There are 4 roads leading from Bluffton to Hardeeville, 10 roads leading from Hardeeville to Savannah, and 5 roads leading from Savannah to Macon. How many ways are there to get from Bluffton to Macon

Answers

Answer 1

Answer: 200 ways

Step-by-step explanation:

From the given information:

Total number of roads leading from Bluffton to​ Hardeeville = 4

Total number of roads leading from Hardeeville to​ Savannah = 10

Total number of roads leading from Savannah to Macon = 5

We need to find the total number of ways to get from Bluffton to​ Macon.

Total number of ways to get from Bluffton to​ Macon = 4 * 10 * 5

= 200

Therefore, there are 200 required number of ways to get from Bluffton to​ Macon.


Related Questions

Find a set of parametric equations for y= 5x + 11, given the parameter t= 2 – x

Answers

Answer:

[tex]x = 2-t[/tex] and [tex]y = -5\cdot t +21[/tex]

Step-by-step explanation:

Given that [tex]y = 5\cdot x + 11[/tex] and [tex]t = 2-x[/tex], the parametric equations are obtained by algebraic means:

1) [tex]t = 2-x[/tex] Given

2) [tex]y = 5\cdot x +11[/tex] Given

3) [tex]y = 5\cdot (x\cdot 1)+11[/tex] Associative and modulative properties

4) [tex]y = 5\cdot \left[(-1)^{-1} \cdot (-1)\right]\cdot x +11[/tex] Existence of multiplicative inverse/Commutative property

5) [tex]y = [5\cdot (-1)^{-1}]\cdot [(-1)\cdot x]+11[/tex] Associative property

6) [tex]y = -5\cdot (-x)+11[/tex]  [tex]\frac{a}{-b} = -\frac{a}{b}[/tex] / [tex](-1)\cdot a = -a[/tex]

7) [tex]y = -5\cdot (-x+0)+11[/tex] Modulative property

8) [tex]y = -5\cdot [-x + 2 + (-2)]+11[/tex] Existence of additive inverse

9) [tex]y = -5 \cdot [(2-x)+(-2)]+11[/tex] Associative and commutative properties

10) [tex]y = (-5)\cdot (2-x) + (-5)\cdot (-2) +11[/tex] Distributive property

11) [tex]y = (-5)\cdot (2-x) +21[/tex] [tex](-a)\cdot (-b) = a\cdot b[/tex]

12) [tex]y = (-5)\cdot t +21[/tex] By 1)

13) [tex]y = -5\cdot t +21[/tex] [tex](-a)\cdot b = -a \cdot b[/tex]/Result

14) [tex]t+x = (2-x)+x[/tex] Compatibility with addition

15) [tex]t +(-t) +x = (2-x)+x +(-t)[/tex] Compatibility with addition

16) [tex][t+(-t)]+x= 2 + [x+(-x)]+(-t)[/tex] Associative property

17) [tex]0+x = (2 + 0) +(-t)[/tex] Associative property

18) [tex]x = 2-t[/tex] Associative and commutative properties/Definition of subtraction/Result

In consequence, the right answer is [tex]x = 2-t[/tex] and [tex]y = -5\cdot t +21[/tex].

If y varies directly with x and y = 5 when x = 4, find the value of y when x = -8

Answers

Answer:

-10

Step-by-step explanation:

y : x

= 5 : 4

4z = -8

= -8 / 4 = -2 = z

y : x

= 5 * -2 : 4 * -2

= -10 : -8

For what value of x does (x + 3)^2-5=0

Answers

Answer:

x = -3±sqrt( 5)

Step-by-step explanation:

(x + 3)^2-5=0

Add 5 to each side

(x + 3)^2-5+5=0+5

(x + 3)^2 = 5

Take the square root of each side

sqrt((x + 3)^2 )=±sqrt( 5)

x+3 = ±sqrt( 5)

Subtract 3 from each side

x+3-3 = -3±sqrt( 5)

x = -3±sqrt( 5)

Evaluate S_5 for 600 + 300 + 150 + … and select the correct answer below. A. 1,162.5 B. 581.25 C. 37.5 D. 18,600

