Look at the figure below:If siny - and tan yo =9-what is the value of cos yº? O cos y 90cos yOcos yO cos y® - 90

We know that the ratio of pink markers to total markers is 1:3.

This means that for every 3 markers, one of them is pink. The other 2 will be yellow markers.

We can write that the ratio of pink markers to yellow markers is 1:2, based on the last sentence. This means that if we have N yellow markers, we will have N/2 pink markers.

Then, if we have 16 yellow markers, then we will have 16/2=8 pink markers.

The frequency means how many times specific data shows up in a set of values.

Score Frequency

1-6 2

7-12 4

13-18 5

...

And so on.

The probability that the entire cargo will be approved is 0.078 = 7.8% using the Binomial probability distribution, while 92.2% will be refused. As a result, many will be rejected.

By Binomial probability distribution,

P(X = x) = [tex]C_{n,x}[/tex] × [tex]p^{x}[/tex] × [tex](1-p)^{n-x}[/tex]

[tex]C_{n,x}[/tex] , various combinations of x items from a collection of n elements given by,

[tex]C_{n,x}[/tex] = n! ÷ x! (n - x)!

n=42, as 42 tablets are tested.

p=0.06 as 6% is defective.

If at most there is 1 defective piece then it will be accepted.

Therefore,

P(X ≤ 1) = P(X = 0) + P(X = 1)

P(X = x) = [tex]C_{n,x}[/tex] × [tex]p^{x}[/tex] × [tex](1-p)^{n-x}[/tex]

P(X = 0) = [tex]C_{42,0}[/tex] × [tex](0.06)^{0}[/tex] × [tex](0.94)^{42}[/tex] = 0.074

P(X = 1) = [tex]C_{42,1}[/tex] × [tex](0.06)^{1}[/tex] × [tex](0.94)^{41}[/tex] = 0.0047

Thus,

P(X ≤ 1) = P(X = 0) + P(X = 1)

P(X ≤ 1) = 0.074 + 0.0047

P(X ≤ 1) = 0.0787

The probability that the entire shipment will be approved is 0.078 = 7.8%, while 92.2% will be refused.

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1) Picking points G( 14,13) , H (-11, 0) and R(-3,7) , S(-4,-5) let's find their slopes using the slope formula

And R(-3,7) , S(-4,-5)

Since the condition to be parallel is share the same slope, and to be perpendicular one line must have the reciprocal and opposite slope in comparison to the first one. We can state that neither that line is parallel nor perpendicular.

3) So the answer is GH is not parallel nor perpendicular.

Since in this group of ordered pairs shown above, the x-values are inputs and the y-values are outputs, all the statements that are true include the following:

A. There is only one input for every output.

B. There is only one output for every input.

An ordered pair can be defined as a pair of two (2) elements or points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate or x-axis (abscissa) and the y-coordinate or y-axis (ordinate) on the coordinate plane of any graph.

Generally speaking, the values on the x-coordinate or x-axis (abscissa) of any graph represents all of the input values while the values on the y-coordinate or y-axis (ordinate) of any graph represents all of the output values.

In this context, we can reasonably and logically deduce that there is a unique input for every output and a unique output for every input.

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Step 1: State the given in the question

Given that 3 out 20 cars passing through an intersection did not fully stop

Step 2: State what to be determined

We are to determine the probability that a car arriving at this intersection that will not fully stop

Step 3: State the formula for finding probability

The formula for finding the probability of an en event, E, from a sample S, is the ratio of the number of elements of event E to the total number of elements in the sample S.

This can be represented mathematically as

Step 4: Use the formula to solve the probability

If the event E is cars passing through an intersection did not fully stop. Then, the number of elements in the event E is given as 3. That is:

The sample is the total number of cars, which is given as 20. This means that

Therefore, the probability of the event occuring would be P(E). This is as calculated below:

Hence, the probability that a car arriving at this intersection will not fully stop is 3/20 or 0.15

Based on the time spent for the soccer game, the calculated degree of the soccer portion is found to be 72°.

How to find the soccer portion of the pie chart?

In mathematics, the complete pie chart is 360° and to calculate the soccer portion using standard formula which states that the division of the total hours spent on soccer and total sports hours multiply with 360°.

According to the question, the given data states that the pie chart is 360° which represents the total sports hours as 50 hours.

Therefore, the soccer portion is:

= Total hours spent on walking / Total sports hours x 360°

= 10 / 50 x 360°

= 72°

Based on the time spent for the soccer game, the calculated degree of the soccer portion is found to be 72°.

