The entrance to an accessibility ramp is at ground level
The first section of the ramp covers a horizontal distance of 18 feet and rises to a
landing 1.5 feet above the ground
The second section of the ramp begins at the landing, it rises at a slope of t; and
covers another 9 feet of horizontal distance to reach the door
Second section
First section
Door
13 feet
ber
NOTE Sketch not drawn to scale
Answer the questions to compare the sections of the ramp
1. What is the slope of the ramp from the ground to the landing? Write your answer
as a fraction with a whole number numerator and denominator
Write your answer in the space below.

Answer:

The distance between T and S is 10 units.

Step-by-step explanation:

Given the points

[tex]\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]

The distance between T and S is:

[tex]=\sqrt{\left(2-2\right)^2+\left(6-\left(-4\right)\right)^2}[/tex]

[tex]=\sqrt{\left(2-2\right)^2+\left(6+4\right)^2}[/tex]

[tex]=\sqrt{0+10^2}[/tex]

[tex]=\sqrt{10^2}[/tex]

[tex]=10[/tex]              ∵ [tex]\mathrm{Apply\:radical\:rule\:}\sqrt[n]{a^n}=a,\:\quad \mathrm{\:assuming\:}a\ge 0[/tex]

Therefore, the distance between T and S is 10 units.

Answer:

16

Step-by-step explanation:

I am doing Prepworks Basic triangles as well :D

Answer:

15 yards.

Step-by-step explanation:

This is because there are 3 feet in one yard, and 5x3= 15.

Answer:

1.66667

Step-by-step explanation:

Answer:

x = 12

Step-by-step explanation:

Answer:

Step-by-step explanation:

The given equation is:

f(x) = 3 - 48x + 4x²      [5,7]

where; f(x) is continous and derivable in [5,7]

f'(x) = -48x + 8x

f(5) = 3 - 48(5) + 4(5)² = -137

f(7) = 3 - 48(7) + 4(7)² = -137

Thus, it satisfies the hypotheses of Rolle's Theorem

f'(x) = f'(c) = 0

-48 + 8c = 0

c =48/8

c = 6

Answer:

95% Confidence Interval = (0.037, 0.104)

Step-by-step explanation:

The formula for Confidence Interval if a proportion is:

p ± z × √p(1 - p)/n

z = z score of a 95% confidence interval = 1.96

p = proportion = x/n

x = 16, n = 227

p = 16/227

p = 0.0704845815

≈ 0.0705

Confidence Interval

= 0.0705 ± 1.96 × √0.0705(1 - 0.0705)/227

= 0.0705 ± 1.96 × √0.0002886773

= 0.0705 ± 0.0333013921

Confidence Interval

= 0.0705 - 0.0333013921

= 0.0371986079

≈ 0.037

= 0.0705 + 0.0333013921

= 0.1038013921

≈ 0.104

Hence, 95% Confidence Interval = (0.037, 0.104)

Answer:

There are 5 sales per minute!

Step-by-step explanation:

A unit rate is a ratio between two different units with a denominator of 1. To calculate the unit rate, divide the numerator by the denominator. The resulting decimal number is the unit rate. Basically 5 is the unit rate! 5/1 is 5!

Answer:

B: A

He earns $90 in 3 weeks.

C

He shelves 90 books in 3 hours.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

The probability is  [tex]P( p < 435.82 ) = 0.54094[/tex]

Step-by-step explanation:

From the question we are told that

   The population proportion is  p =  54% = 0.54

    The sample size is  n  =  808

Generally the distribution of the population with college degree follows a binomial distribution  

i.e  

         [tex]X  \~ \ \ \  B(n , p)[/tex]

Generally the mean is mathematically represented as

       [tex]\mu = n * p[/tex]

=>    [tex]\mu = 808 * 0.52[/tex]

=>    [tex]\mu = 420.16[/tex]

Generally the standard deviation is mathematically represented as

        [tex]\sigma = \sqrt{np(1- p )}[/tex]

=>      [tex]\sigma = \sqrt{808 * 0.52(1- 0.52 )}[/tex]    

=>      [tex]\sigma = 14.2[/tex]

Generally 54% of the population proportion is

         [tex]\^ p = 0.54 * 808[/tex]

=>     [tex]\^ p = 436.32[/tex]

Generally by normal approximation of the binomial distribution the probability that the proportion of persons with a college degree will be less than 54% is mathematically evaluated as

      [tex]P(p < \^ p ) = P(\frac{p - \mu }{\sigma } < \frac{\^ p - \mu }{\sigma } )[/tex]

[tex]\frac{X -\mu}{\sigma }  =  Z (The  \ standardized \  value\  of  \ X )[/tex]

=>  [tex]P(p < 436.32 ) = P( Z < \frac{436.32 - 420.16 }{14.20 } )[/tex]

applying continuity correction

      [tex]P(p < (436.32-0.5) ) = P( Z < \frac{(436.32-0.5) - 420.16 }{14.20 } )[/tex]

=>  [tex]P(p < (435.82 ) = P( Z < \frac{435.82 - 420.16 }{14.20 } )[/tex]

=>  [tex]P(p < (435.82 ) = P( Z < 0.1028 )[/tex]

From the z table  the area under the normal curve to the left corresponding to 0.1028  is

   [tex]P( Z < 0.1028 ) = 0.54094[/tex]

=> [tex]P( p < 435.82 ) = 0.54094[/tex]

Answer

n= 0

Explanation

- 3 (n - 3) = 3n + 9−3(−3)=3+9

−3+9=3+9

−3=3

-3n=3n−3n=3n

−3−3=3−3

−6=0

Answer:

3

Step-by-step explanation:

(x₁ , y₁) = (-1 , -2)   &    (x₂ , y₂) = (3 , 10)

[tex]Slope =\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

         [tex]= \frac{10-[-2]}{3-[-1]}\\\\=\frac{10+2}{3+1}\\\\=\frac{12}{4}\\\\=4[/tex]

m  = 4

y - y₁ = m (x - x₁)

y - [-2] = 4(x - [-1])

y + 2 = 4(x + 1)

y + 2 = 4x + 4

    y = 4x + 4 - 2

    y = 4x + 2

Answer:

The answer is yes, since the graph is an equal line throughout.

Step-by-step explanation:

Answer:

He has been saving for 41 weeks.

Step-by-step explanation:

492 is the total, we need to divide 492 by 12 to get how many weeks, 41 is the answer

9514 1404 393

Explanation:

The decimal equivalent of a fraction will terminate if its denominator can be factored using only the prime numbers 2 and/or 5.

1/4 = 1/(2·2) will terminate

1/15 = 1/(3·5) will not terminate

Answer:

The sum of two numbers is 78. If four times the smaller number is subtracted from the larger number, the result is 13. What are the two numbers?

Step-by-step explanation:

EQUATION:

x+ y = 78

x-4y = 13

-------------

solve by any method to get:

x = 65

y = 13

Answer:haha no

Step-by-step explanation:

Answer:

The probability that the sample mean will be between 25.5 and 27 years is 0.1359.

Step-by-step explanation:

Let X denote of age of JSOM students.

The information provided is:

[tex]\mu=24\\\sigma=9\\n=36[/tex]

According to the Central Limit Theorem if an unknown population is selected with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from this population with replacement, then the distribution of the sample means will be approximately normally.  

Then, the mean of the sample means is given by,

[tex]\mu_{\bar x}=\mu\\[/tex]

And the standard deviation of the sample means is given by,

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

As the sample size is large, i.e. n = 36 > 30, the sampling distribution of the average age of all the JSOM students can be approximated by the normal distribution.

Compute the probability that the sample mean will be between 25.5 and 27 years as follows:

[tex]P(25.5<\bar X<27)=P(\frac{25.5-24}{9/\sqrt{36}}<\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{27-24}{9/\sqrt{36}})\\\\=P(1<Z<2)\\\\=P(Z<2)-P(Z<1)\\\\=0.97725-0.84134\\\\=0.13591\\\\\approx 0.1359[/tex]

Thus, the probability that the sample mean will be between 25.5 and 27 years is 0.1359.

Answer:

A.

Step-by-step explanation:

We have the expression:

[tex]-6a+2(2a+2)[/tex]

First, let’s distribute the 2 on the right:

[tex]=-6a+2(2a)+2(2)[/tex]

Multiply:

[tex]=-6a+4a+4[/tex]

Now, combine like terms:

[tex]=-2a+4[/tex]

Hence, our answer is A.

Answer:

a

Step-by-step explanation:

Answer:

7m

Step-by-step explanation:

In an equilateral triangle all the sides and angles are the same

Answer:

h = 9.99in

Step-by-step explanation:

...

Step-by-step explanation:

Total no. of students = 40

Total no. of girls = 22

Total no. of boys = 40 - 22 = 18

No. of girls walking to school = 9

No. of girls who cycle to school = 22 - 9

No. of boys who cycle to school = 7

No. of students who take the bus = 10

(6 boys and 4 girls)

No. of boys who walk to school = 18 - (7 + 6) = 5

Total no. of students who walk to school = 9 + 5 = 14

The number of students who walked to school was 14 students

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

The equations will be ,

Let the total number of students in the class be A = 40 students

The number of girls in the class = 22 students

The number of boys in class = total number of students - number of girls

                                                = 40 - 22

                                                = 18 students

Now ,

The number of girls who walked to school = 9 students

The number of boys who cycled to school = 7

So , remaining boys = 18 - 7

                                 = 11 students

The number of boys who take bus to school = 6 students

So , remaining boys = 11 - 6

                                 = 5 students

Therefore , the remaining boys in the class walks to school = 5 students

So , the equation will be

And , the total number of students who walked to school =
number of boys in the class that walks to school + number of girls who walked to school

Total number of students who walked to school = 9 + 5

                                                                                = 14 students

Hence , The number of students who walked to school was 14 students

To learn more about equations click :

https://brainly.com/question/10413253

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Answer:

8.35

Step-by-step explanation:

To get absolute value, just make it the opposite

Answer: |-8.35| = 8.35

Step-by-step explanation: |-8.35| = 8.35

Answer:

The distance 'd' between T and S:

Step-by-step explanation:

As the point 'T' is located at (2, -4)

And the point 'S' is located at (2, 6)

The distance 'd' between T and S can be computed using the formula:

[tex]d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]

[tex]=\sqrt{\left(2-2\right)^2+\left(6-\left(-4\right)\right)^2}[/tex]

[tex]=\sqrt{\left(2-2\right)^2+\left(6+4\right)^2}[/tex]

[tex]=\sqrt{0+10^2}[/tex]

[tex]=\sqrt{10^2}[/tex]

[tex]d=10[/tex]

Therefore, the distance 'd' between T and S:

Answer:

t and s

Step-by-step explanation:

Answer:

because ΔMLN ≅ ΔYZX

=> MN = YX = 4

Step-by-step explanation:

Answer:

I think its four

Step-by-step explanation:

Answer:

The first thing you do is make the denominators equal on both sides.

Step-by-step explanation:

As a example if you have the equation:

[tex]\frac{1}{2}[/tex] + [tex]\frac{2}{5}[/tex] =

you would multiply the denominator by the smallest multiple. I would do 2 * 5= 10

this would make the equation

[tex]\frac{x}{10} + \frac{x}{10} = ...[/tex]

next you have to do the same with the numerator.

so sence you multiplied the [tex]\frac{1}{2}[/tex] by five you will get [tex]\frac{5}{10}[/tex]

same with the other fraction except you multiplied it by two.[tex]\frac{2}{5}[/tex] x 2 = [tex]\frac{4}{10}[/tex]

next you add and simplify if needed

Answer:

3 simple steps

Step-by-step explanation:

1.     Make sure the bottom numbers ( the denominators ) are the same

       IF DIFFERENT find the LCD

2.    Add the top numbers (the numerators )

3.    simplify the fraction if needed

ex:  1/4 +1/4 = 2/4  (bottoms were the same) simplify  1/2

       1/3 + 1/6    LCD of 3 and 6 so make the bottom numbers 6

                         so multiply  1/3 x  2 = 2/6

        now you have 2/6 + 1/6 = 3/6    simplify 1/2

Answer: Point D

Step-by-step explanation: Point D is at 3 and 3/4.

I think the answer is point D

Answer:

36:81

Step-by-step explanation:

4 to 36 is times 9, so you have to multiply 9 by 9 to complete the ratio which is how you get 81.

Answer:

F(-3) = -7

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

F(x) = 4x + 5

F(-3) is x = -3

Step 2: Evaluate