A rectangle has a length of 23 yards less than 4 times its width. If the area of the rectangle is 3131 square yards, find the length of the rectangle.

Answer:

100%+15% = 115%

proportionally:

x - 100%

161 - 115%

x = (161 * 100%) / 115% = 140

Answer:

\(\Large\boxed{140}\)

Step-by-step explanation:

\(\sf Let \ x \ be \ the \ number.\)

\(\sf x \ increased \ by \ 15\% \ is \ 161.\)

\(x \times (1+15\%)=161\)

\(x \times (1+0.15)=161\)

\(x \times (1.15)=161\)

\(\displaystyle \frac{x \times (1.15)}{1.15}=\frac{161}{1.15}\)

\(x=140\)

Answer:

There were 60 kids in class.

Step-by-step explanation:

Since the kids had two choices and the ratio between them was for every 3 children that selected "Shin Chan" only 1 selected "Tom and Jerry", then in order to calculate the number of children in the class if 45 kids selected "Shin Chan", we first need to calculate the number of children that selected the other option. To do that we divide the number by 3. We have:

children(Tom and Jerry) = children(Shin Chan)/3

children(Tom and Jerry) = 45/3 = 15

Therefore the number of children in the class is:

children(class) = children(Tom and Jerry) + children(Shin Chan)

children(class) = 15 + 45 = 60

There were 60 kids in class.

A D. simple random sample is a sample in which every member of the population has an equal chance of being chosen.

A. Systematic: In a systematic sample, the population is first ordered or arranged in some systematic way, such as by alphabetical order or numerical sequence. Then, a starting point is randomly selected, and subsequent members are chosen at regular intervals from the ordered list. This method ensures that every member of the population has an equal chance of being selected.

B. Probability: The term "probability sample" is a general concept that encompasses various sampling methods. It refers to any sample in which each member of the population has a known nonzero probability of being selected. Probability sampling methods include simple random sampling, stratified sampling, cluster sampling, and systematic sampling.

C. Stratified: In stratified sampling, the population is divided into distinct subgroups or strata based on specific characteristics or attributes. Then, a random sample is taken from each stratum in proportion to its representation in the overall population. This method ensures that the sample is representative of the population across different subgroups or strata.

D. Simple random: A simple random sample is a sampling method where each member of the population has an equal and independent chance of being selected. It involves selecting individuals randomly and without any specific pattern or grouping. This method ensures that each member of the population has an equal probability of being chosen, leading to unbiased estimates and generalizability to the larger population.

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a. The sum of 3.7 and 4.888 is 8.6.

b. The product of (4.09 × 10²) and (6.33 × 10⁴) is 2.74 × 10⁷.

c. The result of multiplying 3.376, 23, and 0.123 is 9.95.

d. The result of adding 0.0467 to 23.32 and subtracting 22.8 is 0.099.

a. 3.7 + 4.888

Adding 3.7 and 4.888 gives us a sum of 8.588. Since the least number of decimal places in the given numbers is one, we round the answer to one decimal place, resulting in 8.6.

b. (4.09 × 10²) × (6.33 × 10⁴)

Multiplying the given numbers gives us 259.797 × 10⁶. Since the given numbers have two significant figures each, the answer should have two significant figures as well. Therefore, we round it to 2.7 × 10⁷.

c. 3.376 × 23 × 0.123

Multiplying the given numbers results in 9.984552. The number with the fewest significant figures is 23, which has two significant figures. Therefore, we round the answer to two significant figures, giving us 10.

d. 0.0467 + 23.32 - 22.8

Performing the addition and subtraction operations, we get 0.5667. The given numbers have four decimal places in total. Hence, the answer should also have four decimal places, resulting in 0.099.

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Both answers

Answer:

A=9mm

B= 293

The derivative of a function f(x) at a point x = a is defined as the limit of the difference quotient as h approaches zero:

f'(a) = lim (h → 0) [f(a + h) - f(a)] / h

What is derivative?

The derivative of a function in calculus measures the function's sensitivity to changes in its input variable. Specifically, at a particular point, it represents the function's rate of change with respect to its input variable at that moment.

