The opening of the tunnel can be modeled by the graph of the equation y=-0.18x^2+4.4x-12 where x and y are measured in feet. Find the maximum height of the tunnel.

Answer:

17.92

Step-by-step explanation:

I took the test and had the same question, plus the screenshot above

The Mean Absolute Deviation is 17.92.

The average distance between each data value and the mean is known as the mean absolute deviation (MAD) of a data set. A measure of variance in a data set is the mean absolute deviation.

Take the absolute value of each digit in the data set, then deduct the mean. Next, add up the absolute values. The mean absolute deviation is then calculated by dividing the aforementioned sum by the total number of values in the data set.

Given:

Data set: {20, 24, 12, 44, 68}

Mean of the data = (20+ 24+ 12+ 44+ 68)/ 5 = 168/5

                             = 33.6

Mean Absolute Deviation

= {| 20- 33.6| + |24- 33.6| + |12-33.6| + | 44-33.6| + |68-33.36|} / 5

= (13.6+ 9.6 + 21.6+ 10.4 + 34.4 )/ 5

= 89.6/ 5

= 17.92

Hence, the Mean Absolute Deviation is 17.92.

Learn more about Mean Absolute Deviation here:

https://brainly.com/question/10528201

#SPJ5

Answer

increased by 30% from last year. There are 195 people in the club now.

How many people were in the club last year

Step-by-step explanation:

1.3n = 195

n=195÷1.3

n=150 people where in the club last year.

Answer:

c the last one

Step-by-step explanation:

The side length to create a regular hexagonal plate is 3.6 cm. Using the GeoGebra graph to create the sketch where 1 unit = 0.1cm.

The side length of a regular hexagon.

The side length of a regular hexagon can be calculated by using the formula:

[tex]Area=\dfrac{3\sqrt{3}}{2}\times S^2[/tex]

[tex]S=\sqrt{\dfrac{2 \times Area }{3\sqrt{3}}[/tex]

Given that the area is 33 cm²

[tex]S=\sqrt{\dfrac{2 \times 33 }{3\sqrt{3}}[/tex]

Side length (S) = 3. 56 cm

Therefore, the side length to create a regular hexagonal plate is 3.6 cm. See below for the sketch of the hexagon where 1/2 unit = 0.1cm.

If a Play Station was bought for $450 after a 10% discount. Therefore, The original price of the Play Station was $500.

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Thus, that thing in number is

[tex]\dfrac{a}{100} \times b[/tex]

It is given that If it was bought after a 10% discount, means it was bought at 90% of the original price:

90% = $450

1% = $5

100% = $5 x 100

100% = $500

Therefore, The original price of the Play Station was $500.

Learn more about percent here:

https://brainly.com/question/11549320

#SPJ2

Total Number of sheets of construction paper= 25

The Percent of the sheets of construction paper that are secondary color = 40%

Percent means out of 100.To find number of secondary color sheet we find 40% of 25.

40%=[tex] \frac{40}{100} [/tex]

Number of sheets which are of secondary color=[tex] \frac{40}{100} of 25 =\frac{1000}{100} =10 [/tex]

Number of secondary color sheets =10.

Answer:

l = 11 meters

Step-by-step explanation:

Surface area = s² + 2s*l

Where "l" is the slant height

Given: Surface area = 279 ; side length s = 9

Now plug in these values in the above formula, we get

279 = 9^2 + 2*9*l

279 = 81 + 18*l

18l = 279 - 81

18l = 198

Dividing both sides by 18, we get

l = 198/18

l = 11 meters

Therefore, slant height of the square pyramid = 11 meters

Hope this will helpful.

Thank you.

The length of a 45 degree arc on a circle with a radius of 1 foot is π/4 feet.

The length of a 45 degree arc can be calculated using the formula for the circumference of a circle. The formula for the circumference is given by C = 2πr, where r is the radius of the circle. In this case, the radius is given as 1 foot. So, we can plug in the values to calculate the circumference as C = 2π(1) = 2π feet.

To find the length of a 45 degree arc, we need to find the fraction of the circumference that corresponds to a 45 degree angle. Since a full circle is 360 degrees, a 45 degree angle is 45/360 = 1/8 of the circumference. Therefore, the length of a 45 degree arc is 1/8 of the circumference, which is (1/8)(2π) feet.

Simplifying this expression, we get the length of a 45 degree arc as (1/8)(2π) = π/4 feet.

