Which of the following is an example of independent events?

Answer:

5

Step-by-step explanation:

Fifteen years from now Ravi's age will be four times his present age. What is Ravi's present age? So, Ravi′s present age is 5 years.

Answer:

x=31

y=6

Step-by-step explanation:

2x+3y=80

x+y=37

solve by elimination:( multiply second equation by 2) to eliminate x

2x+3y=80

2x+2y=74

subtract the two equations:

2x+3y-(3x+2y)=80-74

2x+3y-3x-2y=6

y=6 (3 point basket)

substitute: x+y=37, x=37-6=31

x=31 (2 point shot)

Answer:

2 point shots: 31

3 point shots: 6

Step-by-step explanation:

to get the 3 point shots:

2x+3(37-x)=80

2x+111-3x=80

x=31

31+y=37

y=6 --> 3 point shot

to get the 2 point shots:

2(37-y)+3y=80

74-2y+3y=80

y=6

x+6=37

x=31 --> 2 point shot

Answer:

[tex]\frac{4}{5}[/tex]

Step-by-step explanation:

Given

[tex]\frac{48}{60}[/tex]

To simplify find the highest common factor of 48 and 60, that is 12

Divide both values by 12

[tex]\frac{48}{60}[/tex] = [tex]\frac{4}{5}[/tex] ← in simplest form

The fraction is in simplest form when no other factor but 1 divides into the numerator and denominator

Answer:

$11

Step-by-step explanation:

[tex]\left\begin{array}{c|ccc}&$Lose \$25&$Gain \$5&$Gain \$45\\$Stock ABC&40\%&15\%&45\%\end{array}\right[/tex]

We want to calculate the expected gain or loss of Stock ABC with the probabilities above.

Note that loss is written in negative.

[tex]E$xpected Value =$ (-25 \times 40\%)+(5 \times 15\%) + (45 \times 45\%)\\=(-25 \times 0.4)+(5 \times 0.15)+(45 \times 0.45)\\=-10+0.75+20.25\\=\$11[/tex]

Stock ABC has an expected gain of $11.

Answer:

C. and F.

Step-by-step explanation:

A scalene triangle is a triangle in which all three sides have different lengths. Also the angles of a scalene triangle have different measures. Some right triangles can be a scalene triangle when the other two angles or the legs are not congruent. Right angle are 90 degrees

Answer:

C and F

Step-by-step explanation:

This triangle is not an equilateral triangle because their lengths are not equivalent to each other. It is not an isosceles triangle because no two lengths are equivalent to each other. It is a right triangle because it has one right angle(A 90 degrees angle.) It is not an obtuse triangle because there isn't an angle that is obtuse(More than 90 degrees but less than 180 degrees angle.) It isn't an acute triangle either because not all three angles are acute(Less than90 degrees angle.) Lastly, it is also a scalene triangle because none of the triangle lengths are equivalent to each other.

Answer:

5

snake population at time zero, or the initial snake population, is 5

Step-by-step explanation:

Since we see point (0, 5) written on the graph, we see that the y-intercept is 5.

That means that the snake population at time zero is 5. The initial snake population was 5.

Answer:

£14.29

Step-by-step explanation:

0.98x=14

x=14.29

Answer:

14.28

Step-by-step explanation:

Answer:

The answer is given below

Step-by-step explanation:

The addition postulate for line segment states that if we have points A, C and a point B on line AC, The distance between points A and C can be given as:

AC = AB + BC

Point A is at -6, point B is at -1, point C is at +2 and point D is at point 8.

Therefore using line segment postulates:

AD = AB + BC  + CD

But AB = -1 - (-6)= -1 + 6 = 5

BC = 2- (-1) = 2 +1 = 3

CD = 8 - (+2) = 8 - 2 = 6

Also AD = 8 - (-6) = 8 + 6 = 14

To prove AD = AB + BC  + CD

AD = 5 + 3 + 6 = 14

Answer: 1.0cm

Step-by-step explanation:

Given the following :

Volume = Mass / Density

Given that:

Mass of spherical grape = 8.4g

Density = 2g/cm^3

Radius of the grape =?

