The table shows the population of a small town over time. The function P = 10,550(1.1)x models the population x years after the year 2000.

A 2-column table with 5 rows. The first column is labeled years after 2000, x with entries 0, 3, 4, 7, 10. The second column is labeled population, P with entries 10,5000; 14,000; 15,500; 20,500; 27,000.
For which year would this model most likely be sufficient to make a prediction of the population?

1950
2005
2025
2050

Answer:

X = ABC+ AB+ ABC

X = AB(C+1+C)

X = AB(2C+1)

The wire breaks if the load [tex]X[/tex] exceeds some amount. So what you're asked to do is find [tex]P(X\ge74)[/tex] and [tex]P(X\ge89)[/tex].

In either case, transform [tex]X[/tex] to the random variable [tex]Z[/tex] that's normally distributed with expected value 0 and standard deviation 1.

[tex]P(X\ge74) = P\left(\dfrac{X-80}3 \ge \dfrac{74-80}3\right) \\ = P(Z \ge -2) \\ = 1-P(Z < -2) \approx 0.9773[/tex]

[tex]P(X\ge89) = P\left(\dfrac{X-80}3 \ge \dfrac{89-80}3\right) \\= P(Z \ge 3) \\= 1 - P(Z < 3) \approx 0.0013[/tex]

The standard error will be equal to 0.75.

The standard deviation of a statistic's sample distribution, or an approximation of that standard deviation, is the statistic's standard error. The term "standard error of the mean" is used when referring to a statistic that is the sample mean.

The standard error will be calculated by using the formula:-

SE = [tex]\sigma[/tex] / √n

Here [tex]\sigma[/tex] is the standard deviation and n is the sample number.

SE = 6.5 / √75

SE = 0.75

Therefore the standard error will be equal to 0.75.

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In logarithmic form, we get In(2e^9)= ln(2)+9.

We are given,

 ln(2[tex]e^{9}[/tex])

We know that, ln(ab) = ln(a) + ln(b)

So we get,

 ln(2[tex]e^{9}[/tex]) = ln(2)+ln([tex]e^{9}[/tex])

Since ln(m^n)=n ln(m)  

And ln(e)= 1, we will get,

ln(2[tex]e^{9}[/tex]) = ln(2) +9 ln(e)

          = ln(2) +9

Hence, the logarithmic form, we get In(2e^9)= ln(2)+9.

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The clock was skipping 3 seconds every 30 minutes from Friday noon to Monday 6 pm.

The clock was still accurate by Friday noon. The clock was late by 468 seconds by Monday, 6 pm.

To solve the problem, we must:

Know how many 30-minutes have passed during the time period.

1 day = 24 hours

1 hour = 60 minutes = 2 × (30 minutes)

1 day = 24 hours × 2 × (30 minutes)

1 day = 48 × (30 minutes)

Thus, there are 48, 30-minutes in a day. On Friday, however, we start counting at noon, which is half of the day. Moreover, on Monday, the mark is only up to 6 pm, which is three-fourths of the day.

Friday = 48 × [tex]\frac{1}{2}[/tex] = 24

Saturday = 48

Sunday = 48

Monday = 48 × [tex]\frac{3}{4}[/tex] = 36

TOTAL = 24 + 48 + 48 + 36 = 156

Therefore, the total number of 30-minutes that have passed is 156. There were 156, 30-minutes that passed during the time period.

Divide the number of total seconds late by the number of 30-minutes passed.

That is, the number of total seconds late= 468 seconds ÷ 156

= 3 seconds  

Therefore, the clock was skipping 3 seconds every 30 minutes from Friday noon to Monday 6 pm.

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Answer:

(0,11)

Step-by-step explanation:

If we let x=0, then -y = -11, and so y=11.

Thus, (0,11) is a solution to the linear equation.

We conclude that the line that passes through (0, 0) and (2, -3) is perpendicular to line l.

Remember that two lines are perpendicular only if the slope of one of the lines is equal to the opposite of the inverse of the slope of the other line.

So, if line l has the slope 2/3.

Then the perpendicular lines have a slope equal to -3/2.

Now, remember that if a line goes through two points (x₁, y₁) and (x₂, y₂), then the slope of that line is:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

So here we just need to find two points (x₁, y₁) and (x₂, y₂) such that the slope is equal to -3/2.

If we define (x₁, y₁) = (0, 0), then the other point must be:

[tex]a = \frac{y_2 - 0}{x_2 - 0} = -3/2\\\\y_2/x_2 = -3/2[/tex]

Then we can write the other point as (2, -3).

So we conclude that the line that passes through (0, 0) and (2, -3) is perpendicular to line l.

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Answer:

Line LM

Step-by-step explanation:

First, we need to know what the slope is of a line that would be perpendicular to a line with a slope of -5/6. To find this, we take the reciprocal and multiply it by -1. Therefore, the line we are looking for needs to have a slope of 6/5.

Based on the fact that the slope is positive, we can eliminate lines PQ and JK as they have a negative slope. This leaves us with lines LM and NO.

To find out whether or not it is between LM and NO, you could eyeball it by looking at the graph and simply counting which might be faster if you understand how to do that (rise/run), or you can use the pair of coordinates given to you on each line to calculate for slope.

Line LM - [tex]\frac{-3-3}{-5-0}=\frac{-6}{-5}=\frac{6}{5}[/tex]

Line NO - [tex]\frac{-5-0}{-6-0}=\frac{-5}{-6}=\frac{5}{6}[/tex]

Based on this, we know that line LM is perpendicular to a line that has a slope of -5/6.

If you need help on calculating slope from two points, I'd suggest watching this video: https://www.brightstorm.com/math/algebra/linear-equations-and-their-graphs/finding-the-slope-of-a-line-from-2-points-problem-1/#:~:text=Use%20the%20slope%20formula%20to,second%20points%20are%20x2%2C%20y2.

Answer:

the answer is 24

Step-by-step explanation:

6x - 48 = 4x

6x - 4x - 48 = 0

2x - 48 = 0

2x = 0 + 48

2x = 48

x = 24

Answer:

56x² + 8x

(second option listed)

Step-by-step explanation:

area: length × width

length: 7x + 1

width: 8x

(8x)(7x + 1)

{distribute 8x}:

(8x)(7x):  8x × 7x = 8 · 7 · x · x = 56 · x · x = 56x²

(8x)(1) = 8x

area = 56x² + 8x

so, the area of this rectangle is 56x² + 8x

Answer:

56x² + 8x

[answer B]

Answer:

15 degrees

Step-by-step explanation:

Answer:

The earth turns 15 degrees in one hour. Hope this helps!

Step-by-step explanation:

Answer:

the answer is L

Step-by-step explanation:

rounding up to any number/decimal requires the digit before the specified digit to be 5 or greater.
rounding down requires the digit to be 4 or less.
if the estimated time to the nearest 0.01 of a second is 35.20 then the actual race time could be from 35.195 to 35.205 since any number between could be rounded to 35.20

The sequence of transformations used to obtain figure A'B'C'D'from figure ABCD are a reflection across the y-axis followed by a horizontal translation 1 unit right

Figure ABCD is transformed to figure A'B'C'D', as shown below: (see attachment)

Which of the following sequences of transformations is used to obtain figure A'B'C'D'from figure ABCD?

From the attached figure, we can see that:

ABCD and A'B'C'D' are on either sides of the y-axis.

This means that ABCD is first reflected across the y-axis.

ABCD is 2 units from the y-axis, while A'B'C'D' is 1 unit from the y-axis.

This means that the reflection is followed by a translation.

The unit of translation is:

Unit = 2 - 1

Evaluate

Unit = 1

1 represents a right translation

Hence, the sequence of transformations are a reflection across the y-axis followed by a horizontal translation 1 unit right

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When h = 0 ,  [f(x + h) - f(x)]/h  = 2x +2 for the given expression.

The missing expression is  f(x) = x² + 2x.

f(x+h)-f(x)/h is called the formula of difference quotient.

When h---> 0 ,

the expression f'(x) = (f(x-h) - f(x)) / h is the equation for tangent to the line

Here the the expression is

f(x) = x² + 2x

Determining f(x + h) by substituting x = x + h on both sides of the given f(x).

Then f(x + h) = (x + h)² + 2(x + h)

= x² + 2xh + h² + 2x + 2h

the difference f(x + h) - f(x).

f(x + h) - f(x) = [x²  + 2xh + h²  + 2x + 2h] - [x² + 2x]

= 2xh + h² + 2h

Divide the difference from h as in the formula of difference coefficient

[f(x + h) - f(x)]/h = (2xh + h² + 2h) / h

= 2x + h + 2

So, when h = 0 ,  [f(x + h) - f(x)]/h  = 2x +2

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The function g(x) is obtained by the transformation of the function f(x) is translated towards left by 1 unit.

A statement, principle, or policy that creates the link between two variables is known as a function.

The function f(x) is given below.

f(x) = 2ˣ

Then the function g(x) is given as

[tex]\rm g(x) = 2^{x + 1}[/tex]

The function g(x) is obtained by the transformation of the function f(x) is translated towards left by 1 unit.

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[tex]\displaystyle\\|\Omega|=\binom{15}{3}=\dfrac{15!}{3!12!}=\dfrac{13\cdot14\cdot15}{2\cdot3}=455[/tex]

a)

[tex]\displaystyle\\|A|=\binom{10}{3}=\dfrac{10!}{3!7!}=\dfrac{8\cdot9\cdot10}{2\cdot3}=120\\\\P(A)=\dfrac{120}{455}=\dfrac{24}{91}\approx26.4\%[/tex]

b)

[tex]\displaystyle\\|A|=\binom{5}{3}=\dfrac{5!}{3!2!}=\dfrac{4\cdot5}{2}=10\\\\P(A)=\dfrac{10}{455}=\dfrac{2}{91}\approx2.2\%[/tex]

c)

[tex]\displaystyle\\|A|=\binom{10}{2}\cdot5=\dfrac{10!}{2!8!}\cdot5=\dfrac{9\cdot10}{2}\cdot5=225\\\\P(A)=\dfrac{225}{455}=\dfrac{45}{91}\approx49.5\%[/tex]

d)

[tex]A[/tex] - at least one is spoilt

[tex]A'[/tex] - none is spoilt

[tex]P(A)=1-P(A')[/tex]

We calculated [tex]P(A')[/tex] in a).

Therefore

[tex]P(A)=1-\dfrac{24}{91}=\dfrac{67}{91}\approx73.6\%[/tex]

Answer:

Step-by-step explanation:

Using slope m = y_2-y_1/x_2-x_1 to find the solution slope that passes through those two-point.

Point-slope form into y-intercept form.

Answer:

For finding slope

we have the formula

m = y2 - y1/ x2 - x1

x1 = (-2)

x2. = ( 8)

y1. = (-1)

y2 =(-3)

putting the value of this in the formula we get,

m = (-3)-(-1)/8-(-2)

m = (-3+1)/8 + 2.

m = (-2)/10

m = (-1)/5.

m = (-1)/5

Answer:

60°

Step-by-step explanation:

since angle on straight line is 180° you take the sum of the exterior angle of R and its interior angle then divide both sides by the coefficient of y to find y then things get easier from there

Answer:

Step-by-step explanation:

Plan

7y and 5y are made on the same straight line. Therefore they are supplementary and add to 180 degrees. <s has to be found by finding 3x and 5y first. Find <s by solving 3y + 5y + x = 180 degrees.

Solution

7y + 5y = 180 degrees               Combine the left

12y = 180 degrees                      Divide by 12

12y/12 = 180/12

y = 15

3y + 5y + x = 180                         Combine the left side

8y + x = 180                                  Substitute 15 for y

8*15 + x = 180                               Combine

120 + x = 180                                Subtract 120 from both sides

120 -120 +x =180 - 120                 Combine

x  = 60

Answer

s = 60 degrees

<TRS = 5y = 75

The maximum number of spherical balloons that can be held in the canopy will be 30.

The canopy is the fabric cover that hangs above a bed. It is a covering that is fastened to or carried over a dignitary or a holy item.

