.

Let's call the distance we're trying to find x.

First, we can find the length of the hypotenuse of the triangle formed by the light bulb, the mirror, and the ceiling.

This is equal to the distance from the light bulb to the mirror plus the distance from the mirror to the ceiling, which is:

= 4ft + 8ft

= 12ft.

Next, we can set up the following proportion:

2ft / x = 4ft / 12ft

Cross-multiplying, we get:

4ft x (x) = 2ft x 12ft

Simplifying, we get:

x = 6ft

So,

The distance from the ceiling to the reflection of the light bulb in the mirror is 6ft.

Now,

To prove that the tangent of the angle of incidence is equal to the tangent of the angle of reflection, we can use the law of reflection, which states that the angle of incidence is equal to the angle of reflection. Let's call these angles θ.

We can draw a diagram to represent the situation, with a ray of light hitting a mirror at an angle of incidence:

         |\

         | \

  d      |  \

--------->|   \

         |θ_i \

         |____\

Here, d is the distance from the light source to the mirror, and θi is the angle of incidence.

Using trigonometry, we can express the tangent of θi as:

tan(θi) = opposite / adjacent

In this case, the opposite side is the vertical distance from the light source to the mirror, which is "h" in the diagram.

The adjacent side is the distance from the mirror to the point where the ray of light reflects off the mirror, which is also d.

tan(θ_i) = h / d

After the light reflects off the mirror, it travels at the same angle as the angle of reflection, θr:

         |\

         | \

  d      |  \

--------->|   \

         |θ_i \

         |____\

           \ θ_r

            \

             \

Using the law of reflection, we know that θi = θr.

So we can write:

tan(θr) = opposite / adjacent

The opposite side is now the vertical distance from the mirror to the point where the ray of light reflects off the mirror, which is also h.

The adjacent side is still d since the distance from the mirror to the point where the ray of light reflects off the mirror is the same as the distance from the light source to the mirror.

So, we have:

tan(θr) = h / d

Since θi = θr, we can substitute tan(θi) for tan(θr) in the equation above:

tan(θi) = h / d = tan(θr)

This means,

The tangent of the angle of incidence is equal to the tangent of the angle of reflection.

Thus,

The distance from the ceiling to the reflection of the light bulb in the mirror is 6ft.

The tangent of the angle of incidence is equal to the tangent of the angle of reflection.

Learn more about reflection of light here:

https://brainly.com/question/2254222

#SPJ1

The area of the pizza box measuring 2/3 feet wide by 4/5 feet long is 8/15 square feet.

The shape of the pizza box is a rectangle. The rectangle is a quadrilateral with opposite sides parallel and equal with an equal angle and of 90°.

The area of a rectangle is considered as:

A = L * B

where L is the length

B is the breadth

Given in the question,

L = 4/5 feet

B = 2/3 feet

The area is calculated by multiplying the fractions. For the multiplication of fractions, we multiply the numerators and denominators separately. And final answer is calculated by simplifying the resulting fraction.

A = 4/5 * 2/3

= 4*2 / 5*3

= 8/15 square feet

Thus, the pizza box has an area of 8/15 square feet

Learn more about the Area:

https://brainly.com/question/24487155

#SPJ4

The value of tan C in the figure is 7/24

Information from the question

The value of tan x is worked using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The figure describes a right angle triangle of

hypotenuse = 50

opposite = ?

adjacent = 14

Using cos, CAH for angle C

sin C = Opposite / hypotenuse

sin C = 14 / 50

x = arc sin (14/50)

Solving for tan x

tan (arc sin (14/50)) = 7/24

Learn more about SOH CAH TOA here:

https://brainly.com/question/29402966

#SPJ1

The trapezoid has only one line of reflectional symmetry.

When we divide the image, the mirror image of one side of the image to the other is known as reflectional symmetry. We can say that one half of the image is the reflection of the other half. Reflection symmetry is also known as mirror symmetry.

