In this problem, you will investigate the relationship between the arcs of a circle that are cut by two parallel chords.
a. Use a compass to draw a circle with parallel chords -AB and -CD . Connect points A and D by drawing segment -AD .

Only [tex]$1\frac{1}{2} - 1\frac{1}{9} = \frac{7}{18}[/tex] is less than 1.

We have a set of mixed numbers.

We have to identify which set of mixed numbers has a difference less than 1.

A mixed number is a whole number, and a proper fraction represented together. It generally represents a number between any two whole numbers. Any mixed fraction can be converted into normal fraction using the formula -

[tex]X\frac{Y}{Z} =\frac{Z\times X+Y}{Z}[/tex]

According to the question -

Let us solve them one by one (for difference to be less than 1, the denominator should be less than numerator) -

Hence, only [tex]$1\frac{1}{2} - 1\frac{1}{9} = \frac{7}{18}[/tex] is less than 1.

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Answer: The answer to this equation is 53.91

The y-intercept is the amount she got as gifts during her graduation.

The equation in slope intercept form is $630 + $60b

The slope intercept form is used to write equations for equations for linear equations with two variables. The graph for a  slope intercept form is a straight line.

The form for  slope intercept form is: y = mx + b

Where:

The y-intercept is the constant. It represents the point where the slope touches the y-axis.

The first step is to determine how much are earnings are and how much the gift is.

The equations that would be used to determine this are:

a +2b = 750 equation 1

a + 4b = 870 equation 2

Where:

a = gift

b = amount earned weekly while working on the golf course

Subtract equation 2 from equation 1: 2b = 120

Divide both sides of the equation by 4: b = $60

Substitute for b in equation 1

a + 2(60) = 750

a + 120 = 750

a = 750 - 120

a = 630

The y-intercept is $630.

The equation in slope intercept form is: $630 + $60w

Where w is the number of weeks that Betty works.

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Answer:

x = 85

Step-by-step explanation:

the exterior angles of a polygon sum to 360°

note the exterior angle at P = 180° - 90° = 90°

sum the 4 exterior angles and equate to 360

x + 72 + 113 + 90 = 360

x + 275 = 360 ( subtract 275 from both sides )

x = 85

The number of ways can five of the nine us supreme court justices agree is 3024 ways.

The number of ways that five of the nine us supreme court justices agree will be calculated thus:

= 9! / 5!

= (9 × 8 × 7 × 6 × 5 × 4 × 3 × 2) / (5 × 4 × 3 × 2)

= 3024

There'll be 3024 ways.

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The model's scale factor if the ant is 1/2 inch long as well as the model is 1 foot long. = 24 inch or 2 foot.

The Scale Factor is employed to scale shapes in different dimensions. Geometry teaches us about numerous geometrical shapes in two and three dimensions. The scale factor is a metric considering similar figures that appear the same but have distinct scales or measures.

The basic formula for computing this same scale factor is, Scale factor = Dimension of the new shape x Dimension of the original shape If indeed the original figure is scaled up, then the formula is expressed as Scale factor = Larger figure dimensions /Smaller figure dimensions.

The size of the ant = 1/2 inch.

the model size is = 1 foot.

                             = 1 foot = 12 inch

The scale factor of the model  =  Larger figure dimensions ÷ Smaller figure dimensions.

                                                  = 12/.5

                                                  = 24 inch or 2 foot

The model's scale factor if the ant is 1/2 inch long as well as the model is 1 foot long. = 24 inch or 2 foot.

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The center of the given ellipse is given as (-1, 2)

Center of the Ellipse

To find the center of the ellipse, we need to rearrange the equation into the standard equation of ellipse.

[tex]4x^2 + 9y^2 + 8x - 36y + 4 = 0\\\frac{(x+1)^2}{2} + \frac{(y-2)}{4} = 1[/tex]

The center of the ellipse is given as

[tex]center = (-1, 2)[/tex]

The foci of the ellipse  are the reference points in an ellipse and it helps to derive the equation of the ellipse. There are two foci for the ellipse i.e F1 and F2

[tex]F_1= (-1 + \sqrt{5}, 2)\\ F_2 = (-1, -\sqrt{5}, 2)[/tex]

The center of the given ellipse is (-1,2) while the foci are stated above.

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The 25th percentile of the data is represented by the 0 to 1 hour range.

48 speakers, or around 25% of the total of 192 speakers, are present.

According to the graph, 60 presenters gave presentations that lasted between 0 and 1 hours.

This means that 48 is between0 and1.

A score that compares a certain score to the scores of the other group members is known as a percentile. It shows the percentage of scores that a particular score outperformed.

A person's performance is gauged by using the percentile calculation to compare it to others. A student's test score is compared to that of other applicants using the percentile approach.

