directions: use the given information to find the desired measurement. a ferris wheel has a diameter of 50 feet. how far has a person traveled when they have moved 270 degrees?

For the parallel lines (l//m), the value of x is equal to 25 and the converse used is the alternate exterior angle theorem.

Parallel lines simply refers to two (2) lines that always have the same or equal distance apart and never meet.

The alternate exterior angle theorem states that when two (2) parallel lines are cut through by a transversal, the alternate exterior angles that are formed are congruent or angles of equal measure and magnitude.

By applying the alternate exterior angle theorem to parallel lines (l//m), we have:

4x - 13 = 2x + 37

4x - 2x = 37 + 13

2x = 50

x = 50/2

x = 25

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The perpendicular bisector of the line segment with endpoints (6, -5) and (-2, -9) is 7x,2y = 6.

Therefore,

The coordinates of the end points:

(6, -5) and (-2, -9)

((6, -5) +(-2, -9))/2

= ((6,-9)/2, (-2, -5)/2)

= (1.5, 3.5)

The difference in endpoint coordinates will be;

(Δx, Δy) = (9-(-5), (-2)-6) = (14, 8)

Then the ratio of these values, so we need to divide both by the common factor of 2:

(Δx, Δy) = (7, 2)

A line perpendicular to this segment through the point (h, k) can be written as;

Δx·x +Δy·y = Δx·h +Δy·k

7x ,2y = 7(2) 2(4)

7x, 2y = 6 .

Hence the standard form equation for the perpendicular bisector will be;  7x ,2y = 6 .

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Answer: angle 1 and 4

Step-by-step explanation:

When the circumference of a circle is 19π cm the area of the circle is

28.27 square centimeters

Information given in the question include

The circumference of a circle is 19π cm

Area of a circle is given by

π r^2

where r = radius

π = constant = 3.124

circumference of a circle is given by 2πr

2πr = 19

πr = 9.5

r = 3.024

r = 3 cm

The area is solved as

= π * 3^2

= 28 .27square centimeters

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By simplifying 2/5  + [tex]a^{2/2}[/tex] C we get the solution as (2a + 5C) / 5.

Given equation ,

2/5  + [tex]a^{2/2}[/tex] C

We know that ,  [tex]a^{2/2}[/tex]  = a

So the equation becomes ,

2/5 a + C

By simplifying,

2a / 5 + C

= 2a / 5 + 5C / 5

By combining fractions ,

(2a + 5C) / 5

Thus solution is (2a + 5C) / 5 .

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The graph of the inequality is attached below.

We are given an inequality. The inequality is linear in nature. An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions. The inequality is given below.

y < 2x - 3

We need to graph the inequality. The first step is to find out the corresponding equation of the straight line. The equation is found by replacing the greater-than or less-than sign with the equal-to sign. The equation is given below.

y = 2x - 3

We plot this equation on the graph with a dotted line. Now we shade the area that satisfies the given inequality. The graph is given below.

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Answer:

Step-by-step explanation: I think it could be 5,0000

The exchange rate if each souvenir costs 200 Jamaican dollars, 38 might be purchased.

The exchange rate refers to the value of one country currency about's currency. It is determined by the foreign currency market, often known as the FOREX market.

Amount needed for vacation = $50 USD = $7,740 JMD

Each souvenir is priced at 200 Jamaican dollars.

One US dollar = 154.8 Jamaican dollars when converted to Jamaican currencies.

50 US dollars = 154.8 × 50

= 7,740 Jamaican dollars

Number of souvenirs you can buy = Amount of money with you for vacation ÷ Cost of each souvenir

= 7,740 Jamaican dollars ÷ 200 Jamaican dollars

= 38.7 souvenirs.

As a result, for 200 Jamaican dollars for each souvenir, about 38 souvenirs may be obtained with 50 US dollars.

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Step-by-step explanation:

Randy is 8 years old. His brother is twice as old as Randy. Randy’s sister is three years younger than Randy. Write an expression to represent the age of Randy’s brother.

