Triangle ABC was dilated using the rule DO,4. Triangle A'B'C' is the result of the dilation. Point O is the center of dilation. Triangle A B C is dilated to create triangle A prime B prime C prime. The length of O B is three-fourths. What is OB'? 1.5 units 3 units 4.5 units 6 units

After the double rotation, the vertices of the quadrilateral MNPQ are transformed to M'', N'', P'', and Q''. The shape of the quadrilateral may have changed, but the order of the vertices remains the same.

When a quadrilateral MNPQ is rotated counterclockwise at 90 degrees about the origin, each vertex undergoes a transformation.

The new positions of the vertices after this rotation can be denoted as M', N', P', and Q'. The order of the vertices remains the same.

Next, when the rotated quadrilateral M'N'P'Q' is further rotated counterclockwise at 270 degrees about the origin, each vertex undergoes another transformation.

The new positions of the vertices after this rotation can be denoted as M'', N'', P'', and Q''. Again, the order of the vertices remains the same.

It's important to note that a 270-degree counterclockwise rotation is equivalent to a 90-degree clockwise rotation.

The result of the double rotation is equivalent to a single clockwise rotation of 90 degrees.

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1.57 meters of barbed wire are needed to fence the circular piece of land with a radius of 25 cm.

We have,

To calculate the amount of barbed wire needed to fence the circular piece of land, we need to find the circumference of the circle.

Given:

Radius (r) = 25 cm

The formula for the circumference (C) of a circle is:

C = 2πr

Substituting the given radius into the formula, we have:

C = 2π x 25 cm

Now, we can calculate the circumference in centimeters.

C = 2 x 3.14 x 25 cm

C ≈ 157 cm

Now,

To convert centimeters to meters, we divide the circumference by 100.

C (in meters) = 157 cm / 100

C (in meters) ≈ 1.57 meters

Therefore,

Approximately 1.57 meters of barbed wire are needed to fence the circular piece of land with a radius of 25 cm.

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The complete question.

A circular piece of land with a radius of 25 cm is going to be fenced. How many meters of barbed wire are needed?

Answer:

The answer is c. 0.027.

Step-by-step explanation:

Answer:

Step-by-step explanation:

0.18*0.15=0.027  choice C

By rewritting the exponential equation, we can see that the correct options are B and C.

We know that the balance is modeled by the exponential equation below:

\(A = 328.23\times e^{0.045*(t - 2)}\)

Now we want to see which of the other equations are equivalent to this one, so we need to rewrite this equation, so let's do that.

First we can rewrite the second part to get:

\(A = 328.23\times e^{0.045\times(t - 2)}\\\\A = 328.23\times(e^{-2*0.045*}\times e^{0.045\times t})\\\\A = 300\times e^{0.045\times t}\)

So that is an equivalent equation.

We also can keep rewritting this to get:

\(A = 300\times e^{0.045\times t}\\\\A = 300\times(e^{0.045})^t\\\\A = 300\times(1.046)^t\)

The correct options are B and C.

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This distribution of snowfall amounts is skewed to the right

Data is said to be skewed to the right or positively skewed, when the tail of the distribution extends more towards the right side of the data. This means that there are a few larger values or outliers that pull the mean or median towards the higher end of the scale, resulting in a longer tail on the right side of the distribution.

In a positively skewed distribution majority of the data is concentrated towards the lower values.

Considering the stemplot the majority of the data is in the lower values

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Answer:

to the second part

18.7 inches

Answer:

312

Step-by-step explanation:

Add the area of each face together

Don't forget the units!

Let's start by finding the right face (12 by 3). From your picture, we can tell its 12m long, and 3m tall. To find the aria of any face, we multiply the length, times the width.
12 x 3 = 36.
Now let's look at where it says 8m. Since that face is just as tall as the first one, we can tell its 3m tall.
8 x 3 = 24.

We can continue this for the top face.
Since the width of the second face we did is 8m, and the width of the first one is 12m, we can tell that the top one is 8 x 12. (96).

We can do this again for the other 3 sides.
A shortcut i like to take, is to do 3 of the sides, (Like the ones we did) and add them together, then double the sum.

36+24+96=156.

156x2=312.

This shortcut should work, because by adding the aria of half the sides together, we get exactly half the answer.

When doing this, it only works to do 3 different sides. it will not work if you do the same side twice, or a parallel side.

I encourage you to let me know if this method works for you! I hope this helps!

The annual interest rate is 7.5%.

What is Simple interest?

Simple interest is a type of interest that is calculated on the principal amount (or the initial amount) of a loan or investment, without taking into account any accumulated interest from previous periods.