Volume of grape = mass of grape / density of grape

Volume = 8.4g / 2g/cm^3

Volume = 4.2cm^3

Volume of a sphere = (4/3)πr^3

4.2 = 4/3 * 3.14 * r^3

4.2 = (12 * r^3) / 3

4.2 × 3 = (12 * r^3)

12.6 = 12r^3

r^3 = 12.6/12

r^3 = 1.05

r = 1.01639635681

r = 1.0 cm ( to the nearest tenth)

Answer:

1.0 cm

Step-by-step explanation:

Answer:

the answer is line RQ and line OP

Answer:

The answer is B: (x-32)

Answer:

B

Step-by-step explanation:

ape.x

Answer:

b

Step-by-step explanation:

C cuts a and b as well.Therefore it will be the transversal of a and b.

plzz mark this answer as brainliest answer

Answer:

b

Step-by-step explanation:

just  did it on edge

Answer:

Step-by-step explanation:

We that the area of a circle is Pi times r^2 where r is the radius

Let A be the area of the first circle and S the area of the second one and T the total one

A=4^2× Pi

S=6^2× Pi

T = Pi( 4^2 +6^2)

= Pi ( 16+36) = Pi× 52

52 is the radius square

So r = root square 52 = 2 root square 13

Answer:

Volume of wheat = 147.26 m³ (check the explanation)

Step-by-step explanation:

The question still lacks some details such as the size of the silo. We will go forward by assuming the size of the silo to aid our calculation. Silos are cylindrical storage structures that range from 3 - 27 m in diameter and 10 - 90 m in height. For the purpose of this question, let's assume that the size of the silo is 5 m (diameter) by 15 m (height).

Let's list out the parameters to be used:

diameter (D) = 5 m; r = D ÷ 2 ⇒ r = 5/2 = 2.5 m,

height (h) = 15 m

Volume of silo = πr²h = π * 2.5² * 15

V (silo) = 294.52 m³

The silo is half full ⇒ ½ * V

Volume of wheat stored is given by half of the silo volume, since the silo is half-full

V (wheat) = ½ * 298.52

V (wheat) = 147.26 m³

Answer:

cot(45 -A) = cot(90 - (45 + A)) =  tan(45 + A) = tan2A + sec2A

Step-by-step explanation:

cot(45 -A) = tan2·(A) + sec2·(A)

We have;

tan2(A) + sec2(A) = sin2(A)/cos2(A) + 1/cos2(A) = (sin2(A) + 1)/cos2(A)

= (sin²(A) + cos²(A) + 2·sin·(A)cos(A))/(cos²A - sin²A)

= (sin(A) + cos(A))²/((cos(A) -sin(A))(cos(A) +sin(A)))

= (sin(A) + cos(A))/((cos(A) -sin(A)))

= (cos(A)(1 + sin(A)/cos(A)))/(cos(A)(1 - sin(A)/cos(A)))

= (1 + tan(A))/(1 - tan(A))

= (tan 45 + tan(A))/(1 - tan(45)·tan(A)) = tan(45 + A)

cot(π/2 - x) = tan(x)

= cot(π/2 - (45 + A)) =  tan(45 + A)

π/2 = 90°

= cot(90 - (45 + A)) =  tan(45 + A)

cot(45 - A) =  tan(45 + A) =  tan(2A) + sec(2A).

Answer:

30, root 3 over 2 or the third option

I did it on my quiz :)

But basically it is 30, root 3 over 2 because sin and cos are complements to one another.

Trigonometric Identities are equalities that utilize trigonometry functions and hold true for all variables in the equation. The correct option is C; 30°, (√3)/2.

Trigonometric Identities are equalities that utilize trigonometry functions and hold true for all variables in the equation. There are several trigonometric identities relating to the side length and angle of a triangle.

