A handicapped ramp is being constructed for the front entrance of First National Bank in Springfield. ADA guidelines requires a rise angle from the foot of the ramp (point furthest from the entrance) not to exceed 4.8 degrees. This means the vertical to horizontal ratio cannot exceed 1:12. If the handicapped ramp must start 15 feet away from the front entrance, contractors estimate the rise to be about 3 feet.

Part A: Explain thoroughly whether or not these ramp dimensions meet the ADA guidelines.

Part B: If the rise estimate does not meet ADA requirements, provide a measurement that would meet the guidelines.​​​

Step-by-step explanation:

2.

it is a square !

what do we know about squares ?

first of all, they are a special rectangle, where length = width, and therefore all 4 sides are equally long.

and secondly, as they are a form of rectangle, every inner angle is 90°.

so,

6x - 12 = 90

6x = 102

x = 102/6 = 17

therefore,

CD = x + 15 = 17 + 15 = 32

many greetings to your teacher, CD is a side, a length, and NOT an angle, so it is NOT measured in degrees (°).

since it is a square and all sides are equally long,

AD = CD = 32

3.

it is a rectangle.

so, it has 4 sides consisting of 2 pairs of equally long sides. that means there are 2 equally long side we call length, and 2 equally long sides we call width.

these equally long sides are always opposite of each other.

that means

2x - 52 = x - 2

x - 52 = -2

x = -2 + 52 = 50

Confidence interval for 68% confidence level = (0.548, 0.572)

Confidence interval for 95% confidence level = (0.536, 0.584)

Confidence interval for 99.99% confidence level = (0.523, 0.598)

The mean of this sample distribution is

Mean = μₓ = np = 0.61 × 1600 = 976

But the sample mean according to the population mean should have been

Sample mean = population mean = nP

= 0.56 × 1600 = 896.

To find the interval of values where the sample proportion should fall 68%, 95%, and almost all of the time, we obtain confidence intervals for those confidence levels. Because, that's basically what the definition of the confidence interval is; an interval where the true value can be obtained to a certain level. of confidence.

We will be doing the calculations in sample proportions,

We will find the confidence interval for the confidence levels of 68%, 95% and almost all of the time (99.7%).

Basically the empirical rule of 68-95-99.7 for standard deviations 1, 2, and 3 from the mean.

Confidence interval = (Sample mean) ± (Margin of error)

Sample Mean = population mean = 0.56

The margin of Error = (critical value) × (standard deviation of the distribution of sample means)

Standard deviation of the distribution of sample means = [tex]\sqrt{[p(1-p)/n]}[/tex] =

[tex]\sqrt{[(0.56\times0.44)/1600]}[/tex] = 0.0124

The critical value for 68% confidence interval = 0.999 (from the z-tables)

The critical value for 95% confidence interval = 1.960 (also from the z-tables)

Critical values for the 99.7% confidence interval = 3.000 (also from the z-tables)

Confidence interval for 68% confidence level

= 0.56 ± (0.999 × 0.0124)

= 0.56 ± 0.0124

= (0.5476, 0.5724)

Confidence interval for 95% confidence level

= 0.56 ± (1.960 × 0.0124)

= 0.56 ± 0.0243

= (0.5357, 0.5843)

Confidence interval for 99.7% confidence level

= 0.56 ± (3.000 × 0.0124)

= 0.56 ± 0.0372

= (0.5228, 0.5972)

Therefore,

Confidence interval for 68% confidence level = (0.548, 0.572)

Confidence interval for 95% confidence level = (0.536, 0.584)

Confidence interval for 99.99% confidence level = (0.523, 0.598)

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Using the angle of elevation, the height of the tower is 9.2 ft.

He is  5 ft tall. The angle of elevation of the tower is 23 degree.

He is standing 10 feet away from the base of the tower.

The height of the tower can be found as follows;

The situation forms a right angle triangle.

The height of the tower can be found using trigonometric ratios.

Hence,

tan ∅ = opposite / adjacent

where

tan 23° = h / 10

cross multiply

h = 10 tan 23°

h = 4.2447481621

h = 4.2 ft

Therefore,

height of the tower = 4.2 + 5 = 9.2 ft

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The algebraic expression of the mentioned statement will be 5x-3.

According to the question,

An unknown number is thought of, multiplied by 5, and then subtracted by 3 from the result.

Let the unknown number be taken as x.

If we have to write the statement mathematically by taking x as a variable, the algebraic expression will be,

x* (5), which is equal to 5x, (by taking the variable x and multiplying it with 5).

For the second step, the expression will be 5x -3, (by subtracting 3 from the previous result, that is, 5x).