The formula for simple interest is:

I = P × r × t

where I is the interest earned, P is the principal (initial amount), r is the annual interest rate as a decimal, and t is the time in years.

In this case, we know I = $562.50, P = $1500, and t = 5 years.

we ca substitute values into the formula,

562.50 = 1500× r ×5

Simplifying, we get:

r = 562.50 / (1500 ×5)

r = 0.075

r = 7.5%

Therefore, the annual interest rate is 7.5%.

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Answer:  C - 15.81

Step-by-step explanation:

pythagorean theorum: a^2 + b^2 = c^2

13^2 + 9^2 = c^2

169 + 81 = c^2

c^2 = 250

root both sides

c = 15.81

it is 4 3 2 1 5 6 4 3 3. 6 5 3 3 5 5 3 4 5 4

Answer:

4

Step-by-step explanation:

Answer:

$4.00

Step-by-step explanation:

I used a calculator.

Therefore, there are approximately 889 faculty members at the college.

Ratio is a mathematical concept that expresses the relationship between two or more quantities or values. It is a way to compare the size of two numbers, by dividing one number by the other. The result of this division is a numerical expression of the relative size of the two numbers.

Ratios are often expressed as a fraction or a colon (:) between the two numbers. For example, if there are 4 red balls and 6 blue balls in a bag, the ratio of red balls to blue balls can be expressed as 4/6 or 4:6. This means that for every 4 red balls in the bag, there are 6 blue balls.

Ratios are commonly used in various fields, such as finance, statistics, and science, to compare different values and make meaningful interpretations.

To solve this problem, we need to use the ratio between faculty members and students, which is given as 1:18. This means that for every one faculty member, there are 18 students.

If there are 16000 students in the college, we can find the number of faculty members by dividing the number of students by the ratio of students to faculty members:

Number of faculty members = 16000 / 18

This gives us 888.888, but since we are asked to round to the nearest whole number, we should round up to 889. Therefore, there are approximately 889 faculty members at the college.

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Answer:

-152

Step-by-step explanation:

-152 < 12

-152 is negative, which means it is less than 1.

12 is positive, which means it is greater than 1.

Therefore, -152 is the lesser of the two given numbers.

Have a great rest of your day! :)

Hi!

-152 is less than 12, because:

\(\mathbb{NUMBER \ LINE}\)

\(_ < \!\!\!\rule{300}{1}\!\!\!_ >\)

     \(-152\)                                                                         \(12\)

Cheers!

Have a nice day!

I hope this helps!

The first ten terms of the Lucas sequence are 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843.

The Lucas sequence or Lucas series are an integer sequence named after the mathematician francois Edouard Lucas, which are similar to the Fibonacci numbers, each Lucas number is defined to be the sum of its two immediate previous terms, thereby forming a fibonacci integer sequence.

Now, the sequence of first 10 numbers of Fibonacci series are-

0, 1, 1 ,2, 3, 5, 8, 13, 21, 34

which are defined as set of integers that starts with zero, followed by a one,then by another one and then by series of steadily increasing numbers,The sequence follow the rule that each number is equal to the sum of preceding two numbers.

And the sequence of Lucas sequence is -

2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843.

which is definedas  the sum of its two immediate previous terms.

The Lucas number may thus be defined as follows;

Ln =    \(\left \{ {{2} ; if n= 0 \atop {1}; if n = 1} \right.\)

Here we can see that Lucas series starts with 2 and 1 whereas Fibonacci series starts with 0 and 1.

Hence,The first ten terms of the Lucas sequence are 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843.

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Answer:

0.88

Step-by-step explanation:

Answer:

write anser is 33/49 1 st one.

Step-by-step explanation:

hope it helps you

Answer:

The correct answer is (second option):

The x-intercept is (6, 0); the y-intercept is (0, –9).

Step-by-step explanation:

Intercepts of a real function

Given a function y=f(x), the x-intercepts of f are those values of x that make y=0. The y-intercepts are those values of y that make x=0.

Our function is:

3x - 2y = 18

To find the x-intercept(s), we set y=0:

3x - 2(0) = 18

3x = 18

Solving:

x = 18 / 3 =6

The x-intercept is the point (6,0)

Now for the y-intercept(s), we set x=0:

3(0) - 2y = 18

-2y = 18

Solving:

y = 18 / (-2) = -9

The y-intercept is the point (0,-9)

The correct answer is (second option):

The x-intercept is (6, 0); the y-intercept is (0, –9).

The x-intercept is (6, 0); the y-intercept is (0, –9).

Answer:

y = 4x + 9

Step-by-step explanation:

First, find the slope of the line, which is the change in y/the change in x:

(-11-1)/(-5-(-2)) = -12/-3 = 4

That leaves you with the equation:

y = 4x

But notice, when x = -2 in the equation, y = -8, but we want it to be 1, so we add 9 to the end of the equation:

y = 4x + 9

I hope this helped.

Answer:

Step-by-step explanation: -15/9 my teacher told me

Answer:

27/250

Step-by-step explanation:

Green grape is 9/25

seedless is 3/10

Since it’s a compound probability you multiple them to get 27/250

Answer:

27/250

Step-by-step explanation:

Answer: 7

Step-by-step explanation:

Since there are 42 tubes and each tray can hold 6 tubes, it will be 42/6 which is 7.

5.06

√25.65 = 5.06458...

so, to round it off to 2.d.p, you just count up to two numbers after the decimal point, these number would be 0 and 6. 6 can not be rounded off because the 4 after it is not bigger than 5.

The function notation of the following are:

f(1) = 5

f(0) = 1

f(-3) = -11

f(8) = 33

Given:

x is the input.

the function is 4x+1

f(x) is the output.

we are asked to determine the values of the following :

a. f(1)

x = 1

so f(x) = 4x+1

f(1) = 4(1)+1

f(1) = 4+1

f(1)=5

b. f(0)

x = 0

so f(x) = 4x+1

f(0) = 4(0)+1

f(0) = 0+1

f(0)=1

c. f(-3)

x = -3

so f(x) = 4x+1

f(-3) = 4(-3)+1

f(1) = -12+1

f(1)= -11

d. f(8)

x = 8

so f(x) = 4x+1

f(8) = 4(8)+1

f(8) = 32+1

f(1)=33

Hence we get the required values.

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Step-by-step explanation:

nice

question

dear

Answer:

9

Step-by-step explanation:

The \(n\)term is \(2n+1\).

\(S_n=\frac{3+2n+1}{2}(n)=99 \\ \\ \frac{n(2n+4)}{2}=99 \\ \\ n(n+2)=99 \\ \\ n^2+2n-99=0 \\ \\ (n+11)(n-9)=0 \\ \\ n=9 \text{ } (n>0)\)

The number of terms that needed to make the sum to 99 is 9

The first term of the arithmetic progression = 3

The common difference = 2

The sum of n term is = (n/2) [2a+(n-1)d]

Where a is the initial term

d is the common difference

Substitute the values in the equation

(n/2) [2(3)+(n-1)2] = 99

(n/2) [6 + 2n - 2] = 99

(n/2)[4+2n] = 99

n(2 + n) = 99

2n + \(n^2\) = 99

\(n^2\) + 2n - 99 = 0

Split the terms

\(n^2\) - 9n +11n - 99 =0

n(n -9) + 11(n - 9) = 0

(n + 11)(n - 9) = 0

n = -11 or 9

Since n cannot be a negative number, therefore n = 9

Hence, the number of terms that needed to make the sum to 99 is 9

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Janet's savings in January is $800

A word problem in math is a math question written as one sentence or more. This statements are interpreted into mathematical equation or expression.

Represent Mary's savings by x and Janet's savings by y

7/4 = x/y

40/100 × x = 40x/100 = 2x/5

New savings for Mary =

x -2x/5 = 5x - 2x)/5 = 3x/5

50/100 × y = y/2

New savings for Janet =

y + y/2 = 3y/2

3y/2 + 3x/5 = 2040

15y + 6x = 20400

7y = 4x

y = 4/7x

Substitute (4/7)x for y

15( 4/7) x + 6x = 20400

(60/7 )x + 6x = 20400

60x + 42x = 142800

102x = 142800

x = 142800/102

x = $ 1400

y = 4/7 × 1400

y = $800

Therefore, the savings for Janet in January is $800.

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The given formula that models the number of songs in Martin's iTunes collection is:

Where m is the number of months.

We can interpret the terms in this formula as: 200 is the current number of songs in Martin's collection, and 15 is the number of new songs Martin adds every month.

We can prove this by replacing m=1, so:

So, in the first month, Martin will have 215 songs, for a total of 15 new songs.

The answer is: Every month, Martin adds 15 new songs.

Answer:we3

Step-by-step explanation:

s

Answer:

\(dauda = x \\ his \: brother = y \\ x + y = 2 \: \: \: (i) \\ 5(3x + y) = 5 \: \: \: (ii) \\ 15x + 5y = 5\)

I don't really remember this very well, because it confusing me