Juan rides the bus to school each day. He always arrives athis bus stop on time, but his bus is late 80% of the time.Juan runs a simulation to model this using a randomnumber generator. He assigns these digits to the possibleoutcomes for each day of the week:• Let 0 and 1 = bus is on time• Let 2, 3, 4, 5, 6, 7, 8, and 9 = bus is lateThe table shows the results of the simulation.

Answer:

The correct answers are below, if you want a more in depth explanation let me know and I will provide

Step-by-step explanation:

- The Diver surfaced 3 min before the Watcher

- When the noticed was received, the Diver was 20 ft deeper than the watcher

- 3 Min after receiving the notice, the diver and the watcher are at the same depth

Answer:A rate of change is a rate that describes how one quantity changes in relation to another quantity. Constant rate is also called as uniform rate which involves something travelling at fixed and steady pace or else moving at some average speed. For example, A car travels 3 hours.

Step-by-step explanation:

Given that the radius r of a circle is written as a function of the area A with the following equation:

The domain of the above function is the area A of the circle.

This is because, in this context, the area is an independent and unique variable.

A is the input value.

we have that the figure of a rectangle and a triangle. So the area of this figure is:

so the answer is 68 in^2

Answer: -33

Step-by-step explanation: I guess he had like debt to pay lol but he would've had to have -33 dollars and added $84 to get a total of $51

The solution of the given system of equation will have infinite many solutions.

In the above question, the following equations are given

4x + 6y = 24

2x + 3y = 8

Now, we need to find the number of solutions that this system of equation will have

We know that,

a1 x + b1 y = c1

a2 x + b2 y = c2

is the general system of equation, and

[tex]\frac{a1}{a2} \neq \frac{b1}{b2}[/tex] then unique solution, or

[tex]\frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2}[/tex] then there will be infinite solutions or,

[tex]\frac{a1}{a2} = \frac{b1}{b2} \neq \frac{c1}{c2}[/tex] then there will be no solution

Now, we'll check for the given system of equations

a1 = 4, b1 = 6 , c1 = 24

a2 = 2, b2 = 3 , c2 = 8

[tex]\frac{a1}{a2} = \frac{b1}{b2} \neq \frac{c1}{c2}[/tex] = 2 = 2 [tex]\neq[/tex] 3

As this condition satisfies the third condition, the solution of the given system of equation will have infinite many solutions.

Now as we multiply the first equation 4x + 6=24 by 3 we get we have 12x+18y=72, the system will still have same solutions as only the equations are multiplied by a constant k = 3 which does not affect the solution.

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Answer:

there is no solution because there aren't any nubmer of X to get linear equation

3X-3X= 12-7

0=5

there aren't solutions so it will be 0

Answer:

6:20 - 2:4 (simplified)

Step-by-step explanation:

20 total slips

6 red slips

For any given angle in a right triangle that is not the 90° angle its sine is given by the quotient between its opposite side and the hypotenuse. For triangle ABC the hypotenuse is BC and the opposite side to theta is AB. Then the sine of this angle is given by the following equation:

Then the answer is the third option, 4/5.

Answer:

===============================

Vertex form of quadratic equation:

Convert the given expression into vertex form by completing the square:

Answer:

[tex]f(x)=\left(x+\dfrac{1}{2}\right)^2+\dfrac{3}{4}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]

To find the vertex form of the given function, complete the square.

Given function:

[tex]f(x)=x^2+x+1[/tex]

Add and subtract the square of half the coefficient of the term in x:

[tex]\implies f(x)=x^2+x+\left(\dfrac{1}{2}\right)^2+1-\left(\dfrac{1}{2}\right)^2[/tex]

[tex]\implies f(x)=x^2+x+\dfrac{1}{4}+1-\dfrac{1}{4}[/tex]

[tex]\implies f(x)=x^2+x+\dfrac{1}{4}+\dfrac{3}{4}[/tex]

Factor the perfect square trinomial formed by the first three terms:

[tex]\implies f(x)=\left(x+\dfrac{1}{2}\right)^2+\dfrac{3}{4}[/tex]

Answer:

1. 6 units

2. 13 units

3. 5 units

Step-by-step explanation:

Answer:

  zero

Step-by-step explanation:

You want Amy Van's average velocity when she swims 50 m to the end of the pool and back.

