Find m∠NAB

a) 55

b) 110

c) 80

d) 95

Base of the ladder is 5.6 m far away from the wall.

What is pythagoras theorem?

The Pythagorean Theorem, also known as the Pythagoras Theorem, is one of the most fundamental theorems in mathematics and it defines the relationship between the three sides of a right-angled triangle. In a right-angled triangle, one of the angles is  90∘, and the side that is opposite to that  90∘  (right) angle is known as the hypotenuse. The other two sides that are adjacent to the right angle are called the legs of the triangle.

It is given that  an 11.0 m ladder leans against the side of a building and ladder reaches up to the bottom of a window 9.5 m above the ground.

Diagram of this problem will be right angled triangle having hypotenuse 11 m and perpendicular 9,5 m

Using pythagoras theorem,

\(H^2=P^2+B^2\)

\((11)^2=(9.5)^2+B^2\)

121 = 90.25 + \(B^2\)

\(B^2\) = 121 - 90.25 = 30.75

B = \(\sqrt{30.75}\) = 5.6 m

Therefore, Base of the ladder is 5.6 m far away from the wall.

To learn more about the pythagoras theorem from the given link.

https://brainly.com/question/343682

#SPJ1

Answer:

Chart:

x           y

-6         11

3           5

15         -3

-12        15

Step-by-step explanation:

The only things you can plug in are the domain {-12, -6, 3, 15}

Plug in the domain into equation to find y.

-6 :

y = -2/3 (-6) +7

y = +47

y=11

(-6,11)

3:

y = -2/3 (3) +7

y = -2 +7

y = 5

(3, 5)

15:

y = -2/3 (15) +7

y =  -10 +7

y = -3

(15 , -3)

-12:

y = -2/3 (-12) +7

y = 8 + 7

y= 15

(-12,15)

Answer:

1) 11

2) 3

3) -3

4) -12

Step-by-step explanation:

eq(1):

\(y = \frac{-2}{3} x + 7\\\\y - 7 = \frac{-2}{3} x\\\\x = (y - 7)\frac{-3}{2} \\\\x = (7-y)\frac{3}{2} ---eq(2)\)

1) x = -6

sub in eq(1)

\(y = \frac{-2}{3} (-6) + 7\\\\y = \frac{12}{3} + 7\\\\y = 4+7\\\\y = 11\)

2) y = 5

sub in eq(2)

\(x = (7-5)\frac{3}{2} \\\\x = 3\)

3) x = 15

sub in eq(1)

\(y = \frac{-2}{3} 15 + 7\\\\y = \frac{-30}{3} +7\\\\y = -10 + 7\\\\y = -3\)

4)

sub in eq(2)

\(x = (7-15)\frac{3}{2} \\\\x = -8\frac{3}{2}\\ \\x = -12\)

The object whose distance is three times its displacement is object Z.  

The distance is defined as a scalar quantity representing the total distance traveled.

Displacement is a vector representing the distance between the end and start points.

Distance, Displacement, Ratio To calculate r = 3

Object    Motion                                    Distance     Displacement  ratio

 X          3 units left, 3 units right        3 + 3 = 6       3 - 3 = 0            ∞

 Y          6 units right, 18 units right    6 + 18 = 24    6 + 18 = 24       1

 W         8 units left, 24 units right      8 + 24 = 32   -8 + 24 = 16     2

 Z          16 units right, 8 units left       16 + 8 = 24    16 - 8 = 8         3

Ratio is calculated by dividing the distance by the displacement.

distance/displacement.

For object Z it is 24/8 = 3. So the object whose distance is three times its displacement is object Z.  

Read more about Object distance at: https://brainly.com/question/17206319

#SPJ1

The slope is positive and equal to 3, there is a positive relationship between X and Y. The remaining statements regarding a horizontal relation, a negative slope, or a vertical relation between X and Y are incorrect.

Based on the given information, we can conclude the following:

1. The slope is positive, and it is equal to 3: The coefficient of X in the equation Y = 390 * 3X is 3, indicating a positive relationship between X and Y. For every unit increase in X, Y increases by 3 units.

2. When X = 0, Y = 390: When X is zero, the equation becomes Y = 390 * 3 * 0 = 0. Therefore, when X is zero, Y is also zero.

3. The relation between X and Y is horizontal: The statement "the relation between X and Y is horizontal" is incorrect. The given equation Y = 390 * 3X implies a linear relationship between X and Y with a positive slope, meaning that as X increases, Y also increases.

4. When Y = 0, X = 130: To find the value of X when Y is zero, we can rearrange the equation Y = 390 * 3X as 3X = 0. Dividing both sides by 3, we get X = 0. Therefore, when Y is zero, X is also zero, not 130 as stated.