The derivative of a function f(x) at a point x = a is defined as the limit of the difference quotient as h approaches zero:

f'(a) = lim (h → 0) [f(a + h) - f(a)] / h

This limit represents the instantaneous rate of change or slope of the function at the point x = a. The difference quotient is the change in the function value divided by the change in the input variable (or the distance between two points on the graph of the function).

The derivative is a fundamental concept in calculus, and it has many applications in various fields of science, engineering, and economics. It allows us to calculate important quantities such as velocity, acceleration, and marginal cost, and it is used to optimize functions and solve many real-world problems.

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We know that the score is obtained by subtracting the number of incorrect answers from twice the number of correct answers. Let's use "x" to represent the number of correct answers.

According to the question, the player answered 40 questions in total. This means that the number of incorrect answers is 40 - x.
Now we can use the formula for the score:
Score = 2x - (40 - x)
We also know that the player obtained a score of 50. So we can set up the equation:
50 = 2x - (40 - x)
Simplifying the equation:
50 = 3x - 40
90 = 3x
x = 30
Therefore, the player answered 30 questions correctly.
To check, we can plug this value back into the formula for the score:
Score = 2x - (40 - x)
Score = 2(30) - (40 - 30)
Score = 60 - 10
Score = 50
So the score of 50 is correct and the player answered 30 questions correctly.

To find out how many questions the player answered correctly in the trivia game with a score of 50, we can use the given information to set up an equation:
Let x be the number of correct answers and y be the number of incorrect answers. According to the question, the score is calculated by subtracting the number of incorrect answers (y) from twice the number of correct answers (2x). The player answered 40 questions in total, so we have:
x + y = 40
2x - y = 50
Now we can solve this system of equations step-by-step:
1. Solve the first equation for x:
x = 40 - y
2. Substitute this expression for x in the second equation:
2(40 - y) - y = 50
3. Simplify the equation:
80 - 2y - y = 50
4. Combine like terms:
80 - 3y = 50
5. Subtract 80 from both sides:
-3y = -30
6. Divide both sides by -3:
y = 10
7. Substitute the value of y back into the expression for x:
x = 40 - 10
x = 30
The player answered 30 questions correctly in the trivia game with a score of 50.

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Answer:

20x the power of 3 -23x to the power of 2 +65x

Step-by-step explanation:

Answer:

b=37

Step-by-step explanation:

if the angles are supplementary then they will add up to equal 180.

to find b you just subtract 143 from 180 to get 37

The number of times Gus needs to fill the bucket will be 3.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Number of times = volume of tank /volume of cylinder

The volume of the cylinder = πr²h

3.14 x 5² x 20 = 1570

4710 /  1570 = 3 times

Therefore, the number of times Gus needs to fill the bucket will be 3

The complete question is given below:-

How many times will Gus need to fill the bucket to completely fill the fish tank if he doesn’t spill a drop? Use 3.14 for pi

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Answer: 3

Step-by-step explanation:

1. This problem calls for the formula for the volume of a cylinder which is 

   V=π\(r^{2}\)h

2. First let's find the volume of one bucket. The bucket has a radius of 5    inches and a height of 20 inches.

V= 3.14 x \(5^{2}\) x 20

  = 3.14 x 25 x 20

  = 1570

3. To find out how many buckets it will take to fill the tank, we can divide the total volume of the fish tank by the volume of each full bucket.

\(\frac{4710}{1570}=3\)

4. Gus will need to fill the bucket 3 times in order to completely fill the fish tank.

Answer:

62

Step-by-step explanation:

all you do for this is take 496 and divide it by 8, which gives you 62, if you still need help explain I can reply with a step by step of showing how to divide

Answer:

19

Step-by-step explanation:

1/2*38=19

Half of 38

50% of 38 = 0.5 × 38 = 19

Answer:

The modal age is 11

The range is the highest minus the Lowe's which is 19-9=10

Answer:

I don't have the options but I know parallel lines will never touch, they have the same slope, and the distance between the lines never changes

Based on the ratios given of 0.3 : 4 = 9 : y, the value of y can be found to be 120

From the given ratios of 0.3 : 4 = 9 : y, we can infer that these are equivalent ratios.

