Find the tangent of

The 75 entries in a costume contest, 31 entrants were dressed as heroes and 31 entrants were wearing a mask. 8: No masks or costumes were worn by contestants .

The possibility of an event occurring is described by the concept of probability. In real life, we frequently have to make predictions about the future. We might know about the result of an occasion.

We declare that there is a possibility that the event will take place when this occurs.

In conclusion, probability can be used in a lot of great ways in business, entertainment, and this new area of artificial intelligence.

By simply dividing the total number of possible outcomes by the favorable number, the probability of an event can be calculated using the probability formula.

n(A)=31 and n(B) = 20 and n(AB) =9

50-42 = 8

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If Cody was 10 %, percent taller than he was on the first day of school last year then he was 150 cm tall on the first day of school last year.

 To find out the height of Cody on the first day of school last year, we need to perform a calculation as follows:

           Let's say their height of Cody on the first day of school last year is 'x'.

           His height of Cody on the first day of school this year is 165 cm.

           Cody is 10% taller than he was on the first day of school last year, so:

                      165 = x + (10% of x)

    Simplifying this equation will give

                        165 = x + 0.1 x 165

                               = 1.1xx

                               = 150

           Therefore, Cody was 150 cm tall on the first day of school last year.

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Answer: x=6

Step-by-step explanation:

Step 1: Add all the 4's together (20) and then you get 20+(5*x)=50

5x6=30+20=50.

Answer:

Step-by-step explanation:

[tex]x^2=17^2-15^2[/tex]     (Pythagoras Theorem)

[tex]x^2=64[/tex]

[tex]x=8[/tex]

The intercepted arcs of the inscribed angle are in proportion to the inscribed angle itself. In other words, the larger the inscribed angle, the more significant the intercepted arc it cuts, and vice versa. So, in an equilateral triangle, each of the inscribed angles of the circle measures 60°, which is half of the central angle of 120° that intercepts the same arc.

The angle measure and intercepted arcs of inscribed angles in an equilateral triangle inscribed in a circle are related, and the relationship between inscribed angles and central angles in a circle is that the inscribed angles are half of the central angle. Let us have a more in-depth understanding of these two angles.An inscribed angle is an angle that has its vertex on the circle and is formed by two chords that intersect at that point. It is half of the central angle that intercepts the same arc.A central angle is an angle whose vertex is at the center of the circle, and the sides of the angle pass through any two points on the circumference of the circle.

For an equilateral triangle inscribed in a circle, each angle measures 60°, and the central angle measures 120°. So, each of the two inscribed angles measures half of the central angle, i.e., 60°.The relationship between inscribed angles and intercepted arcs.

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To make 70 cups of fruit soda with a juice-to-sparkling water ratio of 4:3, Milo will need 40 cups of juice and 30 cups of sparkling water.

If the juice-to-sparkling water ratio is 4:3, then we can write it as 4x:3x, where x is a common factor.

Let's say Milo wants to make a total of 7x cups of fruit soda (since 4x + 3x = 7x). We know that 7x = 70 cups, so x = 10.

Therefore, Milo needs 4x = 40 cups of juice and 3x = 30 cups of sparkling water.

You will therefore need 40 cups of juice and 30 cups of sparkling water to generate 70 cups of fruit soda with a 4:3 juice-to-sparkling water ratio.

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Therefore, the area of triangle XYZ is 2 square units.

Area is a measure of the size of a two-dimensional shape or surface. It is defined as the amount of space inside the boundary of a flat or planar figure, such as a triangle, square, rectangle, or circle. The unit of area is typically square units, such as square meters (m²), square feet (ft²), or square centimeters (cm²).

Here,

To determine the area of triangle XYZ with coordinates (6,1), (2,5), and (10,9), we can use the formula for the area of a triangle:

Area = (1/2) * base * height

where the base is any side of the triangle and the height is the perpendicular distance from the base to the opposite vertex.

Distance between (6,1) and (2,5):

= √((6 - 2)² + (1 - 5)²)

= √(20)

So, the base of the triangle is √(20).

We can use the formula for the distance between a point and a line to do this:

Distance from (10,9) to line passing through (6,1) and (2,5):

= |(10 - 6)(5 - 1) - (2 - 6)(9 - 1)| / √((5 - 1)² + (6 - 2)²)

= 4 / √(20)

So, the height of the triangle is 4 / √(20).