Randy = R = 8 years

Brother =  B

B = 2R

solving:

B = 2R when R = 8

B = 2(8)

B = 16 years old

Answer: Its 16

Step-by-step explanation:

You need to take randy's age twice so you need to calculate 8x2= 16.

The number of books bought by the school is 92.

Here it is given that the school spend $925 to buy new books for the library.

The cost of each book is $9.95

So we have to find the number of books that can be bought.

By dividing the total money spent by the cost of each book we get the number of books bought.

Let n be the number of books bought.

n × 9.95 = Total money spend on the books

As we know the total money spend on the books is $925.

So we get:

925 = n × 9.95

n = 925/ 9.95

= 92

Therefore the total number of books bought is 92.

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The fraction 7/2a+4/a*a can be written as (7 + 8a) / 2a

What is a fraction?

In general, any number of equal pieces is represented by a fraction, which is a portion of the entire. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many pieces of a particular size there are in spoken common English. In other words, a fraction indicates the components of a whole or group of items.

Solution Explained:

First, we simplify the equation

=  [tex]\frac{7}{2a} + \frac{4}{a} X a[/tex]

=  [tex]\frac{7}{2a} + 4[/tex]

= [tex]\frac{7 + 8a}{2a}[/tex]

Therefore, the equation can be written as (7 + 8a) / 2a

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Answer:

190 43/100

Step-by-step explanation:

First, you turn the mixed fractions into improper fractions. 382 3/10 is 3823/10, and 191 87/100 is 19187/100. Then, you need to have a common denominator in order to subtract. This turns 3823/10 into 38230/100. 38230/100 - 9187/100 is 19043/100 since you only subtract the numerators. Finally, you turn it back into a mixed fraction by dividing 19043/100. This equals 190 with a remainder of 43. In conclusion, the answer is 190 43/100. I attached the image where I worked it out to show my thought process a bit more as well. I hope this helped! :D

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-16}~,~\stackrel{y_1}{11})\qquad (\stackrel{x_2}{16}~,~\stackrel{y_2}{4})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~16 - (-16)~~)^2 + (~~4 - 11~~)^2} \implies d=\sqrt{(16 +16)^2 + (4 -11)^2} \\\\\\ d=\sqrt{( 32 )^2 + ( -7 )^2} \implies d=\sqrt{ 1024 + 49 } \implies d=\sqrt{ 1073 }\implies d\approx 32.76[/tex]

Preston left with $5 and correct expression for to find solution is option(B) i.e, 15 - (6.5 + 2 * 1.75)

What is an Algebraic Expression?

An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression. For example, 3x² − 2xy + c is an algebraic expression.

Given,

Total money Preston have = $15

He buys the ticket for = $6.50

And, two snacks = $1.75 each

so the cost of two snacks is = 1.75 * 2 = $3.5

Total cost for ticket and snacks = $3.5 + $6.50 = $10

Now, he spent money on snacks and ticket $10 and he have total money $15 so,

Preston left with = $15 - $10

                           = $5

Therefore, Preston left with $5 and correct expression for to find solution is option(B) i.e, 15 - (6.5 + 2 * 1.75)

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The probability that exactly four of the selected bulbs from the pack of 10 bulbs is defective is 1/120.

For the given question;

Thus, the probability that exactly four of the selected is defective.

P = ⁴C₄  / ¹⁰C₃

P = 1/120

Thus, the probability that exactly four of the selected is defective is 1/120.

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The system of inequalities that best matches the graph is Option C

Step-by-step explanation:

To find the system of inequalities, we simply need to find the equation of each line.

Thus, let's find the inequality that is represented by each line.

Red Line:

First, let’s determine the slope. To do so, we can use the slope formula:

m = (y₂-y₁) / (x₂-x₁)

We can use any two points that's on the Red Line. Using (3, -2) and (6, -4) and substituting them into the slope formula yields:

m = (-4+2) / (6-3)    = -2/3

Therefore, the slope of the red line is 2.

