Factor the expressions 7 – 42

If a student claims that 3.8¯ is an irrational number because it is a non-terminating decimal, then, he/she is incorrect as 3.8¯ can be represented as a fraction which is (35/9).

As per the question statement, a student claims that 3.8¯ is an irrational number because it is a non-terminating decimal.

We are required to determine if the claim is correct or incorrect, and if the claim is correct, then we will have to justify our answer, while if it is incorrect, we will have to determine the fraction that is equal to 3.8¯.

To solve this question, let us first try to convert our concerned decimal 3.8¯ into its equivalent fraction.

Now, 3.8¯ = 3.888...

Let us assume a random variable "x" such that, 3.8¯ = x = 3.888...

Then, 10x = (10 * 3.888...) = 38.888...

Now, [(10x - x) = {(38.888...) - (3.888...)}]

Or, (9x = 35)

Or, x = (35/9)

That is, the non-terminating decimal 3.8¯ can be converted to a fraction which is equal to (35/9).
Hence, the student's claim that that 3.8¯ is an irrational number because it is a non-terminating decimal is incorrect.

To learn more about Irrational Numbers and Non-Terminating Decimals, click on the link below.

https://brainly.com/question/6782325

#SPJ1

Answer:

We now want to find the best approximation to a given function. This fundamental problem in Approximation Theory can be stated in very general terms. Let V be a Normed Linear Space and W a finite-dimensional subspace of V , then for a given v ∈ V , find w∗∈ W such that kv −w∗k ≤ kv −wk, for all w ∈ W.

Step-by-step explanation:

6 weeks from now, you will have $215 in your bank account

The given parameters are:

b = 60 + (20+6)w

When the account balance is $215, we have

60 + (20+6)w = 215

Subtract 60 from both sides

(20+6)w = 155

This gives

26w = 155

Divide both sides by 26

w = 5.96

Approximate

w = 6

Hence, 6 weeks from now, you will have $215 in your bank account

Read more about linear equations at:

https://brainly.com/question/14323743

#SPJ1

Answer:

5.625 inches

Step-by-step explanation:

We Know

A 6-inch candle burns down in 8 hours.

6 / 8 = 0.75 inches burn down per hour

So, we know 0.75 inches burn down per hour

How far has it burned after 7 1/2 hours?

We take

0.75 x 7.5 = 5.625 inches

So, it burned 5.625 inches after 7 1/2 hours.

Answer:

having a sticky surface

Step-by-step explanation:

Just took the tests

We can expect 30 guests to receive free admission out of the 1500 guests expected this weekend.

To determine how many guests can be expected to receive free admission, we need to use the given information about the ratio of guests with coupons to guests without coupons. We can do this by setting up a proportion and solving for the unknown variable.

Let x be the number of guests we can expect to receive free admission.
1/50 = x/1500

Cross-multiplying gives us:
50x = 1500

Dividing both sides by 50 gives us:
x = 30

Therefore, we can expect 30 guests to receive free admission out of the 1500 guests expected this weekend.

Here to learn more about the Ratio and Proportion at the link https://brainly.com/question/12024093

#SPJ11

The exact length of the curve is \(\frac{1}{216}[145^{\frac{3}{2} } -1]\).

The given equation is \($y=1+8 x^{\frac{3}{2}}$\).

The point is \($$0 \leq x \leq 1$.\)

Arc length: To find the arc length of the function y=f(x), use the power rule. After that use the integration.

Let  f(x)  be a smooth function over the interval [a,b] . Then the arc length of the portion of the graph of  f(x)  from the point (a, f(a))  to the point (b, f(b))  is given by

The formula of the arc length is: \($=\int_0^1 \sqrt{1+\left(y^{\prime}\right)^2}$\)

Differentiate this equation

\($$\begin{aligned}& y^{\prime}=8 \frac{\mathrm{d}\left(x^{\frac{3}{2}}\right)}{\mathrm{d} x} \\& =8 \frac{3}{2} x^{\frac{1}{2}} \\& =12 \sqrt{x}\end{aligned}$$\)

Now, find the arc-length.

