A 40-foot ladder is used to reach the top of a 24-foot wall. If the ladder extends 10 feet past the top of the wall, find the
measure of the angle that the ladder forms with the horizontal ground. Answer to the nearest degree

The logarithmic regression equation that models the situation is given as follows:

y = 242.9037 + 23.7097ln(x).

The estimated population in 2010 is of:

313.9 million

Which overestimates the actual amount by 5.2 million.

The prediction for when the population will be of 400 million is of:

Year of 2,744.

The logarithmic regression equation is obtained inserting the points of the data-set into a logarithmic regression calculator.

From the table given by the image at the end of the answer, the points are given as follows:

(0, 248.8), (10, 281.4), (20, 308.7), (30, 331.4), (31, 331.9).

Inserting these points into a calculator, the equation is given as follows:

y = 242.9037 + 23.7097ln(x).

2010 is 20 years after 1990, hence the estimate is given as follows:

y = 242.9037 + 23.7097 x ln(20) = 313.9 million.

The overestimate of the actual value, from the table, is of:

313.9 - 308.7 = 5.2 million.

The prediction for when the population will be of 400 million is obtained as follows:

400 = 242.9037 + 23.7097 x ln(x)

ln(x) = (400 - 242.9037)/23.7097

ln(x) = 6.6258.

x = e^(6.6258)

x = 754.

Hence during the year of 2,744.

The table is given by the image presented at the end of the answer.

More can be learned about logarithmic regression at https://brainly.com/question/26755306

#SPJ1

3/5 or 60% of the prism's volume will be filled with sand.

The volume of each cube is e³ = 5³ = 125 cubic centimeters.

Since the rectangular prism is made up of two cubes, its volume is 2e³ = 2(125) = 250 cubic centimeters.

If Arusha fills the prism with 150 cubic centimeters of sand, the fraction of the prism's volume that will be filled with sand is:

150/250 = 3/5

Therefore, 3/5 or 60% of the prism's volume will be filled with sand.

Read more on fractions here:https://brainly.com/question/386916

#SPJ1

Step-by-step explanation:

sum of four angles=360°

a=128

b=126

c=54

d=?,let d=x

128+126+54+x=360°

308+x=360

find like terms

x=360-308

x=52°

The 5th term of the arithmetic series is  1179/ 19.

The 10th term of the arithmetic series , S is 66.

Using arithmetic formula,

aₙ = a + (n - 1)d

where

Therefore,

66 = a + 9d

The sum of the first 20 terms of S is 1290.

Therefore,

Sₙ = n / 2 (2a + (n - 1)d)

1290 = 10(2a + 19d)

1290 = 20a + 190d

combine the equation

66 = a + 9d

1290 = 20a + 190d

Hence,

a = 66 - 9d

1290 = 20(66 - 9d) + 190d

1290 = 1320 - 180 + 190d

1290 - 1320 + 180 = 190d

190d = 150

d = 150 / 190

d = 15 / 19

Hence,

a = 66 - 9(15  /19)

a = 66 - 135 / 19

a = 1254 - 135/ 19

a = 1119 / 19

Hence, let's find the fifth term.

a₅ = a + 4d

a₅ = 1119 / 19 + 4(15 / 19)

a₅ = 1119 / 19 + 60 / 19

Therefore,

a₅ =  1179/ 19

learn more on arithmetic series here: https://brainly.com/question/16415816

#SPJ1

Answer:

29. x = 5

30. r = 8

31. w = 3

32. a = 7

33. c =4

34. m = 9

Hope it helps and have a great day! =D

~sunshine~

Answer:

Step-by-step explanation:

The length of a rectangular picture frame is 3 inches longer than it's width. If the perimeter of the picture frame is 38 Inches, what is the length and width ?

Given :

Perimeter of rectangle is 38 Inches

lenght is 3 inches more than the breadth.

let, width be x, and length be x+3

So, Breadth is 8 inches and length is 8+3= 11 inches.

Let's verify ::

Thus Solved !!

The expression that shows the total oranges amir got in total is x-12 = 4. And amir got 16 oranges in all

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1. For example, x² is a variable raised to the second power, but x is a variable raised to the first power.

example of linear expression is 2x+2y = 5. This is a linear expression with two variables x and y.

Let's represent the total no of oranges by x.

Therefore ,

2 bags of oranges with 6 in each bag will amount to 2×6 = 12 oranges.

an addition of 4 loose oranges . Therefore the total number of oranges = 12+4 = x

x = 12+4 or x-12 = 4

= 16

therefore amir got 16 oranges in all

learn more about linear expression from

https://brainly.com/question/2030026

#SPJ1

No, we can't conclude that the correlation coefficient differs from zero because the p-value, which is 0.0653 exceeds 0.05. The correct option is a.