Answers

Answer:

  A.  1,162.5

Step-by-step explanation:

Write the next two terms and add them up:

  S5 = 600 +300 +150 +75 +37.5 = 1162.5 . . . . matches choice A

Answer: Choice A 1,162.5

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

Explanation:

{600, 300, 150, ...} is a geometric sequence starting at a = 600 and has common ratio r = 1/2 = 0.5, this means we cut each term in half to get the next term. We could do this to generate five terms and then add them up. Or we could use the formula below with n = 5

Sn = a*(1-r^n)/(1-r)

S5 = 600*(1-0.5^5)/(1-0.5)

S5 = 1,162.5

-----------

Check:

first five terms = {600, 300, 150, 75, 37.5}

S5 = sum of the first five terms

S5 = 600+300+150+75+37.5

S5 = 1,162.5

Because n = 5 is relatively small, we can quickly confirm the answer. With larger values of n, a spreadsheet is the better option.

If the normality requirement is not satisfied​ (that is, ​np(1​p) is not at least​ 10), then a​ 95% confidence interval about the population proportion will include the population proportion in​ ________ 95% of the intervals. ​(This is a reading assessment question. Be certain of your answer because you only get one attempt on this​ question.)

Answers

Answer:

less than

Step-by-step explanation:

If the normality requirement is not satisfied​ (that is, ​np(1​ - p) is not at least​ 10), then a​ 95% confidence interval about the population proportion will include the population proportion in​ _less than__ 95% of the intervals.

The confidence interval consist of all reasonable values of a population mean. These are value for which the null hypothesis will not be rejected.

So, let assume that If the 95%  confidence interval contains the value for the hypothesized mean, then the sample mean  is reasonably close to the hypothesized mean. The effect of this is that the p- value is going to be greater than 0.05, so we fail to reject the null hypothesis.

On the other hand,

If the 95%  confidence interval do not contains the value for the hypothesized mean, then the sample mean  is far away from the hypothesized mean. The effect of this is that the p- value is going to be lesser than 0.05, so we reject the null hypothesis.

You are ordering two pizzas. A pizza can be small, medium, large, or extra large, with any combination of 8 possible toppings (getting no toppings is allowed, as is getting all 8). How many possibilities are there for your two pizzas

Answers

Answer:

1048576

Step-by-step explanation:

Given the following :

Pizza order :

Size = small, medium, large, or extra large = 4 possible sizes

Toppings = any combination of 8 possible toppings (getting no toppings is allowed, as is getting all 8).

Combination of Toppings = 2^8

Four different sizes of pizza = 4

Number of possibilities in ordering for a single pizza :

(4 * 2^8) = 4 * 256 = 1024

Number of possibilities in ordering two pizzas :

(4 * 2^8)^2

(2^2 * 2^8)^2

From indices :

[2^(2+8)]^2

[2^(10)]^2

2^(10*2)

2^20

= 1048576

You have 9kg of oats and cup scales that gears of 50g and 200g. How − in three weighings− can you measure 2kg of the oats?

Answers

Answer: You will need 8 cup scales

Step-by-step explanation:

kg=1000 grams

2000/250=8

In 8 cups it is possible to measure the 2kg or 2000 grams but in three weighs it is not possible to measure the 2kg or 2000 grams.

What is a fraction?

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

You have 9kg of oats and cup scales that gears of 50g and 200g.

Total oats need to measure = 9kg

As we know in 1 kg there are 1000 grams.

1 kg = 1000 grams

9kg = 9000 grams

2kg = 2000 grams

Cup scales that gears: 50g and 200g

The number of cups if consider one cup is of 250 grams( = 200 + 50)

Number of cups = 2000/250

Number of cups = 8

In three weighs it is not possible to measure the 2kg or 2000 grams.

Thus, in 8 cups it is possible to measure the 2kg or 2000 grams but in three weighs it is not possible to measure the 2kg or 2000 grams.

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Find the area of the shaded regions.

Answers

Answer:

7 pi cm^2 or  approximately 21.98 cm^2

Step-by-step explanation:

First find the area of the large circle

A = pi r^2

A = pi 3^2

A = 9 pi

Then find the area of the small unshaded circle

A = pi r^2

A = pi (1)^2

A = pi

There are two of these circles

pi+ pi = 2 pi

Subtract the unshaded circles from the large circle

9pi - 2 pi

7 pi

If we approximate pi as 3.14

7(3.14) =21.98 cm^2

Answer:

[tex]\boxed{\sf 7\pi \ cm^2 \ or \ 21.99 \ cm^2 }[/tex]

Step-by-step explanation:

[tex]\sf Find \ the \ area \ of \ the \ two \ smaller \ circles.[/tex]

[tex]\sf{Area \ of \ a \ circle:} \: \pi r^2[/tex]

[tex]\sf r=radius \ of \ circle[/tex]

[tex]\sf There \ are \ two \ circles, \ so \ multiply \ the \ value \ by \ 2.[/tex]

[tex](2) \pi (1)^2[/tex]

[tex]2\pi[/tex]

[tex]\sf Find \ the \ area \ of \ the \ larger \ circle.[/tex]

[tex]\sf{Area \ of \ a \ circle:} \: \pi r^2[/tex]

[tex]\sf r=radius \ of \ circle[/tex]

[tex]\pi (3)^2[/tex]

[tex]9\pi[/tex]

[tex]\sf Subtract \ the \ areas \ of \ the \ two \ circles \ from \ the \ area \ of \ the \ larger \ circle.[/tex]

[tex]9\pi -2\pi[/tex]

[tex]7\pi[/tex]

determine if the following side lengths create an acute,obtuse,or right triangle. a) 20, 21, 28 b) 3, 6, 4 c) 8, 12, 15

Answers

Answer:

a) 20, 21, 28 : acute

b) 3, 6, 4 : obtuse

c) 8, 12, 15 : obtuse

Step-by-step explanation:

You can see if a triangle is acute, obtuse, or right using the Pythagorean theorem as follows:

If [tex]a^2+b^2=c^2[/tex] , then the triangle is right.

If [tex]a^2+b^2>c^2[/tex] , then the triangle is acute.

If [tex]a^2+b^2<c^2[/tex] , then the triangle is obtuse.

Solve each to find if the given lengths form an acute, obtuse, or right triangle ( The biggest number is the hypotenuse length, since the hypotenuse is always the longest side in a triangle. This is represented by c):

a) 20, 21, 28

Insert numbers, using 28 as c:

[tex]20^2+21^2[/tex]_[tex]28^2[/tex]

Simplify exponents ([tex]x^2=x*x[/tex]):

[tex]400+441[/tex]_[tex]784[/tex]

Simplify addition:

[tex]841[/tex]_[tex]784[/tex]

Identify relationship:

[tex]841>784[/tex]

The sum of the squares of a and b is greater than the square of c. This triangle is acute.

b) 3, 6, 4

Insert numbers, using 6 as c:

[tex]3^2+4^2[/tex]_[tex]6^2[/tex]

Simplify exponents:

[tex]9+16[/tex]_[tex]36[/tex]

Simplify addition:

[tex]25[/tex]_[tex]36[/tex]

Identify relationship:

[tex]25<36[/tex]

The sum of the squares of a and b is less than the square of c. This triangle is obtuse.

c) 8, 12, 15

Insert numbers, using 15 as c:

[tex]8^2+12^2[/tex]_[tex]15^2[/tex]

Simplify exponents:

[tex]64+144[/tex]_[tex]225[/tex]

Simplify addition:

[tex]208[/tex]_[tex]225[/tex]

Identify relationship:

[tex]208<225[/tex]

The sum of the squares of a and b is less than the square of c. This triangle is obtuse.

:Done.

The correct values are,

a) 20, 21, 28  = Acute

b) 3, 6, 4  = Obtuse

c) 8, 12, 15 = Obtuse

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The sides are,

a) 20, 21, 28

b) 3, 6, 4

c) 8, 12, 15

Now,

We know that;

If three sides of a triangle are a, b and c.