In an isosceles trapezoid, the length of the sides is the same which means that the left and the right sides are equal. But, the bases of an isosceles trapezoid are not the same. When a vertical line is drawn in the middle of the isosceles trapezoid, the left side of the image becomes the reflection of the right side. So there is only one line of reflection symmetry.

Therefore, there is only one line of reflectional symmetry in this figure of an isosceles trapezoid.

To learn more about reflectional symmetry;

https://brainly.com/question/2036345

#SPJ4

The complete question is "The figure is an isosceles trapezoid. How many lines of reflectional symmetry does the trapezoid have? The image is given below"

The angles 75° and ∠2 are alternate interior angles.

Option D is the correct answer.

We have,

From the figure,

55°, ∠3, and 75° forms a straight angle.

Alternate angles are pairs of angles formed when a transversal line intersects two parallel lines.

Alternate angles are equal in measure, which means they have the same angle degree value.

So,

75° and ∠2 are alternate angles.

Thus,

75° and ∠2 are alternate angles.

Learn more about angles here:

https://brainly.com/question/7116550

#SPJ1

Answer:

104-18=86 and also  18-104=-86

Step-by-step explanation:

We reject the null hypothesis and conclude that there is strong evidence to support the claim that the mean composite satisfaction rating for the XYZ-Box exceeds 42.

The null and alternative hypotheses are:

H_0: mu <= 42

H_a: mu > 42

Using the sample mean, sample size, and population standard deviation given, we can calculate the test statistic:

z = (x - mu) / (sigma / sqrt(n))

z = (42.85 - 42) / (2.65 / sqrt(68))

z = 2.56

Using a standard normal distribution table or calculator, we can find the critical values for each significance level:

a = 0.10: z_crit = 1.28

a = 0.05: z_crit = 1.645

a = 0.01: z_crit = 2.33

a = 0.001: z_crit = 3.09

Since our test statistic is greater than the critical value at a = 0.10 and a = 0.05, we reject the null hypothesis at these levels. However, we fail to reject the null hypothesis at a = 0.01 and a = 0.001.

To calculate the p-value, we can use a standard normal distribution table or calculator to find the probability that a z-score is greater than or equal to our test statistic:

p-value = P(Z >= 2.56)

p-value = 0.0052

Since the p-value is less than all of the given significance levels, we reject the null hypothesis and conclude that there is strong evidence to support the claim that the mean composite satisfaction rating for the XYZ-Box exceeds 42.

To learn more about hypothesis visit:

https://brainly.com/question/31319397

#SPJ11

Answer:

x+15 dollars

Step-by-step explanation:

x could be any number, but if you add 15 to x, it would be x+15. Since you don't know what x is, you can't do anything else.

The value of j is equal to -9.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the slope of a line, we have the following;

10 = (-5 - 5)/(-10 - j)

10(-10 - j) = -10

(-10 - j) = -1

j = -10 + 1

j = -9

Read more on slope here: brainly.com/question/3493733

#SPJ1

Complete Question:

A line with a slope of 10 passes through the points (j, 5) and (-10,-5). What is the value of j?

We used the chain rule and derivative of an inverse tangent function to find [tex]\frac{dy}{dx} &= \frac{d}{dx} \left[\tan^{-1}\left(\frac{2x}{1+x^2}\right)\right][/tex] and got [tex]$\frac{dy}{dx} = 2\left(\frac{1}{1+4x^2}\right)\left(\frac{1}{1+x^2}\right)$[/tex].

To find [tex]\frac{dy}{dx}[/tex] for [tex]$y = \tan^{-1}\left(\frac{2x}{1+x^2}\right)$[/tex], we can use the chain rule and the derivative of the inverse tangent function:

[tex]$\frac{dy}{dx} = \frac{d}{dx}\left[\tan^{-1}\left(\frac{2x}{1+x^2}\right)\right]$[/tex]

[tex]$= \frac{1}{\left(\frac{2x}{1+x^2}\right)^2+1} \cdot \frac{d}{dx}\left[\frac{2x}{1+x^2}\right] \quad $[/tex] [chain rule]

[tex]$= \frac{1}{\left(\frac{2x}{1+x^2}\right)^2+1} \cdot \frac{(1+x^2)\cdot2 - 2x\cdot2x}{(1+x^2)^2} \quad[/tex] [quotient rule]

[tex]$= \frac{2}{1+4x^2} \cdot \frac{1}{1+x^2}$[/tex]

Therefore, [tex]\frac{dy}{dx} = \frac{2}{1+4x^2} \cdot \frac{1}{1+x^2}$[/tex].

