the perimeter of a school crossing sign is 102 inches what is the length of each side

Final answer:

To find n(A), we count the elements in the set A={0,1,2,3,...,2000} which form an arithmetic sequence. By applying the formula for the number of terms in an arithmetic sequence, we find that n(A) = 2001.

Explanation:

To find n(A), which represents the number of elements in set A, we simply count the elements listed in the given set A={0,1,2,3,...,2000}. These elements form an arithmetic sequence starting from 0 and ending at 2000 with a common difference of 1 between each consecutive number.

The formula for the number of terms n in an arithmetic sequence is given by:

n = (last term - first term) / (common difference) + 1

Applying the formula to our set A:

n = (2000 - 0) / 1 + 1 = 2000 + 1 = 2001

Therefore, n(A) = 2001.

Answer:

30 millimeters

Step-by-step explanation:

Answer:

9760-5220 is more than 4000.

Step-by-step explanation:

Consider the provided numbers.

We need to find 9760-5220 is more or less than 4000.

Subtract the numbers as shown.

 9760

-5220

4540

Now compare the number 4540 and 4000

By comparing it can be concluded that the number 4540 is greater than 4000.

Hence, 9760-5220 is more than 4000.

Answer:

The solution of the given inequality  [tex]|x-4|<\:3\:[/tex] is [tex]1<x<7[/tex]

Step-by-step explanation:

Given inequality [tex]|x-4|<\:3\:[/tex]

We have to find the solution of the given inequality  [tex]|x-4|<\:3\:[/tex]

Using absolute rule, [tex]\mathrm{If}\:|u|\:<\:a,\:a>0\:\mathrm{then}\:-a\:<\:u\:<\:a[/tex], we have,

[tex]-3<x-4<3[/tex]

Rewrite as [tex]x-4<-3\quad \mathrm{and}\quad \:x-4<3[/tex]

Consider , [tex]x-4>-3[/tex]

Adding 4 both side, we have,

[tex]x-4+4>-3+4[/tex]

Simplify, we have,

[tex]x>1[/tex]

Consider , [tex]x-4<3[/tex]

Adding 4 both side, we have,

[tex]x-4+4<3+4[/tex]

Simplify, we have,

[tex]x<7[/tex]

Combining, we have,

[tex]1<x<7[/tex]

Thus, The solution of the given inequality  [tex]|x-4|<\:3\:[/tex] is [tex]1<x<7[/tex]

Final answer:

Simplify the expression √(16 − x²) by substituting x with '4 sin x' to get 4|cos x|. Use trigonometric identities to arrive at the simplified expression.

Explanation:

The expression to simplify is: √(16 − x²) after substituting '4 sin x' for x.

Step-by-step solution:

Replace x with 4 sin x in the expression: √(16 − (4 sin x)²)

Simplify: √(16 − 16 sin² x)

Apply trigonometric identity: √(16 cos² x) = 4|cos x|

Lammer will make $150 after working for 10 hours .

Calculating Earnings Based on Hours Worked

To predict how much Lammer will make after working 10 hours, we first need to determine his hourly wage. From the information given, we know:

We can calculate his hourly wage as follows:

Hourly Wage = Total Earnings / Total Hours Worked

For both inputs, we observe:

This indicates that Lammer's hourly wage is consistent at $15 per hour.

Now, to predict how much he will make after working 10 hours:

Earnings for 10 Hours of Work = Hourly Wage x Number of Hours

Earnings for 10 Hours = $15 x 10 = $150

Therefore, Lammer will make $150 after working 10 hours.

Answer: B.

[tex]a_1=2\\a_n=a_n\times(-5)[/tex]

Step-by-step explanation:

The given geometric sequence : 2, -10, 50, -250

The first term of the sequence : [tex]a_1=2[/tex]

The common ratio between the terms :[tex]r=\dfrac{-10}{2}=-5[/tex]

We know that the recursive formula for geometric progression is given by :-

[tex]a_n=a_{n-1}r[/tex]

Then , the recursive formula for the given geometric progression will be :-

[tex]a_n=a_n\times(-5)[/tex]

Answer:

The mean of sample (21.6) is greater than population mean and the standard deviation of sample (8.4) is also greater than population standard deviation.

Both values, mean and std are greater than corresponding population values. This means, that our sample overestimates or is skewed to the right in the values of population. Also each specific value is farther apart from the mean so variation is much bigger in our sample than in our population.

Step-by-step explanation:

To calculate the mean, we estimate the avergage of the data as

Mean = Sum(data)/n

Where n is the number of observations of sample. We have;

(25 + 32 +  16 + 12 + 11 + 38 + 22 + 21  + 19 + 20)/10 = 21.6

The standard deviation is the square root of variance. Variance is sum of the deviation of each data point to the sample mean.

Variance = sum i= 1 to n (Xi-xmean)/(n-1)

Where n = 10 the # of observations and xi is each specific data point.

If you calculate it in Excel or or by hand you obtain:

Variance = sum i= 1 to n (Xi-21.6)/(10-1) = 8.4

Both values, mean and std are greater than corresponding population values. This means, that our sample overestimates or is skewed to the right in the values of population. Also each specific value is farther apart from the mean so variation is much bigger in our sample than in our population.

Answer:

The mean of the random samples (21.6) is greater than population´s mean (19.4) and the STD of the random samples (7.96) is greater than population´s STD (5.8)

Step-by-step explanation:

To calculate the mean of the random samples, we find the average value of the data set

[tex]Mean=\frac{(\sum_{i=0}^{n}{a_i})}{n}\\[/tex]

Where a is an element of the random example and n is the number of elements in the sample, as follows

Mean = (25+32+16+12+11+38+22+21+19+20)*(1/10) = 21.6

To calculate the STD (Standard Deviation) we need to know the variance, because

[tex]STD=\sqrt{var}[/tex]

The variance is determined as the sum of the deviation from one element of the data to the mean squared, all divided by n as below.

[tex]Var=(\sum_{i=1}^{n}{(a_{i}-Mean)^{2})/n[/tex]

If you calculate this by calculator or with a computer, you should get Var=63.44

And with that value, STD=7.96≈8

Therefore, by comparison, both Mean and STD of the random sample are greater than the population´s parameter

The range at θ = 10⁰ is 155.4 meters.

What is a projectile?

A projectile is an object thrown or projected into the air, subject to gravity, following a curved trajectory.

Given that

v₀ = 500m/s

g = 9.8 m/s²

θ = 10⁰

Substitute into the function

f(θ)=v₀²/g sin πθ/90=25510 sin πθ/90 meters.

f(θ)= 25510sin πθ/90

= 25510sin10π/90

= 25510sinπ/9

= 25510sin(3.142/9)

= 25510sin(0.349)

= 25510 * 0.00609

= 155.4 m

The range at θ = 10⁰ is 155.4 meters.

Complete question

The greater the initial velocity of a projectile, the greater the range, with the maximum range achieved at a 45° angle in the absence of air resistance.

The initial velocity of a projectile has a significant impact on its range. Specifically, the greater the initial speed, ℓ0, the greater the range. The formula for range R on level ground, neglecting air resistance, is given by R = (v0²/g) sin(2θ), where θ is the launch angle, v0 is the initial velocity, and g is the acceleration due to gravity. The maximum range is reached when the launch angle is 45°. With air resistance, the optimal angle decreases to roughly 38°. Additionally, for every angle other than the optimal, there are two different angles that yield the same range, and their sum totals 90°.

Answer:

[tex]y=3x+2[/tex]

Step-by-step explanation:

We are given equation as

[tex](y+4)=3(x+2)[/tex]

Since, we have to write equation in slope-intercept form

so, we can use slope-intercept formula

[tex]y=mx+b[/tex]

where m is a slope

b is y-intercept

so, we can write our equation in this form

[tex](y+4)=3(x+2)[/tex]

Distribute 3

[tex]y+4=3\times x+3\times 2[/tex]

[tex]y+4=3x+6[/tex]

Subtract both sides by 4

[tex]y+4-4=3x+6-4[/tex]

[tex]y+4-4=3x+6-4[/tex]

[tex]y=3x+2[/tex]

So, slope-intercept form of equation is

[tex]y=3x+2[/tex]

The sum of two angles is equal to [tex]180^\circ[/tex] than the angle pairs are known as supplementary angles. Therefore, from the given diagram angle pairs [tex]\rm \angle 3\;and\;\angle6[/tex], [tex]\rm \angle 5\;and\;\angle6[/tex], [tex]\rm \angle 4\;and\;\angle5[/tex], [tex]\rm \angle 3\;and\;\angle4[/tex] and [tex]\rm \angle 7\;and\;\angle 8[/tex] are supplementary angles. So, the correct options are: B), C), and E).

Given :

[tex]\angle 3 = 90^\circ[/tex]

The sum of two angles is equal to [tex]180^\circ[/tex] than the angle pairs are known as supplementary angles.

From the diagram given in the question it can be clearly observe that if [tex]\angle 3 = 90^\circ[/tex] than [tex]\rm \angle 4,\;\angle 5,\;and\;\angle 6[/tex] are also equal to [tex]90^\circ[/tex].

Than according to the definition of supplementary angles:

[tex]\angle 3 +\angle6 = 180^\circ[/tex]

[tex]\angle 3 +\angle4 = 180^\circ[/tex]

[tex]\angle 4 +\angle5 = 180^\circ[/tex]

[tex]\angle 5 +\angle6 = 180^\circ[/tex]

[tex]\angle 7 +\angle8 = 180^\circ[/tex]

Therefore, angle pairs [tex]\rm \angle 3\;and\;\angle6[/tex], [tex]\rm \angle 5\;and\;\angle6[/tex], [tex]\rm \angle 4\;and\;\angle5[/tex], [tex]\rm \angle 3\;and\;\angle4[/tex] and [tex]\rm \angle 7\;and\;\angle 8[/tex] are supplementary angles.

For more information, refer the link given below:

https://brainly.com/question/19281924

To find the cost of the dryer, set up equations based on the given information and solve for the dryer's cost, which results in the dryer being priced at $425.

To solve for the cost of the dryer in the given problem, we can create two equations based on the information provided. Let's denote the cost of the dryer as D and the cost of the washer as W. According to the problem, W = D + $67, and the combined cost of the washer and dryer is $917, so W + D = $917.

Substituting the first equation into the second, we have (D + $67) + D = $917. Simplifying this, we get 2D + $67 = $917. Subtracting $67 from both sides of the equation gives us 2D = $850. Finally, dividing both sides by 2, we find that D = $425.

Therefore, the cost of the dryer is $425.