Sarah lives in Ruthin and works in Oswestry for 5 days a week. each day she travel to and from work. Work how many miles does she commute a week​

When calculating the total area of this unknown figure, you should use (π - r²)/4 for the area of both the semicircle (half circle) and the larger square.

By critically observing this unknown figure, we can logically deduce that it comprises a semicircle, squares, a rectangle and a triangle. Thus, its total area should be calculated by adding the area of each of the geometric figures together.

Total area = A₁ + A₂ + A₃ + A₄

However, you should take note that the diameter of the semicircle (half circle) is equal to the side length of the larger square.

Area of a semicircle = πr²/4

Thus, the total area of both the semicircle (half circle) and the larger square is given by:

Area = πr²/4 - d²

Note: d = 2r

Area = πr²/4 - (2r)²

Area = πr²/4 - 4r²

Area = (π - r²)/4 sq. units.

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Given that, y varies indirectly as the square of x, the value of y when x equal 8 is 2.

Indirect variation is expressed as;

y ∝ 1/x

Given that;

y ∝ 1/x²

y = k/x²

Where k is the proportionality constant.

Given that;

First, we determine the proportionality constant.

y = k/x²

8 = k/4²

8 = k/16

k = 128

Now, we find y when x = 8

y = k/x²

y = 128 / 8²

y = 128 / 64

y = 2

Given that, y varies indirectly as the square of x, the value of y when x equal 8 is 2.

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The total value of the investment is $107,032.16.

The total interest earned is $53,032.16

The inheritance would last the tenure of the university.

The formula that can be used to determine the future value of the 18-year annuity is: annuity factor x amount deposited yearly

Annuity factor = {[(1+r)^n] - 1} / r

Where:

$3000 x [(1.075^18 - 1) / 0.075] = $107,032.16

Amount deposited in the course of 18 years = (3000 x 18) = 54,000

Interest earned = 107,032.16 - 54,000 = $53,032.16

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The correct trigonometry formula to solve for x in the right angled triangle is sin(62°) = 18 / x

An equation is an expression that shows the relationship between two or more variables and numbers.

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

Hence:

sin(62°) = 18 / x

The correct trigonometry formula to solve for x in the right angled triangle is sin(62°) = 18 / x

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Using trigonometric identities, the simplified expression, without quotients, is given as follows:

A. [tex]\cos{\beta}\cot{\beta}[/tex]

The cosecant of an angle is given by one divided by the sine of the angle, hence:

[tex]\csc{\beta} = \frac{1}{\sin{\beta}}[/tex]

The sine and the cosine of an angle are related as follows:

[tex]\sin^2{\beta} + \cos^2{\beta} = 1[/tex]

[tex]\cos^2{\beta} = 1 - \sin^2{\beta}[/tex]

The cotangent of an angle is:

[tex]\cot{\theta} = \frac{\cos{\theta}}{\sin{\theta}}[/tex]

The expression given is:

[tex]\csc{\beta} - \sin{\beta}[/tex]

Simplifying the cosecant:

[tex]\csc{\beta} - \sin{\beta} = \frac{1}{\sin{\beta}} - \sin{\beta} = \frac{1 - \sin^{2}\beta}{\sin{beta}}[/tex]

Then, applying the last two identities in the subsection above to remove the quotient, the simplified expression will be found as follows:

[tex]\frac{1 - \sin^{2}\beta}{\sin{beta}} = \frac{\cos^2{\beta}}{\sin{\beta}} = \frac{\cos{\beta}}{\sin{\beta}} \times \cos{\beta} = \cos{\beta}\cot{\beta}[/tex]

Hence option A is correct.

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The percentage of the can that is not occupied by tennis​ balls is 33.33%.

Given:

Radius of cylinder=3.4cm

First step

Height of cylinder=3.4×2×6

Height of cylinder=40.8 cm

Second step

Volume of cylinder=(3.4)^2×40.8

Volume of cylinder=471.648

Volume of tennis=6×4/3×(3.4)^3

Volume of tennis=314.432

Third step

Percentage=471.648-314.432/471.648×100

Percentage=33.33%

Therefore the percentage of the can that is not occupied by tennis​ balls is 33.33%.

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Answer:

20% increase

Step-by-step explanation:

To find the percent increase, use this formula

New value - original value

----------------------------------------

original value

114-95

-----------

95

19

---- = .2

95

.2 is 20%, so it is a20% increase

The company's current ratio is 2.6.

Current ratio is an example of a liquidity ratio. Liquidity ratios are financial ratios measure a firm's ability to honour its short terms obligations.

Current ratio = current asset /current liability

$65,000 / 25,000 = 2.6

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Answer:

Well a sovial reason is that no one would no what order yo do it in, which would cause arguments

Answer:

without the order of operations, maths literally doesn't work.

Step-by-step explanation:

like whilst some equations don't rely on a particular order for solving, if you for example, don't solve brackets first, then try to multiply them by something else basically the equation breaks and you get the wrong answer. So... kids remember your BODMAS :)

Answer:

C

Step-by-step explanation:

For lines AC and EF, line FC is a transversal.

Angles ACF and EFC are same side interior angles.

Since their measures add to 180°, then the lines are parallel.

Answer: Choice C

The correct set of data are 15, 16, 16, 17, 19, 20, 21, 23, 32, 42.

According to the question

Using the key: 2|4 = 24, the following are the set of data represented by the stem-and-leaf plot showing:

Row one, 1| 5 6 6 7 9 :

This means there are 5 data set for the first row which are:

15, 16, 16, 17, 19

Row two, 2|0 1 3 :

There are 3 data here, which are:

20, 21, 23

Row 3, 3|2: = 32

Row 4, 4|2: = 42

So, The correct set of data are 15, 16, 16, 17, 19, 20, 21, 23, 32, 42.

Correct option is C.

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Answer:

19

Step-by-step explanation:

4(4)+3

16+3=19

Answer:

19

Step-by-step explanation:

4x+3

4(4)+3

16+3

19

hope it helps

Answer:

mother age 37

sons age 12

If the radius of the circle is 5 m and angle subtended by arc LKM is 70° then the length of the arc LNM is 25.29 m.

Given that the radius of the circle is 5 m and angle subtended by arc LKM is 70°.

From the figure given we can estimate that the length of arc LNM can be circumference of circle subtracted by length of arc LKM.

Circulference of the circle is basically the length of whole arc of the circle. It is also know as perimeter of the circle. The formula of calculating circumference of a circle is 2πr in which r is the radius.

So,

length of arc LNM=Circumference of circle-length of arc LKM.

We know that length of an arc =Θr

in which Θ is the angle in radian.

length of arc=70*π[tex]/180*5[/tex]

=70π[tex]/36[/tex]

Circumference of circle=2π*5

=10π

Length of arc LNM=10π-70π[tex]/36[/tex]

=(360π-70π)[tex]/36[/tex]

=290π[tex]/36[/tex]

Put π=3.14

=290*3.14[tex]/36[/tex]

=910.6[tex]/36[/tex]

=25.29m

Hence the length of arc LNM is 25.29 m.

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The area of QOR from the given diagram is 2π square centimeters

A sector is said to be a part of a circle made of the arc of the circle along with its two radii.

The formula for calculating the area of a sector is expressed as;

A = r²β/2

where

r is the radius of the circle

β is the angle subtended

Given the following parameters

<QOR = 180 - <POQ

<QOR = 180 - 135

<QOR = 45 degrees

Determine the radius

L = rβ

π = r(π/4)

1 = r/4

r =  4

Determine the area of QOR

Area = 4²(π)/8

Area = 2π

Hence the area of QOR from the given diagram is 2π square centimeters

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Option C. The correct statement about spatial relationshipo is that Spatial terms such as above, below, behind, and under are used to describe objects in space.

