What is the length of each side of this equilateral triangle? A 2.5 C 15 B5 D 20 7x - 15. one side is 4x, second side is 3x+5, third side is 7x-15

The line plot, histogram, and box plot provide different visual representations of the reading time data. By analyzing these plots, we can observe the distribution and characteristics of the data, such as central tendency, spread, and outliers.

Line Plot:

A line plot displays data points on a number line, representing the frequency or count of each value.

In this case, the line plot will show the minutes spent reading on the x-axis and the count of students on the y-axis.

For the given data, the line plot will show 10, 20, 30, 40, and 60 on the x-axis, with the corresponding counts displayed above each value.

Histogram:

A histogram displays data distribution by dividing the range of values into intervals or bins and representing the frequency of values falling into each bin.

The histogram will have the minutes spent reading on the x-axis and the count or frequency of students on the y-axis.

The intervals will be 10-19, 20-29, 30-39, 40-49, and 50-59, with the last interval being 60+.

The height of each bar in the histogram will represent the number of students falling into each interval.

Box Plot:

A box plot (also known as a box-and-whisker plot) provides a visual representation of the distribution of data, including measures of central tendency and variability.

The box plot will show a horizontal line inside a box, with whiskers extending from the box, and possibly individual data points beyond the whiskers.

The box will represent the interquartile range (IQR), showing the middle 50% of the data.

The line within the box will represent the median value.

The whiskers will indicate the minimum and maximum values, excluding outliers.

By analyzing these plots, you can observe the central tendency, spread, and distribution of the reading time data. For example, you can identify any outliers, notice the most common reading durations, and observe any patterns or trends within the dataset.

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Answer:

170

Step-by-step explanation:

17 dogs per 30 students or 17/30

Same ratio for 300 students:

So 170 students have a dog

The period of \(f(x)\) is \(\boxed{2\pi}\).

Recall that \(\sin(x)\) and \(\cos(x)\) both have periods of \(2\pi\). This means

\(\sin(x + 2\pi) = \sin(x)\)

\(\cos(x + 2\pi) = \cos(x)\)

Replacing \(x\) with \(3x\), we have

\(\sin(3x + 2\pi) = \sin\left(3 \left(x + \dfrac{2\pi}3\right)\right) = \sin(3x)\)

In other words, if we change \(x\) by some multiple of \(\frac{2\pi}3\), we end up with the same output. So \(\sin(3x)\) has period \(\frac{2\pi}3\).

Similarly, \(\cos(5x)\) has a period of \(\frac{2\pi}5\),

\(\cos(5x + 2\pi) = \cos\left(5 \left(x + \dfrac{2\pi}5\right)\right) = \cos(5x)\)

We want to find the period \(p\) of \(f(x)\), such that

\(f(x + p) = f(x)\)

\( \implies \sin(3x + p) + \cos(5x + p) = \sin(3x) + \cos(5x)\)

On the left side, we have

\(\sin(3x + p) = \sin(3x + 2\pi + p - 2\pi) \\\\ ~~~~~~~~ = \sin(3x+2\pi) \cos(p-2\pi) + \cos(3x+2\pi) \sin(p-2\pi) \\\\ ~~~~~~~~ = \sin(3x) \cos(p-2\pi) + \cos(3x) \sin(p - 2\pi)\)

and

\(\cos(5x + p) = \cos(5x + 2\pi + p - 2\pi) \\\\ ~~~~~~~~ = \cos(5x+2\pi) \cos(p-2\pi) - \sin(5x+2\pi) \sin(p-2\pi) \\\\ ~~~~~~~~ = \cos(5x) \cos(p-2\pi) - \sin(5x) \sin(p-2\pi)\)

So, in terms of its period, we have

\(f(x) = \sin(3x) \cos(p - 2\pi) + \cos(3x) \sin(p - 2\pi) \\\\ ~~~~~~~~ ~~~~+ \cos(5x) \cos(p - 2\pi) - \sin(5x) \sin(p - 2\pi)\)

and we need to find the smallest positive \(p\) such that

\(\begin{cases} \cos(p - 2\pi) = 1 \\ \sin(p - 2\pi) = 0 \end{cases}\)

which points to \(p=2\pi\), since

\(\cos(2\pi-2\pi) = \cos(0) = 1\)

\(\sin(2\pi - 2\pi) = \sin(0) = 0\)

The number line that shows the solutions of x < 5

A number line is a visual representation of the real numbers, ordered from left to right, with zero in the middle. It is typically a straight line that extends infinitely in both directions, with evenly spaced markings that represent specific points along the line.

The solution of x < 5 should consist of number less than 5

The inequality used is less than and hence should have values saying less than

Other options has numbers more than 5 such as 6 except option B

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Your answer is attached.

Hope it helps you!

The solutions to x = 4 are: (4, 1). The other ordered pairs are not solutions to the equation.

What is Set theory ?

Set theory is a branch of mathematical logic that deals with the study of sets, which are collections of objects. The objects in a set are called elements or members of the set.

The basic idea of set theory is to study the properties of sets and their relationships with other sets. Set theory provides a foundation for most of modern mathematics, as it provides a way to define mathematical objects in terms of sets and to reason about them using set-theoretic operations.

In set theory, the most basic concepts are sets, elements, and subsets. A set is a collection of distinct objects, which can be anything from numbers to colors to people. An element is a member of a set, and a subset is a set whose elements are all contained in another set.

To determine whether each ordered pair is a solution to x = 4, we need to check whether the value of x in each pair is equal to 4.

Therefore, the solutions to x = 4 are: (4, 1). The other ordered pairs are not solutions to the equation.

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Step-by-step explanation:

1.

10 ft in 2 hours = 10/2 / 1 hour = 5 ft/h

2.

165 miles in 3 hours = 165/3 / 1 hour = 55 m/h or mph

3.

48 bottles in 4 cases = 48/4 / 1 case = 12 bottles per case

4.

$3.60 for 12 oz = 3.6/12 / 1 oz = $0.30 per ounce

Answer: Equilateral

Step-by-step explanation:

It's equilateral because it says that each side of the triangle is 4cm. In simple words, all the sides of triangle are equal. Such a triangle is called an equilateral triangle.

Hope you understood.

Answer:

84 and more

Step-by-step explanation:

84+81+75

=240

240/3

=80

To calculate how much Naruto spends on ramen in 15 days, we need to determine the total cost of ramen per day and then multiply it by 15.

Since Naruto receives a 33.33% discount, he pays 100% - 33.33% = 66.67% of the original price.

66.67% of 45 cents is (66.67/100) * 45 = 30 cents.

So, Naruto spends 30 cents on ramen per day.

To find out how much he spends in 15 days, we multiply the daily cost by the number of days:

30 cents * 15 = 450 cents.

Therefore, Naruto spends 450 cents, which is equivalent to $4.50, on ramen in 15 days.

Answer:

The answer should be 0.66

The length of the fence around the enclosure not including the gates is:2l + 2w + 8 m

To find the length of the fence around the enclosure, we need to first find the perimeter of the rectangle and then subtract the combined length of the two gates from it.

Let's assume the length of the rectangle is 'l' and the width is 'w'.

From the given data, we know that each gate is 4 m wide.

Therefore, the width of the rectangle is:

Width = w + (4 m + 4 m) = w + 8 m

The perimeter of the rectangle is:

P = 2l + 2(w + 8 m) = 2l + 2w + 16 m

Now, we need to subtract the combined length of the two gates from the perimeter:

P - 2 × 4 m = 2l + 2w + 16 m - 8 m = 2l + 2w + 8 m

So, the length of the fence around the enclosure not including the gates is:2l + 2w + 8 m

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Answer:

a. 35

Step-by-step explanation:

x - 18 = 17

x = 35

Answer: The percentage of computing books is 13.33%.

Step-by-step explanation:

The library consist of books on different subjects:

S = {Business, Healthcare, Computing, Psychology, Law,...}

There are a total of N = 60,000 books in the library.

Business (B) = 14,000

Healthcare (H) = 22,000

Psychology and Law (P&L) = 12,000

Remaining = N - B - H - P&L

                  = 60000 - 14000 - 22000 - 12000

                  = 12000

It is provided that computing books make up two thirds of the remainder

Compute the number of computing books as follows:

C = 12000 × (2/3) = 8000

Compute the percentage of computing books as follows:

\(C\)%=\(\frac{8000}{60000}*100=13.33\)\(%\)%

Thus, the percentage of computing books is 13.33%.

Answer:

b. 1 liters of milk

c. 2.4 hours

d. (any number) /10% times 100

Step-by-step explanation:

because of the gravity of the earth

bobo Ampt

The simplification of the expression ab³/a⁴b  +  (c²)³ is determined as b²/a³  +  c⁶.

The given expression is simplified as follows;

The given expression is written as;

ab³/a⁴b  +  (c²)³

To simplify the expression given above, we will divide the fraction with the common factor as follows;

From the numerator; ab³, we will factor out "ab"

From denominator; a⁴b, we will factor out "ab"

The resulting expression becomes;

ab³/a⁴b  +  (c²)³

= b²/a³  +  c⁶

Note: for the power of c, we simplify by multiplying 2 and 3 = 6

Thus, the simplification of the expression ab³/a⁴b  +  (c²)³ is determined as b²/a³  +  c⁶.

