a publisher reports that 76v% of their readers own a particular make of car. a marketing executive wants to test the claim that the percentage is actually different from the reported percentage. a random sample of 200200 found that 71q% of the readers owned a particular make of car. is there sufficient evidence at the 0.010.01 level to support the executive's claim? step 2 of 7 : find the value of the test statistic. round your answer to two decimal places.

The perimeter of the quadrilateral is 46 units, so the correct option is d.

The perimeter is equal to the sum of the lengths of all the sides of the quadrilateral.

Remember that the length of a segment whose endpoints are (x₁, y₁) and (x₂, y₂) is:

L = √( (x₁ - x₂)^2 + (y₁ - y₂)^2)

The length between the first two vertices: (−6, −2), (0, −10)

L₁ = √( (-6 - 0)^2 + (-2 + 10)^2) = 10

The length between the second two vertices:  (0, −10), (5, 2)

L₂ = √( (0 - 5)^2 + (-10 - 2)^2) = 13

The length between the third two vertices:  (5, 2), (−1, 10)

L₃ = √( (5 + 1)^2 + (2 - 10)^2) = 10

The length between the fourth two vertices:  (−1, 10), (−6, −2)

L₄ = √( (-1 + 6)^2 + (10 + 2)^2) = 13

Then the perimeter is:

P = 10 + 13 + 10 + 13 = 46

The correct option is D.

Learn more about perimeter.

https://brainly.com/question/24571594

#SPJ1

The trigonometric expression cos 3x / (sin x · cos x) is equivalent by trigonometric formulas to the trigonometric expression csc x · cos 2x - sec x · sin 2x. (Correct choice: A)

In this problem we find the definition of a trigonometric expression, whose equivalent expression must be found by using algebra properties and trigonometric formulas. First, write the trigonometric function:

cos 3x / (sin x · cos x)

Second, use trigonometric formulas:

cos (x + 2x) / (sin x · cos x)

(cos x · cos 2x - sin x · sin 2x) / (sin x · cos x)

cos 2x / sin x - sin 2x / cos x

csc x · cos 2x - sec x · sin 2x

The equivalent trigonometric expression is csc x · cos 2x - sec x · sin 2x.

To learn more on trigonometric equations: https://brainly.com/question/22624805

#SPJ1

Answer:

y^2

Step-by-step explanation:

a^m/a^n = a^(m - n)

y^5/y^3 = y^2

Solution to the inequality on the number line is y < 4 and y > −4.

What is inequality?

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance.

When resolving an inequality, you can do one of the following:

• Add the same amount to each side;

• Subtract the same amount from each side;

• Multiply or divide each side by the same positive amount.

You must flip the inequality symbol if you multiply or divide each side by a negative number.

Let's solve your inequality step-by-step.

|y| < 4

Solve Absolute Value.

|y| < 4

We know y < 4 and y > −4

y < 4  (Condition 1)

y > −4  (Condition 2)

Learn more about Inequalities click here:

https://brainly.com/question/24372553

#SPJ1

The probability that exactly one of the next four calls results in a reservation being made is 40.75%

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Here, we have

A random call to their reservation phone line results in a reservation being made is 0.31

Now, we find

Exactly one call gets resevervation = 4 * (1-0.31)3(0.31)

= 0.4075 = 40.75%

Now we can simulate an experiment by using random numbers from 0 to 100,000 as probability values between 0 and 31,000 are p to reservation otherwise they don't.

Hence, the probability that exactly one of the next four calls results in a reservation being made is 40.75%

To learn more about the probability from the given link

https://brainly.com/question/24756209

#SPJ4

The number of runs up and runs down for the preceding data is 5.

Runs up refers to the number of observations that are higher than the number of observations before them.

Runs down refers to the number of observations that are lower than the number of observations before them.

As 2nd observation is higher than 1st observation, 4th observation is higher than 3rd observation and 6th observation is also higher than 5th observation so 2nd, 4th,6th observation should be included in runs up.

Therefore,

Runs up = 2nd + 4th + 6th observations

             = 3

As 3rd observation is lower than 2nd observation,5th observation is also lower than 4th observation so 3rd,5th observation should be included in the runs down

Therefore,

Runs down= 3rd +5th observations

                 =2

Therefore,

Runs up + Runs down  =3+2

                                        =5

To know more about Runs up and Runs down:

https://brainly.com/question/17569821

#SPJ4

The average angular velocity during the dive is 10.78 rad/sec.