\($$\begin{aligned}& \text { Arc-length }=\int_0^1 \sqrt{1+\left(y^{\prime}\right)^2} \\& =\int_0^1 \sqrt{1+144 x}\end{aligned}$$\)

Use the substitution method.

\($$\begin{aligned}& u=1+144 x \\& d x=\frac{1}{144} d u \\& =\frac{1}{144} \int_1^{145} \sqrt{u} d u \\& =\frac{1}{144}\left[\frac{u^{\frac{3}{2}}}{\frac{3}{2}}\right]_1^{145} \\& =\frac{1}{216}\left[145^{\frac{3}{2}}-1\right]\end{aligned}$$\)

Hence, the exact length is \(\frac{1}{216}\left[145^{\frac{3}{2}}-1\right]\).

For more such questions on Length of curve

https://brainly.com/question/28187225

#SPJ4

The concavity of a function can change at inflection points, where the concavity transitions from concave up to concave down or vice versa. Inflection points occur when the second derivative is equal to zero or undefined.

To determine whether a function is concave up or concave down using the second derivative, you can follow these steps:

Find the second derivative of the function. This involves taking the derivative of the first derivative of the function. The second derivative is often denoted as f''(x) or d²y/dx².

Identify the critical points of the function. These are the points where the first derivative is equal to zero or undefined. You can find the critical points by setting the first derivative equal to zero and solving for x.

Evaluate the second derivative at the critical points. Plug the critical points into the second derivative equation and calculate the resulting values.

Analyze the sign of the second derivative at the critical points. If the second derivative is positive at a critical point, the function is concave up at that point. If the second derivative is negative at a critical point, the function is concave down at that point.

By examining the signs of the second derivative at the critical points, you can determine the concavity of the function in the corresponding intervals.

Remember that this method applies specifically to functions whose second derivative is continuous. In cases where the second derivative is discontinuous or undefined, additional analysis may be needed.

To know more about function:

https://brainly.com/question/29073659

#SPJ4

Answer:

The 3rd and the 5th

2(3+9i) , 6(1+3i)

Step-by-step explanation:

Problem 5

The missing interior angle of the triangle is also x because the base angles are congruent for any isosceles triangle. The triangle is isosceles because of the two tickmarks indicating those sides are the same length.

The angle 115 is supplementary to that angle x mentioned, so,

115+x = 180

x = 180-115

x = 65

Now to find y, we'll use the idea that adding the angles of any triangle always gets to 180

x+x+y = 180

65+65+y = 180

130+y = 180

y = 180-130

y = 50

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

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

Problem 6

We use the same idea as the previous problem. The missing angle is x because it's a congruent base angle. This missing angle x is supplementary to the 135 degree angle

x+135 = 180

x = 180-135

x = 45

Now add up the interior angles of the triangle, set the sum equal to 180 and solve for x

x+x+y = 180

45+45+y = 180

90+y = 180

y = 180-90

y = 90

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

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

Problem 8

This triangle is equilateral since all sides are the same length. Consequently, all angles are the same measure and equal to 180/3 = 60 degrees each.

Setting the bottom left angle equal to 60 and solving leads to

3y = 60

y = 60/3

y = 20

Do the same for the bottom right angle

2x = 60

x = 60/2

x = 30

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

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

Problem 9

The x and 110 degree angles are supplementary. They form a straight angle of 180 degrees

x+110 = 180

x = 180-110

x = 70

Focusing on the smaller right triangle on the right side, we have the upper acute angle x = 70, and the bottom acute angle y, and a right angle of 90 degrees.

These three angles must add to 180

x+90+y = 180

70+90+y = 180

160+y = 180

y = 180-160

y = 20

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

Answer:

5555555555/100000000000

Step-by-step explanation:

I guess I am not sure though.

Can you help me with my question?

PLS HELP ASAP!!!!

A restaurant wants to study how well it's salads sell. the circle graph shows the sales over the past few days. If 15 of the salads sold were caesar salads, how many total salads did the restaurant sell Caesar 30% Garden 58% Cobb 12%?