(a) To find [tex]\frac{dy}{dx} = (e^x\sqrt{2x})^4$[/tex], we can use the chain rule and the power rule:

[tex]\frac{dy}{dx} = \frac{d}{dx}\left[(e^x\sqrt{2x})^4\right][/tex]

[tex]= 4(e^x\sqrt{2x})^3 \frac{d}{dx}[e^x\sqrt{2x}][/tex]

[tex]= 4(e^x\sqrt{2x})^3 \left(e^x\frac{1}{2}(2x)^{-1/2} + e^x\sqrt{2x}\frac{1}{2}(2x)^{-3/2}\right) \quad[/tex] [chain rule]

[tex]= 2(e^x\sqrt{2x})^2\frac{1+\sqrt{2x}}{x}[/tex]

Therefore, dy/dx = [tex]= 2(e^x\sqrt{2x})^2\frac{1+\sqrt{2x}}{x}[/tex]

(b) To find [tex]\frac{dy}{dx} \quad[/tex] for [tex]\quad e^{xy} + \ln(xy) = 0[/tex] we can use implicit differentiation:

[tex]\quad e^{xy} + \ln(xy) = 0[/tex]

Taking the derivative of both sides with respect to x, we get:

[tex](e^{xy})(y + x\frac{dy}{dx}) + \frac{1}{xy}(xy' + y) = 0[/tex]

Simplifying and solving for [tex]\frac{dy}{dx}[/tex], we get:

[tex]\frac{dy}{dx} = \frac{-e^{xy} - \frac{y}{x^2y+1}}{xe^{xy}}[/tex]

Therefore, [tex]\frac{dy}{dx} = \frac{-e^{xy} - \frac{y}{x^2y+1}}{xe^{xy}}[/tex].

To find the indefinite integral of [tex]e^x sin2x[/tex], we can use integration by parts:

Let u = sin2x and [tex]\frac{dv}{dx} = e^x[/tex]. Then du/dx = 2cos2x and v = e^x.

Using the formula for integration by parts, we get:

[tex]\int e^x \sin 2x \ dx = e^x \sin 2x - \int 2e^x \cos 2x \ dx[/tex]

We can now integrate by parts again, letting u = cos2x and dv/dx = e^x. Then du/dx = -2sin2x and v = e^x.

Using the formula again, we get:

[tex]\int e^x \sin 2x \ dx = e^x \sin 2x - 2e^x \cos 2x + 4\int e^x \sin 2x \ dx[/tex]

Rearranging terms and dividing by 5, we get:

[tex]\int e^x \sin 2x \ dx = \frac{e^x}{5} (\sin 2x - 2\cos 2x) + C[/tex]

Therefore, the indefinite integral of e^x sin2x is [tex]\frac{e^x}{5} (\sin 2x - 2\cos 2x) + C[/tex]

To learn more about chain rule

https://brainly.com/question/28972262

#SPJ4

The answer is not one of the choices provided.

The distribution of sample means follows a normal distribution with a mean equal to the population mean (11) and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

So, for a sample size of 35, the distribution of sample means is normal with a mean of 11 and a standard deviation of 4.7/sqrt(35) = 0.795.

We need to find the probability that the mean blood pressure of the 35 people will be less than 122. We can standardize the distribution of sample means to a standard normal distribution with mean 0 and standard deviation 1 using the z-score formula:

z = (x - mu) / (sigma / sqrt(n))

where x is the sample mean, mu is the population mean, sigma is the population standard deviation, and n is the sample size.