Average velocity is the ratio of the change in position to the amount of time over which that change occurs. When Amy ends up where she started, she has not changed position at all, so her average velocity is ...

  Vave = (change in position)/time = 0/time = 0

Her average velocity is zero.

x ∈ ( -π/2 + 2kπ ; π/2 + 2kπ) ; k ∈ Z

The domain of f(x)=ln(cosx) =  x ∈ ( -π/2 + 2kπ ; π/2 + 2kπ) ; k ∈ Z

Given function,

            f(x)=ln(cosx)

When cos(x) is positive, the domain is.

(cos(x)) > 0

since,

cos0 = 1

cos π/2 = 0

cos π = -1

cos 3π/2 = 0

cos 2π = 1

cos 3π/2 = 0

The values of cos(x) are then between -1 and 1.

That is domain of  f(x)=ln(cos x)

= cos x ∈ (0;1] -> x ∈ ( -π/2 + 2kπ ; π/2 + 2kπ) ; k ∈ Z

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The Solution.

The correct answer is y = 0.34x - 0.9 (option A ).

Step 1:

First, we shall determine the slope of the line by picking two coordinates from the table.

Answer:

y = 3x+3

Step-by-step explanation:

The rate of change, or slope, in this case, is 3, as we can either count the increase in y-values or perform the Δy/Δx (slope equation: [tex]\frac{9-3\\}{2-0}[/tex])to yield three, meaning that the (3x) in this equation would be the slope. Since the y-intercept is the constant in the equation and the y-intercept is always when x=0 (when the graph crosses the y-axis) on the XY plane, we can just subtract 3 from the x=1 coordinate, meaning that the y-intercept/x=0 coordinate would be (0, 3), leaving 3 as the constant.

Therefore,

the equation is y = 3x+3.

Given data:

The time taken by Amy is A=30 min.

The expression for the time taken by Julian is,

Substitute the given values in the above expression.

Thus, the time taken by Julian is 48 minutes.

Answer:

600

Step-by-step explanation:

[tex]R(1)=400 \\ \\ R(2)=1000 \\ \\ R(2)-R(1)=600[/tex]

Answer:

100 ×10 =1000

Step-by-step explanation:

10% of 1000 is 100 that's the final answer if am wrong let me know

Answer: A relation is just a relationship between x and y-coordinates. It maps inputs to outputs. A function is just a special kind of relation: any input has exactly one output.

Step-by-step explanation:

Hello

we are given a function and asked to find the reminder when it is divided by a binomial

According to the remainder theorem, f(a) would be the remainder from dividing f(x) by x -a

but our f(x) is given as

From the calculation above, the answer to this question is 31

[tex] { 3 }^{ - 1} \times {3}^{x + 1} - { 3}^{x - 2} + {3}^{ - 2} \times { 3}^{x + 3} = 35 \\ {3}^{ - 1 + x + 1} - {3}^{x - 2} + {3}^{ - 2 + x + 3} = 35 \\ {3}^{x} - {3}^{x - 2} + { 3}^{ - 2 + 3 + x} = 35 \\ { 3 }^{x} - {3}^{x - 2} + {3}^{x + 1} = 35 \\ {3}^{x} - {3}^{x} \times {3}^{ - 2} + {3}^{x} \times {3}^{1} = 35 \\ {3}^{x} (1 - {3}^{ - 2} + 3) = 35 \\ {3}^{x} (3 + 1 - \frac{1}{9}) = 35 \\ \\ {3}^{x} (4 - \frac{1}{9} ) = 35 \\ {3}^{x} ( \frac{35}{9} ) = 35 \\ \frac{ {3}^{x}( \frac{35}{ 9 } )}{ \frac{35}{9} } = 35 \div ( \frac{35}{9} ) \\ {3}^{x} = 9 \\ {3}^{x} = { 3 }^{2} \\ x = 2[/tex]

ATTACHED IS THE SOLUTION.

I USED THE LAWS OF EXPONENTS.

GOODLUCK.

We know that the angle terminates in the fourth quadrant and that the tangent of it is -3/4.

Angles that are on the fourth quadrant have a negative sine and a positive cosine.

