£110 is divided between Sara, Gordon & Malachy so that Sara gets twice as much as Gordon, and Gordon gets three times as much as Malachy. How much does Sara get?

Answer:

Option (2). 14 m

Step-by-step explanation:

Formula to get the area of a circle 'A' = [tex]\pi r^{2}[/tex]

where r = radius of the circle

Given in the question,

Area of the circle = 153.86 square meters

By putting the values in the formula,

153.86 = πr²

r = [tex]\sqrt{\frac{153.86}{\pi } }[/tex]

r = [tex]\sqrt{49}[/tex]

r = 7 meters

Diameter of circle = 2 × (radius of the circle)

                              = 2 × 7

                              = 14 meters

Therefore, diameter of the circle is 14 meters.

Option (2) is the answer.

Answer:

14m

Step-by-step explanation:

Answer:

They are all multiplied by 6

Answer:

Geometric sequence.

Step-by-step explanation:

Here are the terms :

-2/3, -4, -24, -144

Now the first term T1 = -2/3

The second Term T2 = -4

But T2/T1 = -4÷ -2/3 = -4 x -3/2 = 6

Similarly Term 3, T3 = -24

T3/T2 = -24/-4= 6

Hence the expression is a geometric sequence.

a×r^(n-1); a is the first term

r is the common ratio 6

n is the number of terms.

Answer:

h = 16.23 m

The cannonball will hit the wall at 16.23m from the ground.

Step-by-step explanation:

Given;

Initial speed v = 62m/s

Angle ∅ = 25°

Horizontal distance d = 260 m

Height of wall y = 20

Resolving the initial speed to vertical and horizontal components;

Horizontal vx = vcos∅ = 62cos25°

Vertical vy = vsin∅ = 62cos25°

The time taken for the cannon ball to reach the wall is;

Time t = horizontal distance/horizontal speed

t = d/vx (since horizontal speed is constant)

t = 260/(62cos25°)

t = 4.627 seconds.

Applying the equation of motion;

The height of the cannonball at time t is;

h = (vy)t - 0.5gt^2

Acceleration due to gravity g = 9.81 m/s

Substituting the given values;

h = 62sin25×4.627 - 0.5×9.81×4.627^2

h = 16.2264134736

h = 16.23 m

The cannonball will hit the wall at 16.23m from the ground.

Answer:

A

Step-by-step explanation:

Integers are negative and positive whole numbers

Answer: A. 0.8

Step-by-step explanation:

An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3. Examples of numbers that are not integers are: -1.43, 1 3/4, 3.14

Answer:

B.   1 over 8

Step-by-step explanation:

To determine the probability of the spinner landing on 5, we need to first know what probability is,

probability = required outcome/all possible outcome

since the spinner is divided into 8 equal sections and each section contains number from 1-8, this implies there are total of 64 numbers on the spinner.  This implies that all possible outcome = 64

In each section there is 5, since there are 8 sections on the spinner, the number of 5's on the spinner are 8.

This implies that the required outcome = 8

but

probability = required outcome/all possible outcome

probability (of the spinner landing on 5) = 8/64    =1/8

Answer:

b

Step-by-step explanation:

Answer: Point slope form is y-y1=m(x-x1)

Step-by-step explanation:

Here y1=4

x1=-11

m i.e slope=-2

And there you go.

Answer:

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Step-by-step explanation:

Answer:

The quarter circle's area is 38.47 yard²

Step-by-step explanation:

The area of a full circle is pi * r ²

The area of a quarter circle is 1/4 * pi * r ²

Given:

Use 3.14 for pi

Round to the nearest hundredths.

Perimeter of quarter circle is 24.99 yards

For r you must leave it as 'r' because we do not know it for now...

1. Circumference of a full circle = 2* pi * r

2. 1/4 * ( 2 * pi * r )

1/4 * ( 2 * 3.14 * r )

1/2 * 3.14 * r

1.57 * r

3 Since r = 'r'

We have to 2 sides running from the centre of the 'pie' to the left and right of the quarter circle which both have a length of exactly 'r'. So you just add 2 * r.