Substituting the given values, we get:

z = (122 - 11) / (4.7 / sqrt(35)) = 37.98

We can then use a standard normal distribution table or calculator to find the probability of z being less than 37.98. Since the standard normal distribution is symmetric, we can also find this probability as 1 minus the probability of z being greater than 37.98.

Using a standard normal distribution table or calculator, we get:

P(z < 37.98) = 1 (to a very high degree of precision)

Therefore, the probability that the mean blood pressure of 35 people will be less than 122 is essentially 1, or 100%. The answer is not one of the choices provided.

To learn more about standardize visit:

https://brainly.com/question/30054101

#SPJ11

Answer:

Step-by-step explanation:

Solve for x.

4x - 9 = 2x + 5

4x - 2x = 5 + 9

2x = 14

x = 14 : 2

x = 7

-----------------

check   (replace "x" with "7")

4 * 7 - 9 = 2 * 7 + 5                  (remember PEMDAS)

28 - 9 = 14 + 5

19 = 19

the answer is good

Answer:

hence the required value of x is 7.

The x-coordinate of the point that the line passes through is x = 0.

We can use the point-slope form of a linear equation to solve this problem.

The slope of the line can be found using the two given points:

slope  (change in y) / (change in x)

slope = (-3 - (-9)) / (12 - x)

slope = 6 / (x - 12)

Now we can use the point-slope form of the linear equation, with the y-intercept of 6:

y - 6 = slope * (x - 0)

Substituting the slope we just found:

y - 6 = (6 / (x - 12)) * x

Simplifying:

y - 6 = 6x / (x - 12)

Multiplying both sides by (x - 12):

y(x - 12) - 6(x - 12) = 6x

Distributing:

xy - 12y - 6x + 72 = 6x

Moving the x terms to one side:

xy - 12y - 12x + 72 = 0

Now we can substitute the y-coordinate of the other given point, (-9), and solve for x:

x(-9) - 12(6) - 12x + 72 = 0

Simplifying:

-9x - 72 - 12x + 72 = 0

-21x = 0

x = 0

Therefore, the x-coordinate of the point that the line passes through is x = 0.

To learn more about line passes  visit: https://brainly.com/question/18434275

#SPJ11

The value of x in the parallelogram is 1/3.

PQRT is a parallelogram

PT = 8x, TR = 6y, QT = 2x + 2, TS = 2y

We have to find the value of x

In a parallelogram the opposite sides are equal

8x=2x+2

Subtract 2x from both sides

6x=2

Divide both sides by 6

x=2/6

x=1/3

Hence, the value of x in the parallelogram is 1/3.

To learn more on Parallelogram click:

https://brainly.com/question/29147156

#SPJ1

The surface area of the given cylinder is 200.96 square centimeters.

Given that the radius of the cylinder is 4 cm and the height of the cylinder is also 4 cm,

The surface area of the cylinder can be found using the formula:

SA = 2πr² + 2πrh, where r is the radius of the circular base and h is the height of the cylinder.

Substitute given values into the formula to get:

SA = 2π(4)² + 2π(4)(4)

= 2π(16) + 2π(16)

= 32π + 32π

= 64π

= 64(3.14)

= 200.96

Therefore, the surface area of the cylinder is 200.96 square centimeters.

Learn more about the surface area of the cylinder here:

https://brainly.com/question/27983648

#SPJ1

The complete question is as follows

What is the surface area of the cylinder?

Here, the radius of the cylinder is 4 cm and the height of the cylinder is 4 cm

Apply the formula SA = 2πr² + 2πrh.

It is proved that if g is not cyclic, all elements of g have order 1, 2, or 3, and there must be an element of order 3.