5. The slope is -3: The statement "the slope is -3" is incorrect. In the given equation Y = 390 * 3X, the slope is positive and equal to 3, as mentioned earlier.

6. The relation between X and Y is vertical: The statement "the relation between X and Y is vertical" is incorrect. A vertical relationship between X and Y would imply that there is no change in Y with respect to changes in X, which contradicts the given equation that shows a positive slope of 3.

7. As X goes up, Y goes down (downward sloping or negative relationship between X and Y): This statement is incorrect. The equation Y = 390 * 3X indicates a positive relationship between X and Y, meaning that as X increases, Y also increases.

Learn more about slope at: brainly.com/question/3605446

#SPJ11

If a line is perpendicular to one of the

two given parallel lines then it is also perpendicular to the other line.

As we know that by the theorem of perpendicular transversal theorem that in the plane, if a transverse is perpendicular to one or two parallel lines, then it is perpendicular to the third line. ... Since, they do not touch or interact with each other they are said to be parallel to each other.

Answer:

4 teachers

Step-by-step explanation:

If there is one teacher for every 18 students, you would divide the total number of students on the trip (72) by 18..

72/18= 4

so the answer is 4

For the answer of factors of expression (12 + 54), in the form of a(b + c), where a is the GCF of 12 and 54 is equals to 6( 2 + 9).

In math, to factor a number means to express it as a product of (other) whole numbers, called its factors. For example, if 7x5 = 35, 7 and 5 are both factors. The divisors that give the remainder to be 0 are the factors of the number. We have an expression of numbers, 12 + 54. We have to write this expression in form of a( b + c), where a is GCF of 12 and 54. Now, we can write the factors of 12 and 54 are 12 = 2×2×3

54 = 2×3 ×3×3

The greatest common factor, GCF of 12 and 54 is 2×3 = 6. So, 12 + 54 = 6× 2 + 6×9

Taking out the common factor 6 from above expression, 6( 2 + 9) which is required form a( b + c). Hence, required expression is 6( 2 + 9).

For more information about factor, visit :

https://brainly.com/question/28765863

#SPJ4

Based on the given sample data, it can be concluded that the average experience of the 250 applicants is statistically significantly greater than 2.5 years.

What is sample data ?

Sample data refers to a subset of observations or measurements collected from a larger population.

To determine whether it can be concluded that the mean of the 250 applicants is greater than 2.5 years, we can perform a hypothesis test.

Let's define the null hypothesis (H0) and the alternative hypothesis (H1) as follows:

\(H_0\): The mean experience of the 250 applicants is less than or equal to 2.5 years.

\(H_1\): The mean experience of the 250 applicants is greater than 2.5 years.

We will conduct a one-sample t-test since we have a sample mean, population standard deviation, and want to compare it to a specified value (2.5 years).

t ≈ 3.46

To determine whether the test statistic is statistically significant, we compare it to the critical value from the t-distribution table at the specified significance level.

At a significance level of 0.05 (α = 0.05) and with degrees of freedom (df) = n - 1 = 25 - 1 = 24, the critical value for a one-tailed test is approximately 1.711.

Since our test statistic (3.46) is greater than the critical value (1.711), we reject the null hypothesis (\(H_0\)) in favor of the alternative hypothesis (\(H_1\)). This means we have sufficient evidence to conclude that the mean of the 250 applicants is greater than 2.5 years at a significance level of 0.05.

In other words, based on the given sample data, it can be concluded that the average experience of the 250 applicants is statistically significantly greater than 2.5 years.

Learn more about standard deviation :
https://brainly.com/question/29115611

#SPJ4

Step-by-step explanation:

20 animal balloons in every 15min

number of ballon in 1min =20/15=1.33

now,

15=20

6×1.33=8

45×1.33=59

Answer:

B

Step-by-step explanation:

203.95 is equal to 4 of the tickets plus 11.95

You can write this as

203.95=4(price of ticket)+11.95

4(price of ticket)=192

Divide by 4

The price of a ticket is 48.

The equation would be 11.95+48t because its 48 times the amount of ticket plus the service fee.

Answer: x=4

Step-by-step explanation:

Answer:

51380000 mg

Step-by-step explanation:

10 - 3 = 7

7.34 x 7 = 51.38

1 kg = 1000000 mg

51.38 x 1000000 = 51380000

When \(7.34 \times 10^{-3} kg\) is converted to milligrams the result is 7340 mg.

Given, that kilograms to be converted to milligrams.

