3. The probability of winning a balloon dart game is 0.25. The odds of winning a ring toss game are 2:7. Which game gives you a better chance of winning?

Please help ​

Answer:

The value of sin 30 degrees is 0.5. Sin 30 is also written as sin π/6, in radians. The trigonometric function also called as an angle function relates the angles of a triangle to the length of its sides.

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Sin 0 Degree Trigonometry Formulas

Inverse Cosine Law of Sines Formula

#1

Scale ratio

#2

Unknown is actual length

So the ratio is

#3

The proportion is

#4

Must be multiplied with 0.75

#5

Actual length is 7.5ft

Answer:

Question 1

Given scale:  1 in = 10 ft

[tex]\textsf{Therefore, the scale as a ratio}=\sf \dfrac{\boxed{10}\:ft}{\boxed{1}\:in}[/tex]

Question 2

The ratio of the garden's actual length to its length in the drawing:

[tex]\sf \dfrac{x\:ft}{0.75\:in}[/tex]

Question 3

Therefore, the proportion is:

[tex]\sf \dfrac{10\:ft}{1\:in}=\dfrac{x\:ft}{0.75\:in}[/tex]

Question 4

Multiply both sides of the proportion by 0.75 to find x

Question 5

[tex]\begin{aligned}\textsf{Proportion}: \quad \quad \;\sf \dfrac{10\:ft}{1\:in} & = \sf \dfrac{x\:ft}{0.75\:in}\\\\\textsf{Mulitply both sides by 0.75}: \quad \sf 0.75\cdot \dfrac{10}{1} & = \sf 0.75 \cdot \dfrac{x}{0.75}\\\\\textsf{Simplify}: \quad \quad \quad \sf 7.5 & = \sf x\end{aligned}[/tex]

Therefore, the actual length of the garden is 7.5 ft

Answer:

152.3 approximately

Step-by-step explanation:

A polygon with 13 sides (and angles too) would be called tridecagon

Now, the sum of interior angles in a polygon is calculated by dividing the number of angles minus 2 by 180 [(n-2)*180]

(13-2)/180 = 1.980 and to find what is the measure of one angle, we divide the sum by the number of angles the polygon has

1.980/13 = 152.3 approximately

Work Shown:

x³ + x² + x + 1

(x³ + x²) + (x + 1)

x²(x+1) + 1(x + 1)

(x² + 1)(x + 1)

The basic outline is to pair up the terms into two groups. We factor each group separately, and then factor out the overall GCF (x+1). You can use the FOIL rule to verify the answer.

The factored form of x³ + x² + x + 1 is (x²+1)(x+1).

A number or other mathematical item is factored (or factorised; see English spelling changes) or factored by a number of factors, usually smaller or simpler things of the same kind.

We have,

x³ + x² + x + 1

Now, making groups as

(x³ + x²) + (x + 1)

= x² (x + 1) + (x+1)

= (x²+1)(x+1)

So, resulting expression is  (x²+1)(x+1).

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Answer:

D is the correct option.

All the best!

Answer:

A, C, and D

Step-by-step explanation:

Hope this helps!

If not, I am sorry.

Step-by-step explanation:

Since , internal sum of angle of triangle is 180°

So,

66 + x +49 + x+83 = 180

or, 198 + 2x = 180

or, 2x = 180 -198

or, 2x = -18

hence, x = - 9

Now angle A = x + 49

= (-9) + 49

= 40

Hence measure of angle A is 40°.

Answer:

40

Step-by-step explanation:

From triangle law ,

66 + x +49 + x+83 = 180

or, 198 + 2x = 180

or, 2x = 180 -198

or, 2x = -18

hence, x = - 9

Now angle A = x + 49

= (-9) + 49

= 40

Hence, answer is 40.

Answer:

31.73 grams

Step-by-step explanation:

70.83 g - 39.1 g = 31.73 g

Answer:

hope you can understand

The supplies travelled 45ft and it took 0.6min to get to the next floor.

Trigonometry is the branch of mathematics dealing with the relationship between the sides of a triangle and the angles.

Analysis:

The supplies distance travelled, distance of first floor from second floor and the ground form a right angled triangle.

so that sin 60 = 39/distance travelled by supplies

distance travelled by supplies = 39/sin 60 = 39/0.866 = 45 feet.

speed = distance / time

time = distance / speed = 45/70 = 0.6 min

In conclusion, the distance and time time taken for the supplies to get to the next floor is 45feet and 0.6 min respectively.

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Answer:

Slope= - 7/9

Step-by-step explanation:

m=rise/run

m=8-1= 7

    -3-6=-9

m=7/-9

- 7/9

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to find the slope of

[tex]\star\mathrm{(6,1)}\star[/tex]

[tex]\star\mathrm{(-3,8)}\star[/tex]

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

Here's the formula:

[tex]\star\boxed{\mathrm{\cfrac{y2-y1}{x2-x1}}}\star[/tex]

Where:

[tex]\star[/tex] y2 and y1 are y-coordinates

[tex]\star[/tex] x2 and x1 are x-coordinates

So substitute the values accordingly:

[tex]\star\mathrm{\cfrac{8-1}{-3-6}}[/tex]

Simplify!

[tex]\star\mathrm{\cfrac{7}{-9}}[/tex]

Which is the same thing as...

[tex]\star\mathrm{-\cfrac{7}{9}}[/tex]

Hope it helps you out! :D

Ask in comments if any queries arise.

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~Just a smiley person helping fellow students :)

g(x) = ¹/₂f(x - 2) -------> y-intercept at (0, - ¹/₂)

h(x) = f(x - ¹/₂) ------->  x-intercept at (1.5, 0)

j(x) = f(x) - ¹/₂ ------->  vertical asymptote at x = 0

m(x) = function decreases as x increases

We are given the function;

f(x) = In (x)

Now, from the given tiles and when we punch the respective values for the given functions, we can say that;

g(x) = ¹/₂f(x - 2) -------> y-intercept at (0, - ¹/₂)

h(x) = f(x - ¹/₂) ------->  x-intercept at (1.5, 0)

j(x) = f(x) - ¹/₂ ------->  vertical asymptote at x = 0

m(x) = function decreases as x increases

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Answer:

C angle H = 75.4

Step-by-step explanation:

In order to find the measure of angle H we must first find the value of x

Firstly it's good to know that the sum of the angles in a quadrilateral always add up to 360 degrees

Knowing this we can create an equation.

Since the angle measures must add up to 360 degrees we know that angle F + angle E + angle H + angle G = 360

Plugging in the given expressions for each angle we acquire

14x - 11 + 5x + 21 + 6x + 16 + 8x - 7

We can now solve for x

==> combine like terms

33x + 19 = 360

==> subtract 19 from both sides

33x = 341

==> divide both sides by 33

x = 10 1/3

Now that we have identified the value of x and we can plug in x = 10 1/3 into the given expression of angle H and evaluate to get the measure

Angle H = 8x - 7

==> plug in x = 10 1/3

Angle H = 8(10 1/3) - 7

==> multiply 8 and 10 1/3

Angle H = 82.7 - 7

==> subtract 7 from 82.7

Angle H = 75.6

C is the closest answer

Answer:

C. m∠H = 75.4°

Step-by-step explanation:

all sides of a quadrilateral add up to 360°

So, (5x + 21) + (14 - 11) + (6x + 16) + (8x - 7) = 360

Add like terms:

33x + 19 = 360

33x = 360 - 19

33x = 341

x = 341/33

x = 10.33...

Substitute:

∠H = 8x - 7

∠H = 8(10.3) - 7

∠H = 75.4°

The amount of plywood that he needs to buy will be 21 square feet.

Let the prism with a length of L of the rectangular surface.

And the dimension of the triangle is A, B, and C. Then we have

SA = 2(area of triangle) + 3(area of rectangle surface)

A triangular prism.

The rectangular sides are 3 feet by 2 feet, 3 feet by 2.5 feet, and 3 feet by 1.5 feet.