These are the types of relationships that are used to relate objects to the location of somethings else. It makes use of words like under, above etc.

It is one of the knowledge that children need in the preoperational stage to learn how to use logical operations.

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The equation 2•x² + 4•y² + 8•x - 16•y + F = 0, at a value of F is the graph of an ellipse when we have;

a. A value of F that results in the equation of an ellipse is; F = 23

b. A point on the ellipse is ((-2), 2.5)

The equation of an ellipse can be presented as follows;

[tex] \frac{(x - h) ^{2} }{ {a}^{2} } + \frac{(y - k) ^{2} }{ {b}^{2} } = 1[/tex]

The given equation can be presented as follows;

2•x² + 4•y² + 8•x - 16•y + F = 0

Collecting like terms, gives;

2•(x² + 4•x) + 4•y² - 16•y + F = 0

Adding a constant value to both sides, we get;

2•(x² + 4•x + 4) + 4•y² - 16•y + 16 + F = 24

2•(x + 2)•(x + 2) + (2•y - 4)•(2•y - 4) + F = 24

2•(x + 2)² + 4•(y - 2)² + F = 24

2•(x + 2)² + 4•(y - 2)² + F - 23 = 24 - 23 = 1

When F = 23, we have;

2•(x + 2)² + 4•(y - 2)² + 23 - 23 = 1

Which gives;

[tex] \mathbf{\frac{(x + 2) ^{2} }{ \left( {\frac{1}{ \sqrt{2} }} \right)^{2}} + \frac{(y - 2) ^{2} }{ \left( {\frac{1}{ 2} } \right)^{2}} } = 1[/tex]

Where;

b) A point on the ellipse can be found as follows;

When x = -2

2•((-2) + 2)² + 4•(y - 2)² = 1

0 + 4•(y - 2)² = 1

y - 2 = √(1/4) = 1/2

A point on the ellipse is therefore;

When y = 2

2•(x + 2)² + 4•(2 - 2)² = 1

2•(x + 2)² + 0 = 1

2•(x + 2)² = 1

(x + 2)² = 1/2

x + 2 = √(1/2)

x = √(1/2) - 2

Another point on the ellipse is therefore;

((√(1/2) - 2), 0)

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Answer:

7 : 20

Step-by-step explanation:

2km = 2000m

Then the ratio of 700m to 2 km​ is :

700 / 2000

Then the ratio in simplest form is :

7 / 20

The value of x from the figure is 70°

It is important to note that alternate angles are equal and angles in a triangle sum up to 180°

We then have that,

x + 50 + 60 = 180 °

x + 110 = 180°

Make 'x' subject

x = 180 - 110

x = 70 °

Thus, the value of x from the figure is 70°

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The time it takes between when the rock was dropped and when it landed is 1.33 seconds.

The time it takes the rock to land on the ground from where it is dropped can be determined by using the function given.

The height of the function when it hits the ground will be zero, so the function can be written as:

[tex]\mathbf{h(t) =36t^2 -64}[/tex]

[tex]\mathbf{0 =36t^2 -64}[/tex]

64 = 36t²

[tex]\mathbf{t^2 = \dfrac{64}{36}}[/tex]

t² =1.778

[tex]t = \sqrt{1.778}[/tex]

t = 1.333 seconds

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Answer:

-42

Step-by-step explanation:

Assuming you want the dot product,

(8)(-6)+(2)(3)= -42

Answer:

D = 50t

Step-by-step explanation:

we see, with every additional hour the distance increases by 50.

that means in general that the number of hours are multiplied by 50 to get the distance.

in other words, this just calculates for a vehicle going constantly 50 miles per hour the distance it is traveling.

The linear equation graphed is given by:

y - 5 = 3(x - 1).

A linear function is modeled by:

y = mx + b

In which:

In point-slope form, considering a point [tex](x_0, y_0)[/tex], the equation is:

[tex]y - y_0 = m(x - x_0)[/tex]

The line goes through points (0,2) and (1,5), hence the slope is:

m = (5 - 2)/(1 - 0) = 3.

Since the line goes through point (1,5), the equation is:

y - 5 = 3(x - 1).

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Using the Factor Theorem and limits, the end behavior of g(x) is that the function decreases to the left and increases to the right.

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

Considering the table, the roots are given as follows:

[tex]x_1 = -4, x_2 = 5, x_3 = 12[/tex]

Hence the function is:

f(x) = a(x + 4)(x - 5)(x - 12).

f(x) = a(x² - x - 20)(x - 12)

f(x) = a(x³ - 13x² - 32x + 240).

When x = 0, y = 1, hence the leading coefficient is found as follows:

240a = 1

a = 0.004167

Then:

f(x) = 0.004167(x³ - 13x² - 32x + 240).

The end behavior is given by the limits of f(x) as x goes to infinity, hence:

Hence the end behavior is that the function decreases to the left and increases to the right.

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Answer:

Step-by-step explanation:

Hello : let A(0,-6) B(8,-8)

the slope is : (YB - YA)/(XB -XA)

(-8+6)/(8-0) = -2/8=-1/4

an equation is : y=ax+b a is a slope

y = (-1/4)x +b

the line through point A (0;-6) : -6 = (-1/4)(0)+b

b = -6            the equation is : y =(-1/)4x-6

Answer:

x² + 1 = 0

a = 1

b = 0

c = 1

[tex]x1.2 = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]

[tex]x1.2 = \frac{ - 0 ±\sqrt{ {0}^{2} - (4.1.1) } }{2.1} [/tex]

[tex]x1.2 = \frac{0± \sqrt{0 - 4} }{2} [/tex]

[tex]x1.2 = \frac{± \sqrt{ - 4} }{2} [/tex]

There is no real solution because the discriminant is negative

Note.

Formula diskriminan

√b² - 4ac.

if the diskrimanan is negatif, so the quadratic equatoin dont have solution

The computation shows that the the hospital in-patient admission rate for the employees of the Prendergast Corporation is 104.5 admissions per 1000 employees.

The in-patient admission rate for Ramsey Manufacturing company = 100 admissions per 1000 employees.

It is given that the in-patient rate of Prendergast will be 10% higher than Ramsey's.

So, in-patient rate of Prendergast:

= 100 + 10% of 100

= 110 admissions

Now, it is also given that out of total in-patients, 5% are for tonsillectomies (which are not in-patient).

So, in-patient admission rate for Prendergast:

= 110 - 5% of 110

= 110 - 5.5

= 104.5 admissions per 1000 employees

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Complete question:

The hospital in-patient admission rate for employees of the Ramsey Manufacturing Company is 100 admissions per 1000 employees per year.

The Prendergast Corporation has older employees and is told that its hospital in-patient admission rate will be 10% higher than Ramsey’s. At the same time, however, all tonsillectomies will be done in the hospital’s outpatient department instead of requiring the patient to be admitted as an in-patient. Given that 5% of all in-patient admissions are for tonsillectomies, what is the hospital in-patient admission rate for the employees of the Prendergast Corporation?

A. 110.0 B. 115.0 C. 109.5 D. 100.0 E. 104.5 F. 117.0

The value of x is 22

Based on the description in the question,

The angles 5x -40 and 5x are angles on a straight line

So, we have:

5x - 40 + 5x = 180

Evaluate the like terms

10x = 220

Divide by 10

x = 22

Hence, the value of x is 22

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The amount of time between interest payments is know as period.

Period is the time between when interests are paid. Period can vary depending on the terms of the investment. Periods can be yearly, quarterly, semi-annually, biweekly or weekly.

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