A 36-inch string is to be cut so that one piece is 9 inches longer than the other. What is the length of the shorter piece?
The shorter plece has a length of inches.

Answer:(6, 5)

Give me brainliest

The side RS is 7 cm. For a similar triangle, the ratio of the opposite side of the two similar triangle are the same.

ΔABC ~  ΔDEF only if the ratio of two sides of ΔABC and corresponding two sides of ΔDEF is equal, and the angle included in both sides are congruent.

Suppose the two sides of ΔABC are AB and BC, and that of DEF be DE and EF, then for SAS similarity, we need

For the similar triangle;

\(\rm \frac{HG}{TS} = \frac{FG}{RS} \\\\ \frac{12}{4} =\frac{21}{RS} \\\\ RS= 7 cm\)

Hence, the side RS is 7 cm.]

To learn more about the SAS similarity theorem, refer to link;

https://brainly.com/question/22472034

#SPJ1

The completed sequence is: 3/k, 3/k, 3/k, 9/2k.To complete the sequence of numbers with a constant difference between adjacent numbers, we can calculate the common difference by subtracting the first term from the second term.

Let's denote the missing terms as A and B.

The given sequence is: 3/k, A, B, 9/2k.

The common difference can be found by subtracting 3/k from A or B. Therefore:

A - 3/k = B - A = 9/2k - B.

To simplify, we can equate the two expressions for the                     common difference:

A - 3/k = 9/2k - B.

Next, we can solve for A and B using this equation.

Adding 3/k to both sides gives:

A = 3/k + 9/2k - B.

Now, we can substitute the value of A into the equation:

3/k + 9/2k - B - 3/k = 9/2k - B.

Simplifying further, we have:

9/2k - 3/k = 9/2k - B.

Cancelling out the common terms, we find:

-3/k = -B.

Multiplying both sides by -1, we get:

3/k = B.

For more such questions on Adjacent numbers:

https://brainly.com/question/28207765

#SPJ8

Answer:

The slope is 2.

Step-by-step explanation:

Slope = rise / run, meaning that when you move 2 units up, you move 1 unit right. The slope here is positive.

Answer:

5/6 + 5/3 = 5/2

Step-by-step explanation:

Answer: q1=11 q2=15 q3=20

Step-by-step explanation:

6 tables are required. Each prime number attender should serve 3 customers each.

The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

All the numbers other than prime numbers are composite numbers.

The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.

Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables

Therefore, 6 tables are required.

Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.

Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.

Thus, each prime number attender should serve 3 customers each.

For more questions on prime number

https://brainly.com/question/145452

#SPJ8

Since AB is parallel to CD, we have alternate interior angles forming when transversal CE intersects the parallel lines. Therefore,

mZDCE = mZECB (Alternate Interior Angles)

(7x + 2) = (x + 8) (Substitute in the given angle measures)

Solving for x, we get:

7x + 2 = x + 8

6x = 6

x = 1

Now, we can use x to find the measure of angle ZDCE:

mZDCE = (7x + 2)

= (7*1 + 2)

= 9

Therefore, the measure of angle ZDCE is 9 degrees.

Answer: 40 pupils

Step-by-step explanation:

 35           14

-------   =   --------

100             ?

find the denominator.

multiply 14 and 100:

14 x 100 = 1400

divide 1400 by 35

1400/35 = 40

Therefore there are 40 students

Answer:

The area of the complex figure is approximately 210.92 square units.

Step-by-step explanation:

Let's calculate the area of the complex figure with the given information.

We can break the figure down into three components: an equilateral triangle, a right triangle, and a rectangle.

1. Equilateral Triangle:

The height of the equilateral triangle is given as 4.33 units. We can calculate the area using the formula:

Area of Equilateral Triangle = (base^2 * √3) / 4

In this case, the base of the equilateral triangle is also the length of side d, which is given as 13 units.

Area of Equilateral Triangle = (13^2 * √3) / 4

Area of Equilateral Triangle ≈ 42.42 square units

2. Right Triangle:

The right triangle has two sides with lengths a (5 units) and b (5 units), and its hypotenuse has a length of side c (also 5 units).

Area of Right Triangle = (base * height) / 2

In this case, both the base and height of the right triangle are the same and equal to a or b (5 units).

Area of Right Triangle = (5 * 5) / 2

Area of Right Triangle = 12.5 square units

3. Rectangle:

The rectangle has a length equal to side d (13 units) and a width equal to side e (12 units).