Given that:

p-value  = 0.0653                        

Level of significance (p) = 0.05  

The null hypothesis is a typical statical theory that suggests that no statical relationship and significance exists in a set of given single observed variables, between two sets of observed data and measured phenomena.

The null hypothesis is significant because it offers a rough description of the phenomena inferred from the available evidence. It enables researchers to empirically test the relationship statement in a study.

Example: The null hypothesis is that the population density is the same across all states.

The hypothesis is

H0: p=0 vs HA: p \(\neq\) 0

We observe that,

p-value > p (level of significance)

So, fail to reject the null hypothesis (H0).

The correlation coefficient differs from zero when the p-value is less than 0.05.

Therefore, we can not conclude that the correlation coefficient differs from zero.

To learn more about the null hypothesis visit: https://brainly.com/question/28920252

#SPJ4

False is the statement, "Polygon endpoints need not conform to snap points, like the boundaries of a filled-in region."

The surface's perimeter is defined by the edge of a filled-in area. An area is a two-dimensional space that any surface can cover. Typically, the edges of the space serve as the surface's boundary. To create a closed area or surface, the edges or the boundary must link.

Similar to end points, snap points are the ends of a polygon's sides. A closed figure can only be formed when these endpoints are connected. A closed polygon is one that has n sides.

Know more about polygon

https://brainly.com/question/1592456

#SPJ4

Answer:

Take a look at the attachment...

Hope this helps! :)

Answer:

1. What are the numbers?

2. 80

3. 26

4. 57

Step-by-step explanation:

Answer: 57

80

26

80-26=54

Step-by-step explanation:

thank you! I think I did the last one correct but I’m not sure so if I’m not then sorry.

Answer:

y = -x + 8

Step-by-step explanation:

Let's break down the equation step by step to understand it better.

The equation in point-slope form is given as:

y - y1 = m(x - x1)

In this case, we have:

y - 0 = -1(x - 8)

The point-slope form uses a specific point (x1, y1) on the line and the slope (m) of the line.

Here, the point (x1, y1) is (8, 0), which represents a point on the line. This means that when x = 8, y = 0. The graph has a point at (8, 0), which confirms this information.

The slope (m) is -1 in this equation. The slope represents the rate at which y changes with respect to x. In this case, since the slope is -1, it means that for every unit increase in x, y decreases by 1. The negative sign indicates that the line has a downward slope.

By substituting the values into the equation, we get:

y - 0 = -1(x - 8)

Simplifying further:

y = -x + 8

This is the final equation of the line in slope-intercept form. It tells us that y is equal to -x plus 8. In other words, the line decreases by 1 unit in the y-direction for every 1 unit increase in the x-direction, and it intersects the y-axis at the point (0, 8).

If the graph has points at (0, 8) and (8, 0), the equation y = -x + 8 accurately represents that line.

Answer:

110

Step-by-step explanation:

Suppose lines EH and BD are parallel:

Angle <GFE and angle <ABC are supplementary so their sum is equal to 180

2x + 10 + x  + 20 = 180 add like terms

3x + 30 = 180 subtract 30 from both sides

3x = 150 divide both sides by 3

x = 50

We are asked the value of <ACD

<ABD and <ACD are also supplementary so we can find the value od <ACD:

x + 20 + <ACD = 180 we know x = 50 so we can replace x with that

50 + 20 + <ACD = 180

70 + <ACD = 180 subtract 79 from both sides

<ACD = 110

When edge D connects with edge X, this net is folded into a cube, which is obtained by folding the given figure in cube.

A cube is a solid shape with six square faces. Each side of a square  has the same side length, so all  faces are the same size.

A cube has 12 sides and 8 vertices. Each vertex refers to the angle where the three edges of the cube meet.

Shape Properties of  Cube  

Thus, when edge D connects with edge X, this net is folded into a cube.

Know more about the cube

https://brainly.com/question/19891526

#SPJ1

Answer:

D

Step-by-step explanation:

Each top part of the fraction counts as one jump thingy, which is from one stick to another. Since the first jump skips 3 sticks, that is the (3/7), and so on...

Answer:

67

Step-by-step explanation:

The measure of the angle supplement of TOK is 131°.

Supplementary angles refer to the pair of angles that always sum up to 180°. These two angles are called supplements of each other.

Now the given angle is,

m TOK = 49°

Let the supplement of 49° be x.

