a dart board is a regular octagon divided into regions as shown. suppose that a dart thrown at the board is equally likely to land anywhere on the board. what is the probability that the dart lands within the center square?

[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=60\\ k=50 \end{cases}\implies y=a(x-60)^2+50\qquad \textit{we also know that} \begin{cases} x=0\\ y=30 \end{cases} \\\\\\ 30=a(0-60)^2 + 50\implies -20=a(-60)^2\implies -20=3600a \\\\\\ \cfrac{-20}{3600}=a\implies -\cfrac{1}{180}=a\hspace{5em}\boxed{y=-\cfrac{1}{180}(x-60)^2+50} \\\\\\ \textit{when x = 80, what is "y"?}\qquad y=-\cfrac{1}{180}(80-60)^2+50 \\\\\\ y=-\cfrac{20^2}{180}+50\implies y=-\cfrac{20}{9}+50\implies y=\cfrac{430}{9}\implies y=47\frac{7}{9}[/tex]

The simplification of the trigonometric expression (sec(t) - cos(t))/sin(t) is; tan (t)

There are different trigonometric ratios such as;

sin x

tan x

cos x

sec x

cosec x

cot x

Now, we want to simplify the trigonometric expression;

(sec(t) - cos(t))/sin(t)

We know that;

sec (t) can be written as 1/cos t

Thus;

(sec(t) - cos(t))/sin(t) = [(1/cos t) - cos t]/ sin t

= (1/(sint cos t) - cos t/ sin t

= (1 - cos²t)/(sin t cos t)

= sin²t/(sin t cos t)

= sin t/cos t

= tan t

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Answer:

5 1/4 // 5.25

Step-by-step explanation:

OR

Answer:

  5 1/4

Step-by-step explanation:

You want the product of 6 and 7/8.

Your written-out version of the question gives you a clue how to solve it:

  six times seven eighths

The associative property of multiplication lets you rearrange this to ...

  (six times seven) eighths = forty-two eighths

That is, the product is formed by multiplying the integer by the numerator, and expressing the whole thing over the denominator:

  [tex]6\times\dfrac{7}{8}= \dfrac{6\times7}{8}=\dfrac{42}{8}\\\\=\dfrac{40+2}{8}=\dfrac{40}{8}+\dfrac{2}{8}=5+\dfrac{1}{4}\\\\=\boxed{5\dfrac{1}{4}}[/tex]

The improper fraction is converted to a mixed number by looking at the quotient and remainder from the division: 42/8 = 5 r 2 = 5 2/8 = 5 1/4.

__

Alternate solution

Sometimes, it can be helpful to look at the problem another way.

  6 × 7/8 = 6 × (1 -1/8) = 6 -6/8

  = 6 -3/4 = 5 1/4

Answer:

No

Step-by-step explanation:

The sum of the squares of the lengths of the two shorter sides is [tex]10^2+12^2=244[/tex].

The square of the length of the largest side is [tex]14^2=196[/tex].

Because these two values are not equal, the side lengths do not satisfy the Pythagorean theorem. Therefore, the triangle is not a right triangle.

If the fishes are divided to be in tenths, then the total pieces of fishes that would be available would be 1730

It is assumed that Jorge has 173 fish that he intends to cut up into smaller portions for his dog sled team.

The amount of fish pieces that would remain if Jorge divided each fish into tenths must be determined.

We are aware that there are 10 pieces to every fish.

There are a total of 173 fish available for the dog.

The product of the number of fish that are available and the number of pieces that each fish is divided into results in the total number of fish.

173 * 10

= 1730 pieces of fish.

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Complete question

Jorge has 173 fish for his dog sled team that he wants to divide into smaller pieces. how many pieces of fish would there be if jorge divided each fish into tenths.

The transformation that occurs from the graph (y = x²) to the graph of [y = (x − 5)² + 7] is (D) a vertical shift up 7 units and a horizontal shift right 5.