4. The outcome of step 2 + step 3 is the perimeter of quarter circle, which was given as 24.99 inch

1.57 * r + 2 * r = 24.99

( 1.57 + 2 ) * r = 24.99

3.57 * r = 24.99

Divide left and right of the = sign by 3.57

3.57 / 3.57 * r = 24.99 / 3.57

1 * r = 24.99 / 3.57

r = 7

The area of a quarter circle is 1/4 * pi * r ²

1/4 * pi * 7²

1/4 * 49 * pi

49/4 * pi

49/4 * 3.14

38.465

Round to the nearest hundredths gives 38.47 yard²

The quarter circle's area is 38.47 yard²

Answer:

see below

Step-by-step explanation:

We'll cal the first integer x and then the rest of them will be x + 1, x + 2, x + 3 and x + 4. We can write x + 5(x + 2) = 3(x + 1 + x + 3 + x + 4) - 41.

x + 5x + 10 = 3(3x + 8) - 41

6x + 10 = 9x + 24 - 41

6x + 10 = 9x - 17

3x = 27

x = 9

The numbers are 9, 10, 11, 12, 13.

Answer:

4 1/2

Step-by-step explanation:

5 apples - 1/2 apple =

4 1/2 apple

or

9/2

Answer:

(a)123 km/hr

(b)39 degrees

Step-by-step explanation:

Plane X with an average speed of 50km/hr travels for 2 hours from T (Kano Airport) to point U in the diagram.

Distance = Speed X Time

Therefore: Distance from T to U =50km/hr X 2 hr =100 km

It moves from Point U at 9.00 am and arrives at the airstrip A by 11.30am.

Distance, UA=50km/hr X 2.5 hr =125 km

Using alternate angles in the diagram:

[tex]\angle U=110^\circ[/tex]

(a)First, we calculate the distance traveled, TA by plane Y.

Using Cosine rule

[tex]u^2=t^2+a^2-2ta\cos U\\u^2=100^2+125^2-2(100)(125)\cos 110^\circ\\u^2=34175.50\\u=184.87$ km[/tex]

Plane Y leaves kano airport at 10.00am and arrives at 11.30am

Time taken =1.5 hour

Therefore:

Average Speed of Y

[tex]=184.87 \div 1.5\\=123.25$ km/hr\\\approx 123$ km/hr (correct to three significant figures)[/tex]

b)Flight Direction of Y

Using Law of Sines

[tex]\dfrac{t}{\sin T} =\dfrac{u}{\sin U}\\\dfrac{125}{\sin T} =\dfrac{184.87}{\sin 110}\\123 \times \sin T=125 \times \sin 110\\\sin T=(125 \times \sin 110) \div 184.87\\T=\arcsin [(125 \times \sin 110) \div 184.87]\\T=39^\circ $ (to the nearest degree)[/tex]

The direction of flight Y to the nearest degree is 39 degrees.

1 × 18/100 = 12/100(g+11), is the equation. The answer is 12/100 gallons

Answer:

E. 400

Step-by-step explanation:

So this is how we set this up, and how we solve

[tex]0.25x=100\\x=100/0.25\\x=400[/tex]

Hope this helps!

So you are solving for circumference of a quarter circle: [tex]\frac{1}{4}2 \pi r[/tex]

r= 28

[tex]\pi=3.14[/tex]

[tex]\frac{1}{4}2(87.92)=\\43.96[/tex]

The number line model that represents the expression -2/5 + 4/5 is: Option B

To plot an inequality, such as x > 2, on a number line, first draw a circle over the number (e.g., 2). Then if the sign includes equal to (≥ or ≤), fill in the circle. If the sign does not include equal to (> or <), leave the circle unfilled in.

Now, in this case, the operation to solve is:

-2/5 + 4/5

Solving this gives 2/5

Now, since the operation shows a negative and positive fraction with the solution being positive, then we can easily say that Option B is the correct answer to the problem

Read more about Inequality on number line at: https://brainly.com/question/24372553

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Answer:

x = 20

Step-by-step explanation:

3x + 6x = 180, if you make them supplementary then they will be parallel

9x = 180

x = 20

Answer:

[tex]\frac{7}{3}[/tex]

Step-by-step explanation:

csc(Ф) is equivalent to the inverse of sin(Ф)

Since sin(Ф) = 3/7, the inverse of this would be 7/3

So, [tex]csc = \frac{1}{\frac{3}{7} }=\frac{7}{3}[/tex]

Answer:

1.75

Step-by-step explanation:

Divide the ounces by 16 to get the value.