Area of Rectangle = length * width

Area of Rectangle = 13 * 12

Area of Rectangle = 156 square units

Now, to get the total area of the complex figure, we add the areas of each component:

Total Area = Area of Equilateral Triangle + Area of Right Triangle + Area of Rectangle

Total Area = 42.42 + 12.5 + 156

Total Area ≈ 210.92 square units

Therefore, the area of the complex figure is approximately 210.92 square units.

Answer:

dollar amount in decimal is 0.55

in fraction form is 11/20

Answer:

506

Step-by-step explanation:

8³-9×2÷3

= 512 - 9 × 2 ÷3

= 512 - 9 × ⅔

= 512 - 3 × 2

= 512 - 6

= 506

PEDMAS rule

P: Parentheses

E: Exponent

D: Division

M: Multiplication

A: Addition

S: Substraction

Answer:

11.295

11.29 and 11.30 are already two digit decimals, we can not get another 2 digit decimal. We have to make a 3 digit decimal.

11.295 falls between 11.29 and 11.30.

Hope this helps you!

Answer:

11.295

Step-by-step explanation:

cmon now. That was pretty easy lol

The true statement, regarding the signal of the graphed function, is given by:

F(x) > 0 over the interval (–∞, –4).

Looking at it's graph, we have that:

Researching this problem on the internet and looking at the graph of the function, the function is negative for all values to the right of x = -4,  and positive to the left, hence the correct statement is given by:

F(x) > 0 over the interval (–∞, –4).

More can be learned about the signal of a function at brainly.com/question/25638609

#SPJ1

Tamara should expect the sum of the two cubes to be equal to 7 around 30 times when rolling the two number cubes 180 times.

To determine how many times Tamara should expect the sum of the two number cubes to be equal to a certain value, we need to analyze the chart and calculate the probabilities.

Let's examine the chart and count the number of times each sum occurs:

Sum: 2, Occurrences: 1

Sum: 3, Occurrences: 2

Sum: 4, Occurrences: 3

Sum: 5, Occurrences: 4

Sum: 6, Occurrences: 5

Sum: 7, Occurrences: 6

Sum: 8, Occurrences: 5

Sum: 9, Occurrences: 4

Sum: 10, Occurrences: 3

Sum: 11, Occurrences: 2

Sum: 12, Occurrences: 1

Now, let's calculate the probabilities of each sum occurring.

Since there are 36 possible combinations when rolling two number cubes, the probability of each sum is the number of occurrences divided by 36:

Probability of sum 2 = 1/36

Probability of sum 3 = 2/36

Probability of sum 4 = 3/36

Probability of sum 5 = 4/36

Probability of sum 6 = 5/36

Probability of sum 7 = 6/36

Probability of sum 8 = 5/36

Probability of sum 9 = 4/36

Probability of sum 10 = 3/36

Probability of sum 11 = 2/36

Probability of sum 12 = 1/36

To find out how many times Tamara should expect a certain sum when rolling the two number cubes 180 times, we can multiply the probability of that sum by 180.

For example, to find the expected number of times the sum is 7:

Expected occurrences of sum 7 = (6/36) \(\times\) 180 = 30

Similarly, we can calculate the expected occurrences for all other sums.

For similar question on probabilities.

https://brainly.com/question/30768613  

#SPJ8

The statement which best describes the data given is C) The data can be modeled by a quadratic function.

Given a data,

The numbers of customers that visited a store each hour for several hours after the store opened at 8 am are shown in the table.

It is clear that the number of customers increases to 18 for the first 4 hours and then decreases to 0 after 9 hours.

So this data cannot be modeled by a linear function or an exponential function.

Also since the number of customers arriving is not constant, this cannot be expressed as constant function.

So it is quadratic function.

Hence the correct option is c.

Learn more about Quadratic Functions here :

https://brainly.com/question/18958913

#SPJ1

Answer:

Hello your question is poorly written below is the complete question

An actuary has discovered that policyholders are three times as likely to file two claims as to file four claims. If The number of claims filed has a Poisson distribution. Compute the variance of the number of claims filed. You can use, without a proof, what is the variance of a Poisson distribution is equal to its mean

answer : variance = 2

Step-by-step explanation:

compute the variance of the number of claims filed

x = number of claim filed

For Poisson distribution

mean = variance = Л

∴ Variance = 2

Answer:

Null hypothesis : Option C

Alternative Hypothesis: Option A

Step-by-step explanation:

In statistics, basically null hypothesis states that there is no statistical difference between the two variables in question whereas alternative hypothesis states that there is a significant statistical difference between both variables.

Null hypothesis: There is no difference in price between emeralds and rubies.