Given that sin(60°) is (√3)/2. Therefore, the value of cos can be written as,

sin(60°) = (√3)/2

cos(90° - 60°) = (√3)/2 {Cos(90° - x) = Sin(x)}

cos 30° = (√3)/2

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Answer:

bearing of A from C is - 65.24°

the distance |BC| is 187.84 m

Step-by-step explanation:

given data

girl walks AB = 285 m (side c)

bearing angle B = 78°

girl walks AC = 307 m (side a)

solution

we use here the Cosine Law for getting side b that is

ac² = ab² + bc² - 2 × ab × cos(B)     ...............1

307² = 285² + x²  - 2 × 285 cos(78)

x = 187.84 m

and

now we get here angle θ , the bearing from A to C get by law of sines

sin (θ) = [tex]\frac{187.84}{307} \times sin(78)[/tex]

sin (θ) =  0.5985  

θ = 36.76°

and as we get here angle BAC that is

angle BCA = 180 - ( 36.76° + 78° )

angle BCA = 65.24°

and here  negative bearing of A from C so - 65.24°

Answer:

1) 2 (11) - 1/2

Step-by-step explanation:

Given the following:

A line “t” is parallel to 3y = 6x + 9

Equation of a line;

y = mx + c

Where the Coefficient of x, 'm' is the gradient or slope and c is the intercept.

From the equation;

3y = 6x + 9

Divide through by 3

y = 2x + 3

Comparing the line equation with the equation provided :

Coefficient of x = 2, therefore 2 = slope

Since line t is Parallel to y = 2x + 3

Then, slope of line 't' is the same as that of y:

Slope of line 't' = 2

(11) For perpendicular lines :

Slope of original line : 3y = 6x + 9

Divide through by 3

y = 2x + 3

Compare to line equation:

y = mx + c

m = gradient/ slope, c = intercept

Gradient of original line, m = 2

For a line 'r' perpendicular to y = 2x + 3

Gradient, m of line r equals to the negative reciprocal of the gradient of original line

Therefore, gradient of r equals :

-1/2

Answer:

b) 1/6

Step-by-step explanation:

You need to multiply the results from the question a) by 2.

1*2=2

----------

6*2=12

=2/12

now simplify it

2/12

=1/6

Hope this  helps <3

Answer: 199.5 ft

Step-by-step explanation:

Given: A scientist was in a submarine below sea level studying ocean life over the next 10 minutes she went down 58 ft.

If she was 141.5 ft below sea level after she went down , then she had been (141.5 ft + 58 ft) = 199.5 ft below sea level.

Hence, If she was 141.5 ft below sea level after she went down , then she had been 199.5 ft below sea level.

Answer:

A.) 25.2

Step-by-step explanation:

Given the following :

Times in first four races :

26.3, 28.4, 25.6 and 29.1

The range of a list of values is the difference between the maximum and minimum value of the list or data.

In her first four races :

Range = 29.1 - 25.6 = 3.5

Value of range in her first four races = 3.5

In other to make the range larger:

Either she has a value less than the least time in her previous four races or she has a value greater than the maximum value of her previous race in her next race.

With a time of 25.2 in her next race : least value in the data will be 25.2

Range = 29.1 - 25.2 = 3.9

With a time of 26.1 in her next race :

Range = 29.1 - 25.6 = 3.5

With a time of 28.0 in her next race :

Range = 29.1 - 25.6 = 3.5

With a time of 29.1 in her next race :

Range = 29.1 - 25.6 = 3.5

Answer:

25.2

Step-by-step explanation:

Your friend swims on the school team.

In her first four races, her times are 26.3, 28.4, 25.6, and 29.1 seconds.

Which time listed for her next race would make the range larger?

Answer:

8/10

Step-by-step explanation:

There's ten numbers altogether and there are two numbers with the digit one, 1 and 10. 10-2=8

8/10

Answer: (i) Interval for proportion of underpaid nurses: 0.15 ± 0.0415.