Answer:

\(\frac{1}{18}\)

Step-by-step explanation:

We require to create 2 equations with the repeating number placed after the decimal point.

let x = 0.055555 ( multiply both sides by 10 and 100 )

10x = 0.555555 → (1)

100x = 5.55555 → (2)

Subtract (1) from (2) to eliminate the repeating decimal

90x = 5 ( divide both sides by 90 )

x = \(\frac{5}{90}\) = \(\frac{1}{18}\)

Answer: 6

Step-by-step explanation:

I assume you meant to write 8xy − 9x2y − 5x + 6. The constant term in an expression is defined as a number by itself that contains no variables. Therefore, the answer is 6.

Using the slope formula, we can conclude that the slope of the line is m = 2.

So, the slope of the line is:

Now, put the values and solve for the slope as follows:

Therefore, using the slope formula, we can conclude that the slope of the line is m = 2.

Know more about slope here:

brainly.com/question/3493733

#SPJ13

The box and whisker plot of the prices of some DVDs:

Minimum: 9.99

First Quartile: 12.99

Median: 15.99

Third Quartile: 19.99

Maximum: 26.99

The box and whisker plot shows that the median price of a DVD is $15.99. The prices range from $9.99 to $26.99. There are two outliers, one at $9.99 and one at $26.99.

The box and whisker plot can be used to identify the distribution of the data. In this case, the data is slightly skewed to the right, meaning that there are more DVDs priced at the lower end of the range than at the higher end.

The box and whisker plot can also be used to compare different sets of data. For example, we could compare the prices of DVDs from different stores or from different years.

Overall, the box and whisker plot is a useful tool for visualizing and summarizing data.

For such more questions on Median

https://brainly.com/question/26177250

#SPJ8

Y: 1 Y is 1 becuase 1 +2 =3 so y=3

Answer:

2x + 8

Step-by-step explanation:

Step 1: Define expression

-5 + x + x + 13

Step 2: Combine like terms (x)

-5 + 2x + 13

Step 3: Combine like terms (constants)

2x + 8

Answer:

my wattapp number

is 7667587493

Step-by-step explanation:

I think the answer is 8

The phrase "He went to get milk but never came back" is often used as a humorous way to explain someone's absence or to imply that someone is unreliable or untrustworthy.

The phrase likely originates from a common experience where a child's parent, often their father, promises to go out to get something, like milk, but never returns. This can be a source of disappointment and confusion for the child, and the phrase has since been used in a joking manner to explain someone's failure to show up or fulfill a promise.

However, it is important to recognize that this experience can also be a source of trauma and should not be used to make light of someone's pain or loss.

To know more about Milk:

https://brainly.com/question/15601108

#SPJ4

Parallel lines are defined as lines that do not intersect or meet at any point in a plane. They are always parallel and equidistant from one another.

What is answer parallel line?

In geometry, parallel lines can be defined as two lines in the same plane that are at equal distance from each other and never meet. They can be both horizontal and vertical.

Parallel lines are two lines in the same plane that are equal distance apart and never intersect.

Real-world parallel line examples include railroad tracks, sidewalk edges, street markings, zebra crossings, the surface of pineapple and strawberry fruit, staircases and railings, and so on.

Parallel lines are lines in a plane that never meet, no matter how far they are extended. The distance between the parallel lines is constant because they never meet.

Parallel lines are defined as lines that do not intersect or meet at any point in a plane. They are always parallel and equidistant from one another.

these are 8 parallel lines

2x+3y = 6

2x+3y = 4

2x+3y = 1

2x+3y = 2

2x+3y = 3

2x+3y = 8

2x+3y = 7

2x+3y = 5

learn more about of lines here

https://brainly.com/question/22224495

#SPJ4

Answer:

2

Step-by-step explanation:

Answer: 4. 3. 9. = 2. 1. 10. = 3. 1. 11. = 10. 8. 12. = 3. 2. Rename each percent as a decimal: 13. 8% = 14. 60% = 15. 11% = 16. 12% = 17. 40% = 18. 95% = 6.

Step-by-step explanation: Good luck!