Given,

displacement of the diver = 10.4m

as the diver falls freely then the acceleration will be g=9.8 [tex]m/s^2[/tex]

To find average angular velocity during dive use formula,

[tex]\omega=\frac{\theta}{t}[/tex]

where, θ=angular displacement and t= time taken to reach water

the diver makes 2.5 revolutions, here 1 revolution is 2π radians then total angular displacement is

θ=2.5* 2π=15.7 radian

To find time taken, use formula [tex]s=ut+\frac{1}{2}gt^2[/tex]

here u=initial velocity=0

s=displacement of diver=10.4m

[tex]10.4=0+\frac{1}{2}9.8t^2\\\\10.4=4.9t^2\\\\2.122=t^2\\\\t=1.456 s[/tex]

angular velocity, [tex]\omega=\frac{15.7}{1.456}=10.78\ rad/sec[/tex]

Thus, the average angular velocity during the dive is 10.78 rad/sec.

To learn more about angular velocity refer here

https://brainly.com/question/14769426

#SPJ4

The formula for the line passing through the intersection of (3, 2) and A B (5 , 6) equals y = 2x - 4

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line can be used to calculate the slope of any line.

The ratio of "vertical change" to "horizontal change" between two different points on a line is calculated using the slope of a line formula.

We will comprehend the slope-finding method and its applications in this article

According to our question-

Let A be the initial point ( 3 , 2 )

Let B be the second point ( 5 , 6 )

A ( x₁ , y₁ ) = A ( 3 , 2 ) ( 3 , 2 )

B ( x₂ , y₂ ) = B ( 5 , 6 ) ( 5 , 6 )

The slope of the line is now determined by,

Slope m is equal to (y2 - y1) / (x2 - x1)

By changing the values, we obtain

Slope m is equal to (6 - 2)/(5 - 3)

= 4 / 2

= 2

Slope of the line therefore equals 2.

The equation for the line is now y - y1 = m (x - x1).

By changing the values, we obtain

y - 2 = 2 ( x - 3 ) ( x - 3 )

y - 2 = 2x - 6

2 is added to both sides of the equation to get

y = 2x - 4

HENCE, The formula for the line passing through the intersection of (3, 2) and A B (5 , 6) equals y = 2x - 4.

learn more about slope click here:

brainly.com/question/3493733

#SPJ4

If this line cuts the curve y = x^3 – 2x^2 – 3x – 8 at x = 3, find the equation of the line would be 2x + y + 2 = 0

The slope of a line and a position upon that line can be used to generate the equation of a line. Let us learn more about the gradient of the line and the required point on the line in order to better grasp the formulation of a line equation. The slope of the line, which can be stated as a numeric integer, fraction, or the tangent of  angle it makes with the positive x-axis, is the line's inclination with respect to the positive x-axis. The poiny of coordinate with the x and y values is referred to as the point.

How to solve?

here it is provided that x = 3

substitute for x in y = x^3-2x^2-3x-8

y =(3)^3-2(3)^2-3(3)-8

y = - 8

Now all you have to do is plug y in each of the answers until you get 3 for x.

A. 2x - ( - 8) + 2 = 0

    2x + 10 = 0

    2x = - 10

     x = - 5

B. 2x + ( - 8 ) + 2 = 0

   2x - 6 = 0

   2x = 6

   x = 3

C. 2x + ( - 8 ) - 2 = 0

   2x - 10 = 0

   2 x = 10

    x = 5

To learn more about the equation of line, visit:

https://brainly.com/question/14576922

#SPJ4

The result of the following Boolean expression, if x equals 5, y equals 3, and z equals 8 not (x < y or z > x) and y < z will be false.

It is defined as the combination of constants and variables with mathematical operators.

Finally, keep in mind that two negatives add up to a positive. This would print that the compound expression is False because it contains one negative The first step, and one positive expression 2-4 as a whole.

Expression 1 is False because (x=5) (y=3)

The value must now be reversed according to the first step. the current value is true (-) False

Both sub-expressions 1 and 2) must be true for the AND= operator #3. The sub-expression 2 in (y=3) (z=8) is true.

Thus, the result of the following Boolean expression, if x equals 5, y equals 3, and z equals 8 not (x < y or z > x) and y < z will be false.

Learn more about the expression here:

brainly.com/question/14083225

#SPJ1

MAIN ANSWER: using strong induction that every positive integer can be written as sum of distinct powers of two is 20=2²+2⁴

supporting answer The statement is true for all positive integers by mathematical induction. Strong induction can be used to demonstrate that every positive integer n can be written as a sum of distinct powers of two, that is, as a sum of a subset of the

2²=4

2⁴=16

4+16=20

final answer is 20=2²+2⁴

to learn more about strong induction link

https://brainly.com/question/26144295

#SPJ4

Using strong induction that every positive integer can be written as sum of distinct powers of two is 20=2²+2⁴

What is positive integer?

Natural numbers are those in mathematics that are utilised for counting and ordering. Cardinal numbers are those used for counting, and ordinal numbers are those used for ordering.

The statement is true for all positive integers by mathematical induction. Strong induction can be used to demonstrate that every positive integer  can be written as a sum of distinct powers of two, that is, as a sum of a subset of the

2²=4

2⁴=16

4+16=20

Final answer is 20=2²+2⁴

To learn more about strong induction link

brainly.com/question/26144295

#SPJ4

The football field is longer than soccer field.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.

We have a soccer field that is 105 meters long and a football field is 120 yards long.

In one yard, we have -

1 yard = 0.9144 meters

Then, in 120 yards, we will have -

120 x 0.9144 = 109.728 meters

Now, 109.728 meters > 105 meters.

Therefore, the football field is longer than soccer field.

To solve more questions on dimensions and unit conversion, visit the link below -

brainly.com/question/4613077

#SPJ1

The value of the function g(f(2)) is 29 and 2.f(g(x)) is (x - 1)(2x - 2).

When the output of one function is given to the input of another function they are called composite functions.In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).

Given, f(x) = 4x² - 1. and g(x) = 2x - 1.

Now, g(f(2)) is the output of f(2) is the input of g(x).

∴ f(2) = 4(2)² - 1.

f(2) = 15.

Now, g(f(2)) = 2(15) - 1.

g(f(2)) = 29.

Also given,

f(x) = x² and g(x) = x - 1.

Now, 2.f(g(x)).

2.f(g(x)) = 2.f(x- 1).

2.f(g(x)) = 2(x - 1)².

2.f(g(x)) = 2(x² - 2x + 1).

2.f(g(x)) = 2x² - 4x + 2.

2.f(g(x)) = 2x² - 2x - 2x + 2.

2.f(g(x)) = 2x(x - 1) - 2(x - 1).

2.f(g(x)) = (x - 1)(2x - 2).

There is no restriction to the domain of this quadratic function.

learn more about domain and range here :

https://brainly.com/question/28135761

#SPJ1

Answer:

p=8

Step-by-step explanation:

[tex]2(p+1)=18\\\frac{2(p+1)}{2}=\frac{18}{2}\\p+1=9\\p+1-1=9-1\\p=8[/tex]

Answer:P=8

Step-by-step explanation:

I TOOK THE TEST

Answer: Yes

Step-by-step explanation:

y=4x+1
(2,9) 2 is x, 9 is y
9=4(2)+1
9=8+1
9=9

The expression that uses the greatest common factor and distributive property to write the given expression, 18 + 24, is 6(3 + 4)

From the question, we are to determine the expression that uses the greatest common factor and the distributive property to write the given expression.

The given expression is

18 + 24

First, we will determine the greatest common factor of 18 and 24

18 = 2 × 3 × 3

24 = 2 × 2 × 2 × 3

Thus,

The greatest common factor is 2 × 3 = 6

Now, we will write the expression using the greatest common factor and the distributive property

18 + 24

6(3 + 4)

Hence, the expression is 6(3 + 4)

Learn more on Writing an expression here: https://brainly.com/question/28401321

#SPJ1

Set I is the set of ordered pairs which is a function. Choose A.

A function is a relationship between inputs where each input is related to exactly one output.

Based on the definition of function as seen above. Let's check the set of ordered pairs:

Given:

I. { (3, 7), (-1, 9), (-5, 11)}

II. { (9, -5) , (4, -5) , (-1, 7)}

III. { (-2, 1) , (3, -4) , (-2, -6)}

In set I, each input (i.e. 3, -1 and -5 ) has different output (i.e. 7, 9 and 11 ). Thus, set I is a function

In set II, two inputs (9 and 4) have the same output (i.e. -5). Thus, set II is not a function

In set III, the same input (i.e. -2 ) has different outputs (i.e. 1 and -6). Thus, set III is not a function

Therefore, the set of ordered pairs which is a function is I. So option A. is the answer

Learn more about function on:

brainly.com/question/29352039

#SPJ1

The minimum monthly payment for Brian is $25.

The minimum payment is the smallest amount of money you must pay each month to maintain the status of your account. The statement balance is your total account balance for that billing cycle. The current balance is the sum of your most recent bill plus any charges.

From the information, the minimum monthly payment for Brian's credit card is 3.5% of his balance or $25

Since the balance was $722, the amount will be:

= 3.5% × $722

= 0.035 × $722

= $25.27

Since $25.27 is more than $25, the minimum monthly payment is $25.

Learn more about percentages on:

brainly.com/question/24877689

#SPJ1

Brody reads 8 books each month.

The slope of a line indicates the direction and the steepness of the line. The formula for the slope of a line passing through the points (x₁,y₁) and (x₂, y₂) is m = (y₂-y₁)/(x₂-x₁).

Give the graph of the line.

The graph of the line passes through points (0,15) and (5,55)

To find the number of books Brody read each month, find the slope of the line.

The slope of the line is:

m  = (55 - 15)/ (5 - 0)

m = 8

Hence, Brody reads 8 books each month.

To learn more about slopes, click here:

https://brainly.com/question/3605446

#SPJ1

Answer: $21.33

Step-by-step explanation: 50 - 28.67 = 21.33

[tex]tan(\alpha - \beta) = \cfrac{tan(\alpha)- tan(\beta)}{1+ tan(\alpha)tan(\beta)} \\\\[-0.35em] ~\dotfill\\\\ cos(\alpha )=\cfrac{\stackrel{adjacent}{3}}{\underset{hypotenuse}{5}}\qquad \textit{let's find the opposite} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}[/tex]

[tex]\pm\sqrt{5^2 - 3^2}=b\implies \pm 4=b\implies \stackrel{IV~Quadrant}{-4=b}~\hfill tan(\alpha)=\cfrac{\stackrel{opposite}{-4}}{\underset{adjacent}{3}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]tan(\alpha - \beta) \implies \cfrac{\stackrel{tan(\alpha)}{-\frac{4}{3}}- \stackrel{tan(\beta)}{\frac{4}{3}}}{1+ \stackrel{tan(\alpha)}{\left( -\frac{4}{3} \right)}\stackrel{tan(\beta)}{\left( \frac{4}{3}\right)}}\implies \cfrac{~~ \frac{-8 }{3 } ~~}{1-\frac{16}{9}}\implies \cfrac{~~ \frac{-8 }{3 } ~~}{\frac{-7}{9}} \\\\\\ \cfrac{-8}{3}\cdot \cfrac{9}{-7}\implies \cfrac{24}{7}\implies {\Large \begin{array}{llll} 3\frac{3}{7} \end{array}}[/tex]

By taking the quotients between the legs of the triangles, we will see that the pair that has hypotenuses with equal slopes are triangles 1 and 4.

Any two triangles where the quotient between the lenghts of the two legs are equal, have hypotenuses with equal slopes.

Here we will take the quotients between the heights and the bases of the triangles.

For triangle 1 the quotient is:

q₁ = 4/2 = 2

For triangle 2 the quotient is:

q₂ = 6/6 = 1

For triangle 3 the quotient is:

q₃ = 3/6 = 1/2

For triangle 4 the quotient is:

q₄ = 8/4 = 2

So we can see that the two triangles where the slopes of the hypotenuses are equal are triangles 1 and 4.

Learn more about triangles:

https://brainly.com/question/2217700

#SPJ1

Answer:

Step-by-step explanation:

[tex]\tt 6(x-2)(x-3) + 4(x-2)(x - 5)[/tex]

When, x = -3

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

To find the value of 6(x-2)(x-3) + 4(x-2)(x - 5), we need to substitute x with -3.

[tex]\tt 6\left(-3-2\right)\left(-3-3\right)+4\left(-3-2\right)\left(-3-5\right)[/tex]

[tex]\tt (6)(-5)(-3-3)+4(-3-2)(-3-5)[/tex]

[tex]\tt -30\left(-6\right)+4\left(-3-2\right)\left(-3-5\right)[/tex]

[tex]\tt -30\left(-6\right)+4\left(-5\right)\left(-3-5\right)[/tex]

[tex]\sf -30\left(-6\right)+4\left(-5\right)\left(-8\right)[/tex]

[tex]\tt 180+4\left(-5\right)\left(-8\right)[/tex]

[tex]\tt 180-\left(-160\right)[/tex]

[tex]\tt 180-\left(-160\right)[/tex]

[tex]\tt =340[/tex]

Therefore, the value of 6(x-2)(x-3) + 4(x-2)(x - 5) is 340!

____________________

Hope this helps!

Have a great day!