The 2 triangular sides have a base of 2 feet and a height of 1.5 feet.

Then the area of the triangle will be

⇒ 1/2 x 2 x 1.5

⇒ 1.5 square feet

The area of the rectangles will be

⇒ 3 x 2 + 3 x 2.5 + 3 x 1.5

⇒ 18 square feet

Then the surface area of the triangular prism will be

Surface area = 2 x 1.5 + 18

Surface arae = 3 + 18

Surface area = 21 square feet

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Answer: B. 28.26 ft2

Step-by-step explanation: I did this in school and got it right.

Answer:

B. 28.26 ft²

Explanation:

Here given:

Area of the fountain:

By definition of percentages, we conclude that Montraie has 10 coins saved in his box that come from a collection with a total of 50 coins.

In this question we know the quantity of coins in a box and such coins are part of the coin collection. By definition of percentage we have the total quantity of coins in the collection:

x = 10*(100/20)

x = 50

By definition of percentages, we conclude that Montraie has 10 coins saved in his box that come from a collection with a total of 50 coins.

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The minimum and maximum mass measurement is calculated as 1.467 kg and 1.533 kg respectively.

The minimum and maximum mass measurement is determined from the uncertainty in the measurement.

For a given uncertainty of 2.2%, the minimum and maximum mass measurement is calculated as follows;

2.2% of 1.5 kg = 0.022 x 1.5 kg = 0.033 kg

minimum mass = 1.5 kg - 0.033 kg = 1.467 kg

maximum mass = 1.5 kg + 0.033 kg = 1.533 kg

Thus, the minimum and maximum mass measurement is calculated as 1.467 kg and 1.533 kg respectively.

The complete question is below:

what is the minimum and maximum mass of 1.5 kg if the uncertainty in measurement is 2.2%?

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Using the normal distribution, it is found that there is a 62.4% probability that a data value is between 37 and 41.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem, the mean and the standard deviation are given, respectively, by:

[tex]\mu = 38, \sigma = 2[/tex]

As a proportion, the probability that a data value is between 37 and 41 is the p-value of Z when X = 41 subtracted by the p-value of Z when X = 37, hence:

X = 41:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{41 - 38}{2}[/tex]

Z = 1.5

Z = 1.5 has a p-value of 0.933.

X = 37:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{37 - 38}{2}[/tex]

Z = -0.5

Z = -0.5 has a p-value of 0.309.

0.933 - 0.309 = 0.624,

0.624 = 62.4% probability that a data value is between 37 and 41.

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Answer: Hope this explains everything for you!

y= -2x+3

Step-by-step explanation:

y= 2x-1 is wrong

First, we will start by identifying the y-int, the y-int is when x is zero. The y-int is 3 since when x is 0, y is 3, (0,3).

y= 2x+3 (So that means -1 is actually 3)

Plus even if your slope is 2, since from the 2 points you go up 2 and run by 1, if you're not going to calculate it with 2 points, you need to see if its uphill, downhill, etc. (More info in the image below) The slope is actually negative meaning it is -2.

So the equation of the line is actually y= -2x+3

x 's measure is already given

x=20°

Answer:

∡x = 20°

∡y = 160°

∠z = 160°

Step-by-step explanation:

Angles on a straight line sum to 180°

⇒ ∠z + 20° = 180°

⇒ ∠z = 180° - 20°

⇒ ∠z = 160°

The central angle measure equals the corresponding arc measure.

⇒ ∡x = 20°

⇒ ∡y = ∠z = 160°

Based on the entries into the TVM solver, the expression that will return the same value for PV is [tex]\frac{(620) (( 1 + 0.066)^{108} - 1) }{(0.066) (1 + (0.066))^{108}}[/tex].

The formula for present value for this series of cashflows is:

= [tex]\frac{(Payment) (( 1 + Interest rate)^{Number of years} - 1) }{(Periodic interest) (1 + (Periodic interest))^{Number of years}}[/tex]

Based on the P/Y and the C/Y being 12, the number of periods given in the graphing calculator will be the same in the formula, which is 108 periods.

The interest rate of 6.6% will also be the same in the formula.

The best option is therefore option B which has all these figures and so will give the same present value.

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Answer: 0.0055 and 108

aka ($620) ((1+0.0055)^108 -1 / (0.0055) (1+0.0055)^108

Step-by-step explanation: Just did it, Good luck! :)

[tex]\sqrt{-1} + 2 = i+2 = 2+i[/tex]

The surface area of the triangular prism is 153 cm².

Area = A + B + C

       =(9 × 15) + (0.5×6×3) + (0.5×6×3)

       = 135 + 9 + 9

       = 153 cm²

Hence, the surface area of the triangular prism is 153 cm².

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The closest among the choices is Choice C. $105.  Differences in amount may vary in the rounding off of the decimal numbers.

The complete question is given below as:-

Marcia has two credit cards and would like to consolidate the two balances into one balance on the card with the lower interest rate. The table below shows the information about the two credit cards Marcia currently uses.

Card A

Card B

Amount

$1,879.58

$861.00

APR

14%

10%

Monthly Payment

$43.73

$18.29

After 5 years, how much will Marcia have saved in interest by consolidating the two balances?

a.

$1,526.40

b.

$2,422.80

c.

$105.00

d.

$227.40

The amount received by an employee by giving the service or work to any frim will be termed as the income.

Given:

Card A - 1,879.58 ; APR 14%; monthly -43.73

Card B -    861.00 ; APR 10% ; monthly -18.29

5 years x 12 months/yr = 60 months.

Card A = 43.73 x 60 = 2,623.80

Card B = 18.29 x 60 = 1,097.40

Total : 2,623.80 + 1,097.40 = 3,721.20

Lowest APR is 10%. monthly rate: 0.83%

Total Card balance: 1,879.58 + 861 = 2,740.58

A = P * (r(1+r)^n) / [(1+r)^n -1]

A = 2,740.58 * [0.0083 (1.0083)^60] / [(1.0083)^60 - 1]

A = 2,740.58 * 0.014/0.64

A = 2,740.58 * 0.022

A = 60.29 monthly payment.

60.29 x 60 = 3,617.40

Separate cards: 3,721.20

Consolidated:     3,617.40

Difference: 103.80

Therefore closest among the choices is Choice C. $105.  Differences in amount may vary in the rounding off of the decimal numbers.

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The value of x from the given right triangle in rational form is 14√

This is a way of determining the sides and angles of a right triangles

From the given triangle

Opposite = 7√4 = 14

Hypotenuse = x

acute angle = 45 degrees

Using the theorem

sin 45 = 14/x

x = 14/sin45

x = 14√2

Hence the value of x from the given right triangle in rational form is 14√2

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The x-intercepts of f(x) are common to those of g(x) .

The x-intercept is the point on the coordinate at which a line, curve or plane intersect with the x-axis. The value of y is equal to zero at x-intercept.

For me, it helps to graph everything on the same xy coordinate system. Start with the given graph and plot the points shown in the table. You'll get what you see in the diagram below.

The blue point C in that diagram is on the red parabola. This point is the x intercept as this is where both graphs cross the x axis. Therefore, they have a common x intercept.

Choice 1 is not true due to choice 4 being true. We have f(x) = g(x) when x = 2, which is why f(x) > g(x) is not true for all x.

Choice 2 is not true. Point B is not on the parabola.

Choice 3 is not true. There is only one known intersection point between f(x) and g(x), and that is at the x intercept mentioned above. Of course there may be more intersections, but we don't have enough info to determine this.

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The measure of center that will be used to emphasize the average height of the students is frequency of the numbers.

The average height of the students is calculated as follows;

Average = total height/number of students

total height = 135  + 130 + 170 + 170 + 160 + 90 = 855

Average = (855)/(6)

Average = 142.5 cm

From the given heights of the students, 170 cm has the highest frequency and will influence the average height more.

Thus, the measure of center that will be used to emphasize the average height of the students is frequency of the numbers.

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Answer:

.................................................

Step-by-step explanation:

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