If a, b, c, and d are coplanar lines and a ∥ b, b ⊥ c, and c ∥ d​, then which statement must be true?

Answer:

6.67

Step-by-step explanation:

Because in the park there are 30 people OK

15 were walking

7 were playing

6 were running.

15 + 7 + 6=28

Meaning there are still 2 people left so that is 6.67 =% of the people.

Hope it helps have a great afternoon:)

Answer: 7%

Step-by-step explanation:

15 + 7 + 6 = 28

Fraction of no activity is 2/30

divide 2/30

0.06666667

Round up

0.07 = 7%

Answer:

2(3/2)+ .5 - (0-1)

Step-by-step explanation:

Answer:

x = 95°

y = 40°

z = 95°

Step-by-step explanation:

The first part of the question asks for the integral of \(f(x) = 7x / (x^2 + 4) dx\). The second part asks for the derivative of f(x) = (x^2 + 1)(7x - 3). The third part involves a manufacturer's production model, P(d) = 3 + 15(1 - \(e^0^.^2^d\)), where P(d) represents the number of items produced per day by an employee with d days of experience.

The graph of P(d) is requested, and specific questions are asked: (a) the approximate production of a beginning employee per day, (b) the production of an experienced employee per day, and (c) the marginal production rate of an employee with 5 days of experience, including the units and interpretation of the answer.

(a) For a beginning employee with no experience (d = 0), the approximate production per day can be found by substituting d = 0 into the production model P(d). Thus, P(0) = 3 + 15(1 - \(e^0^.^2^\times^0\)) = 3 + 15(1 - \(e^0\)) = 3 + 15(1 - 1) = 3 + 15(0) = 3.

(b) To find the production per day for an experienced employee, we need to determine the limit of P(d) as d approaches infinity. As d approaches infinity, the exponential term \(e^0^.^2^d\) approaches 0, resulting in P(d) approaching 3 + 15(1 - 0) = 3 + 15 = 18.

(c) The marginal production rate represents the rate of change of production with respect to experience. It can be found by taking the derivative of P(d) with respect to d. Taking the derivative of P(d) = 3 + 15(1 - \(e^0^.^2^d\)) yields P'(d) = 0.2 * 15 * \(e^0^.^2^d\). Substituting d = 5 into P'(d) gives P'(5) = 0.2 * 15 * \(e^0^.^2^\times ^5\). The units of P'(5) are items per day per day, which can be simplified to items per day squared. This result represents the rate of change in the production rate for an employee with 5 days of experience.

Learn more about integral here:

https://brainly.com/question/31109342

#SPJ11

A. P(6, then 1) = 1/90

B. P(even, then 5) = 1/18

C. P(8, then odd) = 1/18

D. P(3, then prime) = 2/45

E. P(prime, composite) = 4/15

F. P(even, then 3, then 5) = 1/144

Given:

Total number of cards: 10

A. P(6, then 1):

P(6, then 1) = 1/10 x 1/9

= 1/90

B. P(even, then 5):

Number of favorable outcomes: 5 x 1 = 5

P(even, then 5) = 5/10 x 1/9

= 1/18

C. P(8, then odd):

Number of favorable outcomes: 1 x 5 = 5

P(8, then odd) = 1/10 x 5/9

= 1/18

D. P(3, then prime):

Number of favorable outcomes: 1 x 4 = 4

P(3, then prime) = 1/10 x 4/9

= 2/45

E. P(prime, composite):

Number of favorable outcomes: 4 x 6 = 24

P(prime, composite) = 4/10 x 6/9

= 4/15

F. P(even, then 3, then 5):

Number of favorable outcomes: 5 x 1 x 1 = 5

P(even, then 3, then 5) = 5/10 x 1/9 x 1/8

= 1/144

Learn more about Probability here:

brainly.com/question/32117953

#SPJ1

Answer:

33.33 %

Step-by-step explanation:

( 1/3 )* 100 = 33.33...

In this scenario, the shape of the sampling distribution of X-bar is approximately normal.

The sampling distribution of the sample mean, X-bar, can be determined by the Central Limit Theorem. In this case, since the sample size is large (n = 64) and the underlying distribution (X) is approximately normal, the sampling distribution of X-bar will also be approximately normal. The Central Limit Theorem states that regardless of the shape of the population distribution, as the sample size increases, the sampling distribution of X-bar tends to become more and more normal. Therefore, in this scenario, the shape of the sampling distribution of X-bar is approximately normal.