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We are given that "x" and "y" vary inversely. This means that the variables follow the next relationship:

Where "k" is a constant to be determined. To determine "k" we will use the given values:

Now, we plug in the values:

Now, we solve for "k" by multiplying both sides by 3:

Therefore, the value of "k" is 18. Now, we substitute in the relationship:

And thus we get the equation.

Answer:

900

Step-by-step explanation:

because I know answer

Answer:

f(2) = 4

Step-by-step explanation:

Hello!

We can find f(2) by substituting 2 for x in the equation.

The value of f(2) is 4.

Mrs. long bought 4 types of fruits at the market:

- 2 cantaloupes that weighed 2.3 pounds each:

that is, a total of 2.3x2 = 4.6

- 6 peaches that weighed a total of 1.7 pounds.

- 4 apples that weighed a total of 1.25 pounds.

- and 3 pounds of grapes.

The total weight of the four fruits is:

4.6 + 1.7 + 1.25 + 3 = 10.55 pounds.

The statement which is true about the graph shown is that: B. The equation c = 0.4w is correctly represented by the graph.

Mathematically, a proportional relationship can be modeled by the following linear equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for this graph:

k = y/x

k = 0.8/2

k = 0.4.

In this context, the proportional relationship which models the cost of mailing a package to the weight of the package is given by this linear equation:

c = 0.4w

where:

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Answer:

Step-by-step explanation:

The statement which is true about the graph shown is that: B. The equation c = 0.4w is correctly represented by the graph.

How to determine the equation of a proportional relationship?

Mathematically, a proportional relationship can be modeled by the following linear equation:

y = kx

Where:

y and x are the variables.

k represents the constant of proportionality.

Next, we would determine the constant of proportionality (k) for this graph:

k = y/x

k = 0.8/2

k = 0.4.

In this context, the proportional relationship which models the cost of mailing a package to the weight of the package is given by this linear equation:

c = 0.4w

where:

c is the total cost.

w is weight in ounces.

The height of cylinder when volume of 480 cubic meters is  480/r^2.

Volume serves as a measure for an object's storage capacity. For instance, a cup's volume is said to be 100 ml if it can hold 100 ml of water when filled to the brim. The amount of space a three-dimensional object occupies is another way to define volume.

A solid's volume can be calculated by counting how many unit cubes it contains, such as in the case of a cube or cuboid. The best way to understand volume is to think of it as the area surrounded or occupied by any solid object or object with three dimensions. This can be seen by performing the following easy exercise at home:

volume of cylinder V is = πr²h

where, r  = radius of cylinder

h = height of cylinder

V = 480π cubic meters

Now, calculate its height in terms of cylinder radius using the volume of cylinder formula:

V = πr²h

480π =  πr²h

h = 480π/ πr²2

h = 480/r²

Therefore, The height of cylinder when volume of 480π is  480/r².

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ANSWER and EXPLANATION

We want to draw a quadilateral that has 2 pairs of congruent parallel sides and 4 right angles.

There are 2 quadilaterals that fit this description:

A square and a rectangle

[tex]21 + 21 \leqslant - 4z \\ - 4z \geqslant 42 \\ \frac{ - 4z}{ - 4} \geqslant \frac{42}{ - 4} \\ z \leqslant - 10.5[/tex]

ATTACHED IS THE SOLUTION

BE AWARE THE SIGNS <> ONLY CHANGE SIGN WHEN YOU MULTIPLY OR DIVIDE BY A NEGATIVE NUMBER.

A relationship between two expressions or values that are not equal to each other is called 'inequality. Z≤ -10.5 is the solution for inequality 21 ≤ −4z − 21.

A relationship between two expressions or values that are not equal to each other is called 'inequality.

The given inequality is twenty one lesser or equal to minus four z minus twenty one.

21 ≤ −4z − 21.

We need to solve for z

Let us add twenty one on both sides

21+21≤ −4z − 21+21

42≤ −4z

Divide both sides by 4

10.5≤ -Z

-10.5≥Z

Z≤ -10.5

Hence Z≤ -10.5 is the solution for inequality 21 ≤ −4z − 21.

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Let's begin by listing out the information given to us:

Jaylen's beta volume = 4 1/2 gallons = 4.5 gal

Time taken = 1 7/8 minutes = 1.785 min

Flow rate = volume / Time taken = 4.5 / 1.875 = 2.4 gal/min

You will need to make b the subject of the formula:

This you do by subtracting 0.25 from both sides of the equation:

b + 0.25 = 1.15 becomes:

Given the equation : 2x + 3y = 12?

We will find the slope of the equation by re-arranging the equation into the standard form of slope intercept formula:

Re-arranging the equation will be :

Take into account that vector v can be written as follow:

where (x,y) and (xo,yo) are two points on the vector.

In this case, we can use (xo,yo) = R(-2,12) and (x,y) = S(-7,6). By replacing these values into the expression for vector v, we obtain:

Now, consider that the magnitude of v is the square root of the sum of the squares of the components. Then, we have for the magnitud of v:

Hence, the magnitude of v is approximately 7.810.

Now, consider that the tangent of the angle of the direction of the vector is equal to the quotient between the y component over the x component of the vector:

Hence, the direction of vector v is approximately 230.194 degrees.

The probablity that first one selected is a criminal justice major is,

Now, the probablity that second one is a criminal justice major is when selected without replacement,

Simirally,

Thus, using the multiplication theorem,

Thus, the above equation gives the requried probablity.

Answer:

Step-by-step explanation:

You want the initial population and the population after 4 hours if its doubling time is 15 minutes, and the population is 60,000 after 110 minutes.

We like to use the numbers in the problem when writing the exponential equation. Here, we are given a doubling time and a population that is ...

  (minutes, population) = (110, 60000)

We can put these numbers in the form ...

  p(t) = (value at t1) · (growth factor)^((t -t1)/(growth period))

where the growth factor (2) is applicable over the growth period (15 minutes).

This makes our equation ...

  p(t) = 60000(2^((t-110)/15))

We want to find p(0) and p(240). (240 is the number of minutes in 4 hours). The attachment shows the calculations.

The population at t=0 was about 372.

The population after 4 hours will be 24,382,480.

__

Additional comment

A lot of times, you'll see this rewritten as an exponential equation with 'e' as the base. Here, that would be ...

  p(t) = 372·e^(0.0452098t)

where 372 = p(0) = 60000·2^(-110/15), and 0.0452098 ≈ ln(2)/15

These rounded numbers don't give the problem statement values exactly:

  p(110) = 53743, not 60000, for example. You would get a population of 60000 after 112.4 minutes (approximately).

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Answer:

Yes

Explanation:

A set S is said to be closed under addition if:

For a, b in S, a+b is in S.

If we add two even numbers, the result will always be an even number.

Therefore, the set of even number is closed under the operation of addition

Answer:

this is true

Step-by-step explanation:

The number of people who ride the bus is 70 students.

From the information, at the school, there are 7 students who ride the bus to school for every 4 students who do not ride the bus.

Therefore, the number of people who ride the bus if there are 40 people who do not take the bus will be represented by x.

This will be illustrated as:

4/7 = 40/x

Cross multiply

4x = 40 × 7

4x = 280

Divide

x = 280/4

x = 70

Therefore there are 70 students.

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At Everton Middle School, there are 7 students who ride the bus to school for every 4 students who do not ride the bus. How many people ride the bus of there are 40 people who do not take the bus?

We have a line defined by two points, P(-4,9) and Q(12,1).

Knowing two points of the line, we can calculate the slope with the formula:

In this case, the slope will be:

With the slope and one point we can express the equation in slope-point form:

The x-intercept is the value of x that makes the function f(x) become 0.

In this case, we have to find x so that y = 0.

We can replace y in the equation and calculate x as:

Then, for the x-intercept is x = 14.

Answer:

a) The equation of the line is y = (-1/2)*x+7

b) The x-intercept is x = 14.

[tex] ({x}^{2} + 8x + 16) \\ bring \: out \: the \: x \: and \: ivide \: the \: 8 \: by \: 2[/tex]

Equivalent linear expressions are expressions that have the same value. That is, if you have two linear expressions that are equivalent to one another, and you plug the same value in for the variable in each of them, you will get the same result in each of them.

In the case of this question, the equaivalent expression can be gotten by factorizing the expression

The equation of a linear model to describe the data is 14x - y = 26904

To find a linear equation of the provided data,

Let us put the number of legislature on the y axis and the year corresponding at the x axis,

According to provided information,

In year 2003, the number of legislature is 1138.

In year 2009, the number of legislature is 1222.

So here we have two points,

A(2003,1138) and B(2009,1222).

As we have two points now,

We can use the two point form of the line to find the equation of line,

It says if we have two point (a,b) and (c,d), then the equation of line is,

(y-b)/(x-a) = (d-b)/(c-a)

So, our equation of line is with points A and B is,

(y - 1138)/(x-2003) = (1222-1138)/(2009-2003)

(y-1138)/(x-2003) = 14

y - 1138 = 14x - 28042

14x - y = 26904

When,

x = 2000, y = n,

14(2000) - n = 26904

n = 1096.

The Linear Equation is 14x - y = 26904

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