Answer:

8551.56

Step-by-step explanation:

[tex]A=5300(1+(0.08)/12)^{(12)(6)} \approx 8551.56[/tex]

By using implicit differentiation:

∂z/∂x=yz/4[tex]e^{4z}[/tex]-xy

∂z/∂y=xz/4[tex]e^{4z}[/tex]-xy

Without first having to solve the supplied equation for y, implicit differentiation enables you to determine the derivative of y with respect to x. Because we assume that y may be represented as a function of x, the chain rule must always be applied whenever the function y is being differentiated. If you need to determine the derivative dy/dx but x and y are not related to one another in a straightforward way, such as y = x, implicit differentiation is incredibly helpful (x). Instead, it's possible that x and y are related by a more challenging equation, such as sin(x + y) = x, where it may be challenging to describe y in terms of x.

Given function is,

[tex]e^{8z}[/tex]=xyz

By using implicit differentiation,

We have to differentiate with respect to x, we get:

∂/∂x([tex]e^{4z}[/tex])=∂/∂x(xyz)

[tex]e^{4z}[/tex](∂/∂x(4z)=yz(1)+xy(∂z/∂x)

4[tex]e^{4z}[/tex]∂z/∂x=yz+xy∂z/∂x

(4[tex]e^{4z}[/tex]-xy)∂z/∂x=yz

∂z/∂x=yz/4[tex]e^{4z}[/tex]-xy

Now, we have to differentiate again implicitly with respect to y, we get:

∂/∂y([tex]e^{4z}[/tex])= ∂/∂y(xyz)

[tex]e^{4z}[/tex](∂/∂y(4z)=xz(1)+xy(∂z/∂y)

4[tex]e^{4z}[/tex]∂z/∂y=xz+xy∂z/∂y

(4[tex]e^{4z}[/tex]-xy)∂z/∂y=xz

∂z/∂y=xz/4[tex]e^{4z}[/tex]-xy

To know more about implicit differentiation, visit:

https://brainly.com/question/11887805

#SPJ1

Answer:

p=45-2.5f

Step-by-step explanation:

5f+2p=90

We have to isolate p in one side

5f+2p=90

-5f. -5f

2p=90-5f

/2. /2. /2

p=45-2.5f

Hopes this helps please mark brainliest

Answer:

4.33

Step-by-step explanation:

See picture attachment.

The weighted average of points is M = 5.4

The mean value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.

Mean = Sum of Values / Number of Values

Given data ,

Let the weighted average be represented as M

Now , the value of M is

The points A, B, and C, shown on the number line, have weights 1, 1,

and 3 respectively.

A = 2 , B = 4 and C = 7

To find the weighted average of points A, B, and C with the given weights, we need to use the formula:

The weighted average M = (weight of A * value of A + weight of B * value of B + weight of C * value of C) / (total weight)

Plugging in the given values, we get:

The weighted average M = (1 * 2 + 1 * 4 + 3 * 7) / (1 + 1 + 3)

The weighted average M = (2 + 4 + 21) / 5

The weighted average M = 27 / 5

The weighted average M = 5.4 (rounded to one decimal place)

Hence , the weighted average of points A, B, and C with the given weights is 5.4

To learn more about average or mean click :

https://brainly.com/question/15526777

#SPJ2

A possible first step Vivi could take is multiply each term in the second equation by 2 and she can also multiply each term in the second equation by 4. The correct option is d. Both a and c could work.

From the question, we are to determine the statement that correctly describes a possible first step Vivi could take

From the given information,

The given system of equations is

4x + 6y = -14

-x + 3y = -10

To eliminate y, we can multiply each term in the second equation by 2 and then subtract

2 × [-x + 3y = -10

-2x + 6y = -20

Then, subtract

4x + 6y = -14

-{ -2x + 6y = -20

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

6x = 6

To eliminate x, we can multiply each term in the second equation by 4 and add the equations,

4 × [-x + 3y = -10

-4x + 12y = -40

Then, add

4x + 6y = -14

+{ -4x + 12y = -40

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

18y = -54

Hence, we can multiply each term in the second equation by 2 and we can also multiply each term in the second equation by 4.

Learn more on Elimination method here: https://brainly.com/question/25427192

#SPJ1

The function in the context of this problem is modeled as follows:

t(r) = 12/(6 + r)

In which the input and output of the function are given, respectively, by:

Then the numeric value at t = 3 represents the time in hours it takes for the boat to cross the river when the velocity of the river is of 3 kilometers per hour.

The vertical asymptote of a function are the values of the input for which the function is not defined.

A fraction is not defined at the zeros of the denominator, hence:

t + 6 = 0

t = -6 is the vertical asymptote of the function.

More can be learned about functions at https://brainly.com/question/24808124

#SPJ1