So, the transformation from:

First, plot both graphs.

(Refer to the graph attached below)

Therefore, the transformation that occurs from the graph (y = x²) to the graph of [y = (x − 5)² + 7] is (D) a vertical shift up 7 units and a horizontal shift right 5.

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The probability that it takes at most 1 hour of machining time to produce a randomly selected component  is  0.04074

we are provided  with  the  independent  time which are 15, 20, and 30 min and the respective standard deviations which are 2, 1, and 1.8 min.So the total  mean X= 15+20+30 =65, as we know that

Variance = ( standard deviation )²

=> Variance = 2² + 1² + 1.8² = 8.24

since standard deviation = √variance

=>Standard deviation = 2.87

so the z score = X -mean /standard deviation

since here X = 1 hour = 60 mintues

z = 60-65/2.87 =  -1.74216

So the probability, P( z≤ -1.74216) = 0.04074

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Answer:

The answer is (1, 6)

Step-by-step explanation:

The probability that the size of the family is 4 or more rounded to three decimal places is 0.361.

Given that families are selected at random, to find the probability that the size of family 4 we need to select and add those probabilities whose family size is more than and equal to 4.

P(X ≥ 4) = P(4) + P(5) + P(6) + P(7)

P(X ≥ 4) =  19.2 + 11.6 + 3.3 + 2.0

P(X ≥ 4) = 36.1

Since we need the answer rounded off to three decimal places, we can divide the answer by 100 which will give the final answer which is 0.361.

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The equation that shows the total cost, depends on the number of students going is y = 21.25 + 14.75x

Equation:

An equation is made up of two expressions connected by an equal sign.

For example, y = 3x + 6 is an equation.

Given,

The president of the Huerta Middle School science club suggested a field trip to the local aquarium. Tickets will cost $21.25 for the club adviser and $14.75 for each student who goes.

Here we need to find the equation that shows the total cost depends on the number of students.

Let us consider x be the number of students and y be the cost for x number of students.

Here we know that, there is one club advisor whose ticket cost is $21.25 and the cost per student is $14.75.

So, based on these details, the equation for the total cost is calculated as,

=> y = 21.25 + 14.75x

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80°,20° or 50°,50° are possible for the other two angles.

Given:

One angle of an isosceles triangle measures 80°.

we assumed that the 80° is one of the equal angles, then there is another 80° angle.That makes 160°.

Since a triangle always totals 180°,

180° - 160° = 20°.

if the 80° was the only different angle instead,the two remaining angles total:

180 - 80 = 100

Since we have two identical angles remaining, we need only divide the 100° in half to get the final answer:

100/2 = 50°.

Therefore 80°,20° or 50°,50° are possible for the other two angles.

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The following are features of the parabola shown in the diagram:

Vertex:  (2, -1)

Axis of symmetry: x = 2

The parabola opens downward.

The vertex of a graph is the coordinates of the point where the tip of the parabola lies at.

What is the Axis of Symmetry of a Parabola?

The axis of symmetry of a parabola passes through the vertex and is it expressed as the x-coordinate of the vertex of the parabola.

The tip of the parabola shown in the image above is at (2, -1), and the parabola as can be seen opens downward.

Therefore:

The vertex of the parabola is (2, -1)

The axis of symmetry would be expressed as x = 2. The parabola opens downward as well.

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Answer:

£22.80

Step-by-step explanation:

To work out how much Ross has to pay for his ticket, you first need to calculate how much the 1/3 of the full price is.
To do this, you divide the 34.20 by 3.
34.2 / 3 = 11.4
So Ross gets a discount of £11.40
To work out the price, that Ross has to pay, we substract the discount from the normal price:
34.2 - 11.4 = 22.8
So Ross pays £22.80 for his ticket.

Answer:

Step-by-step explanation:

5 dollars and 25 cents

Turning of head is rooting reflex.