Then, We get;

If a² + b² = c², then the triangle is right triangle.

If a² + b² > c², then the triangle is acute triangle.

If a² + b² < c², then the triangle is obtuse triangle.

Here, For option a;

⇒ 20, 21, 28

Clearly, a² + b² = 20² + 21²

                       = 400 + 441

                       = 841

And, c² = 28² = 784

Thus, a² + b² > c²

Hence, It shows the acute angle.

For option b;

⇒ 3, 6, 4

Clearly, a² + b² = 3² + 4²

                       = 9 + 16

                       = 25

And, c² = 6² = 36

Thus, a² + b² < c²

Hence, It shows the obtuse angle.

For option c;

⇒ 8, 12, 15

Clearly, a² + b² = 8² + 12²

                       = 64 + 144

                       = 208

And, c² = 15² = 225

Thus, a² + b² < c²

Hence, It shows the obtuse angle.

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Help me please thank y’all

Answers

Answer: x=60°

Step-by-step explanation:

The sum of the angles of a triangle is 180°. With this, we can find x°.

33+87+x=180                         [combine like terms]

120+x=180                               [subtact both sides by 120]

x=60°

Answer:

60 degrees

Step-by-step explanation:

All the angles in a triangle add up to 180 degrees.

We know two angles, 33 degrees and 87 degrees.

Now we have to find the last one.

So we make an equation to solve this.

33 + 87 + x = 180

120 + x = 180

Subtracting 120 fr0m both sides get us,

120 - 120 + x = 180 -120

x = 60

60 degrees

We can check by adding all three angles by substituting 60 for x,

33 + 87 + 60 = 120 + 60 = 180 degrees

Is it ever possible that after an elastic collision (where a moving mass (1) strikes a stationary mass (2)) that the two objects will have exactly the same final speeds? If so, how must the two masses compare? (Hints, 1st : there are two possibilities as to how the speeds could be equal, 2nd : equations below should be helpful).V1f=V1o (m1-m2/m1+m2) V2f=V1o (2m1/m1+m2)

Answers

Answer:

Step-by-step explanation:

It is possible that after an elastic collision a moving mass (1) strikes a stationary mass (2) and the two objects will have exactly the same final speed.

During an elastic collision, the momentum and kinetic energy are both conserved. Since one of the object is a stationary object, its velocity will be zero hence the other moving object will collide with the stationary object and cause both of them to move with a common velocity. The expression for their common velocity can be derived using the law of conservation of energy.

Law of conservation of energy states that the sum of momentum of bodies before collision is equal to the sum of momentum of the bodies after  collision.

Since momentum = mass*velocity

Before collision

Momentum of body of mass m1 and velocity u1  = m1u1

Momentum of body of mass m2 and velocity u2  = m2u2

Since the second body is stationary, u2 = 0m/s

Momentum of body of mass m2 and velocity u2  = m1(0) = 0kgm/s

Sum of their momentum before collision = m1u1+0 = m1u1 ... 1

After collision

Momentum of body of mass m1 and velocity vf  = m1vf

Momentum of body of mass m2 and velocity vf  = m2vf

vf is their common velocity.

Sum of their momentum before collision = m1vf+m2vf ... 2

Equating 1 and 2 according to the law;

m1u1 = m1vf+m2vf

m1u1 = (m1+m2)vf

vf = m1u1/m1+m2

vf s their common velocity after collision. This shows that there is possibility that they have the same velocity after collision.

Find the slope of a line perpendicular to the line defined by the equation 3x-5y=12

Answers

Answer:

-5/3

Step-by-step explanation:

Note the slope intercept form: y = mx + b

Note that:

y = (x , y)

m = slope

x = (x , y)

b = y-intercept

Isolate the variable, y. First, Subtract 3x from both sides:

3x (-3x) - 5y = 12 (-3x)

-5y = -3x + 12

Next, divide -5 from both sides. Remember to divide from all terms within the equation:

(-5y)/-5 = (-3x + 12)/-5

y = (-3x/-5) + (-12/5)

Simplify.

y = (3x/5) - 12/5

y = (3/5)x - 12/5

You are trying to find the perpendicular slope to this line. To do so, simply flip the slope (m) as well as the sign:

Original m = 3/5

Flipped m = -5/3

-5/3 is your perpendicular slope.

Answer:

          5                                

m =  - ----    perpendicular slope

          3

Step-by-step explanation:

3x - 5y = 12 -------->> convert to y = mx + b

- 5y = - 3x + 12

- 5y = - (3x + 12) --- eliminate the negative

5y = 3x + 12

   

     3x + 12

y = -------------

         5

       3           12

y = -----x  +   -----

       5            5  

the above equation is the form of  y = mx + b

where m is the slope and b is the intercept

   

                            5                                

therefore,  m =  - ----    perpendicular slope

                             3                        

The time between consecutive uses of a vending machine is exponential with an average of 15 minutes. a)Given that the machine has not been used in the previous 5 minutes, what is the probability that the machine will not be used during the next 10 minutes

Answers

Answer5

Step-by-step explanation:

A charity organization is holding a food drive with a goal to collect at least 1,000 cans of
food by the end of the month. It currently has 565 cans from donations and is having an
event where 87 guests will attend and bring cans. Which solution set represents the
number of cans each guest must bring to meet the goal?
+
OA
++
0
1
2
3
4
5
6
7
8
9
10
---
+
OB. 4
+
0
1
2
3
4
5
6
7
8
9
10
OC.
+
1
2
3
5
6
7
8
9
10
OD. +
+
++
-
6
+
7.
+
0
1
2
3
4
5
8
9
10

Answers

Answer:

Each guest must bring 5 cans.

Step-by-step explanation:

1000-565=435

435/87=5

What is the equation of the following line? Be sure to scroll down first to see all answer options.



A.
y = - x

B.
y = -2x

C.
y = 2x

D.
y = x

E.
y = -4x

F.
y = - x

Answers

Answer:

The answer is option F

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To calculate the equation of the line first find the slope

Slope of the line using points

(0 , 0) and (4 , -2) is

[tex]m = \frac{ - 2 - 0}{4 - 0} = \frac{ - 2}{4} = - \frac{1}{2} [/tex]

Now use the formula

y - y1 = m(x - x1) to find the equation of the line using any of the points

Using point (0,0)

That's

[tex]y - 0 = - \frac{ 1}{2} (x - 0)[/tex]

The final answer is

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

Hope this helps you

Answer:

F

Step-by-step explanation:

Solve 2 - (7x + 5) = 13 - 3x (make sure to type the number only)

Answers

Answer:

x = -4

Step-by-step explanation:

2 - (7x + 5) = 13 - 3x

add the binomial (7x +5) to both sides

2 = (7x + 5) + 13 - 3x

combine like terms

2 = 4x + 18

subtract 18 from both sides

-16 = 4x

divide by 4

x = -4

Answer:

-4

Step-by-step explanation:

Distribute the negative signs to the values in the parentheses

2 -7x - 5 = 13 - 3x

Add like terms:

-7x - 3 = 13 - 3x

Add 3x to both sides:

-4x - 3 = 13

Add 3 to both sides:

-4x = 16

Divide both sides by -4:

x = -4

f(x )=x square +6x + 5 what is the x intercept to graph f(x)

Answers

Answer:

(-5, 0)

(-1, 0)

Step-by-step explanation:

x-intercepts are points where the graph intersects the x-axis (or when y = 0)

Step 1: Write out function

f(x) = x² + 6x + 5

Step 2: Factor

f(x) = (x + 5)(x + 1)

Step 3: Find binomial roots

x + 5 = 0

x = -5

x + 1 = 0

x = -1

Alternatively, you can graph the function and analyze the graph for x-intercepts:

12. Consider the function ƒ(x) = x^4 – x^3 + 2x^2 – 2x. How many real roots does it have?
options:
A) 2
B) 1
C) 3
D) 4

Answers

Answer:

Step-by-step explanation:

Hello, let's factorise as much as we can.