Alternative Hypothesis: There is a significant difference in the price of emeralds and rubies

A person would need to buy 60 square yards of carpet for a rectangular room with dimensions of 10 yards by 18 feet.

How to determine the amount of carpet needed for a rectangular room?

To determine the amount of carpet needed for a rectangular room, you need to convert the measurements to the same unit of measurement. Since the carpet is sold in square yards, we need to convert the dimensions of the room to yards.

The length of the room is given in yards, so we don't need to make any conversions for that dimension. However, the width of the room is given in feet, so we need to convert it to yards by dividing by 3 (since there are 3 feet in a yard),

18 feet ÷ 3 feet/yard = 6 yards

So the dimensions of the room in yards are 10 yards by 6 yards.

To find the total area of the room, we need to multiply the length and width,

10 yards × 6 yards = 60 square yards

Therefore, a person would need to buy 60 square yards of carpet for a rectangular room with dimensions of 10 yards by 18 feet.

Learn more about rectangle here,

https://brainly.com/question/25292087

#SPJ9

Answer:

A. y=-2x+1

Step-by-step explanation:

rise over run rise(up or down) 2 run(right or left) 1

-2a+6

Hope it helps.

Do comment if you have any query.

Answer:

\(G(y) = 4\ln(2y+1) - \frac{1}{2}\ln(y^2 + 1)\)

Step-by-step explanation:

Given

\(G(y) = \ln(\frac{(2y+1)^4}{\sqrt{y^2 + 1}})\)

Required

Rewrite as sum and difference

Apply laws of logarithm:

\(G(y) = \ln(2y+1)^4 - \ln({\sqrt{y^2 + 1})\)

Rewrite the exponents

\(G(y) = \ln(2y+1)^4 - \ln(y^2 + 1)^\frac{1}{2}\)

Convert exponents to coefficients

\(G(y) = 4\ln(2y+1) - \frac{1}{2}\ln(y^2 + 1)\)

Answer:

Part A:

The probability of hitting the black circle is the ratio between the area of the black circle and the white square (including the black circle)

Area of circle:

Ac = pi x r^2 = pi x (2/2)^2 = pi (diameter = 2)

Area of square:

As = side^2 = 11^2 = 121 (side = 11)

=> P = pi/121 = ~0.025 (P = 0.025 < 0.5 => P is closer to 0 than 1)

Part B:

The probability of hitting the white portion could be calculated in a similar way as shown in part A. However, the event of hitting the white portion is the complement event of the event of hitting the black circle.

Because P(event) + P(complement of event) = 1

=> P = 1 - 0.025 = 0. 975 (P = 0.975 > 0.5 => P is closer to 1 than 0)

Using rules for exponents we can simplify the expression to get:

\(16*x^{-1/3}\)

Here we need to use two rules for exponents, these rules are:

\(x^n*x^m = x^{n + m}\)

In the product of two powers with the same base we just need to add the two exponents togheter.

And:

\((x^n)^m = x^{n*m}\)

When we have the exponent of a power, we need to take the product between the two exponents.

Here we want to simplify the following expression:

\(x*(2x^{-1/3})^4\)

Using the second rule we can rewrite the expression as follows:

\(x*(2x^{-1/3})^4 = x*(2^4*x^{-4/3})\)

Now we can use the first rule, now we will get:

\(x*(2^4*x^{-4/3}) = 16*x^{-4/3 + 1} = 16*x^{-1/3}\)

Learn more about exponents:

https://brainly.com/question/847241

#SPJ1

Answer:

= 1799   or   224.875

     8

Step-by-step explanation:

5³ − (6/48) + 10²

= 125 - (0.125) + 100

= 224.875

or

5³ − (6/48) + 10²

= 125 - 1/8 + 100

= -1/8 + 225

= (225 * 8)/8 - 1/8

= (225 * 8-1) / 8

= 1799   or   224.875

     8

Answer:

\(\huge \boxed{\frac{1799}{8} }\)

\(\rule[225]{225}{2}\)

Step-by-step explanation:

\(\displaystyle 5^3-(\frac{6}{48} )+10^2\)

Solving for exponents:

\(\displaystyle 125-(\frac{6}{48} )+100\)

Adding or subtracting:

\(\displaystyle -(\frac{1}{8} )+100+125\)

\(\displaystyle -(\frac{1}{8} )+225\)

\(\displaystyle -(\frac{1}{8} )+\frac{1800}{8}\)

\(\Rightarrow \ \displaystyle \frac{1799}{8}\)

\(\rule[225]{225}{2}\)

The word that describes the slope of the line representing the data in the table is "negative."

