If you have a distribution of 50 scores, and you want 5 intervals, what should be the size of your class interval?

Final answer:

The 55th derivative of y = cos(3x) is recognized by repeating the derivative patterns of cosine functions and is found to be -27cos(3x).

Explanation:

The 55th derivative of y = cos(3x) can be found by recognizing that the derivatives of sine and cosine functions repeat every four steps. Considering the pattern cos(x) -> -sin(x) -> -cos(x) -> sin(x) -> cos(x), and that the derivative of cos(3x) is -3sin(3x), we can determine that the pattern repeats every four derivatives with a factor of 3n, where n is the number of times the derivative is taken.

The 55th derivative will be the same as the third derivative in the cycle, but with an iteration count of 55/4, which leaves a remainder of 3, so the 55th derivative will be -27cos(3x).

Final answer:

To find the product of three consecutive nonzero integers, multiply the first number by the next two numbers in the sequence.

Explanation:

If the first integer is n, the next will be n+1 and the next to it will be n+2

The product of three consecutive nonzero integers can be calculated using the formula:

n * (n+1) * (n+2)= n(n^2 + 3n+ 2)=n^3 +3n^2 + 2n

where 'n' represents the first integer. For example, if we take 'n' as 2, the three consecutive nonzero integers would be 2, 3, and 4. So, the product would be 2 * 3 * 4 = 24= (2)^3+  3*(2)^2+ 2*2

Answer: The answer is biased :)

Answer:

99.064  miles of coastline are in Georgia.

Step-by-step explanation:

Consider the provided information.

The united states has 12,383 miles of coastline and 0.8% of the coastline is located in Georgia.

Now we need to find about how many miles of coastline are in Georgia.

Thus solve this as shown:

0.8% of 12,383

[tex]\frac{0.8}{100} \times 12,383[/tex]

[tex]0.008 \times 12,383[/tex]

[tex]99.064[/tex]

Hence, 99.064  miles of coastline are in Georgia.

Answer: a=-3b

                  2

Step-by-step explanation:

get all letters on the same side so:

7a-5a (because when you cross the = you do the opposite)=-b+2b

2a=b

you are solving for a so: 2a/2=b/2

so the 2 cancel out and you have a=1/2b

29/1

Improper fractions have a greater numerator.

29 > 1

Step 1

Find the slope of the given line

we have

[tex]3x+4y=15[/tex]

Isolate the variable y

Subtract [tex]3x[/tex] both sides

[tex]3x+4y-3x=15-3x[/tex]

[tex]4y=-3x+15[/tex]

Divide by [tex]4[/tex] both sides

[tex]y=-\frac{3}{4}x+ \frac{15}{4}[/tex]

the slope of the given line is

[tex]m=-\frac{3}{4}[/tex]

Step 2

Find the equation of the line that passes through  the point [tex](8,-2)[/tex] and is parallel to the given line

we know that

if two lines are parallel, then their slopes are equal

The equation of the line into point-slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=-\frac{3}{4}[/tex]

[tex](x1,y1)=(8,-2)[/tex]

substitute in the equation

[tex]y+2=-\frac{3}{4}(x-8)[/tex]

[tex]y=-\frac{3}{4}x+6-2[/tex]

[tex]y=-\frac{3}{4}x+4[/tex]  or  [tex]3x+4y=16[/tex]

therefore

the answer is

[tex]y=-\frac{3}{4}x+4[/tex]

or

[tex]3x+4y=16[/tex]

Answer:

3x+4y=16

Clarifying because other explanation was confusing

Just took review

Step-by-step explanation:

The answer to the first question is "b. one," according to Euclid's First Postulate. The answer to the second question is "c. infinitely many," according to Euclid's Second Postulate. These principles form the foundation of Euclidean geometry.

In Euclidean geometry, there are fundamental postulates and theorems that govern the behavior of lines and angles in triangles. Let's address your questions:

1. How many lines can be drawn through point A perpendicular to segment BC?

Answer: There can be only one line drawn through point A that is perpendicular to segment BC. This follows from Euclid's First Postulate, which states that a straight line can be drawn between any two points. In this case, the straight line from point A to any point on segment BC is unique and perpendicular.

2. How many lines can be drawn through point C perpendicular to segment AB?

Answer: Infinitely many lines can be drawn through point C that are perpendicular to segment AB. This is based on Euclid's Second Postulate, which states that a straight line can be extended infinitely in both directions. So, you can draw as many lines as you like, all of which are perpendicular to segment AB, and they will extend infinitely in both directions.

Learn more about Euclidean geometry here:

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To find the value of x and BC, set up the equation CB + BD = CD and solve for x. The value of x is 3 and BC is 3.

To find the value of x and BC, we can set up the equation CB + BD = CD and solve for x.

Substituting the given values CB = 4x - 9, BD = 3x + 5, and CD = 17, we get (4x - 9) + (3x + 5) = 17.

Combining like terms, we have 7x - 4 = 17. Solving for x, we find x = 3. Plugging this value back into CB = 4x - 9, we get BC = 4(3) - 9 = 12 - 9 = 3.

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The midpoint of the range of frequencies given is:

midpoint =  (82.4 + 659.2) / 2 = 370.8 Hertz

Then the difference from midpoint to the other end is:
370.8 - 83.4 = 288.4 Hertz

Therefore the inequality formula is
|f - 370.8| <= 288.4

Answer:

Gina=35, Sara=33

Step-by-step explanation:

Gina's number is 2 more than Sara's.

Lets start by saying cookies as the number.

Sum = 2 numbers add together. The answer to the equation. Lik 5+5=10. 10 is the sum.

You only know that Gina has 2 more cookies than Sara.

If Sara has 3 cookies then Gina has 5 cookies. Whats the Sum? 8.

So, you figure out an random big number but, smaller than 68.

Lets do 68 to try now.  So you do 68/2 = 34. You remember that Gina has 2 more than Sara. So, 35 cookies for Gina. So, you can guess that Sara has 33 cookies.

1.50x+0.80y≤20 is inequality represents how many hot dogs and how much water you can buy

A relationship between two expressions or values that are not equal to each other is called 'inequality.

Given,

a hot dog costs $1.50 each and water costs $0.80 each.

Let  x be the amount of hot dog

y be the amount of water

As hot dog costs $1.50 each, 1.50x

water costs $0.80 each, so 0.80y

You want to buy food and water for yourself and your friends but do not want to spend more than $20

1.50x+0.80y≤20

Hence, 1.50x+0.80y≤20 is inequality represents how many hot dogs and how much water you can buy

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Answer:

Atleast 53

Step-by-step explanation:

We are given that your basketball team has a goal  to collect atleast 160 blanket for a shelter.

Team member bought blankets on Monday =42

Team member bought blankets on Wednesday=65

We have to write an inequality and find the number of blankets  has to collect on Friday.

Let x be the number of blankets  bought by team members on Friday

According to question

[tex]42+65+x \geq 160[/tex]

[tex]107+x \geq 160[/tex]

Subtract 107 on both sides

[tex]107-107+x\geq 160-107[/tex]

[tex]x\geq 53[/tex]

Hence, team members bought atleast 53 blankets on Friday .