We can start with the cot():

We can relate the cosine with the tangent as:

We can now calculate the sine of the angle as:

We can now calculate the sec() and csc() as:

Answer:

sin() = -3/5

cos() = 4/5

cot() = -4/3

sec() = 5/4

csc() = -5/3

The answer of the expression is 3 -4 and the sum is -1

Given,

In the figure, given a number line.

And, write an addition expression represented by number line. Then find the sum.

Now, According to the question:

To solve for an expression is:

Calculate the principle based on the number line .

We can figure out the formula .

= 3 - 4

[Moving to the right is positive and moving to the left is negative ]

To find the sum:

3 - 4 = -1

According to the figure , the end point of the movement is -1 and the answer is correct.

Hence, The answer of the expression is 3 -4 and the sum is -1

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We can see that if we rotate P 90° counterclockwise it would be located in the first quadrant. So it can be A or B. But A forms a 90° with the position of point P. So, the answer is A.

Based on the sequence given of 3,5,8,12,17, it would be incorrect to say that the sequence is arithmetic. The sequence is not arithmetic.

In an arithmetic sequence, one would find that the number that separates each of the figures in the sequence is the same. In other words, the common difference between each figure is the same.

For instance, 2, 5, 8, 11, 14 has the common difference of 3 so this is an arithmetic sequence.

The sequence given of 3,5,8,12,17 is not arithmetic because the difference between each number is not common and instead increases.

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Not true, true, true, true, true, true, true, not true, true, true

See explanation below

From the diagram, we noticed a change in lengths when all four vertex was dragged.

This means the 4 sides will not always be the same (congruent).

Not always true: The four sides are congruent

From both diagrams. we found the opposite sides are the same (congruent)

Always true: The opposite sides are congruent

Since they opposite sides arecongruent, this also means the opposite sides are parallel

Always true: opposite sides are parallel

All four angles from both diagrams are equal (congruent)

Always true: all four angles are congruent

SInce all four angles areequal, then the angles opposite each other will also be equal.

Always true: opposite angles are congruent

The diagonals of both shapes bisect each other. Hence, they are congruent.

Always true: Diagonals are congruent

Always true: diagonals bisect each other

Diagonals of a square (the shapethat has all sides equal ) intersect at a right right angle.

Diagonals of a rectangle ( the shape with opposite sides equal) don ot intersect at right angle.

Not always true: Diagonals intersect at a right angle

The interior angles were split by the two diagonals in both shapes.

Always true: Diagonals bisect interior angles

The sum of angles in a quadrilateral is equal to 360°

Both shapes are quadrilaterals. Hence, the sumof their angles is 360°.

Always true: sum of all angles equal 360°

The overall percentage reduction in the price of the radio is 40%.

Percentage is the fraction of an amount expressed as a number out of hundred. Percentage is a measure of frequency. The sign that is used to represent percentages is %.

Let's assume that that initial price of the radio is 100.

Price of the radio after the 20% decline in price = (1 - 0.2) x 100

0.8 x 100 = 80

Price of the radio after the 25% decline in price = (1 - 0.25) x 80

0.75 x 80 = 60

The percentage decline in price = (initial price / final price) - 1

(60 / 100) - 1 = 0.4 = 40%

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The mixed fraction can be 3 2/3 and the improper fraction would be 11/3 for the same mixed fraction.

A mixed fraction is one that is represented by its quotient and remainder. 2 1/3, for example, is a mixed fraction in which 2 is the quotient and 1 is the remainder. A mixed fraction is thus the product of a whole number and a proper fraction.

An improper fraction is one in which the numerator (top number) exceeds or equals the denominator (bottom number). Fractions like 651/14 are "incorrect." They are simply another way to write a mixed number.

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Given the line which passes through the points (2, 3) and (5,8) and the line that passes through the points (-7, 5) and (-12, 8).

To determine the relationship which best describes the line, the first thing we do is find the gradients of the lines.

For point A and B with coordinates:

For points (2, 3) and (5,8)

For the points (-7, 5) and (-12, 8)

• Two lines are said to be ,parallel, ,if their gradients are the same.

• Two lines are said to be ,perpendicular ,if the ,product of the gradients is -1.

Product of the two gradients

Since the product of the gradients is -1, the two lines are said to be perpendicular.

The correct option is D