[tex]x^4-x^3 + 2x^2-2x\\\\=x(x^3-x^2+2x-2)\\\\=x(x-1)(x^2+2)[/tex]

So, the solutions are

[tex]0, \ 1, \ \sqrt{2}\cdot i, \ -\sqrt{2}\cdot i[/tex]

There are only 2 real roots.

Thank you.

Answer:

So, the solutions are

There are only 2 real roots.

Step-by-step explanation:

According to the website www.costofwedding, the average cost of flowers for a wedding is $698. Recently, in a random sample of 40 weddings in the U. S. it was found that the average cost of the flowers was $734, with a standard deviation of $102. On the basis of this, a 95% confidence interval for the mean cost of flowers for a wedding is $701 to $767.
Choose the statement that is the best interpretation of the confidence interval.
I. That probability that the flowers at a wedding will cost more than $698is greater than 5%.
II. In about 95%of all samples of size 40,the resulting confidence interval will contain the mean cost of flowers at weddings.
III. We are extremely confident that the mean cost of flowers at a wedding is between $701and $767
A) II only
B) I only
C) III only
D) II and III are both correct

Answers

Answer:

D) II and III are both correct.

Step-by-step explanation:

The Probability distribution is the function which describes the likelihood of possible values assuming a random variable. The cost of flowers for a wedding is $698. The 95% of all samples of size is 40 and the confidence interval will be mean cost of flowers at wedding. There is confidence that mean cost of wedding flowers is between $701 to $767.

If the random variable X is normally distributed with mean of 50 and standard deviation of 7, find the 9th percentile.

Answers

Answer:

The 9th percentile is 40.52.

Step-by-step explanation:

We are given that the random variable X is normally distributed with a mean of 50 and a standard deviation of 7.

Let X = the random variable

The z-score probability distribution for the normal distribution is given by;

                            Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean = 50

           [tex]\sigma[/tex] = standard deviation = 7

So, X ~ Normal([tex]\mu=50, \sigma^{2} = 7^{2}[/tex])

Now, the 9th percentile is calculated as;

            P(X < x) = 0.09         {where x is the required value}

            P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{x-50}{7}[/tex] ) = 0.09

            P(Z < [tex]\frac{x-50}{7}[/tex] ) = 0.09

Now, in the z table the critical value of x that represents the below 9% of the area is given as -1.3543, i.e;

                     [tex]\frac{x-50}{7}=-1.3543[/tex]

                     [tex]x-50=-1.3543 \times 7[/tex]

                     [tex]x=50 -9.48[/tex]

                      x = 40.52

Hence, the 9th percentile is 40.52.

The average daily volume of a computer stock in 2011 was ų=35.1 million shares, according to a reliable source. A stock analyst believes that the stock volume in 2014 is different from the 2011 level. Based on a random sample of 30 trading days in 2014, he finds the sample mean to be 32.7 million shares, with a standard deviation of s=14.6 million shares. Test the hypothesis by constructing a 95% confidence interval. Complete a and b A. State the hypothesis B. Construct a 95% confidence interval about the sample mean of stocks traded in 2014.

Answers

Answer:

a

   The  null hypothesis is  [tex]H_o : \mu = 35 .1 \ million \ shares[/tex]

    The  alternative hypothesis  [tex]H_a : \mu \ne 35.1\ million \ shares[/tex]

b

 The   95% confidence interval is  [tex]27.475 < \mu < 37.925[/tex]

Step-by-step explanation:

From the question the we are told that

      The  population mean is  [tex]\mu = 35.1 \ million \ shares[/tex]

      The  sample size is  n = 30

       The  sample mean is  [tex]\= x = 32.7 \ million\ shares[/tex]

       The standard deviation is  [tex]\sigma = 14.6 \ million\ shares[/tex]

     

Given that the confidence level is  [tex]95\%[/tex] then the level of significance is mathematically represented as

                  [tex]\alpha = 100-95[/tex]

                  [tex]\alpha = 5\%[/tex]