Reflex is defined as the action which is performed without thought. In other words, it is an unconscious behaviour or involuntary movement. Newborns have different reflexes such as rooting reflex, moro reflex, stepping reflex, tonic neck reflex and grasp reflex.

Rooting reflex acts on touch. Based on this, babies feed themself. They start sucking when the roof of their mouth is touched. Moro reflex occurs on sudden sound or movement of high intensity. Tonic neck reflex results in fencing position of baby. Grasp reflex is seen when baby closes their fingers and stepping reflex concerns legs.

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The two values of x which are root of the given equation are; x = (-3 + √29)/2 and x = (-3 - √29)/2.

It follows from the task content that the two values of x which are roots of the given quadratic equation be determined.

Recall that the roots of quadratic equations are given by the formula;

x = {-b ± √(b² - 4ac)} / 2a

Since the given equation is; x² + 3x - 5; it follows that; a = 1, b = 3 and c = -5.

Therefore, the roots are as follows;

x = {-3 ± √(3² - 4•1•-5)} / 2(1)

x = (-3 ± √29)/2

Therefore, the required roots are;

x = (-3 + √29)/2 and x = (-3 - √29)/2

Ultimately, the roots of the given quadratic equation x² + 3x - 5 are; x = (-3 + √29)/2 and x = (-3 - √29)/2.

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The age of Marcus now is 20 years as 8 years ago Marcus was 12 years old.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical sentence with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10. A mathematical equation that depicts the connection between two expressions on opposite sides of the sign. It generally consists of one variable and one equal to symbol. 2x - 4 = 2 is an example. x is a variable in the preceding example.

Let his age now be x.

x-8=12

x=20

Marcus is currently 20 years old, although he was 12 years old eight years ago.

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A double-blind placebo control group study is used to control for observer bias and eliminate testing effects. So option c is correct.

A double-blind placebo control group study is one in which subjects are randomly assigned to either a control group, who receive a placebo, or an experimental group, who receive the treatment being studied. The researcher is not aware of which subjects are in which group, and neither are the subjects. This design is used to control for observer bias and eliminate testing effects.

This type of study is important because it allows researchers to test the efficacy of a new treatment without the risk of bias. By eliminating the possibility that the researcher or the subjects will know who is receiving the treatment and who is receiving the placebo, any expectations or preconceptions about the treatment can be avoided. This type of study is also important because it helps to control for the placebo effect, which is the phenomenon whereby subjects in the control group may experience some benefits from the placebo itself.

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Answer:

-2x+18, and -2(x-9)

Step-by-step explanation:

4x+18-6x

4x-6x+18

-2x+18

-2(x-9)

-2x+18

Use the compass to join the two circles together, this statement is not a step used when constructing an inscribed equilateral triangle.

A polygon having three vertices and three sides are called a triangle. The triangle's angles are created by joining its three sides end to end at a single point.

The triangle's construction does not include claim D, which is the case. Use the compass to join the two circles together.

It is necessary to keep the compass at a width equal to the circle's radius and to position it at the point where the circle and radius connect while building an inscribed equilateral triangle.

Additionally, it's crucial to pivot an arc the radius's length away from the circle's point. It is not a part of the steps to join the two circles using the compass.

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The expected number of classes a student will take in a given semester is 1.89

Expected value is defined as the predicted value of a variable, calculated as the sum of all possible values each multiplied by the probability of its occurrence.

Given :

x|  0       1        2       3      45  

p| 0.4 0.25  0.15  0.08  0.02

where x = number of classes

p = probability

The expected value of x, E(x) =Σ xp

E(x) = (0×0.4) + (1×0.25) + (2×0.25) + (3×0.08) + (45×0.02)

E(x) = 0 + 0.25 + 0.5 + 0.24 + 0.9

E(x) = 1.89

Therefore, the expected number is 1.89.