This means that y is to 9, what 4 is to 0.3.

The value of y can therefore be found by direct proportion:

0.3 : 4

9 : y

Cross multiplying gives:

0.3 y = 36

y = 36 / 0.3

y = 120

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Given:-

To find:-

Solution:-

Here the sum of the two unknown angles will be 90° as they are the angles which make up 90° . So that;

\(\implies x^o + 42^o + 3x^o = 90^o \\\)

\(\implies 4x^o = 90^o - 42^o \\\)

\(\implies 4x^o = 48^o \\\)

\(\implies x =\dfrac{48}{4} \\\)

\(\implies \boxed{ x = 12} \\\)

Hence the value of x is 12 .

and we are done!

Answer:

4 1/2

Step-by-step explanation:

The origional question is ¨A turtle travels 1/2 mile in 1/9 hour. At this rate, how far can the turtle travel in an hour¨ To be honest i have no clue how to explain it but that is the awanser.

The turtle will travel  \(4\frac{1}{2}\) in an hour.

A proportion is an equation in which two ratios are set equal to each other.

Given that, a turtle travels 1/2 mile in 1/9 hour. we need to find, at this rate, how far can the turtle travel in an hour.

We will solve this by using proportionality, since, rate is constant,

Let the turtle travels x miles in an hour,

Therefore,

x / 1 = (1/2) / (1/9)

x = 1/2 × 9

x = 9/2

x = \(4\frac{1}{2}\)

Hence, the turtle will travel  \(4\frac{1}{2}\) in an hour.

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Answer:

Please find below. Fill in the table with the values of y given below.

Step-by-step explanation:

For question 5, you should substitute the different values of x into the equation y =x^2 +4

So, when

x = -3, y = (-3)^2 +4 = 9+4 = 13

x = -2, y = (-2)^2 +4 = 4+4 = 8

x = -1, y = (-1)^2 + 4 = 1+4 = 5

x = 0, y = 0^2 + 4 = 4

x = 1, y = 1^2 +4 = 1+4 = 5

x = 2, y = 2^2 +4 = 8

x = 3, y = 3^2 + 4 = 13

x = 4, y = 4^2 + 4 = 20

For question 6, you need to find the nth term or a formula of y in terms of x.

For this, find the common difference between each of the consecutive values of y.

This is 5

So, the start if our equation is going to be ‘y = 5x’

Now, to find the ‘+c’ part, can be calculated by substituting the value of y when x = 1 into the y = 5x

So,

y = 5x + c

13 = 5 + c

Rearrange the find that c = 8

Therefore, the nth term formula = 5x + 8

Hope this helps

Answer: The model of the Cape Hatteras Lighthouse is 7 feet tall, as it follows a scale of 8 inches = 30 feet. The actual lighthouse is 210 feet, so to calculate the height of the model, you would divide the actual lighthouse's height by the scale that is used. 210 feet divided by 30 equals 7 feet, which is the height of the model. This is why models are made to a specific scale, as it allows us to calculate the size of the model accurately, without having to measure every single dimension.

After solving the equation, the number obtained is 4/3 and its reciprocal will be 3/4.

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.

Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.

As per the data mentioned in the question,

Let the number be x.

Then the sum and reciprocal of the number is 25/12.

So, the equation will be,

x + 1/x = 25/12

(x² + 1)/x = 25/12

12x² + 12 = 25x or,

12x² - 25x + 12 = 0

Now, find the roots:

D = b² - 4ac

(-25)² - 4× 12× 12

D = 49

Then,

-(b ± √D)/2a

(25 ± 7)/24

So, the roots are,

(25 + 7)/24 = 4/3 and,

(25 - 7)/24 = 3/4

Then, the number is 4/3 and its reciprocal is 3/4.

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Answer:

5 is your answer sweetheart

Step-by-step explanation:

We know that the range to a data set is the difference between the maximum data value and the minimum data value .

The given data set :  29, 30, 28, 32, 28, 31, 27

Maximum value = 32

Minimum value = 27

Then , the range the given data set would be :-

\begin{gathered}\text{Range = Maximum-Minimum}\\\\\Rightarrow\text{Range}=32-27=5\end{gathered}Range = Maximum-Minimum⇒Range=32−27=5

Hence, the range of her distances = 5

Answer:

5

Step-by-step explanation:

A graphical plot with sales on the Y axis and time on the X axis is a:

a. Scatter diagram.

Using a single variable on each axis, the scatter diagram plots pairings of numerical data in an effort to identify any relationships between them. A line or curve will be formed by the points if the variables are correlated. The points will hug the line closer the more highly correlated the data is. You may also visualise the strength of any relationship. If the researcher believes there may be a correlation, a line of greatest fit can also be drawn on the graph.

Data points are shown on a horizontal and vertical axis using scatter plots in an effort to demonstrate the degree to which one variable is influenced by another.

Thus, correct option: a

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Answer:

The 3rd answer

Step-by-step explanation:the

180-30\2

....

=75

30+2*75=

...

180

Answer:

30 + 2x = 180

Step-by-step explanation:

This is becuase we know this triangle is an isosceles triangle. (The two markings on the sides prove that.) An isosceles triangle is when two sides (so naturally also two angles) are the same. This means the other angle is x. We know that if we add all of the angles, we'll get 180. So, 30 + x + x = 180 or "30 + 2x = 180".

Also, x = 75.

Here:

30 + 2x = 180

30 - 30 + 2x = 180 - 30

2x = 150

2x / 2 = 150 / 2

x = 75

HOPE THIS HELPED!! HAVE AN AWESOME DAY!

The length of the vegetable garden as a function of its length will be given as:

The expression of the garden width in terms of the width of the tomato patch is given as:

If Melissa wants the length of  the garden to exceed three times the length of the tomato patch by 2 feet, the length of the vegetable garden as a function of its length will be given as:

If she also wants the garden's width  to exceed the width of the tomato patch by 5 feet,  the expression of the garden width in terms of the width of the tomato patch is given as:

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Answer:

50.32 square units

Step-by-step explanation:

To find the area of a triangle, given the measures of two of its side lengths and the included angle, use the Sine Rule.

\(\boxed{\begin{minipage}{6 cm}\underline{Sine Rule - Area of a triangle} \\\\$A=\dfrac{1}{2}ab \sin C$\\\\where:\\ \phantom{ww}$\bullet$\;\;$a$ and $b$ are the sides.\\ \phantom{ww}$\bullet$\;\;$C$ is the incl\:\!uded angle. \\\end{minipage}}\)

From inspection of the given triangle:

Substitute these values into the formula and solve for A:

\(\begin{aligned}A&=\dfrac{1}{2} \cdot 8 \cdot 15 \cdot \sin 123^{\circ}\\\\&=4 \cdot 15 \cdot \sin 123^{\circ}\\\\&=60 \cdot \sin 123^{\circ}\\\\&=50.3202340...\\\\&=50.32\; \sf square\;units\;(nearest\;hundredth)\end{aligned}\)

Therefore, the area of the given triangle is 50.32 square units (rounded to the nearest hundredth).

PART 1

The exponential decay model is given to be:

where a is the initial value and r is the decay rate.

In the question, the initial value is 15,500 and drops at a rate of 3%. This means that we have the following parameters:

Therefore, the exponential model is gotten to be:

PART 2

The graph of the function is shown below:

At x = 8000, we have the time as shown below:

The time will be 21.7 years.

Answer:

5. False.

Look at the graph.

Every one day, the cost jumps $30 instead of $60.

Therefore, it is false.

6. True.

Like I said, Every one day, the cost jumps $30.

So when x increases by 1, y increases by 30.

So, y = 30x is correct.

7. False.

Use the equation in the 6th question.

y = 30x.

Put x = 7.

You get y = 210, not 200.

So. it is false.

8. True

Again, same thing.

Use the equation in the 6th question.

y = 30x.

Put x = 9.

You get y = 270.

So the statement is correct.

Pls mark as brainliest for no apparent reason. Cheers