Multiplication: It is the basic mathematical operation among subtraction, division and addition. Multiplication follows associative and distributive property.

Exponential multiplication:

a) \(10^{-3} = \frac{1}{1000}\)

b) \(10^3 = 1000\)

Conversion factors:

1 Kg = 1000 grams

1 Gram = 100 milligrams

1 kg = 1000000 mg

Apply unitary method to convert Kg to mg.

1 kg = 1000000 mg

Multiply both sides by  \(7.34 \times 10^{-3} kg\)

\(7.34 \times 10^{-3} kg\) × 1 = \(7.34 \times 10^{-3} kg\) × 1000000

Here the kilograms is converted to equivalent milligrams.

\(7.34 \times 10^{-3} kg\) = 7340 milligrams

Thus the total milligrams in \(7.34 \times 10^{-3} kg\) are 7340 .

Know more about unit conversion, here:

https://brainly.com/question/14614674

#SPJ3

The length of each latus rectum of the hyperbola is 10.5. So, the correct option is G. 10.5.

The given hyperbola is `(y²/21) - ((x + 3)²/4) = 1`.

In a hyperbola, a latus rectum is defined as the line segment perpendicular to the principal axis that passes through a point on the hyperbola and whose endpoints lie on the hyperbola. If a hyperbola's center is at the origin, the length of each latus rectum is `2b²/a`.

Given equation of the hyperbola is `(y²/21) - ((x + 3)²/4) = 1`. We can write `(x + 3)²/4 - y²/21 = -1`

Comparing the given equation with the standard form of the hyperbola `(x - h)²/a² - (y - k)²/b² = 1`, we have `h = -3`, `k = 0`, `a²/4 = 1`, and `b²/21 = 1`. Therefore, `a² = 4` and `b² = 21`.

The length of each latus rectum of the hyperbola is `2b²/a`.`

2b²/a = 2(21)/4 = 21/2 = 10.5`. Hence, the correct option is G. 10.5.

To know more about hyperbola refer here:

https://brainly.com/question/27799190#

#SPJ11

Answer:

-2xy+7x^2-7y

i recommend m a t h w a y :)

Step-by-step explanation:

Answer:

7x^2−2xy−7y

Step-by-step explanation:

First Simplify

(−8x)(y)+3x2−5y+4x2−2y+6xy

=−8xy+3x2+−5y+4x2+−2y+6xy

Then Combine Like Terms:

=−8xy+3x2+−5y+4x2+−2y+6xy

=(3x2+4x2)+(−8xy+6xy)+(−5y+−2y)

=7x2+−2xy+−7y

The equation that is approximately 13.52 milligram remains is f(x) = 50(0.5)⁽¹⁰/⁵°³)

Equation:

Equation also known as expression is the combination of numbers, variables and mathematical operators.

Given,

The function gives the mass, m, of a radioactive substance remaining after h half-lives. Cobalt-60 has a half-life of about 5. 3 years.

Here we need to find the equation gives the mass of a 50 mg Cobalt-60 sample remaining after 10 years, and approximately how many milligrams remain.

Here we know that, when the mass is 50 mg, it means that:

=> m = 50

So, the equation is written as,

=> f(x) = 50(0.5)⁽ᵃ/ᵇ⁾

Here they said that when 10 years remain in the life of the substance, it means that:

So, the value of t = 10 and the value of half life is 5.3

Then the equation is rewritten as,

=> f(x) = 50(0.5)⁽¹⁰/⁵°³⁾

To evaluate the equation

f(x) = 13.52

Therefore, the required equation is f(x) = 50(0.5)⁽¹⁰/⁵°³) and approximately 13.52  milligram remains

To know more about Equation here.

https://brainly.com/question/10413253

#SPJ4

Answer:

192.5 in³

Step-by-step explanation:

The cardboard is 10 by 20 before removing a square from each end. Assuming that the square is x inches wide. Therefore, the 20 in side gets reduced by x inches on both sides, or say it becomes 20 - 2x inches. On the other hand, the 10 in side is also reduced by 2x. The x value we get happens to be the height of the box when the sides are folded up.

Thus the volume V = lbh =

V = (20-2x)*(10-2x)*(x)

V = 4x³ - 60x² + 200x

On differentiating, we have dv/dx to be

dv/dx = 12x² - 120x + 200

Using general formula to find the roots of this equation, we can solve that x = 7.886 and x = 2.113

This roots we got are possible values of x, the square we cut. Since 7.886 * 2 = 15.772 inches, this is more than the 10 inch side, henceforth x = 2.113 inches.

You cut 2.113 inches from each corner to obtain the maximum volume.

The sizes of the cubes are

20 - (2 * 2.113) = 15.774

10 - (2 * 2.113) = 5.774

2.113

The volume of the cube is 15.774 * 5.774 * 2.113 = 192.5 cubic inches.

True, The objective function in linear programming is formulated to either maximize or minimize a specific value or quantity.

The goal of linear programming is to optimize this objective function by finding the optimal values for the decision variables within the given constraints. Whether it is maximizing profit, minimizing cost, maximizing production, or minimizing waste, the objective function is designed to achieve the desired optimization outcome.

The objective function in linear programming serves as the goal or target to be achieved. It can involve maximizing profits, minimizing costs, maximizing efficiency, minimizing waste, or any other measurable quantity. The objective function guides the optimization process by defining the objective to be pursued in the linear programming problem.

Learn more about linear programming at

https://brainly.com/question/30763902

#SPJ4

Answer:

Mr.Green washed the most laundry with .375 of it done

what remains is .291

Step-by-step explanation:

3/8 or 3 divided by 8 is .375

1/3= .3333 repeating or rounded to .334

.375+.334= .709

1.000 - .709= .291

hopes this helps

Answer:

1. Mr. Green washed more laundry 2. 7/24 of the laundry still needs to be washed

Step-by-step explanation:

If you find a common denominator you can compare them. I used the common denomiator of 24. Next, you need to change both fractions so that they have the same denominator. To do that we have to multiply both the numerator and denominator of 3/8 by 3. When you do that, you end up with 9/24. Then you have to do the same for 1/3 but this time multiplying the numerator and the denominator by 8. That will leave us with 9/24 and 8/24 which proves that Mr. Green did more laundry.

For the second question, we will need to add the two amounts of laundry already washed and then find out how much remains from there. We can use the fractions that already have a common denominator from the explanation above. Now we have to add 9/24 and 8/24 together. Once we add them together, we will get 17/24 which is how much laundry is already done. Now, we need to take the remaining amount from 17/24 which is 7/24, and that represents how much laundry sitll needs to be washed.

(sorry if this is confusing but I hope it helped!)

Answer:

Step-by-step explanation:

Lets assume the smallest angle measure is x.

Then the largest angle is 12x and the middle angle is 5x.

We know that sum of interior angles of a triangle is 180°.

Set the following equation and solve for x:

The smallest angle is 10°.

The largest angle is:

The middle angle is:

Answer:

Smallest angle = 10°

Middle angle = 50°

Largest angle = 120°

Step-by-step explanation:

Sum of interior angles of a triangle = 180°

Let x = smallest angle

Given

   x + 5x + 12x = 180

⇒ 18x = 180

⇒ x = 180 ÷ 18

⇒ x = 10

Smallest angle = x = 10°

Middle angle = 5x = 5 x 10 = 50°

Largest angle = 12x = 12 x 10 = 120°

Answer:f

Step-by-step explanation:

its not that hard

The function is concave up for  x < 1 and concave down for x > 1 because the second derivative is positive for x < 1 and negative for x > 1. As a result, the critical point at x  < 1 is a relative maximum.

A function is an equation with just one solution for y for every x. A function produces exactly one output for each input of a certain type. Instead of y, it is common to call a function f(x) or g(x). f(2) indicates that we should discover our function's value when x equals 2. A function is an equation that depicts the connection between an input x and an output y, with precisely one output for each input. Another name for input is domain, while another one for output is range.

Here,

The derivative of the function f(x) can be found by taking the derivative of the expression e^(-x) (x^2 + 2x) using the product rule:

f'(x) = -e^(-x) (x^2 + 2x) + e^(-x) (2x + 2) = 2e^(-x) - 2xe^(-x) (x + 1)

Setting f'(x) equal to zero and solving for x gives us the critical points:

0 = 2e^(-x) - 2xe^(-x).(x + 1)

2xe^(-x).(x + 1) = 2e^(-x)

x(x + 1) = e^x

x^2 + x - e^x = 0

Next, we determine the concavity of the function at the critical points by analyzing the second derivative of the function:

f''(x) = 2e^(-x) + 2xe^(-x) + 2xe^(-x).(x + 1) - 2e^(-x).(x + 1)

= 2e^(-x).(1 - x)

Since the second derivative is positive for x < 1 and negative for x > 1, the function is concave up for x < 1 and concave down for x > 1. Thus, the critical point at x < 1 corresponds to a relative maximum.

To know more about function,

https://brainly.com/question/28193995

#SPJ4

Answer: 1

Step-by-step explanation:

25+23=48

48=73+25Y

-73        = -25

divide = 1

Answer:

2.1 m²

Step-by-step explanation:

Area of Sector

-21x + 6x (i'm pretty sure)

The set of observations on a variable measured at successive points in time or over successive periods of (c) time series .