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A store received shipment of 37 tvs valued at 625 each what is the total value of the shipment?

37 * $625 = $23,125

Answer:

Step-by-step explanation:

Given,

No. of nails the factory makes = 600

Time taken by the factory to make 600 nails = 3 minutes

So,

Time taken by the factory to make 1 nail = [tex]\frac{3}{600}[/tex] minutes

∴ Time taken by the factory to make 27000 nails

= ( [tex]\frac{3}{600}[/tex] × [tex]27000[/tex] ) minutes

= ( [tex]\frac{1}{2}[/tex] × [tex]270[/tex] ) minutes

= 135 minutes

Or,

As we know ,  [ 1 minute =  [tex]\frac{1}{60}[/tex] hour]

So, 135 minutes = [tex]\frac{135}{60}[/tex] hours

= 2.25 hours

Now, [1 hour = 60 minutes]

0.25 hours = [tex]\frac{1}{4}[/tex] hours

= [tex]\frac{1}{4}[/tex] × 60 minutes

= 15 minutes

Hence,

The time taken by the factory to make 27000 nails is 2 hours 15 minutes (Ans)

Answer:

2.25 hours or 2 hours 15 minutes

Step-by-step explanation:

600 nails / 3 minutes = 200 nails / minute

27,000 nails / 200 nails/minute = 135 minutes

1 hour = 60 minutes

135 minutes × 1 hour / 60 minutes = 2.25 hours

2.25 hours = 2 hours  + 0.25 hours × 60 minutes/hour = 2 hours 15 minutes

Answer: 2.25 hours or 2 hours 15 minutes

No. of coins in jar of nickels is 207 and of dimes is 103.

Let the no. of coins of dimes = x

No. of coins of nickels = 2x

Total = 310

x + 2x = 310

     3x = 310

       x = 310/3

          = 103.33

          ≈ 103

No. of coins of dimes = 103

No. of coins of nickels = 310 - 103

                                     = 207

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The distance and bearing of the boat from the port areas follows;

The boat is locates at approximately 157.15 kilometers and on a bearing of 150° from the port.

A bearing in mathematics is an angle that is measured clockwise, from the north or y-axis direction.

The speed at which the Coast Guard cutter travels = 30 knots

Bearing of the Coast Guard cutter Angelica = 95°

The time the coast guard travels in the initial direction = 2 hours

The direction the Coast Guard cutter changes to = 185°

Time of traveling in the new direction = 2 hours

30 knots = 55.56 km/hr

The distance traveled in the first direction = 55.56 km/hr × 2 hr = 111.12 km

The distance traveled in the second direction = 55.56 km/hr × 2 hr = 111.12 km

From the attached drawing, we have that the figure formed by the path of the Coast Guard cutter is an isosceles triangle

The distance from the port to the location of the boat, given by Pythagorean theorem is; l = √(111.12² + 111.12²) ≈ 157.15

The distance f the boat from the port is approximately 157.15 kilometers

The base angles of an isosceles right triangle are 45°

Therefore, the bearing is 95° + 45° = 150°

The bearing from the port to the boat is 150°

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Answer:

y=5 x= -2 z=1 the procedure Is in the picture

Answer:

y=-0.4x - 1.2

Reason:

The digit in the tens place is 1. Just to the right is 5, which tells us to bump the 15 up to 20.

We can say that 15.0872 is closer to 20, than it is to 10.

Be sure not to mix up "tens place" with "tenths place".

The round-off from the number 15.0782 to the nearest 10 will be 20.

When a number is rounded off, its value is maintained but is brought closer to the next number, simplifying the number. For entire numbers as well as decimals at different places of hundreds, tens, tenths, etc., it is done.

A number can be rounded off to its lower value if the number after the decimal is between 0 and 4. The number will be rounded off to its higher value if the number after it is between 5 and 9.

Given that the number is 15.0782. The round-off to the nearest 10 will be 20 for the number.

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