The base layer of spheres in a square pyramidal arrangement has n2 balls, where n is the number of balls that make up a square's side.

n=4 inch

The total number of spheres in the pyramid is;

⇒n(n+1)(2n+1)/6

⇒4(4+1)(2×4+1)/6

⇒(4×5×9)/6

⇒30

Hence, in the canopy, 30 spherical balloons are the most that may be accommodated.

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Step-by-step explanation:

Easy buddy....

_________________________________

Remember, from now on, wherever the function domain is asked

They mean the same inputs or xs of the function.

Now you can answer them yourself but I like to help you to do it buddy.

_________________________________

The first function's domain is :

D = { -6 , -1 , 0 , 3 }

°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°

The second function's domain is :

D = { -7 , -6 , -2 , -1 , 0 , 1 , 3 , 9 }

_________________________________

And we're done.

Thanks for watching buddy good luck.

♥️♥️♥️♥️♥️

The domain of the function in the table given is:

A. {x|x = -6, -1, 0, 3}.

In any given function, all x-values (input) make up the domain of the function, while corresponding y-values (output) make up the range of the function.

In the table given, the x-values (input) are -6, -1, 0, and 3.

Therefore, the domain of the function in the table given is:

A. {x|x = -6, -1, 0, 3}.

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Step-by-step explanation:

Very easy the value are given apply the value for X and y

The solution for the first inequality is a ≥ 2 or a ∈ [2, ∞), and for the second inequality the solutions are b < -5 or b ∈ (-∞, -5)

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have two inequalities:

a.) -12a +7 ≤31

b.) -9 > 3b +6

a)  -12a +7 ≤ 31

-12a ≤ 31 - 7

-12a ≤ 24

-a ≤ 2

a ≥ 2  (sign changed because multiplied by a negative number)

a ∈ [2, ∞)

b.) -9 > 3b +6

-15 > 3b

-5 > b

or

b < -5

b ∈ (-∞, -5)

Thus, the solution for the first inequality is a ≥ 2 or a ∈ [2, ∞), and for the second inequality the solutions are b < -5 or b ∈ (-∞, -5)

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Answer:

x-intercepts: -5 +/-[tex]\sqrt{21}[/tex]. y-intercept: 4

Step-by-step explanation:

For x-intercepts use the quadratic equation

[tex]x= (-b +/-\sqrt{b^2-4ac} )/2a[/tex]

Fill in your values:

[tex]x= (-10 +/-\sqrt{100-16} )/2[/tex]

And solve

[tex]x=-5 +/- \sqrt{21}[/tex]

For y-intercepts set x=0 and solve. In this case, setting x= 0 gives you y=4.

Answer:

l

Step-by-step explanation:

Answer:

Lines L and n are parallel

Explanation -

In the question it is given that angle 7 and angle 5 are supplementary.

which means that sum of this angle is 180°

so line L and n are parallel

The true option about the system of linear equation is that the system can only be independent and consistent.

It should be noted that the system is consistent as it can illustrate more than a solution.

Also, it can't be independent and dependent at the same time as depicted in some of the option given.

In this case, true option about the system is that the system can only be independent and consistent.

The complete question is:

Given that (1, 0, 1) is a solution to a system of three linear equations, which of the following is true about the system?

The system can be either inconsistent or consistent.

The system can be either independent or dependent.

The system can only be independent and consistent.

The system can only be dependent and inconsistent.

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Answer:

[tex]\frac{1}{18}[/tex]

Step-by-step explanation:

The best way to solve this problem is to simplify each factorial one by one!

Starting at the numerator, the factorial for 2! is just 2, while the factorial for 5 is 120.

At the denominator, the factorial of 6! is 720, while the factorial for 3 is 6.

To write this out, we're given: [tex]\frac{(2) (120)}{(720) (6)}[/tex]

Just simply multiply and then divide, and we are given 1/18

Answer:

3x²-2x+1=?

3(4²)-2(4)+1=?

3(16)-8+1=?

48-8+1=?

40+1=41

Answer:

18

Step-by-step explanation:

Using order of operations:

[tex] \frac{15 - 9}{3} (19 - 10)[/tex]

[tex] \frac{6}{3} (9)[/tex]

[tex]2(9) = 18[/tex]