Therefore, the 0 to 1 hour period contains the data's 25th percentile.

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The equation in point-slope form of the line having the given slope that contain the given point m=[tex]-\frac{3}{4}[/tex] and (8,-1) is [tex]y+1=-\frac{3}{4}(x-8)[/tex]

Given,

m = [tex]\frac{-3}{4}[/tex]

The point = (8,-1)

The point-slope form of the line

[tex](y-y_{1} )=m(x-x_{1})[/tex]

Substitute the values in the equation

[tex](y-(-1))=-\frac{3}{4}(x-8)\\ y+1=-\frac{3}{4}(x-8)[/tex]

Hence, the equation in point-slope form of the line having the given slope that contain the given point m=[tex]-\frac{3}{4}[/tex] and (8,-1) is [tex]y+1=-\frac{3}{4}(x-8)[/tex]

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Answer$550.32

Step-by-step explanation: 7day = $320

commission = 8% of 2879

=230.32

 total earnings = 320 + 230.32

= 550.32

Answer:

m = 5d

Step-by-step explanation:

m = 5d

The term "length" is used to describe an object's size or the separation between two points. Lindsey must buy 4 feet of the board for the ramp itself.

The term "length" refers to the measurement or size of something from end to end. In other terms, it is the greater of the upper two or third dimension of a geometric shape or object.

Distance exists estimated in length. The length contain the dimension of distance in the International System of Quantities. The majority of measurement systems select a base unit for length from which all other units exists derived. The meter serves as the foundational unit of length in the International System of Units.

A rectangle, for instance, has length and width as its dimensions.

1/x = 15°

x = 1/sin 15°

simplifying the above equation, we get

x = 3.9ft

x ≈ 4 ft

Therefore, the value of x ≈ 4 ft.

Lindsey must buy 4 feet of the board for the ramp itself.

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Answer:

3 1/2 ÷ 1 1/4

7/2 ÷ 5/4

7/2 · 4/5

28/10

2.8

Step-by-step explanation:

Using trigonometric functions, the value of 2 cos x is equals to √3.

One of the six mathematical functions used to express the side ratios of right triangles, the trigonometric function includes the sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc). The graphic shows these six trigonometric functions in respect to a right triangle.

Cos (π/6) = √3/2

So. f(x) = 2 cos x

⇒ f(x) = 2 cos(π/6)

⇒ f(x) = 2 × √3/2

f(x) = √3

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The 100–meter backstroke swimming times of the 8 swimmers during the semifinal and the finals of the Olympic games gives;

First part;

The center of the semifinal round is approximately 57.3625

The variability in the semifinal round is 0.0998

Second part;

The center of the final round is approximately 57.0125

The variability in the final round is 0.3336

The times of the swimmers in the semifinal round are;

56.7, 57.2, 57.3, 57.3, 57.4, 57.5, 57.7, 57.8

The central value is given by the mean of the data, is found as follows;

(56.7+57.2+57.3+57.3+57.4+57.5+57.7+57.8)/8 = 57.3625

The variability is given by the standard deviation which is found by the formula;

[tex] \sigma = \sqrt{ \frac{ x_{i} - \mu}{n} } [/tex]

Where;

[tex]x _{i} = the \: ith \: value[/tex]

[tex] \mu = the \: mean[/tex]

The standard deviation found using the given values above and an online tool is presented as follows;

[tex] \sigma = \sqrt{ \frac{ x_{i} - 57.3625}{8} \approx 0.316 } [/tex]

Second part;

In the final, we have the following values from the dot plot;

56, 56.6, 56.6, 57, 57.1, 57.2, 57.7, 57.9

From the above values, using an online calculator, the center, which is taken as the mean is 57.0125

The variance for the final, [tex] \sigma^2 [/tex] ≈ 0.3336

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45% of 315 = 141.75

When you are using a % number convert it into a decimal ( 45% would be 0.45 or 55% would be 0.55 ). After you convert it into a decimal you can multiply it by the number ( Here it would be 315 )

0.45 x 315 = 141.75

Answer:

141.75

Step-by-step explanation:

To do this question, first, we can write 45% as 45/100.

Now, we have to multiply.

45/100x315

=141.75

Hope that helped!

:D

Answer: 81

Step-by-step explanation: The square root and the squared function cancel each other out

The constant percent rate of change in the case of a deposit of $400 into a savings account is compounded annually.  

With an example, what is compound interest?

Principal - $400

rate of interest is compounded annually

g(x) =  400( 1.03)ˣ equation 1.

Formula used

A = P( 1 + r )ⁿ

here n = x

Solution:

Putting the value of n, and principal in the formula

A = P( 1 + r )ⁿ ................... equation 2

now comparing both equation 1 and equation 2,

400( 1.05)ˣ =  400( 1 + r )ˣ

( 1.05)ˣ = ( 1 + r  )ˣ

1.05 = 1 + r

r = 1.05 - 1

r = 0.05

r % = 0.05 × 100

r % = 5 %

thus, the constant percent rate of change =  5 %

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The wavelength of the waves on a string that is vibrating at 220 MHz is 2.20 m. These waves move at a 4840 rpm rate as they move up and down the string.

A waveform signal that is carried in space or down a wire has a wavelength, which is the separation between two identical places (adjacent crests) in the consecutive cycles. This length is typically defined in wireless systems in meters (m), centimeters (cm), or millimeters (mm) (mm). According to the available data, the wavelength is more frequently expressed in nanometers (nm), which are units of 10-9 m, or angstroms (), which are units of 10-10 m, for infrared (IR), visible light (VL), ultraviolet (UV), and gamma radiation ().

V=∧F

V=220×22

V=4840m/s

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The given statement is not correct because anyone above 18 years can vote.

It is given that if you are over 18 years old, then you vote in all elections.

We have to determine the truth value , if you are 21 years old and do not vote.

What is the truth value ?

Truth value is the attribute which states that whether the statement is true or false.

As per the question ;

If you are over 18 years old , then you vote in all elections, and if you are 21 years old and do not vote.

The criteria to vote in the elections is to be over 18 years.

Here ;

21 years age is greater than 18 years criteria , that's why it is not possible that you can't vote if you are 21 years old.

The statement is not correct.

Thus , the given statement is not correct because anyone above 18 years can vote.

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The given lograthimic expression  log₃ y + 4 log₃ t can be written as log₃(yt^4).

According to the given question.

We have an logarithmic expression

log₃ y + 4 log₃ t

As we know that, a logarithmic expression is an expression that involves the logarithm of an expression containing a variable.

Also according to the product  and power rule we know that

log(mn) = logm + logn

Thereofore, the given lograthimic expression  log₃ y + 4 log₃ t can be written as

log₃ y + 4 log₃ t

= log₃ y + log₃ t ^4

= log₃(yt^4)

Hence, the given lograthimic expression  log₃ y + 4 log₃ t can be written as log₃(yt^4).

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Answer:

14x cannot be simplified any further.

Answer:

No, 14x can not be further simplified.

Step-by-step explanation:

I hope this helps.

The initial amount and rate of change given a table for a linear function are $332 and $22.5, respectively

The table of linear function represents the given parameter

On the table, we have the following points

(x, y) = (6, 467) and (10, 647)

The rate of change is calculated as

Rate = (y2 - y1)/(x2 - x1)

So, we have

Rate = (647 - 467)/(10 - 2)

Evaluate

Rate = 22.5

This means that the rate of change is $22.5

The initial amount is calculated as

y = m(x - x1) + y1

Where

m = 22.5

So, we have

y = 22.5(x - x1) + y1

Using one of the points, we have

y = 22.5(x - 6) + 467

Set x = 0

So, we have

y = 22.5(0 - 6) + 467

Evaluate

y = 332

Hence, the initial amount and rate of change given a table for a linear function are $332 and $22.5, respectively

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Answer: 660 miles

Step-by-step explanation:

66 miles * 10 hours/1 hour =

66*10/1=

66*10=660 miles

Answer:

It will take approximately 20 years for the investment to double. The amount after 10 years will be $17,033.

Step-by-step explanation:

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The inequality which can be used to determine the number of gigabytes is 58 + 3x < 70 and the solution is  x < 4

The given parameters are

Flat cost = $58

Rate = $3 per gigabyte

Budget = Under $70

The equation is represented as:

Total cost = Flat cost + Rate * Number of gigabyte

So, we have

y = 58 + 3x

The budget is under 70

So, we have

58 + 3x < 70

Subtract 58 from both sides

So, we have

3x < 12

Divide both sides by 3

So, we have

x < 4

Hence. the inequality which can be used to determine the number of gigabytes is 58 + 3x < 70 and the solution is  x < 4

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Answer:

1470 in³, 716 in²

Step-by-step explanation:

The figure is a cylinder, and it's volume can be found using the following formula:

Volume of cylinder

= area of circle base ×height

= πr²h

Identify the value of r and h:

From the diagram, the radius (r) is 6 in. while the height (h) is 13 in.

Using the formula,

volume of cylinder

= π(6²)(13)

= 468π

= 1470 in³ (3 s.f.)

The surface area of a cylinder is the total area of all its faces, i.e. the sum of the area of its two circular bases and its curved surface area.

Formula

Surface area of cylinder

= 2πr² +2πrh

Surface area of cylinder

= 2(π)(6²) +2(π)(6)(13)

= 72π +156π

= 228π

= 716 in² (3 s.f.)

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