Answer:

a. Discrete random variable

b. Discrete random variable

c. Discrete random variable

d. Discrete random variable

e. Continous random variable

f. Continous random variable

Step-by-step explanation:

a. The number of points scored during a basketball game.

This is a random variable, that only takes integer values, so it is a discrete random variable.

b. The number of free dash throw attempts before the first shot is made.

This is a count, so it is a discrete random variable.

c. The response to the survey question "Did you smoke in the last week question mark".

This is a boolean random variable (only two values), and can be considered discrete.

d. The number of people in a restaurant that has a capacity of 150.

This is a count of people, so it is a discrete random variable.

e. The time it takes for a light bulb to burn out.

Time is continous, so it is a continous random variable.

f. The height of a randomly selected giraffe.

Height, as it is a distance, is also a continous variable, so it is a continous random variable.

Answer:

|-a|=|a|

Step-by-step explanation:

The lines beside the a's mean that you are trying to find the absolute value of what's inside. The absolute value of something is the distance it is from 0. You can't have a negative distance so anything inside of absolute value line are positive.

Therefor this is how we can solve this.

|-a| __ |a|

  a __ a

a=a

Answer:

The answer is 13

Step-by-step explanation:

Two positive and consecutive old numbers are x and x - 2.

=> x(x - 2) = 143

=> x^2 - 2x - 143 = 0

=> x^2 + 11x - 13x - 143 = 0

=> x(x + 11) - 13(x + 11) = 0

=> (x + 11)(x - 13) = 0

=>  x = -11 (invalid)

or x = 13 (valid), the remaining number is 13 - 2 = 11

=> The two numbers are 11 and 13, and the greater number is 13.

Hope this helps!

:)

Answer:

top: 2

bottom: 13

Step-by-step explanation:

step

by

step

explanation

Answer:

[tex]y=\frac{(-\frac{4}{x}+1)^2-3 }{4}[/tex]

Step-by-step explanation:

We are given the following information. y have the point [tex](-2,\frac{3}{2} )[/tex] and [tex]\frac{dy}{dx} =\frac{\sqrt{4y+3} }{x^2}[/tex]

First, we need to separate the variables to their respective sides

[tex]\frac{1}{\sqrt{4y+3} } dy=\frac{1}{x^2} dx[/tex]

Now, we need to integrate each side

[tex]\int \frac{1}{\sqrt{4y+3} } dy=\int\frac{1}{x^2} dx[/tex]

But first, let us rewrite these functions

[tex]\int (4y+3)^{-\frac{1}{2} } dy=\int x^{-2} dx[/tex]

Before we can integrate, we need to have the hook for the first function. When we integrate [tex](4y+3)^{-\frac{1}{2} }[/tex], we must have a lone 4 within the integral as well.

[tex]\frac{1}{4} \int4 (4y+3)^{-\frac{1}{2} } dy=\int x^{-2} dx[/tex]

Now we can integrate each side to get

[tex]\frac{1}{4} \sqrt{4y+3} =-\frac{1}{x} + c[/tex]

Now is the best time to use the given point in order to find the value of c.

[tex]\frac{1}{4} \sqrt{4(\frac{3}{2}) +3} =-\frac{1}{-2} + c\\\\\frac{1}{4}\sqrt{6+3} =\frac{1}{2} +c \\\\\frac{3}{4}=\frac{1}{2} +c\\ \\c=\frac{1}{4}[/tex]

Now we can plug in our value for c and then solve for y

[tex]\frac{1}{4} \sqrt{4y+3} =-\frac{1}{x} + \frac{1}{4} \\\\\sqrt{4y+3}=-\frac{4}{x} +1\\ \\4y+3=(-\frac{4}{x} +1)^2\\\\4y=(-\frac{4}{x} +1)^2-3\\\\y=\frac{(-\frac{4}{x} +1)^2-3}{4}[/tex]

Answer:

d. 85%

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The higher the confidence level, the higher the value of z, which means that the margin of error will be higher and the interval will be wider,

Which confidence interval would be the narrowest?

The one with the lowest confidence level. So the answer is d.