A Time Series is a set of observations on a variable that is measured at successive points in time or over successive periods.

Which means that the values of the variable that are recorded at regular intervals or successive points, such as daily, weekly, monthly, or annually, and are analyzed to identify the patterns, trends, and relationships over time.

The Time series analysis can be used in various fields, including economics, finance, engineering, and the natural sciences, to make predictions, identify cause-and-effect relationships, and inform decision-making.

The given question is incomplete , the complete question is

A set of observations on a variable measured at successive points in time or over successive periods of

(a) geometric series

(b) time invariant set

(c) time series

(d) logarithmic series

Learn more about Time Series here

https://brainly.com/question/29737000

#SPJ4

Answer:

hi so can you explain it better i will know what to do thanks i will let you know when i have it

Step-by-step explanation:

Answer:

both are parallel to each other

Step-by-step explanation:

When the line to be examined's slope is known, and the provided point also serves as the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b).

When should you use point-slope form?

When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). The y value of the y intercept point is represented by b in the equation.

One of the three ways we can express a straight line is using the point slope form, also known as the point-gradient form. By merely knowing one point on the line and the slope of the line, we may use this form to get the equation of the line.

The slope and y-intercept of the matching line can be rapidly determined when we have a linear equation in slope-intercept form. This enables us to graph it as well.

The equation of a line can be represented in either slope-intercept form or point-slope form.

Slope-intercept form:

The slope-intercept form of a line is given by y = mx + b, where m is the slope of the line and b is the y-intercept.

To find the equation of the line passing through the points (3,5) and (6,11) in slope-intercept form, we can use the point-slope formula to find the slope and then use one of the points to find the y-intercept.

Point-slope form:

The point-slope form of a line is given by y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line.

To find the equation of the line passing through the points (3,5) and (6,11) in point-slope form, we can use the point-slope formula and one of the points.

Using the point-slope formula, the slope of the line is (11 - 5) / (6 - 3) = 6/3 = 2.

So, the equation of the line in slope-intercept form is:

y = 2x + b

We can use the point (3,5) to find the y-intercept:

5 = 2 * 3 + b

Solving for b, we get b = -1.

So the equation of the line in slope-intercept form is:

y = 2x - 1

In point-slope form, using the point (3,5), the equation of the line is:

y - 5 = 2(x - 3)

Both forms represent the same line, just in different ways.

To learn more about point-slope form refer to:

brainly.com/question/6497976

#SPJ1

Answer:

198 in²

Step-by-step explanation:

triangle (A=1/2)bh [A=1/2(22×8)] b=22 H=8

rectangle (A=bh) [A= 22×5] B=22 H=5

triangle = 88

rectangle = 110

So, 88+110 = 198

The given figure represents a quadrilateral. The sum of the interior angles of a quadrilateral is equal to 360°. This is our working concept to solve for the value of x on the given figure. All we need to do is, to sum up, all the interior angles on the problem and their sum are equal to 360 °. This is written in an equation as

Simplify the equation and compute, we get

Hence, the value of x on the problem is 52 degrees.

Given:

Consider the given function is:

\(P(t)=4000(1.2)^t\)

To find:

a. The type of exponential function (growth or decay).

b. Percentage change in population.

c. Population after 5 years.

Solution:

a. The general exponential function is:

\(P(t)=P_0(1+r)^t\)          ...(i)

Where, \(P_0\) is the initial population and r is the rate of change in decimal.

If r<0, then the function represents exponential decay and if r>0, then the function represents exponential growth.

We have,

\(P(t)=4000(1.2)^t\)

It can be written as:

\(P(t)=4000(1+0.2)^t\)          ...(ii)

On comparing (i) and (ii), we get

\(P_0=4000\)

\(r=0.2\)

Since r>0, therefore the given function represents exponential growth.

b. From part (a), we have

\(r=0.2\)

So, the rate of change in the population is 0.2. Multiply is by 100 to get the percentage change in population.

\(r\%=0.2\times 100\)

\(r\%=20\%\)

Therefore, the yearly percentage change in population is 20%.

c. We have,

\(P(t)=4000(1.2)^t\)

Substitute \(t=5\) in the given function to find the population living on the island after 5 years.

\(P(5)=4000(1.2)^5\)

\(P(5)=4000(2.48832)\)

\(P(5)=9953.28\)

\(P(5)\approx 9953\)

Therefore, the estimated population living on the island after 5 years is 9953.