Now, we can plug in the values for the base and height into the formula for the area of a triangle:

Area = (1/2) * base * height

= (1/2) * √(20) * (4 / √(20))

= 2

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Answer:

The answer to your problem is, y = 1

Step-by-step explanation:

2(4y - 1) = 6, use distributive property: a(b - c) = ab - ac

8y - 2 = 6, add 2 to both sides

8y = 8, divide both sides by 8

Y = 1

Thus the answer to your problem is, y = 1

Answer:

1 is the answer

I took the test

3 x 10-2 is 30,000 times less powerful than 9 x 10-2. If 3 x 10 towards the negative 2 power equals times as much as 9 x 10 to a second power, then

Another way to put it is 2 + 3 = 6. As we've seen, is equivalent to 2 3. The multiplier is the quantity that multiplies the number of these equal groups by the multiplicand, the quantity of items in each group.

Given that 10-2 is 1/100 and 10-2 is 100, we may rephrase the formulas as follows:

9 x 100 = 900

3 x 1/100 = 0.03

At this point the values are comparable:

How many times more than 0.03 is 900?

We may calculate it by dividing 900 by 0.03: 900 0.03 = 30,000

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Answer:

HHH, HHT, HTH, HTT, THH, THT, TTH, TTT

Step-by-step explanation:

You have to construct a probability tree diagram.

Answer: 2,000

Step-by-step explanation:

4 x 100 = 400

6 x 100= 600

400 + 600= 1,000

10 x 100= 1,000

1,000 + 1,000= 2,000

After calculation, we know that the time taken by the lorry is 3 hours and 20 minutes.

Time is the ongoing progression of existence and things that happen in what seems to be an irrevocable order from the past, present, and forward into the future.

Military time starts with 0000, also known as "zero hundred hours" or just "zero hundred," at the stroke of midnight.

Then, multiply each hour by one hundred, such that 1 a.m. is equal to 0100 (zero one hundred) hours, 2 a.m. is equal to 0200 (zero two hundred) hours, and so on.

So, we need to calculate the time as follows:

Leaving time = 14:55

Arriving time = 18:15

Then,

14:55 to 15:15 = 20 minutes

Then, 15:15 to 18:15 = 3 hours

Then, the total time taken would be:

3 hours and 20 minutes

Therefore, after calculation, we know that the time taken by the lorry is 3 hours and 20 minutes.

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Complete question:

On the return journey, the lorry leaves at 14 55 and arrives at the factory at 18 15. Calculate the time taken.

Therefore, they took in $43.10 selling watermelons that day.

Describe the dollar sign($)?

The dollar sign, also referred to as the peso sign, is a symbol that looks like a capital "S" crossed with one or two vertical strokes ($ or Cifro symbol depending on typeface), and it's used to denote the unit of many different currencies around the world, including the majority of currencies denominated in "pesos" and "dollars." The Portuguese word for the specifically double-barred Cifro symbol is cifro.

The sign is also present in a number of compound currency symbols, including those for the Nicaraguan córdoba (C$) and the Brazilian real (R$).

If they sold 5/6 of the watermelons, then they sold 8/6 of the watermelons. So, they sold 4/3 of the watermelons.

If they sold 4/3 of the watermelons for $5.75 each, then they sold each watermelon for $4.31.

They sold 5/6 of the watermelons for $5.75 each,

so they sold

5/6 × 4/3

= 20/18 = 10/9 of the watermelons for $4.31 each.

$4.31 * 10 = $43.10 That day.

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Yes, there are enough evidence to show mean CO2 emission is lower in 2010 than in 2004.

The random variable is mean CO2 emission per capita , population parameter is CO2 emission per capita in population and null hypothesis is rejected as p-value is smaller than significant value.

The random variable is represented as the mean CO2 emission per capita.

The population parameter represented as the interest is the true mean CO2 emission per capita in the population in 2010.

Let μ_0 be the population mean CO2 emission per capita in 2004

And μ_1 be the population mean CO2 emission per capita in 2010.

The null hypothesis is,

There is no difference in the mean CO2 emissions per capita between 2004 and 2010,

H0: μ_0 = μ_1

The alternative hypothesis is,

The mean CO2 emissions per capita in 2010 are lower than the mean CO2 emissions per capita in 2004,

Ha: μ_0 > μ_1

To determine whether there is enough evidence to reject the null hypothesis,

Collect data on CO2 emissions per capita in 2010 and perform a hypothesis test .

Using a suitable statistical test such as a one-sample t-test.

If the test results in a p-value that is smaller than the chosen significance level (typically 0.05).

Reject the null hypothesis .

And conclude that there is enough evidence to show that the mean CO2 emissions per capita are lower in 2010 than in 2004.

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The probability of selecting green, blue, red, and yellow marbles from the bag is 1/35.

To find the probability of choosing specific marbles from the bag, we first need to find out the total number of ways in which four marbles can be selected from seven marbles.

The total number of ways in order to select 4 marbles from 7 marbles is given by the combination formula:

C(7,4) = 7!/(4!3!) = 35

There are 35 ways in which four marbles which will be selected from the bag. We need to find out the number of ways in which we can select green, blue, red, and yellow marbles.

We have only one way to select these specific four marbles from the bag. Number of ways to select green, blue, red, and yellow marbles is 1.

Probability of selecting green, blue, red, and yellow marbles:

P = (Number of ways to select green, blue, red, and yellow marbles) / (Total number of ways to select 4 marbles)

P = 1/35

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If the altitude of a triangle is increasing at a rate of 3 centimeters/minute while the area of the triangle is increasing at a rate of 1 square centimeter/minute. then the Base of the triangle is changing at a rate of 28.2 cm/min when the altitude is 10 cm and the area is 94 sq cm.

The given data is the altitude of a triangle is increasing at a rate of 3 centimeters/minute while the area of the triangle is increasing at a rate of 1 square centimeter/minute. then the rate of the base of the triangle changing when the altitude is 10 centimeters and the area is 94 square centimeters is calculated as,

  Area of a triangle = 1/2 * base * height

    The given area of the triangle is 94 square centimeters.

 Area of the triangle = 1/2 * base * altitude

 94 = 1/2 * b * 10b

      = 18.8 centimeters

Differentiate w.r.t t 94 = 1/2 * b * hdb/dt

                                     = -94 / 5 dA/dt

                                     = 1 square centimeter/minute

                                     = dh/dt * b / 2dh/dt

                                      = (2 / b) * dA/dt

             Substitute the values in the above equation,

                         3 = (2 / 18.8) * dA/dtdA/dt

                           = (3 * 18.8) / 2

                           = 28.2

        square centimeters/minute Base of the triangle is changing at a rate of 28.2 cm/min when the altitude is 10 cm and the area is 94 sq cm.

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Therefore , the solution of the given problem of unitary method comes out to be least quantity of paint (40 fl oz) and the purple jar has the most (80 fl oz). (36 fl oz).

To accomplish the task, one may use this generally accepted ease, preexisting variables, as well as any significant components from the original Diocesan customizable query. If so, there might be an opportunity to interact with the item once more. Otherwise, every significant factor that affects how algorithmic evidence behaves will be gone.

Here,

We must convert all the measurements to the same units in order to evaluate the amounts of paint in each jar. All quantities should now be expressed in fluid ounces (fl oz):

=> 2 gallons 4 liquid ounces = 36 liquid ounces.

=> 80 fluid ounces = 5 glasses

=> equivalent to 39 fluid ounces

The quantities of paint in the jars are as follows:

=> 36 fl oz. blue container

=> 80 fl oz. purple container

=> 39 fl oz. green container

As a result, the blue jar has the least quantity of paint (40 fl oz) and the purple jar has the most (80 fl oz). (36 fl oz).

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Answer: the answer is A

reason:  224294 * 43 / 100 = around 96320

Answer:

The answer is Sin B

Step-by-step explanation:

I remember in 8th grade doing this

Finally, use the sum of interior angles equation again to find the measure of angle Y:
m∠Y = 180° - m∠X - m∠Z

Hello! To find the measure of each angle in triangle XYZ, we need to use the fact that the sum of the interior angles of a triangle is 180°. We are given that m∠X = (32x)° and m∠Z = (6.5x)°. Let's represent the measure of angle Y as m∠Y.

Now we can write an equation:

m∠X + m∠Y + m∠Z = 180°
(32x)° + m∠Y + (6.5x)° = 180°

We need to find the value of x and m∠Y. First, combine the x terms:

38.5x° + m∠Y = 180°

Now, we'll solve for x and then find m∠Y using the equation above. To find x, subtract m∠Y from both sides:

38.5x° = 180° - m∠Y

After finding the value of x, substitute it back into the expressions for m∠X and m∠Z to find the measures of angles X and Z.

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Answer:

We can use trigonometry to solve this problem. Let's call the distance from point A to the boat "x" and the distance from point B to the boat "y". Then we have:

In triangle AOC, tan(12) = OC / x

In triangle BOC, tan(64) = OC / y

We want to find the distance from point A to point B, which is the difference between x and y:

Distance AB = y - x

To solve for x and y, we need to eliminate OC. We can do this by setting the two expressions for OC equal to each other and solving for OC:

tan(12) = OC / x

OC = x tan(12)

tan(64) = OC / y

OC = y tan(64)

x tan(12) = y tan(64)

y = x tan(12) / tan(64)

Now we can substitute this expression for y into the equation for Distance AB:

Distance AB = y - x

Distance AB = x tan(12) / tan(64) - x

We can simplify this expression by factoring out an x:

Distance AB = x (tan(12) / tan(64) - 1)

Now we just need to plug in the values and calculate:

Distance AB = x (0.2174 - 1)

Distance AB = -0.7826 x

Since distance cannot be negative, we know that x > 0. Therefore, the boat is between point A and point B, and the distance from point A to point B is:

Distance AB = x (0.2174 - 1)

Distance AB = -0.7826 x

Distance AB ≈ 1.28 x

We don't know the actual value of x, but we can see that the distance from point A to point B is approximately 1.28 times the distance from point A to the boat when Jaxson measured the angle of depression to be 12 degrees.

Step-by-step explanation:

Answer:434

Step-by-step explanation:It’s correct

Answer:

Step-by-step explanation:129412515968569028414 m

Answer:

The value of the percentage increase = 6.7% × 59

The new value = 59 + The value of the percentage increase

Step-by-step explanation:

The new value =

59 + The value of the percentage increase =

59 + (6.7% × 59) =

59 + 6.7% × 59 =

(1 + 6.7%) × 59 =

(100% + 6.7%) × 59 =

106.7% × 59 =

106.7 ÷ 100 × 59 =

106.7 × 59 ÷ 100 =

6,295.3 ÷ 100 =

62.953 ≈

62.95

Answer:

3

Step-by-step explanation:

According to the given situation in the question the cost of one pen is £1.02 and the cost of one pencil is £0.12 .

Let the cost of one pen be x.

Let the cost of one pencil be y.

So, from the given condition given in question the equations are :-

The cost of 3 pens and 2 pencils is £3. 30 can be written in the equation, 3x + 2y = 3. 30 —-- (1)

The cost of 3 pencils and 2 pens is £2. can be written in the equation, 2x + 3y = 2 —--- (2)

So by solving equation (1) and (2),

3×equation (2) - 2×equation(1)

Now subtract 6x+4y=6.6 from 6x + 9y=6

5y = 0.6

y = 0.12

Put y = 0.12 in equation(1) then x = 1.02

Hence the cost of one pen is £1.02 and the cost of one pencil is £0.12.

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—-------- Correct question format is given below —--------

(Q). The cost of 3 pens and 2 pencils is £3. 30. The cost of 3 pencils and 2 pens is £2. 95.What is the cost of one pencil and one pen?

Step-by-step explanation:

The y-axis is where x = 0 ....so the y-axis intercept occurs at x = o

 put  in   '0' for 'x'

y = 0^2 + 2(0) + 10       <===== 10 is the y-axis intercept

The number of possible ways to select two vehicles = 55

Let m represents the number of cars and n represents the number of trucks.

An auto dealer has 5 different cars and 6 different trucks.

This means that m = 5 and n = 6

so, the total number of vehicles (t) would be,

t = m + n

t = 5 + 6

t = 11

Let us assume that p represents the number of possible ways to select two vehicles.

We use the combination formula.

[tex]^{n}C_r=\frac{n!}{r!(n-r)!}[/tex]

here, n = 11 and r = 2

Using combination formula,

p = [tex]^{11}C_2[/tex]

p = [tex]\frac{11!}{2!\times (11-2)!}[/tex]

p = 55

Therefore, the number of possible ways = 55

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(1)/(x)=(1)/(y)-(1)/(z) is an example of an equation that can be used to express z in terms of x and y. z can be expressed in terms of x and y as z= xy+1/y-x.

It is typically written using an equals sign “=” to show that the two expressions on either side of the equals sign are the same.

To solve the equation, it must first be rearranged so that z is on its own side of the equation.

This can be done by multiplying both sides of the equation by x and then subtracting (1)/(y) from both sides.

(1)/(x)=(1)/(y)-(1)/(z)

1-1/y= (x/y-x/z)-1/y

This yields the equation

y-1/y=(x/y-1/y)-(x/z+1/y)

y-1/y= (x-1/y)-(xy+1/zy)

(y-1/y)-(x-1/y)= (-xy)+1/zy

y-x/y= xy+1/zy

y-x=(xy+1)y/zy

Once the equation has been rearranged, the next step is to solve for z.

z= xy+1/y-x

z= xy+1/y-x

Therefore, z can be expressed in terms of x and y as z= xy+1/y-x.

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The equation of the function in vertex form is given by f(x)=-2(x-2)²-7/2.

It is the point at which the maximum or minimum value of a function is achieved. It is also known as the turning point of the graph of the function.

The equation of the function in vertex form is given by f(x)=a(x-h)²+k.

Using the given table, we can calculate the values of a, h and k.

Substituting the values of x and f(x) from the table, we get:-

-3/2=a(-1/2-h)²+k

-9/4=a(0-h)²+k

-5/2=a(1/2-h)²+k

-3/2=a(3/2-h)²+k

3/2=a(5/2-h)²+k

15/4=a(3-h)²+k

Solving these equations simultaneously, we get

a=-2, h=2 and k=-7/2

Therefore, the equation of the function in vertex form is given by

f(x)=-2(x-2)²-7/2.

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