Solution,

16.87+(-98.35)

=16.87-98.35

= -81.48

Hope it helps

Good luck on your assignment

Answer:-81.48

Step-by-step explanation:

16.87 + (–98.35)

-81.48

If you stumble in other questions like there you can use a calculator or ask me. :D hope that helps

Answer:it is b

Step-by-step explanation:

Answer:

So if a line was parallel it would have same slope. You can search up what slope-intercept form means. But if you have an equation like this:

y = mx+b

The slope will be m. Your question is written in the form. 2/5 = m.

The slope is 2/5

The y-intercept is 4/5

Answer:

m=2/5

Step-by-step explanation:

Lines that are parallel have the exact same slope.

We have an equation in point slope form.

y=mx+b

where m is the slope and b is the y-intercept.

The slope is the number being multiplied by x. In the equation

y=2/5x+4/5

2/5 and x are being multiplied. Therefore, 2/5 is the slope. A line that is parallel will have the same slope of 2/5.

Answer:

0.0062

Step-by-step explanation:

Find the standard error.

σ = 20 / √100

σ = 2

Find the z-score.

z = (x − μ) / σ

z = (70 − 65) / 2

z = 2.5

Find the probability.

P(Z > 2.5) = 1 − 0.9938

P(Z > 2.5) = 0.0062

Answer:

A.

Step-by-step explanation:

So first you need to find the slope:

[tex]\frac{-2-6}{3+2} =-\frac{8}{5}[/tex]

Since it's point slope, you have to use a point:

It's either:

[tex](y - 6)=-\frac{8}{5}(x+2)[/tex]

or

[tex](y+2)=-\frac{8}{5}(x-3)[/tex]

Check which answer has those:

A.

The solution is Option A.

The equation of line is y - 6 = ( -8/5 ) ( x + 2 ) where the slope is -8/5

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( -2 , 6 )

Let the second point be Q ( 3 , -2 )

The slope of the line between the point is given by m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 6 - ( - 2 ) ) / ( -2 - 3 )

On simplifying the equation , we get

Slope m = ( 8 / -5 ) = -8/5

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 6 = ( -8/5 ) ( x - ( -2 ) )

On simplifying the equation , we get

y - 6 = ( -8/5 ) ( x + 2 )

Hence , the equation of line is y - 6 = ( -8/5 ) ( x + 2 )

To learn more about equation of line click :

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Answer:

= ( $18.2, $18.8)

Therefore, the 98% confidence interval (a,b) = ( $18.2, $18.8)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = $18.50

Standard deviation r = $6.10

Number of samples n = 2253

Confidence interval = 98%

z(at 98% confidence) = 2.33

Substituting the values we have;

$18.5+/-2.33($6.1/√2253 )

$18.5+/-2.33($0.128513644290)

$18.5+/-$0.299436791196

$18.5+/-$0.3

= ( $18.2, $18.8)

Therefore at 98% confidence interval (a,b) = ( $18.2, $18.8)

Answer:

  see below

Step-by-step explanation:

In my opinion, Antoinette should make use of a graphing calculator to find the solution. (second attachment)

__

Slope-intercept form can be useful for graphing, so it often works well to start with equations in that form. If that is Antoinette's strategy, she should rewrite the first equation to that form. The second equation is already in slope-intercept form.

In doing that rewrite, she will want to get the y-term on one side of the equal sign by itself. She can do that by subtracting 2x from the first equation:

  -7y = -2x +56

As a final step in her rewrite, she would divide by -7 to get ...

  y = 2/7x +56

This 2nd equation has a positive slope of 2/7. The slope of the second equation is similarly the x-coefficient, -2.5. Neither is 4 and they have different signs.

The appropriate answer choices are shown checked below.

Answer:

B and D

Step-by-step explanation:

I got it right m8. Good day

Answer:

–2(5 – 4x) < 6x – 4

<=>

-10 + 8x < 6x - 4

<=>

2x < 6

<=>

x < 3

Hope this helps!

:)

Answer:

Step 1: –10 + 8x < 6x – 4

Step 2: –10 < –2x – 4

Step 3: –6 < –2x

Step 4: ________

What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?

A. x < –3  

B. x > –3

C. x < 3

D. x > 3

Step-by-step explanation:

The correct answer here is C. x < 3