To write the equation of the red line, we can use the slope-intercept form:

y = mx + c

Notice that our y-intercept of our red line is (0, 3). Therefore, b = 3 and we already determined that m = -2/3:

y = ((-2/3)x) + (-3)

y   = (-2/3)x -3

Now, we need to determine our sign. Notice that the shaded region is below the red line. Therefore, y is less than our equation.

And since our line is shaded, our sign will be less than or equal to. Therefore:

y ≤ (-2/3)x - 3

Blue line:

Again, let’s first find the slope. We can use the two points (3,0) and (0, -3). Hence:

m = (-3-0) / (3-0)  = -3/3  = -1

So, the slope is -1.

We can now use the slope-intercept form. Notice that our y-intercept is (0, 0). Thus, we will substitute -1 for m and 0 for b. This yields:

y = -1x + 0

y = -x

Finally, we will determine our sign. Since the shaded region is above the blue line, our y is lesser than our equation. Therefore, our equation is:

y < -x

Thus, all together, our inequalities are:

y ≤ (-2/3)x - 3

y < -x

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All the statements about Arithmetic sequence and linear function are correct.

What is Arithmetic sequence and linear function?

When used in mathematics, the term "linear function" describes two different but related ideas: A linear function, also known as a polynomial function of degree zero or one, is a function in calculus and related fields that has a graph that is a straight line.

In an Arithmetic Sequence the difference between one term and the next is a constant. In other words, we just add the same value each time.

Since the  Linear Function has a y-intercept.

Also all the points on a Linear Function connect.

When a line slopes down from left to right, it has a negative slope. This means that a negative change in y is associated with a positive change in x.

That means the Domain of the Linear Function includes negative numbers when the function is decreasing.

Therefore, all the statements are correct.

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Answer/Step-by-step explanation:

[tex]-\frac{8}{27} a^{15} = (-\frac{2}{3})^{3} * (a^3)^5 = (-\frac{2}{3} a^{5})^3[/tex]

I hope this helps!

Answer:

x=2

Step-by-step explanation:

add the x onto the other side so it is positive : 7=5+x

then subtract the 5 from both sides so you can isolate the x : 2=x

rewrite the equation: x=2

☆ Hello ☆

The value of x is 2.

[tex] \red{ \sf \underline {\underline{Explantation: }}}[/tex]

¿What are equations?

The equations represent an equality between two mathematical expressions that have at least one variable called unknown.

[tex] \sf \:Solution:[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \begin{gathered}\boldsymbol{\mathsf{7 - x = 5}}\\\boldsymbol{\mathsf{ - x = 5-7}}\\\boldsymbol{\mathsf{ - x = -2}}\ \\ {\mathsf{ x = 2}}\end{gathered}[/tex]

[tex] \bf \:Verification:[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \begin{gathered}\boldsymbol{\mathsf{7 - 2 = 5}}\\\boldsymbol{\mathsf{ 5=5}}\end{gathered}[/tex]

[tex]\green{ \sf \: The \: result \: is} \: \red{\longmapsto} \blue 5[/tex]

P(The aircraft is discoverd and has no locator) = P(discovered)  x P(no locator/discoved =0.28)

The information is based on the disappearance of the of the light aircraft in the flight in the in a certain country . 70% of the aircraft that disapear while in the flight were discovered . The probability that there is an emergency locator        

in the aircraft given that it is discovered is 60% and the probability that the aircraft that has not discovered have an emergenncy locator is 90%.

a) To determine probiblity it wount be discoverd

Calculation

P(the aircraft is discovered and has a locator) = P(discovered) X P(locator/discovered)

The probability of the flight discovered and has locator is obatained as given below:

P(The aircraft is discoverd and has no locator) = P(discovered)  x P(no locator/discovered)

The probability of the flight not discovered and has a locator is obatained below.

P(The aircraft is not discovered and has a locator) = P(not discovered) x P (locator  | not discorverd)    = 1-0

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Answer:

D

Step-by-step explanation:

Multiply both sides by 3

x − 1 = 9

Add 1 to both sides

x = 10

Answer:

Step-by-step explanation:

5.40/12= 0.45

6.72/16=0.42

Answer:

The 16 pack

Step-by-step explanation:

Pack 1: $5.40 for 12

Pack 2: $6.72 for 16

Therefore the 16 pack is the better buy because you purchase an extra 4 sodas for $0.03 less.