To prove that if g is not cyclic, all elements of g have order 1, 2, or 3, and show that there must be an element of order 3, follow these steps,

1. Assume that g is a finite group and is not cyclic.
2. Recall that the order of an element a in group g is the smallest positive integer n such that a^n = e, where e is the identity element in g.
3. If g were cyclic, it would have an element a with order equal to the order of the group itself (|g|). However, we are given that g is not cyclic, so the order of any element in g must be less than |g|.
4. We now consider the possibilities for the order of elements in g. If all elements of g have order 1, then g is the trivial group, which is cyclic, contradicting our assumption.
5. If there is an element of order 2, there must be an element of order 3 as well. This is because, according to Cauchy's theorem, if a prime number p divides the order of a finite group g, then g has an element of order p. Since we have assumed that g is not cyclic, |g| must be divisible by at least two prime numbers. The smallest possible case is when |g| is divisible by the primes 2 and 3.
6. By Cauchy's theorem, since 2 and 3 both divide |g|, there must be elements in g of order 2 and order 3.
7. Therefore, if g is not cyclic, all elements of g have order 1, 2, or 3, and there must be an element of order 3.

Learn more about "order": https://brainly.com/question/1094377

#SPJ11

1/5

you take 1/4÷ 1 1/4 and you get 1/5

The perimeter of the square based on the dimensions of the diagonal is 145.27 millimeters.

We will begin with calculating the side of square from the diagonal of square. It will form right angled triangle and hence the formula will be represented as -

diagonal² = 2× side²

Keep the value of diagonal

(37✓2)² = 2× side²

Side² = 2638/2

Side² = 1319

Side = ✓1319

Side = 36.32 millimetres

Perimeter of the square = 4 × side

Perimeter = 145.27 millimeters

Thus, the perimeter of the square is 145.27 millimeters.

Learn more about square -

https://brainly.com/question/479529

#SPJ4

The graph is  both graph A and graph B, because both curves are above the horizontal axis, and their areas are positive

Density curves are visuals that demonstrate the probability distribution of a data set.

It is a liquid, uninterrupted line that illustrates the variability of a constant haphazard element - with the entire locality below the curve accounting for 1.

In other words, the region underneath the curve denotes the likelihood of registering a precise or scope of values inside the depth of the grouping.

Read more on density curve here:https://brainly.com/question/26559908

#SPJ1

The statements that is correct is: C. Both functions are decreasing and have different rates of change.

A function is said to be decreasing if the value of y decreases for every value of x that increases.

In the first function given, as x values increased from 3 to 4, the y value decreases from 3 to 0. So it is a decreasing function.

Rate of change = 3 - 0 / 3 - 4

= 3/-1

= -3.

In the second function, as x values increases from -4 to 0, the y value decreases from 0 to -1. It is also a decreasing function.

Rate of change = change in y / change in x = 0 - (-1) / -4 - 0

= 1/-4

= -1/4.

Therefore, they both have the same rate of change.

Learn more about decreasing function on:

https://brainly.com/question/29745804

#SPJ1

The net force on a vehicle is directly proportional to its acceleration and mass, according to Newton's Second Law of Motion. Therefore, we can use the equation F = ma, where F is the net force, m is the mass of the vehicle, and a is the acceleration.

We know that the net force on the vehicle is 1800 and its acceleration is 1.5. Substituting these values into the equation, we get:
1800 = m × 1.5

To solve for m, we need to isolate it on one side of the equation. Dividing both sides by 1.5, we get:

m = 1800 ÷ 1.5

m = 1200

Therefore, the mass of the vehicle is 1200 kilograms to the nearest kilogram

Net force = mass × acceleration

In this case, the net force on the vehicle is 1800 N (Newtons), and it is accelerating at a rate of 1.5 m/s² (meters per second squared). We can rearrange the formula to solve for mass:

Mass = net force ÷ acceleration

Now, plug in the given values:

Mass = 1800 N ÷ 1.5 m/s²

Mass ≈ 1200 kg

To the nearest kilogram, the mass of the vehicle is approximately 1200 kg.

Learn more about mass at : brainly.com/question/15959704

#SPJ11

A. The 95% confidence interval is 0.291 < p < 0.435. B. The 80% confidence interval is (0.303, 0.397). C. A 99% confidence interval is 0.613 < p < 0.703.