Now, 49° + x = 180°

Taking alike terms together we get,

⇒ x = 180° - 49°

Solving we get,

⇒ x = 131°

which is the required supplement of TOK.

Thus, the measure of the angle supplement of TOK is 131°.

To learn more about the supplementary angles visit:

brainly.com/question/28312114.

#SPJ2

Answer:

B

Step-by-step explanation:

Because

(c) 15i + 4b ≥ 100 inequality represents this scenario.

To represent the scenario described in the problem, we need to use an inequality that relates the amount of money Emily spends on ink and brushes to the total amount of money she has available. Let's call the amount of ink Emily buys "x" and the number of brushes "y". Then the total amount of money she spends is:

Total cost = 8x + 18y

We want to know when this total cost is less than or equal to $100, so we can write:

8x + 18y ≤ 100

This inequality means that the total cost of ink and brushes must be less than or equal to the amount of money Emily has available. Therefore, the answer is (c) 15i + 4b ≥ 100.

Correct Question :

Emily has $100 extra to spend on supplies for her T-shirt-making business. She wants to buy ink, i, which costs $8 a bottle, and ne brushes, b, which are $18 each. Which inequality below represents this scenario?

a) 4i+100 ≤ 15b

b) 15i + 4b ≤ 100

c) 15i + 4b ≥ 100

d) 4i + 15b ≤ 100

To learn more about inequality here:

https://brainly.com/question/30231190

#SPJ1

The odds ratio of income is 1.00320, rounded to 5 decimal places.

The odds ratio of income can be calculated using the formula given below:

odds ratio = odds of personal loan when income increases by 1 unit

Odds of a personal loan is the ratio of probability of acceptance to probability of rejection.

Odds of personal loan = P(personal loan=yes) / P(personal loan=no)P(personal loan=yes) = 0.0122

P(personal loan=no) = 1 - P(personal loan=yes) = 0.9878

Odds of personal loan = 0.0122 / 0.9878 = 0.0124

The logistic regression model estimated as P(personal loan=yes|income=x) = 1 / (1 + e(-6.3525+0.0392x))

Hence, P(personal loan=yes|income=x) = 1 / (1 + e(-6.3525+0.0392x)) = 0.0122

P(personal loan=yes|income=x+1) = 1 / (1 + e(-6.3525+0.0392(x+1))) = 0.012414

We have, odds ratio = odds of personal loan when income increases by 1 unit

odds ratio = 0.012414 / 0.0124 = 1.0032 ≈ 1.00320

Round the answer to 5 decimal places = 1.00320

The odds ratio of income is 1.00320, rounded to 5 decimal places.

for such more question on odds ratio

https://brainly.com/question/24223396

#SPJ11

Answer:

The third answeer

Step-by-step explanation:

Also nice talk

Answer:

1244 DCD

Step-by-step explanation:

There must be some questions following the table.The answers will depend on the questions.

The domain and the range of the function represented by the graph are [-2, 2) and (-4, 4]

In mathematics, the domain and range of a function are used to describe the set of possible input and output values of the function, respectively.

From the graph, we have the set of input values to be

Input = From -2 (closed circle) to 2 (open circle)

This means that the domain is

[-2, 2)

From the graph, we have the set of output values to be

Output = From -4 (open circle) to 4 (closed circle)

This means that the range is

(-4, 4]

Read more about domain and range at

https://brainly.com/question/2264373

#SPJ1

Check the picture below.

so the composite is really a trapezoid and two triangles, let's get their area and sum them all up.

\(\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a = 2\\ b = 5\\ h = 7 \end{cases}\implies A=\cfrac{7(2+5)}{2} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{\LARGE Areas}}{\stackrel{yellow~trapezoid}{\cfrac{7(2+5)}{2}}~~ + ~~\stackrel{blue~triangle}{\cfrac{1}{2}(\stackrel{b}{3})(\stackrel{h}{5})}~~ + ~~\stackrel{orange~triangle}{\cfrac{1}{2}(\stackrel{b}{10})(\stackrel{h}{2})}} \\\\\\ 24.5~~ + ~~7.5~~ + ~~10\implies \text{\LARGE 42}\)

Answer:

40

Step-by-step explanation:

Angles opposite congruent sides in a triangle are congruent, so the other base angle is also 70 degrees.

This means that the interior angles are 70, 70, and x

Since the sum of the measures of the angles of a triangle is 180 degrees,

70+70+x=180

140+x=180

x=40

Answer:

the answer is 45 because there are four marbles so it would be a 50/50

Answer:

a

Step-by-step explanation:

simple mat h