To determine the slope of the line representing the data in the table, we need to examine the relationship between the number of cards sold and the remaining amount of money needed.

Looking at the given data, we observe that as the number of cards sold increases, the remaining amount of money needed decreases. This indicates an inverse relationship between the two variables.

The slope of a line represents the rate of change between two variables. In this case, the slope is negative because the line decreases as we move from left to right.

Therefore, the word that describes the slope of the line representing the data in the table is "negative."

for such more question on slope

https://brainly.com/question/27877215

#SPJ8

All four consecutive integers will be 9, 10, 11, and 12 and can be found out by high common sense.

A pattern is a specific arrangement of numbers or any term which will follow a specific code or hint.

For example 2,4,6,8 in this, the difference between any two-term is only 2 and this will be its specific pattern.

Given that,

8 times the sum of the first and the third  =  8( 1st + 3rd)

40 greater than 10 times the fourth = 40 + 10(4th)

So,

8( 1st + 3rd) = 40 + 10(4th)

Now if we look right and side then it will come out as any number with the unit placed as 0.

So it means on the left side also the unit place must be 0.

By thinking of  1st + 3rd = 10 /20 because at 45 it will be 40 which is not equal to the right-hand side.

Now by hit and trial method, we need to guess it 20 = 9 + 11

Then

8(9 + 11) = 40 + 10(12)

One equation can never give us three unknowns hence it will be the correct way.

Hence so the four consecutive integers will be 9, 10, 11, and 12.

For more information about the pattern

brainly.com/question/14013716

#SPJ1

In the following option n log n seems to grow the fastest amongst all according to the size of inputs.

In computer science and mathematics, the running time or complexity of an algorithm is often measured in terms of the size of the input, usually denoted by n. The notation O(f(n)) is used to describe the upper bound on the running time of an algorithm, where f(n) is a function of n.

In the context of comparing growth rates of functions, we usually only consider the highest-degree term of the function. For example, we would say that f(n) = n^2 + n grows as O(n^2), because n^2 grows much faster than n and dominates the running time as n grows larger.

Now, let's consider the functions n, n / log n, n - log n, n log n, and n^2. As n grows, each of these functions grows at a different rate.

1. n grows linearly with n, so it takes more time as the size of the input grows.

2. n / log n grows faster than n, but slower than n log n. This is because logarithms grow much slower than linear functions, but as n grows larger, the difference between n and log n becomes larger, so n / log n grows faster.

3. n - log n grows slower than n and n / log n, because log n grows much slower than n, so as n grows larger, n - log n becomes closer to n.

4. n log n grows faster than n, n / log n, and n - log n, but slower than n^2. This is because logarithms grow much slower than linear functions, but as n grows larger, the difference between n and log n becomes larger, so n log n grows faster.

5.n^2 grows much faster than n, n / log n, n - log n, and n log n, so as n grows larger, n^2 becomes much larger than any of these functions.

So, of the options given, n log n grows the fastest, meaning that an algorithm that takes time proportional to n log n will become slower faster as the size of the input grows than an algorithm that takes time proportional to n, n / log n, or n - log n.

To learn more about algorithms click here:

brainly.com/question/27522570

#SPJ4

List of possible integral roots = 1, -1, 2, -2, 3, -3, 6, -6

List of corresponding remainders = 0, -16, -4, 0, 0, 96, 600, 1764

Check out the table below for a more organized way to represent the answer. The x values are the possible roots while the P(x) values are the corresponding remainders.

====================================================

Explanation:

We'll use the rational root theorem. This says that the factors of the last term divide over the factors of the first coefficient to get the list of all possible rational roots.

We'll be dividing factors of 6 over factors of 1. We'll do the plus and minus version of each. Since we're dividing over +1 or -1, this means that we're basically just looking at the plus minus of the factors of 6.

Those factors are: 1, -1, 2, -2, 3, -3, 6, -6

This is the list of possible integral roots.

Basically we list 1,2,3,6 with the negative versions of each value thrown in as well.

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

From there, you plug each value into the P(x) function

If we plugged in x = 1, then,

P(x) = x^4 - 3x^3 - 3x^2 + 11x - 6

P(1) = (1)^4 - 3(1)^3 - 3(1)^2 + 11(1) - 6

P(1) = 1 - 3 - 3 + 11 - 6

P(1) = 0

This shows that x = 1 is a root, since we get a remainder 0. Do the same for the other possible rational roots listed above. You should find (through trial and error) that x = -2 and x = 3 are the other two roots.