addison runs around a circle track 4 times. if the track has a radius of 30 feet, how far did addison run?

The coordinates of the vertices for the image of the pre image is translated 4 units right are: ’(-1, 2), B’(5, 3), and C’(1, 0).

Translation on the coordinate plane is sliding a point or figure in any direction without any changes in size or shape.

During translation, the coordinates of the vertices of a figure or point change, and they slide left or right, up, or down without changing size or shape.

Given the question above, we need to find the coordinates of the vertices for the image of the pre image that are translated 4 units right.

So,

\(\rightarrow\sf \boxed{\boxed{-5+4=1=\bold{(-1,2)}}}\)

\(\rightarrow\sf \boxed{\boxed{1+4=5=\bold{(5,3)}}}\)

\(\rightarrow\sf \boxed{\boxed{-3+4=1=\bold{(1,0)}}}\)

Thus, the coordinates of the vertices for the image of the pre image is translated 4 units right are: ’(-1, 2), B’(5, 3), and C’(1, 0).

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Answer:

Triangles in Geometry

Step-by-step explanation:

Answer:

\(Var = 1.9\)

Step-by-step explanation:

Given

\(p = \frac{1}{20}\)  i.e. 1 per 20cc of water

\(n = 40\) -- sample size

Required

The variance

This is calculated using:

\(Var = np(1 - p)\)

So, we have:

\(Var = 40 * \frac{1}{20} * (1 - \frac{1}{20})\)

\(Var = 40 * \frac{1}{20} * \frac{19}{20}\)

\(Var = 2 * \frac{19}{20}\)

\(Var = \frac{38}{20}\)

\(Var = 1.9\)

Answer:

what? I don't understand what your trying to say

The interest eared from the given amount, rate of interest and time period is $426.883.

Given that, amount = $700, rate of interest = 4% and time period = 2 years.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

The formula used to find the compound interest is \(Amount=Principal(1+\frac{r}{100})^{nt}\)

Let the money deposited be x.

So, \(700=x(1+\frac{4}{100} )^{2\times12}\)

⇒ \(700=x(1+0.04)^{24}\)

⇒ \(700=x(1.04)^{24}\)

⇒ 700 = 2.563x

⇒ x=700/2.563

⇒ x=$273.117

So, interest = 700-273.117

= $426.883

Therefore, the interest eared from the given amount, rate of interest and time period is $426.883.

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The true statements about the polynomial function graphed are:

Its leading coefficient is positive.

It has an odd degree.

None of the zeroes have even multiplicity.

From the given options, the true statements about the polynomial function graphed are:

Its leading coefficient is positive.

It has an odd degree.

None of the zeroes have even multiplicity.

Let's analyze each statement:

Its leading coefficient is positive:

The leading coefficient of a polynomial is the coefficient of the term with the highest degree.

From the graph, if the polynomial is going upwards on the right side, it indicates that the leading coefficient is positive.

It has an odd degree: The degree of a polynomial is the highest power of the variable in the polynomial expression.

If the graph has an odd number of "turns" or "bumps," it indicates that the polynomial has an odd degree.

None of the zeroes have even multiplicity:

The multiplicity of a zero refers to the number of times it appears as a factor in the polynomial.

In the given graph, if there are no repeated x-intercepts or no points where the graph touches and stays on the x-axis, it implies that none of the zeroes have even multiplicity.

The other statements (its leading coefficient is negative, it has an even degree, it has exactly two real zeroes, it has exactly three real zeroes, and none of the zeroes have odd multiplicity) cannot be determined based solely on the information given.

Therefore, the true statements about the polynomial function graphed are:

Its leading coefficient is positive.

It has an odd degree.

None of the zeroes have even multiplicity.

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The measure of the central angle is 0.75 radians

An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.

The area of a figure is the amount of space it occupies in its two dimensional state.

The length of an arc with an angle of Ф is given by:

Length of arc = (Ф/360) * (π * diameter)

The diameter is 16 cm and intercepted arc length is 6 cm, hence:

Length of arc = (Ф/360) * (π * diameter)

6 = (Ф/360) * (π * 16)

Ф = 42.97°

Ф = 42.97° * π/180 = 0.75 radian

The measure of the central angle is 0.75 radians

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Answer:

m = ½

y = ½x - 3

Step-by-step explanation:

m = (-12 + 14)/(‐18 + 22)

m = ½

y + 14 = ½(x + 22)

y = ½x + 11 - 14

y = ½x - 3

Answer:

Below

Step-by-step explanation:

Area of square - area of circle = remnant               area of circle = pi r^2

(40 x 40) - pi (20^2) = 343 . 4 in^2  left over

( this assumes the circle touches the edges of the square)

Answer:

3.10686

Step-by-step explanation:

Divide the kilometer by 1.609

9514 1404 393

Answer:

  3 1/8 miles

Step-by-step explanation:

Using your conversion factor ...