For more information on uniform distribution visit: brainly.com/question/15301850

#SPJ11

SOLUTION

Consider the graph shown:

From the graph the equation is:

Therefore the approximate equation is:

Substitute x=4 into the equation:

Step-by-step explanation:

A sequence is defined recursively using the equation f(n + 1) = f(n) – 8. If f(1) = 100, what is f(6) ?

Since, A sequence is defined recursively using the equation f(n + 1) = f(n) – 8. If f(1) = 100,we have to find the value of f(6).

Consider

f(n+1) = f(n)-8

Let n =1, we get

f(1+1) = f(2) = f(1) - 8 = 100-8 = 92

Let n =2, we get

f(2+1) = f(3) = f(2) - 8 = 92-8 = 84

Let n =3, we get

f(3+1) = f(4) = f(3)-8 = 84 - 8 = 76

Let n =4, we get

f(4+1) = f(5) = f(4)-8 = 76 - 8 = 68

Let n =5, we get

f(5+1) = f(6) = f(5) - 8 = 68-8 = 60

Therefore, the value of f(6) is 60.

Answer: C, 60

Step-by-step explanation: Just took the quiz :)

Answer:

x = 0

Step-by-step explanation:

Using the rule of exponents

\(a^{0}\) = 1

Given

\((2^{6}) ^{x}\)

= \(2^{6x}\)

The only way for this to equal 1 is for x to be zero

Thus x = 0

Answer:

= 9/10

Step-by-step explanation:

- × - = +

Then:

2×1/5 = (2×1)/5 = 2/5 = 12/30

-(-3×1/6) = +(3*1)/6 = 3/6 = 15/30

Then:

2×1/5-(-3×1/6) = 2/5 + 3/6 = 12/30 + 15/30 = (12+15)/30 = 27/30

27/30 = 9/10

The graph is a graph of one to one function

A one to one function, is a type of mathematical function that maps each element of its domain to a unique element in its range.

In other words, if f is a one-to-one function, then no two distinct elements in its domain are mapped to the same element in its range.

As in the graph each element has a unique domain values and hence this is a one to one function.

Learn more about one to one function at:

https://brainly.com/question/28911089

#SPJ1

the antiderivative of the function f(x) = 2 csc(x) cot(x) sec(x) tan(x) is F(x) = 2x + C.

To find the antiderivative F(x) of the function f(x) = 2 csc(x) cot(x) sec(x) tan(x), we can simplify the expression and integrate each term individually.

We know that csc(x) = 1/sin(x), cot(x) = 1/tan(x), sec(x) = 1/cos(x), and tan(x) = sin(x)/cos(x).

Substituting these values into the expression:

f(x) = 2 * (1/sin(x)) * (1/tan(x)) * (1/cos(x)) * (sin(x)/cos(x))

= 2 * (1/sin(x)) * (1/(sin(x)/cos(x))) * (sin(x)/cos(x)) * (sin(x)/cos(x))

= 2 * (1/sin(x)) * (cos(x)/sin(x)) * (sin(x)/cos(x)) * (sin(x)/cos(x))

= 2 * 1

= 2

The antiderivative of a constant function is simply the constant multiplied by x. Therefore:

F(x) = 2x + C

where C represents the constant of the antiderivative.

to know more about function visit:

brainly.com/question/30721594

#SPJ11

Answer:

here is the answer

Step-by-step explanation:

The number of toy cars are in 1,000 boxes is 25000 and the place value of 25 increases by 4 places to the left.

It should be noted that place value is used to know the value of the numbers that are given in a data.

In this case, toy company puts 25 toy cars in each box, the number of toy cars that are in 1,000 boxes will be:

= 25 × 1000

= 25000

Learn more about place values on:

brainly.com/question/1654524

#SPJ1

Answer:

it is b

Step-by-step explanation:

Answer:

it is b

Step-by-step explanation:

i solved it tsk tsk tsk

Answer:

5.7x10^-8

Step-by-step explanation:

Move the decimal 8 places to the right.

Hope this helps

Answer:

3 gallons

Step-by-step explanation:

Length of the rectangular wall = 23.6 feet

Width of the rectangular wall = 19.2 feet

Surface area of the wall = 23.6 × 19.2

                                        = 453.12 square feet

∵ 200 square feet of the wall is covered by the amount of paint = 1 gallon

∴ 1 square feet of the wall will be covered by the amount of paint = \(\frac{1}{200}\) gallons

∴ 453.12 square feet will require the amount of paint = \(\frac{453.12}{200}\)

                                                                                         = 2.2656 gallons

Therefore, minimum 3 gallons will be required to paint the wall.

The number 1.07  × 10⁸ in standard form is 107,000,000.

To write 1.07 × 10⁸ in standard form, we need to move the decimal point to the left or right such that there is only one non-zero digit to the left of the decimal point.

In this case, we have 1.07 × 10⁸, which means we have a value of 1.07 times 10 raised to the power of 8. To convert this to standard form, we need to move the decimal point 8 places to the right since 10 is being raised to the power of 8.

1.07 × 10⁸ = 107,000,000

Learn more standard form on:

https://brainly.com/question/17136267

#SPJ1

Math SAT scores explain about 98.7% of the variation in the total SAT scores.

In statistics, correlation or dependence exists as any statistical relationship, whether causal or not, between two random variables or bivariate data.

A correlation exists as a statistical measure (expressed as a number) that defines the size and direction of a relationship between two or more variables. A correlation between variables, however, does not automatically mean that the change in one variable exists as the cause of the change in the values of the other variable.

Since r² exists = (0.9935)² = 0.9870, we interpret r² as 98.7% of the variation in the y variable exists explained by the x variable.

In context, math SAT score explains about 98.7% of the variation in total SAT score.

To learn more about correlation refer to:

https://brainly.com/question/4219149

#SPJ4

Answer:

4,950

Step-by-step explanation:

The 4 is in the thousands place,

the 9 is in the hundreds place,

the five is in the tens place,

and lastly the two is in the ones place.

To round 4,952 to the tens place you round down since 2 is a number under 5. Hope this helps!

Answer: over 23 mins a little bit 23.157

Step-by-step explanation:

Smart

which means that the net force acting on the skydiver is zero, and the forces are balanced. Therefore, the answer is C) Part I of the descent only.

Step 5: Draw the segments AB and AC to create two tangent lines to the circle.

Step 1: Draw segment OA.

Step 2: Find the midpoint, M, of OA by constructing the perpendicular bisector of OA.

Step 3: Draw a circle centered at point M with radius MA or MO (where A and O are the endpoints of segment OA).

Step 4: Let the points B and C represent the points where the two circles meet.

Step 5: Draw the segments AB and AC to create two tangent lines to the circle.

Based on the information given, we can infer that the skydiver experienced unbalanced forces during Part 1 of the descent only. This is because the diagram shows that the speed of the skydiver is increasing during Part 1,

which means that there must be a net force acting on the skydiver in the downward direction (i.e., the force of gravity is greater than the air resistance). In contrast, during Part 2,

the speed is constant, which means that the net force acting on the skydiver is zero, and the forces are balanced. Therefore, the answer is C) Part I of the descent.

To know more about circle visit:

https://brainly.com/question/11833983

#SPJ1

Answer:

The percentage increase from 8000 to 10000 is 25%.

The percent of increase from 8000 to 10000 is given as 25%.

A percentage is a value that indicates 100th part of any quantity.

A percentage can be converted into a fraction or a decimal by dividing it by 100. The percent of increase or decrease can be found by taking the ratio of the increased or decreased value to the initial value.

The given numbers are 8000 and 10000.

The percent increase can be obtained as follows,

The increased value ÷ Initial number × 100

⇒ (10000 - 8000) ÷ 8000 × 100

⇒ 2000 ÷ 8000 × 100

⇒ 25%

Hence, the percent increase is obtained as 25%.

To know more about percentage click on,

brainly.com/question/29306119

#SPJ2

the solution to the system of equations is x = 2 and y = 1.

To solve the system of equations by substitution, we will solve one equation for one variable and substitute it into the other equation.

Given the system of equations:

1) y = 6x - 11

2) -2x - 3y = -7

Step 1: Solve equation (1) for y.

  y = 6x - 11

Step 2: Substitute the value of y from equation (1) into equation (2).

  -2x - 3(6x - 11) = -7

Step 3: Simplify and solve for x.