A. Using the formula:

CI = p ± zsqrt(p(1-p)/n)

where p is the sample proportion, n is the sample size, and z is the critical value from the standard normal distribution. For a 95% confidence level, z is 1.96.

Putting the values:

CI = 131/396 ± 1.96sqrt((131/396)(265/396)/396)

Simplifying:

CI = 0.291 < p < 0.435

Therefore, the 95% confidence interval for the population proportion p is 0.291 to 0.435.

B. For an 80% confidence level, z is 1.282.

Putting the values:

CI = 0.35 ± 1.282sqrt((0.35)(0.65)/367)

Simplifying:

CI = (0.303, 0.397)

Therefore, the 80% confidence interval for the population proportion p is (0.303, 0.397).

C. For a 99% confidence level, z is 2.576.

Putting the values:

CI = 384/600 ± 2.576sqrt((384/600)(216/600)/600)

Simplifying:

CI = 0.613 < p < 0.703

Therefore, the 99% confidence interval for the population proportion p is 0.613 to 0.703. Writing it in tri-inequality form, we get:

0.613 < p < 0.703

Know more about confidence interval here:

https://brainly.com/question/20309162

#SPJ11

The ONB for the given plane in R3 is ū = [-5/√(26), 1/√(26), 0] and ī = [25/(√(26/13)), -5/(√(26/13)), 0].

To find an orthonormal basis for the plane x + 5y + 4z = 0, we first solve the system and get the parametric solution

x = -5t - 4s

y = t

z = s

Assigning parameters s and t to the free variables and writing the solution in vector form as su + tv, we get

[-5t - 4s, t, s] = t[-5, 1, 0] + s[-4, 0, 1]

Taking u = [-5, 1, 0] and v = [-4, 0, 1], we normalize u to have norm 1 by dividing it by its length

||u|| = √(26)

ū = [-5/√(26), 1/√(26), 0]

To find the component of v orthogonal to u, we take the dot product of v and u, and divide it by the dot product of u and u, and then multiply u by this scalar

v - ((v · u) / (u · u))u

v · u = -5

u · u = 26

v - (-5/26)[-5, 1, 0]

v - [25/26, -5/26, 0]

Finally, we normalize this vector to have norm 1

||v - proj_u v|| = √(26/13)

ī = [25/(2√(26/13)), -5/(2√(26/13)), 0]

Therefore, the orthonormal basis for the plane x + 5y + 4z = 0 is ū = [-5/√(26), 1/√(26), 0] and ī = [25/(√(26/13)), -5/(√(26/13)), 0].

To know more about orthonormal basis:

https://brainly.com/question/30882267

#SPJ4

The probability of a standard normal variable being less than -2.65 is 0.0040. Therefore, P(x < 979) = 0.0040.

To solve this problem, we use the central limit theorem since we have a large enough sample size.

a) Probability that a single randomly selected value is less than 979 dollars

To find the probability that a single randomly selected value is less than 979 dollars, we standardize the value and use the standard normal distribution:

z = (979 - 1046) / 206 = -0.3233

Using a standard normal distribution table or calculator, we find that the probability of a standard normal variable being less than -0.3233 is 0.3736. Therefore, P(X < 979) = 0.3736.

b) Probability that a sample of size n = 66 is randomly selected with a mean less than 979 dollars

To find the probability that a sample of size n = 66 is randomly selected with a mean less than 979 dollars, we use the central limit theorem.

The mean of the sampling distribution of the sample means is the same as the population mean, which is 1046 dollars. The standard deviation of the sampling distribution of the sample means is the standard error, which is:

SE = σ / sqrt(n) = 206 / sqrt(66) = 25.23

To standardize the sample mean, we use the formula:

z = (x - μ) / SE = (979 - 1046) / 25.23 = -2.65

Using a standard normal distribution table or calculator, we find that the probability of a standard normal variable being less than -2.65 is 0.0040. Therefore, P(x < 979) = 0.0040.

To learn more about probability visit:

https://brainly.com/question/15124899

#SPJ11