=>               [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table

    The value is  [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically represented as

                 [tex]E = Z_{\frac{\alpha }{2} } * \frac{ \sigma }{\sqrt{n} }[/tex]

substituting values

                [tex]E = 1.96 * \frac{ 14.6 }{\sqrt{30} }[/tex]

                [tex]E = 5.225[/tex]

The 95% confidence interval confidence interval is mathematically represented as

              [tex]\= x -E < \mu < \= x +E[/tex]

substituting values

               [tex]32.7 - 5.225 < \mu < 32.7 + 5.225[/tex]

                [tex]27.475 < \mu < 37.925[/tex]

       

☆ =
MODULE
The length of a rectangle is eight centimeter less than
twice the width. The area of the rectangle is 24
centimeters squared. Determine the dimensions of the
rectangle in centimeters.

Answers

Answer: The length is 4 centimeters and the width is 6 centimeters.

Step-by-step explanation:

If the length of the  rectangle is eight centimeters less than twice the width then we could represent it by the equation L= 2w - 8 .   And we know that to find the area of a rectangle we multiply the length by the width  and they've already given the area  so we will represent the width by w since it is unknown.

Now we know the length is 2w- 8 and the width is w so we would multiply them and set them equal to 24.

w(2w-8) = 24

2[tex]w^{2}[/tex] - 8w = 24     subtract 24 from both sides to set the whole equation equal zero and solve. solve using any method. I will solve by factoring.

2[tex]w^{2}[/tex] - 8w -24 = 0      divide each term by 2.

[tex]w^{2}[/tex] - 4w - 12 = 0          Five two numbers that multiply to get -12 and to -4

[tex]w^{2}[/tex] +2w - 6w - 12 = 0    Group the left hand side and factor.

w(w+2) -6( w + 2) = 0   factor out w+2

(w+2)(w-6) = 0         Set them both equal zero.

w + 2 =0      or w - 6 = 0  

    -2  -2                + 6   +6

w= -2       or   w=6  

Since we are dealing with distance -2 can't represent a distance so the wide has to 6.  

Now it says that the length is 8 less that twice the width.

So  2(6) - 8 = 12 -8 = 4  So the length in this care is 4.

Check.

6 * 4 = 24

24 = 24

*please help* If multiple forces are acting on an object, which statement is always true?


The acceleration will be directed in the direction of the gravitational force.

The acceleration will be directed in the direction of the applied force.

The acceleration will be directed in the direction of the net force. <-- MY ANSWER

The acceleration will be directed in the direction of the normal force.

Answers

Answer: You are correct. The answer is choice C.

The sum of the vectors is the resultant vector, which is where the net force is directed.

An example would be if you had a ball rolling on a table and you bumped the ball perpendicular to its initial velocity, then the ball would move at a diagonal angle rather than move straight in the direction where you bumped it.

Acceleration is the change in velocity over time, so the acceleration vector tells us how the velocity's direction is changing.

The direction of the acceleration on a body upon which multiple forces are applied depends on the direction of the netforce acting on the body.

When multiple forces acts on a body, such that the different forces acts in different directions.

The acceleration will be in the direction of the netforce.

This is the direction where the Cummulative sum of the forces is greatest.

Acceleration due to gravity is always acting downward, if the upward force is greater than the Gravitational force, then the acceleration won't be in that direction.

Therefore, acceleration will be due in the direction of the netforce.

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write 768,676 in words

Answers

Answer:

seven hundred sixty-eight thousand six hundred seventy-six

hope this answer correct :)

that might be “ seven hundred sixty-eight thousand six hundred seventy-six”

State the correct polar coordinate for the graph shown:

Answers

clearly, r=3 units

and 8 segments (sectors actually) in anti-clockwise direction , with each sector having 30° angle so angle is 240°

so option C

Answer:

Solution :  ( 3, 240° )

Step-by-step explanation:

In polar coordinates the point is expression as the ordered pair ( r, θ ) where r is the directed distance from the pole, and theta is the directed angle from the positive x - axis. When r > 0, we can tell it = 3 as the point lies on the third circle starting from the center. Now let's start listing coordinates for when r is positive ( r > 0 ). There are two cases to consider here.

( 3, θ ) here theta is 60 degrees more than 180, or 180 + 60 = 240 degrees. Right away you can tell that your solution is ( 3, 240° ), you don't have to consider the second case.

What is the solution to the system of equations?
5x – 4y = 6
-5x + 4y = -10
O (4,4)
0 (-2,-5)
O infinitely many solutions
O no solution

Answers

Hey there! I'm happy to help!

We have a 5x is one equation and a -5x in another equation. We can combine the two equations to cancel out the x and then solve! This is called solving by elimination.

5x-4y=6

+

-5x+4y=-10

0= -4

Since we lost our x and y while solving, there cannot be any solution.

Therefore, the answer is no solution.

Have a wonderful day!

The age of some lecturers are 42,54,50,54,50,42,46,46,48 and 48 calculate the mean age and standard deviation

Answers

Answer:

Mean age: 48

Standard deviation: 4

Step-by-step explanation:

a) Mean

The formula for Mean = Sum of terms/ Number of terms

Number of terms

= 42 + 54 + 50 + 54 + 50 + 42 + 46 + 46 + 48+ 48/ 10

= 480/10

= 48

The mean age is 48

b) Standard deviation

The formula for Standard deviation =

√(x - Mean)²/n

Where n = number of terms

Standard deviation =

√[(42 - 48)² + (54 - 48)² + (50 - 48)² +(54 - 48)² + (50 - 48)² +(42 - 48)² + (46 - 48)² + (46 - 48)² + (48 - 48)² + (48 - 48)² / 10]

= √-6² + 6² + 2² + 6² + 2² + -6² + -2² + -2² + 0² + 0²/10

=√36 + 36 + 4 + 36 + 4 + 36 + 4 + 4 + 0 + 0/ 10

=√160/10

= √16

= 4

The standard deviation of the ages is 4


Mary states, "If the diagonals of a parallelogramare congruent, then the
parallelogram is a rectangle." Decide if her statement is wue or false.
A. True
B. False​

Answers

Answer:

True

Step-by-step explanation:

A rectangle is a plane figure with congruent length of opposite sides. Considering a rectangle ABCD,

AD ≅ BC (opposite side property)

AB ≅ CD (opposite side property)

<ABC = <BCD = <CDA = <DAC = [tex]90^{0}[/tex] (right angle property)

Thus,

<ABC + <BCD + <CDA + <DAC = [tex]360^{0}[/tex]

AC ⊥ BD (diagonals are perpendicular to each other)

AC ≅ BD (congruent property of diagonals)

Therefore, the parallelogram is a rectangle.

Which statement best describes what Rutherford concluded from the motion of the particles?

Answers

Answer:

some particle traveled through empty spaces between atoms and some particles were deflected by electrons

Step-by-step explanation:

The motion of particles will be

some particle traveled through empty spaces between atoms and some particles were deflected by electrons.

What was Rutherford Experiment?The vast majority of the alpha particles simply passed through the gold foil.Some of the alpha particles had a slight angle of deflection.Only a tiny fraction of the alpha particles rebounded.

So, the observation made the stamement

He came to the conclusion that the majority of space in an atom was unoccupied since there was very little alpha particle deflection.The fact that very few particles were diverted from their course led him to the further conclusion that positive charge takes up very little space in an atom.

Then, motion of particles will be

some particle traveled through empty spaces between atoms and some particles were deflected by electrons.

Learn more about Rutherford Experiment here:

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Please help me with this

Answers

Answer:

Median; 60

Step-by-step explanation:

For a data plot as shown in the question above, one easier measure of center that can be used for the data set represented is the median.

From the dot plot, we can easily pinpoint the exact median, which can be used as a measure of center.

There are 11 data points represented on the dot plot by 11 dots. The median, that is the median value of the data set, would be the 6th value represented by the 6th dot on the dot plot.

Thus, the middle value is 60.

60 is the median of the data set.

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