Hence, algebraically the final statement will be 5x -3.

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Accupunture is best these days for medication and health therapy.

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Answer:

burgers

Step-by-step explanation:

ahhhhhhhhhhhhhhhhhh

The answer is 15ab

Step-by-step explanation:

Since (x + y)² = (x + y)(x + y) = x² + 2xy + y²

(3a + 2.5b)²

9a² + 2(3a)(2.5b) + 6.25b²

9a² + 15ab + 6.25b²

Hence, (3a + 2.5b)² = 9a² + 6.25b² + 15ab

the correct answer is A

Always concentrate on point where X or G(X) equals Zero.

For example, here point (0,2), G(X)=2 when X=Zero.

If u tried to Replace X and G(X) in the equations below with these numbers, you would figure out the right answer so easily. Have a nice day!

Answer:

Step-by-step explanation:

You have to multiply both sides by 3 so its -9>-5+n. Then add each side by 5. The answer is n<-4 (D)

Answer:

D) n<-4

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

∠ A = ∠ P

∠ C = ∠ R

AC = PR

If 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle, then the triangles are congruent.

The included side is the side between the vertices of the 2 angles.

Then the triangles are congruent by the ASA postulate

The image of (5, 8) after a reflection over the line y = - x is (-5, -8 ).

To see the graph.

Given,

In the question:

What is the image of (5,8) after the reflection over the line y= -x?

Now, According to the question:

The image of (-5,8) after a reflection over the y-axis

When a point is reflected over y axis, then the value of x changes to -x.

the value of y remains the same.

But, It is given that  the reflection over the line y= -x

Hence, The image of (5, 8) after a reflection over the line y = - x is

(-5, -8 ).

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The graph that shows the x- and y-intercepts to graph the equation. y = 1/3x + 1 is added as an attachment

From the question, we have the following equation that can be used in our computation:

y = 1/3x + 1

We set x = 0 to determine the y-intercept

So, we have

y = 1/3 x 0 + 1

Evaluate

y = 1

So, we have

(x, y) = (0, 1)

We set y = 0 to determine the x-intercept

So, we have

0 = 1/3x + 1

Evaluate

1/3x = -1

This gives

x = -3

So, we have

(x, y) = (-3, 0)

So, the intercepts are (0, 1) and (-3, 0)

See attachment for the graph

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The different ways that are there for the students to be ordered in the list so that Ed is higher on the list than Ned is 19,958,400

In the order, if Ned comes first on the list then Ed will not be on the list before Ned. (remember for Ed to be higher than Ned on the list, it should come after Ned on the list).

So if Ned is first on the list, then all the remaining (including Ed) can occur anywhere in the remaining list. Hence the total permutations will be 10!

Ned's corresponding choices: 1 109 8 7 6 5 4 3 -2 1

If Ned comes in the second position, then Ed can't come in the first position. Hence in the first position, there are only 9 choices.

*(excluding Ed) Ned * corresponding choices:

= 9*9!

*(including Ed (including Ed) Ned corresponding choices: *k

= 9*8*8!

Total combinations will be:

10! + 9*9! + 9*8*8! + 9*8*7*7! + 9*8*7*6*6! + 9*8*7*6*5*5! + 9*8*7*6*5*4*4! + 9*8*7*6*5*4*3*3! +9*8*7*6*5*4*3*2*2! + 9*8*7*6*5*4*3*2*1*1! .

= 19,958,400

We can directly compute it. Since there will be a total of 11! combinations in which 11!/2 times Ed comes after Ned and 11!/2 times Ed comes before Ned.

and 11!/2 = 39,916,800/2 = 19,958,400

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If a₁ = 9 and aₙ = 4 + (aₙ - 1) in an arithmetic sequence, then the value of fifth term a₅ is equal to 25.

Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:

aₙ =  a₁ + (n - 1)d

Where:

From the information provided, we know that the common difference is equal to 4.

Substituting the given parameters into the formula, we have;

a₅ =  9 + (5 - 1)4

a₅ =  9 + 4(4)

a₅ =  9 + 16

a₅ =  25

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Complete Question:

If a₁ = 9 and aₙ = 4 + (aₙ - 1), then find the value of a₅.

The value of g(-2) is -2, f(4) is -15.5, f(1/4) is 3.25, g(2.5) is 1.375, the value of x when f(x) = 2 is 0.5 and the value of x when g(x) = 16 is (plus minus)4.