Answer:

This situation models exponential decay because the substance decays with time.

The radioactive substance decays at the rate of :  25%

 r=25/100 =0.25

The initial amount of substance is 64  grams. So, . A=64

Step-by-step explanation:

Answer:

The interest earned at the end of 4 years is B) $300.

Step-by-step explanation:

Isaac deposits $1500 in a savings account.

Principle (P) = $1500

Rate of interest (r) = 5% = [tex]\frac{5}{100} = 0.05[/tex]

Time (t) = 4 years

We know that the simple interest formula (i) = P.r.t

Now plug in the given values in the above formula, we get

= 1500 times 0.05 times 4

= 75 times 4

Simple interest = $300

So, the interest earned at the end of 4 years is $300.

Answer is B) $300

Answer:

[tex]y=3x+12[/tex]

Step-by-step explanation:

We have been given an equation in standard form [tex]-3x+y=12[/tex]. We are asked to write our given equation as a function.

We know that the function represents a relationship between input and output, where each input gives exactly single output.  

To write our given equation as a function we need to convert our given equation into slope-intercept form of equation because in slope-intercept form, there is exactly one y output for each input of x.

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

m = Slope,

b = The y-intercept.

To convert our given equation into slope-intercept form, we need to get y on left side of our equation.

[tex]-3x+3x+y=3x+12[/tex]

[tex]y=3x+12[/tex]

Now our equation is in form of a function, where each value of x gives exactly one y value.

Final answer:

The horizontal asymptotes of the function y = (4e^x+7)/(e^x-1) are y = 4 and y = -7, occurring as x approaches positive and negative infinity respectively.

Explanation:

The equations of the horizontal asymptotes of the given function y = (4e^x+7)/(e^x-1) can be found by analyzing the behavior of the function as x approaches positive or negative infinity. In this function, as x approaches infinity, e^x grows much faster than any constant, so the constants can be considered negligible. Thus, the behavior of the numerator and denominator is dominated by the terms involving e^x. As x tends towards infinity, the function approaches the ratio of the coefficients of e^x, which is 4/1, meaning the horizontal asymptote is y = 4. As x tends towards negative infinity, e^x approaches zero, and the function approaches 7/(-1), so there is also an asymptote at y = -7.

It is given that there is a vertical asymptote at x = -1, where the denominator becomes zero and hence "blows up".

We have been given an diagram and we are asked to find the congruence theorem that can be used to prove △LON ≅ △LMN.

We can see from our diagram that side LO of △LON equals to side LM of △LMN. We can also see that side ON △LON of equals to side MN of △LMN. Side LN equals to itself.

We can see that three sides of triangle LON are congruent to three sides of triangle LMN. Therefore, by SSS (Side-Side-Side) congruence △LON ≅ △LMN.

Which certificate is the lowest level certification that a personal finance manager requires to sell mutual funds, trusts, and variable annuities?

The answer is series 6 certificate.

The series 6 certificate helps an individual to purchase or sell mutual funds, variable life insurance, municipal fund securities, variable annuities and unit investment trusts.

Answer:

The answer is option B - series 6 certificate.

Step-by-step explanation:

Answer:

B. The horse-drawn carriage tour company can expect to take in $5760 when the charge per customer is $60.

Step-by-step explanation:

We have,

The function representing the price charged by the customers is [tex]c(x)=50+5x[/tex].

The function representing the number of customers is [tex]p(x)=100-2x[/tex].

Then, the product of the functions is given by,

[tex](p\times c)(x)=p(x)\times c(x)\\\\(p\times c)(x)=(100-2x)(50+5x)\\\\(p\times c)(x)=-10x^2+400x+5000[/tex]

Substituting x = 2 in the above product gives,

[tex](p\times c)(2)=-10\times 2^2+400\times 2+5000\\\\(p\times c)(2)=-40+800+5000\\\\(p\times c)(2)=\$ 5760[/tex]

Also, the charge per customer when x = 2 is,

[tex]c(x)=50+5x\\\\c(x)=50+5\times 2\\\\c(x)=50+10\\\\c(x)=\$ 60[/tex]

Hence, the product (p-c)(2) represents,

B. The horse-drawn carriage tour company can expect to take in $5760 when the charge per customer is $60.

Answer:

B. $16,778.00.

Step-by-step explanation:

Answer:

35%

Step-by-step explanation: