A professor divided the students in her business class into three groups: those who have never taken a statistics class, those who have taken only one semester of a statistics class, and those who have taken two or more semesters of statistics. The professor randomly assigns students to groups of three to work on a project for the course. Find the requested probability. If 55% of the students have never taken a statistics class, 25% have taken only one semester of a statistics class, and the rest have taken two or more semesters of statistics, what is the probability that the first groupmate you meet has studied some statistics

Answers

Answer 1

Answer:

the probability that the first groupmate you meet has studied some statistics is 0.45

Step-by-step explanation:

From the information given :

A professor divided the students in her business class into three groups

Let consider then to be :

Group            Statistics Class

A                    Never taken a statistics class

B                    Taken one statistics class

C                     Taken two or more statistics class.

If 55% of the students have never taken a statistics class,

Then ;

P(A) = 0.55

25% have taken only one semester of a statistics class

Then P(B) = 0.25

and the rest have taken two or more semesters of statistics

Then P(C) = 1 - 0.55 -0.25

P(C) = 1 - 0.80

P(C) = 0.20

The objective is to determine the probability that the first groupmate you meet has studied some statistics

The probability of the first groupmate you meet has studied some statistics = 1 - P(never taken a statistics course)

Let the  probability of the first groupmate you meet that  has studied some statistics be P(D)

Then P(D) = 1 -  P(A)

P(D) = 1 - 0.55

P(D) = 0.45

the probability that the first groupmate you meet has studied some statistics is 0.45


Related Questions

will mark brainliest!!!plz helppp

Answers

Answer:

(5,-6)

Step-by-step explanation:

ONE WAY:

If [tex]f(x)=x^2-6x+3[/tex], then [tex]f(x-2)=(x-2)^2-6(x-2)+3[/tex].

Let's simplify that.

Distribute with [tex]-6(x-2)[/tex]:

[tex]f(x-2)=(x-2)^2-6x+12+3[/tex]

Combine the end like terms [tex]12+3[/tex]:

[tex]f(x-2)=(x-2)^2-6x+15[/tex]

Use [tex](x-b)^2=x^2-2bx+b^2[/tex] identity for [tex](x-2)^2[/tex]:

[tex]f(x-2)=x^2-4x+4-6x+15[/tex]

Combine like terms [tex]-4x-6x[/tex] and [tex]4+15[/tex]:

[tex]f(x-2)=x^2-10x+19[/tex]

We are given [tex]g(x)=f(x-2)[/tex].

So we have that [tex]g(x)=x^2-10x+19[/tex].

The vertex happens at [tex]x=\frac{-b}{2a}[/tex].

Compare [tex]x^2-10x+19[/tex] to [tex]ax^2+bx+c[/tex] to determine [tex]a,b,\text{ and } c[/tex].

[tex]a=1[/tex]

[tex]b=-10[/tex]

[tex]c=19[/tex]

Let's plug it in.

[tex]\frac{-b}{2a}[/tex]

[tex]\frac{-(-10)}{2(1)}[/tex]

[tex]\frac{10}{2}[/tex]

[tex]5[/tex]

So the [tex]x-[/tex] coordinate is 5.

Let's find the corresponding [tex]y-[/tex] coordinate by evaluating our expression named [tex]g[/tex] at [tex]x=5[/tex]:

[tex]5^2-10(5)+19[/tex]

[tex]25-50+19[/tex]

[tex]-25+19[/tex]

[tex]-6[/tex]

So the ordered pair of the vertex is (5,-6).

ANOTHER WAY:

The vertex form of a quadratic is [tex]a(x-h)^2+k[/tex] where the vertex is [tex](h,k)[/tex].

Let's put [tex]f[/tex] into this form.

We are given [tex]f(x)=x^2-6x+3[/tex].

We will need to complete the square.

I like to use the identity [tex]x^2+kx+(\frac{k}{2})^2=(x+\frac{k}{2})^2[/tex].

So If you add something in, you will have to take it out (and vice versa).

[tex]x^2-6x+3[/tex]

[tex]x^2-6x+(\frac{6}{2})^2+3-(\frac{6}{2})^2[/tex]

[tex](x+\frac{-6}{2})^2+3-3^2[/tex]

[tex](x+-3)^2+3-9[/tex]

[tex](x-3)^2+-6[/tex]

So we have in vertex form [tex]f[/tex] is:

[tex]f(x)=(x-3)^2+-6[/tex].

The vertex is (3,-6).

So if we are dealing with the function [tex]g(x)=f(x-2)[/tex].

This means we are going to move the vertex of [tex]f[/tex] right 2 units to figure out the vertex of [tex]g[/tex] which puts us at (3+2,-6)=(5,-6).

The [tex]y-[/tex] coordinate was not effected here because we were only moving horizontally not up/down.

Help plz down below with the question

Answers

Answer:

The SAS Postulate

Step-by-step explanation:

SAS means Side-Angle-Side; that is, two sides are equal and an angle between those sides are equal. We're given two sides: TK and TL, and we're given that 1 is congruent to 2. Knowing the latter, we can conclude that the angle between them (let's call it 1.5 for our purposes) will be congruent to itself. Since 1.5 is the angle right in the middle of two congruent sides, our answer is SAS.

Opal is collecting data on water levels in different parts of town. She notices that her sample data has a low-value outlier. Which statement must be true?

A. Removing the outlier will not change the spread of the graph of the data set.
B. Removing the outlier will not change the variance of the data set.
C. Removing the outlier will increase the variance of the data set.
D. Removing the outlier will decrease the spread of the graph of the data set.

Answers

Answer:

D.

Step-by-step explanation:

if you remove the low value outlier, the variation from the mean will decrease therefore decreasing the varianc.

Answer:

D. Removing the outlier will decrease the spread of the graph of the data set.

Step-by-step explanation:

Outliers increase the spread of the data set.

So removing an outlier will generally decrease the spread or variance or standard deviation of a data set.

The answer is

D. Removing the outlier will decrease the spread of the graph of the data set.

pls help me I will give BRANLIEST!!!and follow you back (ー_ー゛)its due in 5minutes​

Answers

Answer:

$186.89

Step-by-step explanation:

Let's start by finding the area of the floor.

Area of a trapezium can be found with the formula:

A=(a+b)/2*h

Let's plug our values in.

A=(10+16)/2*7.6

Simplify.

A=26/2*7.6

A=13*7.6

A=98.8

The area of the floor is 98.8 square meters.

Find how many litres of paint are needed.

98.8/1.9=52

He needs 52 liters of paint.

52/5=10.4

He needs 11 5 liter cans of paint.

Each one costs %16.99.

16.99*11=186.89

It would cost $186.89 to buy all the paint he needs.

The system of equations y = negative one-half x + 4 and y = 2x – 1 is shown on the graph below. According to the graph, what is the solution to this system of equations? (2, 3) (3, 2) (–1, 4) (4, –1)

Answers

Answer:

(2, 3 )

Step-by-step explanation:

The solution to a system of equations given graphically is at the point of intersection of the 2 lines.

point of intersection = (2, 3 ) ← is the solution

NEED HELP ASAP WILL AWARD BRAINLIEST!!!!!

Answers

Answer: 69

Step-by-step explanation:

Clarise evaluated this expression.

(66.3 – 14.62) ÷ 0.6 – 0.22

(51.68) ÷ 0.6 – 0.22

(51.68) ÷ 0.42

51.68 ÷ 0.16

32.3

Which errors did Clarise make?

Answers

Answer:

(66.3-14.62)/0.6-0.22

(51.68)/0.6-0.22

(51.68/0.6)-0.22

(86.14667)-0.22

85.92667

What is the coefficient of b in the expression b² - 5b +18

Answers

Answer: -5

Step-by-step explanation:

A coefficient is a number that a variable is multiplied by.

Hope it helps <3

Answer:

well technically, there are two coefficients

the coefficient of (b^2) is 1 and the coefficient of b (itself) is -5.

But if you sre just looking for the coefficient ot just plain b, it is -5

Step-by-step explanation:

the reason I say the coefficient to (b^2) is 1 because if there is no number in front of the variable, it is automatcally assumed to be 1.

now, as for just plain b, it is -5 because the sign, positive or negative, before a number coefficient gets attached to that number.  so, the entire term is -5b, which makes the coefficient to just plain b to be -5

Help please!!!!!! Thank you

Answers

Answer:

1/4

Step-by-step explanation:

Well see how far each points are from each other.

Start at the red triangle and go up 1, go to the right 4.

Thus,

the rise/run is 1/4.

Hope this helps :)

Answer:

1/4

Step-by-step explanation:

To find the rise/run, you first need to pick two points from the line.  You can pick whichever points you want, and you will get the right answer.  I will pick (-8, -3) and (8, 1).

Divide the difference of the y's by the difference of the x's.

-3 - 1 = -4

-8 - 8 = -16

-4/-16 = 1/4

The rise/run is 1/4.

​Claim: Most adults would erase all of their personal information online if they could. A software firm survey of randomly selected 583 adults showed that 58 ​% of them would erase all of their personal information online if they could. Find the value of the test statistic.

Answers

Answer:

Test statistic = 3.863

Step-by-step explanation:

We are told that most adults would erase all of their personal information online if they could. Since the word "most" is used, it means more than 50% or 50 percent.

So, p_o = 0.5

Also, we are told that 58 % of them would erase all of their personal information online if they could.

Thus, p^ = 0.58

Number of randomly selected adults; n = 583

The test statistic formula for hypothesis test for proportion is given by:

z = (p^ - p_o)/[√[p_o(1 - p_o)/n]

Plugging in the relevant values, we have;

z = (0.58 - 0.5)/[√[0.5(1 - 0.5)/583]

z = 0.08/0.02070788416

z = 3.863

Sphere A has a diameter of 6 and is dilated by a scale factor of 2 to create sphere B. What is the ratio of the volume of sphere A to sphere B?

Answers

Answer:

8 : 1

Step-by-step explanation:

From the above question, we are given the following parameters

Sphere A has a diameter of 6 and is dilated by a scale factor of 2 to create sphere B.

Volume of a sphere = 4/3πr³

For Sphere A , diameter = 6

Radius = Diameter ÷ 2 = 6÷ 2 = 3

Volume of Sphere A = 4/3 × π × 3³

= 113.09733553 cubic units

Approximately = 113.1 cubic units

We were given a scale factor (k) of 2

Because we are dealing with volume, the scale factor will be cubed

In order to find the Volume of the sphere B

k³ = Volume of Sphere A/ Volume of Sphere B

2³ = 113.1 / Volume of Sphere B

Volume of Sphere B = 113.1/ 2³

= 14.1375 cubic units.

The ration of the Volume of Sphere A to Sphere B

Sphere A: Sphere B

113.1 : 14.14

= 8: 1

Answer:

1:8

Step-by-step explanation:

Took the test and got it right trust

Write the equation of a function whose parent function, f(x) = x + 8, is shifted 2 units to the right.

Answers

y=f(x-2)+8

This has to do with function transformations. First we can set it up differently, where we are solving for y instead of f(x)
y=f(x)+8
The points of the graph are (x, f(x)+8)
To move the graph to the right, we need to subtract by 2 within the parentheses
y=f(x-2)+8
Now the point would be like (x, f(x-2)+8)

Answer:

[tex]\huge\boxed{f(x - 2) = x + 6}[/tex]

Step-by-step explanation:

f(x) + n - shift the graph n units up

f(x) - n - shift the graph n units down

f(x + n) - shift the graph n units to the left

f(x - n) - shift the graph n units to the right

===========================================

f(x) = x + 8

shift the graph 2 units to the right

f(x - 2) = (x - 2) + 8 = x - 2 + 8 = x + 6

Lydia runs an experiment to determine if a coin is fair by counting the number of times a coin lands heads up. The table shows her data. A 2-row table with 10 columns. The first row is labeled number of coin flips with entries 0, 10, 20, 30 ,40, 50, 60, 70, 80, 90. The second row is labeled number of heads up with entries 0, 7, 12, 18, 23, 30, 35, 38, 42, 45. According to the line of best fit, about how many times would the coin land heads up in 100 flips? 48 50 51 53

Answers

Answer:

b is the right option

Step-by-step explanation:

According to the line of best fit, the coin would land heads up about 52.73 times in 100 flips, which we can round to 53.

What is probability?

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

We can use linear regression to find the line of best fit for the given data, which will give us a linear equation that models the relationship between the number of coin flips and the number of times the coin lands heads up.

Using a calculator or statistical software, we can find that the line of best fit for the given data is:

y = 0.4975x + 2.9825

where y is the number of times the coin lands heads up, and x is the number of coin flips.

To find how many times the coin would land heads up in 100 flips, we can substitute x = 100 into the equation and solve for y:

y = 0.4975(100) + 2.9825

y = 49.75 + 2.9825

y ≈ 52.73

Therefore,

According to the line of best fit, the coin would land heads up about 52.73 times in 100 flips, which we can round to 53.

Learn more about probability here:

https://brainly.com/question/14099682

#SPJ7

Evaluate ƒ(x) = –x2 + 1 for x = –3. a) 4 b) –4 C) –9 D) –8

Answers

[tex]f(x)=-x^2+1[/tex]

Plug in the value [tex]x=-3[/tex] into this function

[tex]f(-3)=-(-3)^2+1[/tex]

[tex]=-(9)+1[/tex]

[tex]=-8[/tex]

Thus, your answer will be D) -8. Let me know if you need any clarifications, thanks!

Answer:

D. -8

Step-by-step explanation:

We are given

f(x)= -x^2+1

and asked to evaluate f(x) for x= -3. Therefore, we must substitute -3 for x in the function.

f(x)= -x^2+1 for x= -3

f(-3)= -(-3^2)+1

Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

First, evaluate the exponent: -3^2

-3^2= -3*-3= 9

f(-3)= -(9)+1

f(-3)=-9+1

Next, add -9 and 1

f(-3)= -8

When f(x)= -x^2+1 is evaluated for x= -3, the result is -8. Therefore, the correct answer is D. -8

find the angle vector (9,7) makes with the x axis​

Answers

Answer:

≈ 37.9°

Step-by-step explanation:

Using the tangent ratio

tanΘ = [tex]\frac{y}{x}[/tex]  where (x, y ) = (9, 7 )

tanΘ = [tex]\frac{7}{9}[/tex] , thus

Θ = [tex]tan^{-1}[/tex] ([tex]\frac{7}{9}[/tex] ) ≈ 37.9° ( to the nearest tenth )

please help :) Which of these numbers is the greatest? A. 1.9 x 10 to the 5 power B. 9.1 x 10 to the 2 power C. 7.9 x 10 to the 4 power D. 89,900

Answers

C. 7.9 x 10 to the 4th power.

Answer: The answer is A.

Step-by-step explanation:

1.9x10^5= 190000

9.1x10^2= 910

7.9x10^4 =79000

The amount that two groups of students spent on snacks in one day is shown in the dot plots below. Which statements about the measures of center are true? Select three choices. The mean for Group A is less than the mean for Group B. The median for Group A is less than the median for Group B. The mode for Group A is less than the mode for Group B. The median for Group A is 2. The median for Group B is 3.

Answers

Answer:

The mean for Group A is less than the mean for Group B. The median for Group A is less than the median for Group B.The mode for Group A is less than the mode for Group B.

Step-by-step explanation:

First, we can find the measures of center for each group.

Group A

Mode: 1

Median: (1 + 2) / 2 = 3 / 2 = 1.5

Mean: (1 * 5 + 2 * 4 + 3) / 10 = (5 + 8 + 3) / 10 = 16 / 10 = 1.6

Group B

Mode: 3

Median: 92 + 3) / 2 = 5 / 2 = 2.5

Mean: (1 * 3 + 2 * 2 + 3 * 4 + 5) / 10 = (3 + 4 + 12 + 5) / 10 = 24 / 10 = 2.4

From here, we can see that...

The mean for Group A is less than the mean for Group B. The median for Group A is less than the median for Group B.The mode for Group A is less than the mode for Group B.

Hope this helps!

Answer:

ABC

Step-by-step explanation:

The area of circle Z is 64 ft^2.
What is the value of r?
Or= 4 ft
O r= 8 ft
O r= 16 ft
O = 32 ft

Answers

Answer:

The answer is

r =4 ft

Step-by-step explanation:

Area of a circle is given by πr²

Where r is the radius

From the question

Area = 64 ft²

So the radius is

64 = πr²

Divide both sides by π

[tex] {r}^{2} = \frac{64}{\pi} [/tex]

Find the square root of both sides

[tex]r = \sqrt{ \frac{64}{\pi} } [/tex]

r = 4 ft

Hope this helps you

Answer: 8

The answer is 8 not 4.5 or 4!!!!!!!!

Step-by-step explanation: It's not just "64" its 64pi. when you posted the question your device could not put the pi symbol so people were thinking that it was just 64.

Determine whether the function shown in the graph is even or odd. The graph starts at the top left, continues down through the x axis at negative two to a minimum around y equals negative five, goes up to a maximum on the x axis at y equals negative one, goes back down to a minimum around y equals negative five, and goes back up through the x axis at two.

Answers

Answer:

Might be D

Step-by-step explanation:

took the test and that was the other one i was thinking

Answer: D: The function is odd because it is symmetric with respect to the origin.

Step-by-step explanation:

The summer has ended and it’s time to drain the swimming pool. 20 minutes after pulling the plug, there is still 45 000L of water in the pool. The pool is empty after 70 minutes. Calculate how much water was in the pool initially

Answers

Answer:

900L per minute

Step-by-step explanation:

1- 70 - 20 = 50

2- in this 50 min the 45000L was drowned

3- 45000L / 50 = 900L

.. ..

Which of the following is an arithmetic sequence?

Answers

Answer:

B: 3,0,-3,-6

Step-by-step explanation:

An arithmetic sequence has constant adding or subtracting. In this case, 3 is being subtracted as a constant.

please i need this answer in two minutes

1. Sarah serves at a restaurant and makes 20% of what she sells as tips. Her base salary is $10.20 an hour. Each hour she sells an average of $60 of food and drinks. She also makes time and a half when she works over 8 hours during a single shift. Her work week contains three 10-hour shifts, one 5-hour shift, and one 11-hour shift. Using the same income deductions as stated in the previous question, what is Sarah’s annual gross income and annual net income.

Answers

Answer: $55,489.20

Step-by-step explanation:

Given the following information :

Base salary = $10.20 per hour

Overtime pay = $10.20 * 1.5 = $15.3

Average sale per hour = $60

Tips = 20% of sale

Regular shift hour = 8hours

Work week:

3 10-hour shift = 24hrs regular (6 hrs overtime)

1 11 - hour shift = 8hrs regular (3 hrs overtime)

1 5 - hour shift = 5 hours

Total hours per week = 37hrs regular, 9hrs overtime

WEEKLY :

Income from tips = $60 * 46 * 0.2 = $552

Regular pay: 37 * 10.20 = $377.40

Overtime: 9 * $15.30 = $137.70

Total = $(137.70 + 377.40 + 552) = $1067.10

Number of weeks in a year = 52

Annual gross = $1067.10 * 52 = $55,489.20

What is the product?

(negative 3 s + 2 t)(4 s minus t)

negative 12 s squared minus 2 t squared
negative 12 s squared + 2 t squared
negative 12 s squared + 8 s t minus 2 t squared
negative 12 s squared + 11 s t minus 2 t squared
Mark

Answers

Answer:

The answer is

negative 12 s squared + 11 s t minus 2 t squared

Step-by-step explanation:

( - 3s + 2t)( 4s - t)

Expand the terms

We have

- 12s² + 3st + 8st - 2t²

Simplify

We have the final answer as

- 12s² + 11st - 2t²

Hope this helps you

Answer:

D. -12s^2+11st-2t^2

the figure is cut into 8 equal pieces shade 3/4 of the figure

Answers

8 pieces divided by 4 is 2. Times that by 3 is 6 therefore the answer is 6

Answer:

You have to shade 6 pieces.

Step-by-step explanation:

Hope it helps!

Please Help! A pair of equations is shown below. x + y = 2 y = one halfx + 5 If the two equations are graphed, at what point do the lines representing the two equations intersect? (4, −2) (−2, 4) (2, 5) (5, −2)

Answers

Answer:

(-2,4)

Step-by-step explanation:

First, put x+y=2 into slope-intercept form: y=-x+2

Second, set the to equations equal to each other: -x+2=1/2x+5

Then, add x to both sides: -x+x+2=1/2x+x+5 to get: 2=3/2x+5

Next, subtract 5 from both sides: 2-5=3/2x+5-5, to get -3=3/2x

Finally, to get the x-value, divide both sides by 3/2: -3(2/3)=3/2x(2/3), to get x=-2

Lastly, substitute -2 for x into one of the equations to find y:

x+y=2

-2+y=2

add 2 to both sides: -2+2+y=2+2, to get y=4

The solution is (-2,4)

Answer:

(- 2, 4 )

Step-by-step explanation:

Given the 2 equations

x + y = 2 → (1)

y = [tex]\frac{1}{2}[/tex] x + 5 → (2)

Substitute y = [tex]\frac{1}{2}[/tex] x + 5 into (1)

x + [tex]\frac{1}{2}[/tex] x + 5 = 2 ( multiply through by 2 to clear the fraction )

2x + x + 10 = 4

3x + 10 = 4 ( subtract 10 from both sides )

3x = - 6 ( divide both sides by 3 )

x = - 2

Substitute x = - 2 into (1) and evaluate for y

- 2 + y = 2 ( add 2 to both sides )

y = 4

Solution is (- 2, 4 )

Find an exact value. tangent of seven pi divided by twelve

Answers

tan
(
7
π
12
)
=

(
2
+

3
)
Explanation:
tan
(
7
π
12
)
=
tan
(
π

5
π
12
)
= #-tan((5pi)/12)
=

tan
(
3
π
12
+
2
π
12
)
=

tan
(
π
4
+
π
6
)
Now using
tan
(
A
+
B
)
=
tan
A
+
tan
B
1

tan
A
tan
B
=

tan
(
π
4
)
+
tan
(
π
6
)
1

tan
(
π
4
)
tan
(
π
6
)
=

1
+
1

3
1

1
×
1

3
Multiplying numerator and denominator by

3
=


3
+
1

3

1
=

(

3
+
1
)
2
(

3

1
)
(

3
+
1
)
=

3
+
1
+
2

3
3

1
=

(
2
+

3

Answer: negative 2 minus radical 3

Step-by-step explanation:

We can use the tangent half-angle formula to find the exact value of tangent of 7π/12:

tan(θ/2) = ±√[(1-cosθ)/1+cosθ)]

Here, θ = 7π/6, and cos(7π/6) = -sqrt(3)/2.

Substituting these values, we get:

tan(7π/12) = ±√[(1-(-sqrt(3)/2))/(1+(-sqrt(3)/2))]

= ±√[(2+sqrt(3))/(2-sqrt(3))]

Multiplying the numerator and denominator by (2+sqrt(3)), we get:

= ±√[(2+sqrt(3))^2/(4-3)]

= ±√[(2+sqrt(3))^2]

= ±(2+sqrt(3))

Since 7π/12 lies in the second quadrant, and tangent is negative in the second quadrant, the exact value of tangent of 7π/12 is - (2+√3)

What is the solution to the equation ? 5{n-1 over 10}= 1 over 2

Answers

Answer:

n = 2

Step-by-step explanation:

Given

5( [tex]\frac{n-1}{10}[/tex] ) = [tex]\frac{1}{2}[/tex] ← distribute parenthesis on left side

[tex]\frac{n-1}{2}[/tex] = [tex]\frac{1}{2}[/tex]

Since denominators are both 2 then equate numerators

n - 1 = 1 ( add 1 to both sides )

n = 2

Rectangle divided into four rectangles. The perimeters of rectangle #1, #2, #3 #4 are 10 cm, 20 cm, 28 cm and 18 cm respectively. Find the perimeter of big rectangle.

Answers

Answer:

The perimeter of the big rectangle is 38 cm

Step-by-step explanation:

Rectangle 1 and rectangle 2 share the same width, let their width be a cm while Rectangle 3 and rectangle 4 share the same width, let their width be b cm

Rectangle 1 and rectangle 3 share the same length, let their length be x cm while Rectangle 2 and rectangle 4 share the same length, let their length be y cm

The perimeter of a rectangle = 2(length + breadth).

For rectangle 1:

Perimeter = 2(a + x) = 10

a + x = 5            1)

For rectangle 2:

Perimeter = 2(a + y) = 20

a + y = 10          2)

For rectangle 3:

Perimeter = 2(b + x) = 28

b + x = 14         3)

For rectangle 4:

Perimeter = 2(b + y) = 18

b + y = 9         4)

Adding equations 1, 2, 3 and 4 gives:

a + x + a + y + b + x + b + y = 5 + 10 + 14 + 9

a + a + b + b + x + x + y + y  =38

2a + 2b + 2x + 2y = 38

2((a + b) + (x + y)) = 38

For the big rectangle, let its width = c = a + b and its length be d = x + y

The perimeter of the big rectangle = 2 (c + d)

Therefore:

2((a + b) + (x + y)) = 38

2(c + d) = 38 cm = The perimeter of the big rectangle

The perimeter of the big rectangle is 38 cm

. What is the solution set for
|k - 6|+17 = 30
A. (-19, 7}
B. (-7, 19)
C. (-19, 19)
D. {-41, 19)

Answers

Answer:

Hope this is correct and helpful

HAVE A GOOD DAY!

Sophie is riding her bike home when she runs over a nail. It gets stuck to the tire of her bike but does not pop the tire. As she continues to cycle home the nail hits the ground every 2 seconds and reaches a maximum height of 48cm. a) Write a sinusoidal equation that models the nails height off the ground in cm, h, in terms of time,t. Sketch one full revolution of the nail, assuming that sophie first runs over the nail at 0seconds . b) Algebraically determine the height of the nail above the ground at 0.8 seconds. Round your answer to the nearest tenth of a cm

Answers

Answer:

a) The sinusoidal equation is;

The function is h = -24·cos[π(t )] + 24

The sketch of one full revolution is attached

b) The height of the nail at 0.8 seconds is 43.42 cm

Step-by-step explanation:

The sinusoidal equation that models the nails height can be given as follows;

y = A·cos[B(x - C)]+D

A = The amplitude = Half maximum height =  48/2 = 24 cm

The period = 2·π/B = Time to complete one oscillation = 2 seconds

∴ B = 2·π/2 = π

x = t  = Time

C = The horizontal shift

D = the vertical shift = 24 cm

y = The height of the nail = h

We have;

h = -24·cos[π(t - C)] + 24

At t = 0, h = 0, therefore, we have;

0 = -24·cos[π(0 - C)] + 24

24·cos[π(0 - C)] = 24

∴ cos[π(0 - C)] = 24/24 = 1

π(0 - C) = 0

C = 0

The function is h = -24·cos[π(t )] + 24

b) The height of the nail at 0.8 seconds is given as follows;

h = -24×cos[π(0.8)] + 24 =

h = 19.42 + 24 = 43.42 cm.

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