According to the question,

We have the following expressions:

f(x) = -5x+9/2

Now, we will find the all the values of f(x) by replacing x with the given digits:

f(4) = -5*4+4.5

f(4) = -20+4.5

f(4) = -15.5

The value of f(1/4):

f(1/4) = -5/4+4.5

f(1/4) = -1.25+4.5

f(1/4) = 1.375

The value of x when f(x) = 2:

-5x+4.5 = 2

-5x = 2-4.5

-5x = -2.5

x = 2.5/5

x = 0.5

g(x) = 1.5[tex]x^{2}[/tex]-8

Now, we will find all the values of g(x) by replacing x with the given digits.

The value of g(-2):

g(-2) = 1.5(-2)(-2)-8

g(-2) = 6-8

g(-2) = -2

The value of g(2.5):

g(2.5) = 1.5*2.5*2.5-8

g(2.5) = 9.375-8

g(2.5) = 1.375

The value of x when g(x) = 16:

1.5[tex]x^{2}[/tex]-8 = 16

1.5[tex]x^{2}[/tex] = 16+8

1.5[tex]x^{2}[/tex] = 24

[tex]x^{2}[/tex] = 24/1.5

[tex]x^{2}[/tex] = 16

x = +4 and -4

Hence, the value of g(-2) is -2, f(4) is -15.5, f(1/4) is 3.25, g(2.5) is 1.375, the value of x when f(x) = 2 is 0.5 and the value of x when g(x) = 16 is (plus minus)4.

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Answer:

15 minutes

Step-by-step explanation:

The 3/4 of an hour is,

→ 60 × (3/4)

→ 180/4 = 45

Now required time spend on rope is,

→ 45 × (1/3)

→ 45/3 = 15 minutes

Hence, he had spend 15 minutes.

A graph of the given system of linear equations is shown in the image attached below.

In Mathematics, a graph can be defined as a type of chart that is commonly used to graphically represent data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate.

Next, we would rewrite the first equation in standard form as follows:

y - 2x = 0

Adding 2x to both sides of the equation, we have the following:

y - 2x + 2x = 0 + 2x

y = 0 + 2x

y = 2x

By critically observing the graph (see attachment), a solution to the given system of linear equations are 2.5 and 5.

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The t-statistic for this hypothesis test will be 1.50 as "the average flight time for the pilots is found to be 8.12 hours. the standard deviation reported by the faa is 0.72 hours, and there were 81 pilots in the sample."

A statistic used in statistical hypothesis testing is known as a test statistic. A test statistic, which can be thought of as a numerical summary of a data set that condenses the data into a single value that can be used to conduct the hypothesis test, is how a hypothesis test is typically expressed. A number derived from a statistical test of a hypothesis is the test statistic. It displays how closely your actual data match the distribution predicted by the statistical test's null hypothesis.

Here,

test statistic t is,

t = (x' - μ)/(σ/√n)

x'=8.12 hours

μ=8 hours

σ=0.72 hours

n=81 pilot

t=(8.12-8)/0.72/(√81)

=0.12/0.08

t=1.5

For this hypothesis test, the t-statistic will be 1.50 as "The pilots' average flight time was found to be 8.12 hours. There were 81 pilots in the sample, and the faa reported a standard deviation of 0.72 hours."

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Step-by-step explanation:

when a line intersects parallel lines, then the intersecting angles must be the same for each of the parallel lines.

so,

y = 139

and the angles y and x are supplementary (or a linear pair). that means together they have 180°.

that is simply because the sum of all angles around a single point on one side of a line must be 180° (because the line is like the diameter of a circle with the "rotation point" being the center, and one side of the line represents the half-circle).

therefore,

y + x = 180

139 + x = 180

x = 41

Based on this if we find the 10% of the population we have:

15000000 × 0.1 = 1500000 And we see that our sample 1600 & lt;

1500000 and we satisfy the 10% condition.

For this case we have the following data given:

n = 1600 represent the sample size select.

dp = 0.43, which,  represent the estimated proportion of high school students that have a part time job

N= 15000000 represent the total population size

And we want to check if the 10% condition is satisfied. So we can use the following definitions for the 10% condition: “We need to have Bernoulli trials must be independent.

If that assumption is not satisfied, it is  still okay to proceed if we have that the sample is smaller than 10% of the population.”"One of the conditions to be checked before using the normal model for sample proportions is, “The sample size, n, must be no larger than 10% of the population.

”So based on this if we find the 10% of the population we have:

15000000 × 0.1 = 1500000

And we see that our sample 1600 & lt;

1500000 and we satisfy the 10% condition.

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Answer:

Step-by-step explanation:

all angles of a triangle add up to 180 degrees, so:

3x-40+x+60 = 180

4x = 180 - 60 + 40

4x = 160

x = 40

Check:

LS:                                    RS:

3(40)-40+40+60              180

= 180

because LS = RS,

x = 40

Hope this helps and you understand!!

24 different seatings are possible when five people are to be seated around a circular table such that two seatings are considered the same if one is a rotation of the other.

A rule used to count the entire number of alternative outcomes in a circumstance is known as the fundamental counting principle. It asserts that if there are n ways to do something and then m ways to do something else, then there are nm methods to do both of these acts. The Fundamental Principle of Counting assists in determining how selection is made based on available options. The Fundamental Principle of Counting streamlines the method to choosing by taking into account all of the available options and their combinations in order to calculate the Probability.

Here,

Since there are 5 peoples,

let us fix the first person and remaining will be set according to that.

this can be arranged in,

(5-1)!=4!

=24 ways

When five persons are sitting around a circular table, 24 distinct seatings are available, with two seatings regarded the same if one is a rotation of the other.

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As replacing a draw is an independent event, the dependent events are

B. drawing a black card and then a red card from a well-shuffled 52-cards deck.

D. Getting two heads when a coin is tossed twice.

If the outcome of one event has an impact on the outcome of another, then two events are dependent. For instance, if you draw two colored balls at random from a bag and don't replace the first ball before drawing the second, the result of the second draw will be influenced by the result of the first.

From the given options we conclude that the dependent events are

Drawing a black card and then a red card from a well-shuffled 52-cards deck.

Getting two heads when a coin is tossed twice.

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Answer:

70,000

Step-by-step explanation:

Round up if the next digit is higher than or equal to 5.

edit: accidentally answered twice

Answer:

70,000

Step-by-step explanation:

Round up if the next digit is higher than or equal to 5.

In the given equation, the value of n is (p - k - m).

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given an equation, p = n + k + m

Solving for n, we get

n = p - k - m

Hence, In the given equation, n = p - k - m

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Using the theories of probability, we got that 0.0260 is the probability  of choosing 4 spades and 2 cards that are not spades and 0.1202 is the probability of choosing 2 red face cards  from a well shuffled deck of 52 playing cards..

We know a deck of 52 playing cards has  13 hearts, 13 clubs, 13 spades,

13 diamonds.

∴  The possibility that she chooses 4 spades and 2 cards that are not spades is,

= ([tex]^1^3C_4[/tex]×[tex]^3^9C_2[/tex])/([tex]^5^2C_6[/tex])

As from the 13 spade cards 4 are chosen, so now we are left with (52 - 4) = 48

and 2 cards that are not spades means out of 9 spades that are left after choosing 4 that is 9 will also be subtracted (48 - 9) = 39.

= (13!/(13 - 4)!×4!)×(39!/(39 - 2)!×2!)/52!/(52 - 6)!×6!

= (13!/9!×4!)×(39!/37!×2!)/(52!/46!×6!)

= (13×12×11×10)/(4×3×2)×(39×38)/2)/(52×51×50×49×48×47)/(6×5×4×3×2)

= (529815)/(20358520)

= 0.026.

Similarly, the probability of choosing 2 red face card is given by

=([tex]^6C_2[/tex]×[tex]^4^6C_4[/tex])/([tex]^5^2C_6[/tex])

=[ [(6! / (2!.4!)] × [46! / (4!.42!)] ]/ [52! / (6!.46!)]

=(15×163185)/20358520

=0.1202.

Hence, the probability of choosing 4 spades and 2 cards by carrie that are not spades is 0.026 and the probability of choosing 2 red face cards by carrie is 0.1202.

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The total number of oranges in the pyramidal stack is 78.

The oranges are stacked by the grocer in a pyramid like shape,

The base of the pyramid is rectangular with a size of 5 by 8 oranges,

So, total number of oranges in the base can be found as,

= 5 x 8

= 40 oranges.

One orange has four oranges below it. So, if there are 40 oranges in the base, the upper layer will have one row of oranges reduced from each side of the rectangular base.

So, every next level will have (L-1)(B-1) oranges, where L and B are the length and breadth of every preceding rectangle.

Hence, Oranges in level 1 = 4x8

Oranges in level 2 = 3x7

Oranges in level 3 = 2x6

Oranges in level 4 = 1x5

Hence, total oranges are, (40+21+12+5) oranges.

Total oranges stacked are 78 oranges.

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Answer:333

Step-by-step explanation:

Since this is a scalene triangle, two sides will equal the same, meaning two angles will equal the same. So 70 has an equal on the other side, meaning 70+70=140, and x will equal the remainder, meaning x=40.

Hope that helps.