Answer:

-7,7

Step-by-step explanation:

The proportion of bottles that will have more than 18 ounces dispensed into them is 0.0228

Proportion relationship:

Proportion means a relationships between two variables where their ratios are equivalent and it is the way to think about them is that, in a proportional relationship, one variable is always a constant value times the other.

Given,

A company that manufactures and bottles apple juice uses a machine that automatically fills 20-ounce bottles. there is some variation, however, in the amount of liquid dispensed into the bottles. the amount dispensed has been observed to be approximately normally distributed with mean 20 ounces and standard deviation 1 ounce.

Here we need to determine the proportion of bottles that will have more than 18 ounces dispensed into them and round the answer to the four decimal places.

Here we have to use tables to determine the proportion of bottles that will have more than 18 ounces dispensed into them.

Let us consider X denote the amount of juice dispensed.

Then it can be written as,

P (X >18) = P (Z > (20 - 18)/1)

=> P (X >18) = P (Z > 2)

=> 1 - Ф(2)

=> 1 - 0.9772

=> 0.0228

Hence the proportion of the bottles that will have more than 18 ounces dispensed into them is 0.0228.

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Yes, a baseball fit in box A.

Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies. Volume is measured in cubic units like m³, cm³, in³, etc.

Volume is simply the amount of space a three-dimensional solid takes up. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

Volume is sometimes referred to as capacity. For instance, a cylindrical jar's volume can be used to calculate how much water it can hold.

Given:

The circumference of a regulation baseball is at least 9 inches but no more than 9.25 inches.

So, the maximum value of Circumference

2πr = 9.5

r= 9.5/ 2 x 3.14

r = 1.472 inch

So, Volume of ball = 4/3 πr³

Volume of ball = 4/3 x 3.14 x (1.472)³

Volume of ball = 13.36 inch³ < 64 inch³

Hence, it will fit inside the box.

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The equivalent expressions using only positive exponents are 1/(7x⁵y⁸)⁵ and (5y³/x⁶)⁵

Expression 1

From the question, the expression is given as

(49x¹⁰y¹⁶)⁻⁵/²

Express the radicals as roots

So, we have

(49x¹⁰y¹⁶)⁻⁵/² = √[(49x¹⁰y¹⁶)]⁻⁵

Take the square root of each of the factor in the bracket

This gives

(49x¹⁰y¹⁶)⁻⁵/² = (7x⁵y⁸)⁻⁵

Apply the negative exponent rule of indices

So, we have

(49x¹⁰y¹⁶)⁻⁵/² = 1/(7x⁵y⁸)⁵

Expression 2

From the question, the expression is given as

(125x⁻¹⁸y⁹)⁵/₃

Express the radicals as roots

So, we have

(125x⁻¹⁸y⁹)⁵/₃ = ∛[(125x⁻¹⁸y⁹)]⁵

Take the cube root of each of the factor in the bracket

This gives

(125x⁻¹⁸y⁹)⁵/₃ = (5x⁻⁶y³)⁵

Apply the negative exponent rule of indices

So, we have

(125x⁻¹⁸y⁹)⁵/₃ = (5y³/x⁶)⁵

Hence, the equivalent expression is  (125x⁻¹⁸y⁹)⁵/₃ = (5y³/x⁶)⁵

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The nearest whole number to the number 5.2 is 5.

Given number:

= 5.2

we can determine the whole number of any decimals using the properties that is,

if decimal part < .5 its nearest whole number is 0.

example = 0.5 whole number is 0.

if decimal part  >  0.5 its nearest whole number is 1.

In this case,

= 5.2

decimal part  = 0.2 < 0

so the nearest whole number is 5.

Therefore the nearest whole number to the number 5.2 is 5.

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Answer: The sum of two prime numbers is always even (which is composite).

Hope this helped :)