  (5 km) × (1 mi)/(1.6 km) = (5/1.6) mi = 25/8 mi = 3 1/8 mi

A 5k race is about 3 1/8 miles.

_____

Additional comment

That estimate that is high by 0.584%, or 29.2 meters.

Using the Pythagorean Theorem, we can determine that the length of CD is 11.62, rounded to the closest hundredth.

When the length of the longest side of a right triangle is squared, the result will be equal to the total of the squares of the lengths of the other two sides of the right triangle that are smaller.

Taking into account the following:

Side AB = 6

Side AC = 12

The perpendicular bisector theory states that AD equals half of AB, which equals half of (6), which equals three.

By using the Pythagorean theorem, we get the following:

The length of the CD is equal to (AC2 - AD2)

The length of the CD is equal to 122 minus 32.

The length of the CD equals (144 - 9)

11.62 is the length of the CD.

Consequently, by using the Pythagorean Theorem, we can determine that the length of the CD is 11.62, rounded to the closest hundredth.

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Answer:

7. 14

15. 30

28. 56

32. 64

18 36

x 2x

1/2y. y

2x. 4x

x+3 2x+9

Step-by-step explanation:

each out is double the in

Answer:

To find the volume of the shipping box in cubic feet, we need to convert the dimensions from inches to feet and then calculate the volume.

Given:

Length = 36 inches

Width = 24 inches

Height = 18 inches

Converting the dimensions to feet:

Length = 36 inches / 12 inches/foot = 3 feet

Width = 24 inches / 12 inches/foot = 2 feet

Height = 18 inches / 12 inches/foot = 1.5 feet

Now, we can calculate the volume of the box by multiplying the length, width, and height:

Volume = Length * Width * Height

Volume = 3 feet * 2 feet * 1.5 feet

Volume = 9 cubic feet

Therefore, the shipping box can hold 9 cubic feet.

Step-by-step explanation:

First convert the units because it's asking for the cubic feet but they give us the measurements in inches.

To convert inches to feet we divide the number by 12.

36 ÷  12 = 3

24 ÷  12 = 2

18 ÷ 12 = 1.5

Now to find the volume, we multiply it all together.

3 × 2 × 1.5 = 9

It can hold 9 cubic feet.

Hope this helped!

Answer: any negative value

Step-by-step explanation:

g(x)= ax², inc on x<0 & dec on x>0

Firstly we need to get the derivative of g(x)

g'(x)=2ax

for inc interval g'(x) should be +ve

x<0 (i.e. x= -ve), then a must be -ve

for dec interval g'(x) should be +ve

x>0 (i.e. x= +ve), then a must be -ve

so in both cases a must be a negative constant

Answer:

5x+4y = 24

Step-by-step explanation:

We know the y intercept = 6

We can find the slope

(0,6) and (4,1)

m = ( y2-y1)/(x2-x1) = ( 1-6)/(4-0) = -5/4

The slope intercept form is y = mx+b where m is the slope and b is the y intercept

y = -5/4x+6

Multiply each side by 4

4y = -5x+24

Add 5x to each side

5x+4y = 24

The standard form of a line is

Ax +By = C  where A,B C are integers and A > 0

Answer:

2y +12

Step-by-step explanation:

5y - 3y =2y and then plus 12

Answer:

C

Step-by-step explanation:

Answer:

Step-by-step explanation:

B=120+12m and P=200-4m

120+12m=200-4m add 4m to each side

16m+120=200, subtract 120 from each side

16m=80, divide each side by 16

m=5

So in five months they will weigh the same.

Answer:

D

Step-by-step explanation:

The credit card company extends you a line of credit. You purchase "stuff" and then have the choice to pay the balance in full or a minimum payment each month.

This is the only one that makes sense because of the last sentence which you have the choice to pay in full or a minimum payment

The option that best describes how a credit card works is D. The credit card company extends you a line of credit. You purchase "stuff" and then have the choice to pay the balance in full or a minimum payment each month.

In conclusion, the correct option is D.

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The event that has a probability other than one-half is choosing a red card from a standard deck of 52 cards, as it has a probability of 26/52 or 1/2. The other events have two, five, and three equally likely outcomes with probabilities of 1/2, 1/5, and 1/3, respectively.

The event that has a probability other than one-half among the given options is choosing a red card from a standard deck of cards.

The probability of choosing a red card from a standard deck of 52 cards is 26/52, which simplifies to 1/2.

The other events have an equal probability of occurring because they are all equally likely outcomes.

Flipping a coin has two possible outcomes, and each outcome has a probability of 1/2.

Choosing a vowel from a bag of tiles that contains one of each letter of the alphabet has five possible outcomes, and each outcome has a probability of 1/5.

Rolling an even number on a number cube that is numbered from 1 to 6 has three possible outcomes (2, 4, or 6), and each outcome has a probability of 1/3.

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There must be 46 chairs in each row and total number of chairs are 1058

To meet the given conditions, we need to find a number that has the following properties:

It should be divisible by 2, as there are an even number of chairs in each row.

It should be divisible by 23, as there are 23 rows of chairs.

It should be the same number in each row.

The smallest number that satisfies these conditions is 46, which is the least common multiple of 2 and 23.

So, we need to set up 46 chairs in each row.

The total number of chairs required will be:

Total number of chairs = 23 rows x 46 chairs per row = 1058 chairs

Hence, the total number of chairs are 1058

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Answer:

t = 6.8 years

Step-by-step explanation:

The formula for compound interest is

\(A(t)=P(1+r/n)^n^t\), where P is the principal/amount invested, r is the interest rate, n is the number of compound periods per year (4 for quarterly), and t in the time in years.

We know that A = $5900, P = $4000, and r = 0.0575 (we must convert the percentage to a decimal).  We must solve for t and round to the nearest tenth:

\(5900=4000(1+0.0575/4)^(^4^t^)\\\\59/40=(1623/1600)^4^t\\\\log(59/40)=log(1623/1600^4^t)\\\\log(59/40)=4t*log(1623/1600)\\\\log(59/40)/log(1623/1600)=4t\\\\1/4(log(59/40)/log(1623/1600))=t\\\\6.80773607=t\\\\6.8=t\)

Answer:

x = 14º 30'   OR  14.5º

Step-by-step explanation:

(x + 14)º = (3x – 15)º

3x -x = 14º +15º

2x = 29º

x = 14º 30'   OR  14.5º

The Least Common Multiple (LCM) for 98 and 231, notation LCM (98, 231), is 3234.

Solution by using the division method:

This method consists of grouping by separating the numbers that will be decomposed on the right side by commas while on the left side we put the prime numbers that divide any of the numbers on the right side. We starting with the lowest prime numbers, divide all the row of numbers by a prime number that is evenly divisible into 'at least one' of the numbers. We stop when it is no longer possible to divide (the the last row of results is all 1's). See below how it works step-by-step.

2 | 98, 231

3 | 49, 231

7 | 49, 77

7 | 7, 11

11 | 1, 11

1 | 1, 1

The LCM is the product of the prime numbers in the first column, so:

LCM = 2 . 3 . 7 . 7 . 11 = 3234

Solution by listing multiples:

This method consists of listing the multiples of all the numbers that we want to find the LCM. Multiples of a number are calculated by multiplying that number by the natural numbers 2, 3, 4, ..., etc. See below:

* The multiples of 98 are 98, 196, 294, 392, 490, 588, ..., 3234

* The multiples of 231 are 231, 462, 693, 924, 1155, ..., 3234

Because 3234 is the first number to appear on both lists of multiples, 3234 is the LCM of 98 and 231.

Hence the answer is The Least Common Multiple (LCM) for 98 and 231, notation LCM (98, 231), is 3234.

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9514 1404 393

Answer:

  no solution

Step-by-step explanation:

The solutions to the equation are ...

  tan(θ/7) +√3 = 0

  tan(θ/7) = -√3

  θ/7 = arctan(-√3) +nπ . . . . . . . for integer n

  θ = 7(-π/3 +nπ) = 7π(n -1/3)

For n=0, θ = -7π/3 -- not in the required interval.

For n=1, θ = 14π/3 -- not in the required interval.

There are no solutions in the required interval.

A quotient is the result of dividing one number by another. For example, the quotient of 6 and 3 equals 6/3 or 2. In your problem above it is asking you to provide the quotient of 10 and 2 meaning you divide the 2 into the ten and end up with 10/2 or 5.

So I think the answer is 10/2 or 5

Answer: 0 = 3

Step-by-step explanation: If y = 7 - 3x, we can plug that in for y in the equation 3x + y = 10 by writing it as 3x + 7 - 3x = 10.

                                                                    - 7            - 7

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

                                                               3x - 3x        = 3

                                                                       0          = 3