(ii) Interval for difference in proportion: 0.03 ± 0.0641

Step-by-step explanation: Confidence Interval for a representation of the proportion is calculated by:

[tex]p_{hat}[/tex] ± z.[tex]\sqrt{\frac{p_{hat}(1-p_{hat})}{n} }[/tex]

(i) [tex]p_{hat}[/tex] is the proportion, in this case, of underpaid nurses: [tex]p_{hat}[/tex] = 0.15

Confidence Interval is 90%, so z = 1.645

The interval is:

0.15 ± 1.645.[tex]\sqrt{\frac{0.15(0.85)}{200} }[/tex]

0.15 ± 1.645*0.0252

0.15 ± 0.0415

Which means that, in 90% of times, the proportion of underpaid nurses wil be between 0.1085 and 0.1915.

(ii) For the difference in proportions:

[tex]p_{hat_1}-p_{hat_2}[/tex] ± z.[tex]\sqrt{\frac{p_{hat_1}(1-p_{hat_1})}{n_{1}}+\frac{p_{hat_2}(1-p_{hat_2})}{n_{2}} }[/tex]

The proportion for the second hospital is [tex]p_{hat_2}[/tex] = 0.12 and, since it is the same confidence interval, z = 1.645.

Calculating:

(0.15-0.12) ± 1.645.[tex]\sqrt{\frac{0.15(0.85)}{200} + \frac{0.12(0.88)}{120} }[/tex]

0.03 ± 1.645*0.0389

0.03 ± 0.0641

The 90% confidence interval for the difference in proportions of nurses being underpaid is between 0.0341 and 0.0941

Answer:

T1=0

T2=2

T3=6

T4=12

T50=2450

59 is not a term in the sequence

Step-by-step explanation:

Tn=n(n-1)

182=n2 - n

0=n2 - n - 182

0=n2-14n+13n-182

0=n(n-14)+13(n-14)

0=(n-14) (n+13)

Since n cannot be negative n is not equal to -13

Therefore,

n=14

Answer:

Step-by-step explanation:

divide 4 and 2 then add 2 and 1

Answer:

y = - 4x + 17

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (4, 1) and (x₂, y₂ ) = (2, 9)

m = [tex]\frac{9-1}{2-4}[/tex] = [tex]\frac{8}{-2}[/tex] = - 4, thus

y = - 4x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (4, 1) , then

1 = - 16 + c ⇒ c = 1 + 16 = 17

y = - 4x + 17 ← equation of line

Answer:

the original price is 500$

Step-by-step explanation:

500*.82*.8=328

Answer:

11

Step-by-step explanation:

sub 23 with m

23 - 12 = 11

Answer:

B. 5

Step-by-step explanation:

[tex] \tan(30 ) = x \div 5 \sqrt{3} = \tan(30) \times 5 \sqrt{3} = 5[/tex]

Answer:

[tex]\large \boxed{9.22}[/tex]

Step-by-step explanation:

The formula for the distance between two points is

[tex]d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}[/tex]

x₂ - x₁ = 4 - (-2) = 9

y₂ - y₁ = 3 - (-4) = 7

The formula, in effect, creates a right triangle, so we can use the Pythagorean theorem to calculate the distance.

[tex]\begin{array}{rcl}AB & = & \sqrt{6^{2} + 7^{2}}\\& = & \sqrt{36 + 49}\\& = & \sqrt{85}\\& \approx & \mathbf{9.220} \end{array}\\\text{The approximate distance between the points is $\large \boxed{\mathbf{9.220}}$}[/tex]

The approximate distance between points A and B will be equal to 9.220.

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. The length of the line segment between two places represents their distance.

Most notably, segments that have the same length are referred to as congruent segments and the distance between two places is always positive.

The formula for the distance between two points is,

[tex]D =\sqrt{(x_2-x_1)+y_2-y_1)^2[/tex]

x₂ - x₁ = 4 - (-2) = 9

y₂ - y₁ = 3 - (-4) = 7

The formula, in effect, creates a right triangle, so we can use the Pythagorean theorem to calculate the distance.

AB = √( 6² + 7² )

     = √ ( 36 + 49 )

     = √85

     = 9.22

Therefore, the approximate distance between points A and B will be equal to 9.220.

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