  -2x - 18x + 33 = -7

  -20x + 33 = -7

  -20x = -7 - 33

  -20x = -40

  x = (-40)/(-20)

  x = 2

Step 4: Substitute the value of x into equation (1) to find y.

  y = 6(2) - 11

  y = 12 - 11

  y = 1

Therefore, the solution to the system of equations is x = 2 and y = 1.

Learn more about Equation here

https://brainly.com/question/31345430

#SPJ4

The solution to the system of equations y = 6x - 11 and -2x - 3y = -7 is x = 2 and y = 1. This is achieved by substituting y into the second equation, simplifying, and solving for x, then substituting x back into the first equation to solve for y.

To solve the system of equations y = 6x - 11 and -2x - 3y = -7 by substitution, we start by substituting the equation y = 6x - 11 into the second equation in place of y, giving us -2x - 3(6x - 11) = -7. Next, simplify the equation by distributing the -3 inside the parentheses to get -2x - 18x + 33 = -7. Combine like terms to get -20x + 33 = -7. Subtract 33 from both sides to obtain -20x = -40, and finally, divide by -20 to find x = 2.

Once we find the solution for x, we substitute it back into the first equation y = 6x - 11. Substituting 2 in place of x gives y = 6*2 - 11, which simplifies to y = 1.

Therefore, the solution to the system of equations is x = 2 and y = 1.

https://brainly.com/question/35467992

#SPJ11

The most appropriate units to describe the cost of the sandbox would indeed be dollars.

When describing the cost of an item or service, it is essential to use the unit that represents the currency being used for the transaction. In this case, the total cost of the sand for the school's sandbox is given in dollars. To maintain consistency and clarity, it is best to express the cost in the same unit it was provided.

Using dollars as the unit for the cost allows for clear communication and understanding among individuals involved in the transaction or discussion. Dollars are widely recognized as the standard unit of currency in many countries, including the United States, where the dollar sign ($) is commonly used to denote monetary values.

Using meters, the unit for measuring the dimensions of the sandbox, to describe the cost would be inappropriate and could lead to confusion or misunderstandings. Mixing units can cause ambiguity and hinder effective communication.

Therefore, it is most appropriate to describe the cost of the sand in dollars, aligning with the unit of currency provided and commonly used in financial transactions. This ensures clarity and facilitates accurate comprehension of the cost associated with the sand purchase for the school's sandbox.

for similar questions on sandbox.

https://brainly.com/question/31290675

#SPJ8

Answer:

  see attached

Step-by-step explanation:

You want the first three terms of sin(x) and cos(x) evaluated for a variety of values of x.

The terms of the series expansion of these trig functions are fairly easily evaluated using a spreadsheet. You write the formula once, then let the spreadsheet evaluate it for the different values of x.

The function PI() is used to obtain the value of π, and the function FACT(3) is used to obtain the value of 3!, for example.

The filled table values (shown to 6 dp) are found in the attachment.

__

Additional comment

Some calculators can operate on lists, so can do this fairly nicely, too. Filling 42 (or so) table entries by hand calculation would be tedious and error-prone. If you're going to try that, you may want to write the expressions in Horner form, for example, ((x^2/(5*4) -1)x^2/(3*2) +1)x. The second attachment shows the evaluation of this for x=π/4.

<95141404393>

Answer: Should be (3, 1) :)

Step-by-step explanation:

Answer: (4,-8)

Step-by-step explanation:

you look at the point it is and flip it to a negative

Answer:

The common ratio of a geometric series is \dfrac14

4

1 ​

start fraction, 1, divided by, 4, end fraction and the sum of the first 4 terms is 170

The first term is 128

Step-by-step explanation:

The common ratio of the geometric series is given as:

\(r = \frac{1}{4}\)

The sum of the first 4 term is 170.

The sum of first n terms of a geometric sequence is given b;

\(s_n=\frac{a_1(1-r^n)}{1-r}\)

common ratio, n=4 and equate to 170.

\(\frac{a_1(1-( \frac{1}{4} )^4)}{1- \frac{1}{4} } = 170\)

\(\frac{a_1(1- \frac{1}{256} )}{ \frac{3}{4} } = 170\\\\ \frac{255}{256} a_1 = \frac{3}{4} \times 170\\\\\frac{255}{256} a_1 = \frac{255}{2} \\\\\frac{1}{256} a_1 = \frac{1}{2} \\\\ a_1 = \frac{1}{2} \times 256\\\\a_1 = \frac{1}{2} \times 256 \\\\= 128\)

Answer:

The first term is 128