Answer: I think its C, yes, all the requirements are met.​

Step-by-step explanation: I might be wrong, so check to make sure

Yes, all the requirements are met.​

The correct option is (C)

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

A graph or table that displays the frequency of various outcomes is called a frequency distribution.

The bell-shaped normal distribution is the norm.

As, the frequency value is lower for scores 5.5000 to 5.5499,

and then it increases 5.5500- 5.7499, then decreases for scores 5.7500-5.7999.

So, the frequency distribution curve looks bell-shaped when plotted.

hence, it  follow a normal distribution.

Learn more about normal distribution here:

https://brainly.com/question/12432168

#SPJ2

its b/13=5 and then to solve you multiply both sides by 13 to get b=65

so 65 bean bags

Answer:

32 Kilometers

Step-by-step explanation:

A Car travels 80 Kilometers in 2 and Half hours.

1 Hour =60 minutes, 2 & Half hours= 2.5*60= 150 minutes

Kilometers travelled by Car in a hour= 80/150*60= 32 Kilometers

Answer:

y=2/3x+5

Step-by-step explanation:

follow the values of x and y

Answer: 10^4 (10 to the fourth)

Step-by-step explanation: I can't see the answer choices but 10,000 is equal to 10^4

The value of f¹(x) = x/5

What is function?

A function in maths is a special relationship among the inputs (i.e. the domain) and their outputs (known as the codomain) where each input has exactly one output, and the output can be traced back to its input.

We are given f(x) = 5x

and we are to find inverse of f(x).

Replace f(x) by y.

So,

y = 5x

Isolate x

x = y/5

Replace x by f'(y)

So,

f'(y) = y/5

Replace all occurrences of y by x.

So,

f'(x) = x/5

Therefore, the inverse of function f(x) = 5x is f'(x) = x/5

To know more about functions, visit:

https://brainly.com/question/9676733

#SPJ9

Answer:

1.5.7909 2. 6.724 3. 9.296 4. 1.416 5. 4.838 6. 1.784 7. 2.793 8. 2.793

Step-by-step explanation: these are the planets in order hope this helps

The converted distances in scientific notation are \(5.7909 * 10^{14}\),\(6.724 * 10^{ 14}\), \(9.296 * 10^{14}\), \(1.416 * 10^{16}\), \(4.838 * 10^{16}\), \(8.907 * 10^{16}\), \(1.784 * 10^{18}\) and \(2.793 * 10^{18}\).

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.

The scientific notation have two parts i.e. a appropriate number multiplied by an appropriate power.

Converted distances in scientific notation are;

Mercury \(= 5.7909 * 10^{14}\)

Venus \(= 6.724 * 10^{ 14}\)

Earth \(= 9.296 * 10^{14}\)

Mars \(= 1.416 * 10^{16}\)

Jupiter \(= 4.838 * 10^{16}\)

Saturn \(= 8.907 * 10^{16}\)

Uranus \(= 1.784 * 10^{18}\)

Neptune \(= 2.793 * 10^{18}\)

To know more about scientific notation click here

https://brainly.com/question/18073768

#SPJ2

The equivalent operation is: b = (a < 5) ? 12 : (d = 30);

The original if/else statement is:

if (a < 5)

   b = 12;

else

   d = 30;

In this statement, the condition (a < 5) is evaluated. If the condition is true (i.e., if the value of a is less than 5), then the statement b = 12; is executed. Otherwise, if the condition is false (i.e., if the value of a is greater than or equal to 5), then the statement d = 30; is executed.

The equivalent operation using the conditional (ternary) operator is:

b = (a < 5) ? 12 : d = 30;

In this statement, the condition (a < 5) is evaluated. If the condition is true, the value 12 is assigned to b. This is indicated by ? in the statement. The : separates the true and false cases.

If the condition is false (i.e., if the value of a is greater than or equal to 5), the value 30 is assigned to d. This is the value assigned after the : in the statement.

The ternary operator statement (a < 5) ? 12 : d = 30; achieves the same outcome as the original if/else statement, providing an alternative way to write the logic based on the condition a < 5.

Learn more about conditionals here:

https://brainly.com/question/17388479

#SPJ8