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The y-intercept of f(x + 4) + 8 is given as follows:

10.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The parent function for this problem is given as follows:

\(f(x) = \log_2{x}\)

The translated function is then given as follows:

\(g(x) = \log_2{x + 4} + 8\)

The y-intercept of the function is the numeric value at x = 0, hence:

\(g(0) = \log_2{0 + 4} + 8\)

g(0) = 2 + 8 = 10.

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Answer:

11. 6

12. The last option, A=1/4, B=7/16, C=5/8, D=3/4

Step-by-step explanation:

11. look at the denominators, and what do you see? I see that 11 is 88 divided by 8. So, let's divide the numerator by 8 as well! 48/8=6

12. 1/4 is half of 1/2, so it would be between 0 and 1/2, or A

     Same thing with 3/4 but this time in the middle of 1/2 and 1, or D

     5/8 is a little over 4/8, or 1/2, so C

     The last one left is 7/16, B

Answer:0.5n

Step-by-step explanation: its to long to explain but correct :)

Answer:

0.5n

Step-by-step explanation:

Answer:

x equals to 10

Step-by-step explanation:

every triangle is 180 degrees, so 180-(79+57)= 44.

4x+4 (reverse it), 44-4= 40, 40÷4= 10. so x=10.

I hope you understand!!!

Answer:

  see attached graph

Step-by-step explanation:

There are a couple of ways you can look at this.

Point-Slope Form

The point-slope form of the equation for a line is ...

  y -k = m(x -h) . . . . . . . line with slope m through point (h, k)

Comparing this to the given equation, we see that ...

  k = -14, m = -7, h = 0

That is, the equation describes a line with slope -7 through point (0, -14).

The slope is the ratio of rise to run. Usually, "run" is considered to be positive in the +x direction (to the right). Here, you run out of room on most graphs if you look for a point that is 7 units down and 1 unit right of the y-intercept at (0, -14). (That point is (1, -21).) So, it is more convenient to start at the y-intercept (0, -14) and go 1 unit left and 7 units up to find another point on the line. That point is (-1, -7). With two points plotted, you can draw the graph.

__

Slope-Intercept form

We discovered above that the y-intercept is -14. You can get there also by putting the equation in slope-intercept form:

  y = mx +b . . . . . . line with slope m and y-intercept (0, b)

Adding -14 to both sides of the given equation gives you this form.

  y = -7x -14

The method of plotting is substantially identical to that described above.

__

Standard form

The standard form of the equation is ...

  ax +by = c

where a > 0, and a, b, c are mutually prime integers.

Adding 7x-14 to both sides of the equation puts it into standard form:

  7x +y = -14

The x- and y-intercepts are found by setting the other variable to zero and solving for the one that is left. Here, that means the x-intercept is ...

  c/a = -14/7 = -2

and the y-intercept is ...

  c/b = -14/1 = -14

These x- and y-intercepts are easily plotted on the x- and y-axes. The graph will be the line drawn through them. The attached graph shows the line and the intercepts.

The solution of the inequality, log₂ 2m > log₂ (m + 5) is {m | m > 5 / 2}.

An inequality is an expression that have <, >, ≤ and ≥ . Therefore, let's solve the logarithmic inequality for the variable m.

Hence,

log₂ 2m > log₂ (m + 5)

Therefore, let's divide both sides by log₂.

Hence,

2m > m + 5

subtract m from both sides of the inequality

2m > m + 5

2m - m > m - m + 5

2m > 5

divide both sides by 2

2m / 2 > 5 / 2

Therefore,

m > 5 / 2

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The wheelchair access ramp must be 216.09 inches long.

To find the length of the wheelchair access ramp, we can use trigonometry.

The tangent function relates the angle of elevation to the ratio of the opposite side (height) to the adjacent side (length of the ramp).

Let's denote the length of the ramp as "x".

The height of the ramp is given as 18 inches.

Using the tangent function:

tan(angle of elevation) = height/length of the ramp

tan(4.8 degrees) = 18/x

To solve for x, we can rearrange the equation:

x = 18 / tan(4.8 degrees)

Using a calculator to evaluate the tangent of 4.8 degrees:

x = 18 / 0.08331

x= 216.09

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Given,

The construction crew took 6 weeks to build 7.68 kilometers of road.

Rate of built the roads,

Therefore, the rate of building the roads is 1.28 per week.

Step-by-step explanation:

you can find the answer by vertical opposite angle

if the value of x is computed and it's equal to 78 you will find the answer

78=(12x+18)^

78=(12×5+18)

78=(60+18)

78=78 the problem is solved

may u get branliest please please

Given the inequality:

-9 < 4x + 3 < 27

we are to solve for x

recall,

if a

Answer: -21

Step-by-step explanation:

Answer:

25 ft tall

Step-by-step explanation:

divide 1250 by 50

i think its right lol.

Answer:

30%

Step-by-step explanation:

150/500 = 0.3

0.3x 100= 30%

Answer:

333.3%

Step-by-step explanation: