A car travels at an average speed of 68 miles per hour. How long does it take to travel 357 miles?

The four ways are 1) Factoring 2) Completing the Square 3) Quadratic Formula  and 4) Graphing

1. Factoring: Factoring is the process of breaking down an expression into its simplest components. To solve a quadratic equation using factoring, you must start by writing the equation in standard form (ax² + bx + c = 0). Then, you must factor the equation into two binomials (x + a)(x + b) = 0. Once this is done, you can solve for x by setting each factor equal to zero and solving for x.

2. Completing the Square: Completing the square is another method of solving a quadratic equation by rewriting it in the form of (x + a)² = b. To do this, you first start by writing the equation in standard form (ax² + bx + c = 0). Then, you must rearrange it so that all the terms are on one side of the equation and the constant is on the other side. Next, divide the coefficient of x² by two and then square this number. Finally, add this number to both sides of the equation, which will then allow you to solve for x.

3. Quadratic Formula: The quadratic formula is a useful tool for solving quadratic equations.

4. Graphing : is another method useful for solving quadratic equation.

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The solutions for all the equations would be

1. p = 30

2. h = 99

3. t = 31.4

4. r = 57

5. t = 5

6. w = 8

7. y = 9

8. p = 7

9. a = 13

10. w = 12

11. h = 24

12. g = 128

13. a = 21

14. y = 39

15. d = 16

16. w = 25

What is an equation?

An equation is a statement that asserts the equality of two expressions. The expressions on either side of the equation are separated by an equals sign (=), and they must have the same value for the equation to be true.

1) 30p = 900

  p = 900/30

  p = 30

2) h/9 = 11

   h = 9 * 11

   h = 99

3) t + 32.4 = 62

   t = 62 - 32.4

   t = 31.4

4) r - 17 = 40

   r = 40 + 17

  r = 57

5)  5t = 25

      t = 25/5

      t = 5

6) 8w = 64

    w = 64/8

   w = 8

7)  9y = 81

     y = 81/9

     y = 9  

8) p + 5 = 12

   p = 12 - 5

   p = 7

9)  a + 2 = 15

    a = 15 - 2

    a = 13

10)  w + 8 = 20

      w = 20 -8

      w = 12

11)  h/6 = 4

    h = 6 * 4

    h = 24

12) g/8 = 16

    g = 16 * 8

    g = 128

13) a/7 = 3

    a = 3 * 7

    a = 21

14) y - 11 = 28

    y = 28 + 11

    y = 39

15) d - 4 = 12

    d = 12 + 4

    d = 16

16) w - 10 = 15

    w = 15 + 10

    w = 25

Hence, solutions for all the equations would be

1. p = 30

2. h = 99

3. t = 31.4

4. r = 57

5. t = 5

6. w = 8

7. y = 9

8. p = 7

9. a = 13

10. w = 12

11. h = 24

12. g = 128

13. a = 21

14. y = 39

15. d = 16

16. w = 25

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Answer: The third one is wrong. The one about it being a republic.

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

30 + 32 + 34 + 36 = 132

Hope this helps!!

Answer:

A

Step-by-step explanation:

It’s the only good answer

There is a 0.0001 percent chance that the average amount of cereal in these boxes is less than 9.65 ounces.

Given that,

Mean µ = 9.70

Sample size = n = 5

standard deviation = σ = 0.03

Its distribution is normal, therefore

σx = σ/

σx = 0.03

σx = 0.0134

We must now determine the z value in order to use the table.

z = (x - µ) ÷ σ

z = (9.65 - 9,70) ÷ 0.0134

z = -3.73

Now

From the probability index tables

So P (z ≤ - 3.73) = 0.0001

Hence, the correct option is e) 0.0001

The complete question is:

A company’s cereal boxes advertise that each box contains 9.65 ounces of cereal. In fact, the amount of cereal in a randomly selected box follows a Normal distribution with mean μ = 9.70 ounces and standard deviation σ = 0.03 ounce. Now take an SRS of 5 boxes. What is the probability that the mean amount of cereal in these boxes is less than 9.65 ounces?

a. 0.4525

b. 0.9522

c. 0.9999

d. 0.0478

e. 0.0001

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Answer:

$18.48

Step-by-step explanation:

Find perimiter of room

4+4+7+7 =22

22•0.84 = 18.48

$18.48

Answer:

Here is the graph to the intercepts.

Step-by-step explanation:

Graph of (6, 4), (4, 3), (-2, 0)

Hope it helps :)

To find the MEAN of Natural numbers, such as  1, 2, 3, 4, 5, 6, 7, 8, 9, and 10, a + b + c3 is the sum of the three numbers a, b, and c. Therefore, 5.5 is the MEAN of the first 10 natural numbers.

Firstly The Given set of numbers Represents Natural numbers,

A natural number is an integer greater than 0. Natural numbers begin at 1 and increment to infinity: 1, 2, 3, 4, 5, etc.

Therefore, the first ten natural numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

And the mean of three numbers a, b, c is a + b + c3

Then the mean of 10 numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 is:-

⇒1+2+3+4+5+6+7+8+9+1010

Adding and dividing we get the value of the above term as,

⇒1+2+3+4+5+6+7+8+9+1010=5510=5.5

Hence, the mean of the first 10 natural numbers is 5.5.

Note: To solve this problem, you must understand that the integers greater than zero are natural numbers and that the mean of the three numbers a, b, and c equals a + b + c3. Knowing how to calculate the average number of elements and being familiar with natural numbers can help you arrive at the correct conclusion.

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The simplified form of 21b − 32 7b − 20b would be 8b - 32.

Reducing an equation is a technique for rewriting it in a more straightforward format. Although some mathematical equations are not in the form of linear equations, they can be converted into linear equations by applying certain mathematical operations to them. These equations can be easily solved after being reduced to linear form, and the value of the unknown can be determined.

21b – 32 + 7b – 20b

= 21b + 7b – 20b – 32

= 28b – 20b – 32 = 8b – 32

21b - 32 + 7b - 20b

= 21b + 7b - 20b -32

= 8b - 32

=8b - 32.

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Using the calculator there are various methods according to the calculator we used and the approach we follow, Basic answer is to select N and generate random number.

Random sampling is a method of selecting a sample from a population in such a way that each member of the population has an equal probability of being selected. This ensures that the sample is representative of the population, and reduces bias in the sampling process. In simple random sampling, a random sample is drawn from a larger population by using random number generators, tables of random numbers, or other methods that ensure that each member of the population has an equal chance of being selected.

A sample is a portion or a subset of a population that is selected for the purpose of studying characteristics of the population. The sample is used to make inferences or conclusions about the population from which it was drawn. The sample is usually smaller in size than the population, and it is selected through a process called sampling. The process of sampling is used to select a sample that is representative of the population, meaning that the sample has similar characteristics as the population.

Define the population size (N) and the sample size (n) that you want to obtain.

Use the calculator's random number generator to generate a random number between 1 and N. This will be the first element of your sample.

Repeat step 2 to generate the remaining elements of the sample, making sure that each element is different from the previous ones.

Record the elements of the sample, which are the random numbers that have been generated.

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Answer:

See below

Step-by-step explanation:

[tex] m\angle ABC = 2\times m\angle AEC = \boxed {60} \degree [/tex]

(By inscribed angle theorem)

[tex] m\widehat{AC} = m\angle ABC = 60\degree [/tex]

(Central angle and its corresponding arc theorem)

[tex] m\widehat {DC} = 180\degree - (60\degree + 80\degree) [/tex]

[tex] m\widehat {DC} = 40\degree [/tex]

[tex] m\angle DBC = m\widehat {DC} = \boxed {40} \degree [/tex]

(Central angle and its corresponding arc theorem)

[tex] m\angle ACE = \boxed {90} \degree [/tex]

(Angle inscribed in a semicircle)

[tex] m\angle DAE = \frac{1}{2}\times 80\degree = \boxed {40}\degree [/tex]

(By inscribed angle theorem)

[tex] m\angle ADE = \boxed {90}\degree [/tex]

(Angle inscribed in a semicircle)

[tex] m\angle FCB = \boxed {90}\degree [/tex]

(By tangent radius theorem)

[tex] m\angle CED = \frac{1}{2}\times 40\degree = \boxed {20} \degree [/tex]

(By inscribed angle theorem)

No, 1, 2, and 3 are not valid side lengths for a triangle. So 1, 2 and 3 cannot make a triangle.                                                                      

In order for a shape to be a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. This is known as the triangle inequality theorem.                                                              

3 + 2 = 5 > 1

3 + 1 = 4 > 2

1 + 2 = 3 not greater than 3

So as 1 + 2 not greater than 3, these set of side lengths does not follow the theorem. Thus a triangle cannot be formed with sides of length 1, 2, and 3.

--The question is incomplete, answering to the question below--

" Can 1, 2 and 3 make the sides of a triangle?"

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The length of tile A is 2.36068 inches.

The quantity of square units required to completely fill a square is known as the area of a square.

The region that lies inside the confines of a flat item or a two-dimensional figure is generally referred to as the area.

The measurement is made using square units, with square meters serving as the standard unit (m^2).

The square unit serves as the unit of area.

Let us recall that the area of a square is given by;

A = side^2

This is because, all the sides of a square are equal hence

When A = 5 square inches

5 = side^2

side = √5

side = 2.36068 inches

Therefore, The length of tile A is 2.36068 inches.

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The distance of each chord from the centre of the circle are √119  and √128 respectively .

Given,

Radius of a circle = 12 cm

AB = 10 cm

CD = 8 cm

Now, we get

BG = 10/2 = 5 cm

HD = 8/2 = 4 cm

(A perpendicular coming from the centre, which is not a diameter, bisects the chord.)

Now,

BE = ED = EF = 12 cm (All radii of a circle are equal.)

Now, by Pythagoras Theorem, we get

H² = P² + B²

For GE —

(BE)² = (GE)² + (BG)²

or, (12)² = GE² + (5)²

or, 144 = GE² + 25

or, GE² = 144 — 25

or, GE² = 119

or GE = ±√119

or GE = √119 (Since, length cannot be negative.)

For HE —

(DE)² = (HE)² + (HD)²

or, (12)² = HE² + (4)²

or, 144 = HE² + 16

or, HE² = 144 — 16

or, HE² = 128

or, HE = ± √128

or, HE = √128 or 8√2(Since, length cannot be negative.)

Hence , the distance of each chord from the centre of the circle are √119  and √128 respectively .

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Answer:

1.5

Step-by-step explanation:

2/2=1 so 2/1=0.5 so answer is 1.5

Answer:

- [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

The additive inverse is the value that requires to be added to make the sum zero, that is

[tex]\frac{3}{2}[/tex] - [tex]\frac{3}{2}[/tex] = 0

The additive inverse is - [tex]\frac{3}{2}[/tex]

Answer:

C

Step-by-step explanation:

70.5 times 3.14 is equal to 221.37 so Ferris Wheel was incorrect

Answer:

The slope would be 3! Hope this helps

Answer:

15

Step-by-step explanation:

dont change the 10 and whats 8 + 7

Answer: Jesus will have 36 dollars after 8 days

Step-by-step explanation: 8 x 8= 64

100-64=36

Answer:

just times every number on there ex:9x2x9x12 etc..

Answer:

18 + 4√15

Step-by-step explanation:

(3√5+√3)(√5+ √3)

= 3√5 (√5+ √3) + √3 (√5+ √3)

= 3√5 √5 + 3√5 √3 + √3  (√5+ √3)

=  3√5 √5 + 3√5 √3 + √3 √5 + √3 √3

= 18 + 4√15

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Answer: [tex]15000\ lbf.ft[/tex]

Step-by-step explanation:

Given

Force acting is [tex]200\ Pounds[/tex]

The direction of action is from [tex](0,0)\ to\ (-75,0)[/tex]

Work done is given by

[tex]W=F\cdot ds[/tex]

As the displacement occurs in the x-direction

[tex]\therefore W=200\cdot 75\\\Rightarrow W=15000\ lbf-ft[/tex]

The 3 parts of a quadratic equation are standard form, factored form and vertex form.

A quadratic equation is a polynomial equation of degree two in one variable of type f(x) = ax² + bx + c where a, b, c, ∈ R and a ≠ 0.

There are three forms of quadratic equations

Standard form of quadratic equation y = ax² + bx + c

factored form of quadratic equation y = a(x − r₁)(x − r₂​)

Vertex form of quadratic equation y = a(x − h)² + k

Each of the above quadratic forms looks unique, allowing the different problems to be more easily solved in one form than another.

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Answer:

48a+24p+66----(a)

48 a= -(24p+66)

a= -(24p+66) /48----(1)

put eq 1 in eq(a)

we get p= 7

again put the value of p in eq (1)

we get a= 12

put values of a and p in eq (1)

48(12)+24(7)+66

576+168+66

810

The function obtained after transformation is given as -x³ + 9x²- 27x + 21.

The graph of a function can be transformed by either shifting it in the right, left, up or down.

When the transformation is rightwards, the function becomes as f(x - a).

For left shifting it is f(x + a).

The function is given as f(x) = x³- 6.

The translation of 3 units towards left can be written as,

f(x + 3) = (x + 3)³ - 6

⇒ x³ + 9x² + 27x + 21

For reflection across y axis replace -x with x as below,

⇒ (-x)³ + 9(-x)² + 27 × -x + 21

⇒ -x³ + 9x²- 27x + 21

Hence, the required form of the transformed function is -x³ + 9x²- 27x + 21.

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Answer:

B. 4, Heads

4, Tails

5, Heads

5, Tails

6, Heads

6, Tails

Step-by-step explanation:

Given that the cube is labelled 1 to 6 and the coin has a head or a tail, the only outcome when the number cube lands on a number greater than 3 means that the cube lands on 4 or 5 or 6.

On the other hand, the coin may give a head or a tail.

In light of this, the possible answers are;

4, Heads

4, Tails

5, Heads

5, Tails

6, Heads

6, Tails

Hence option B is right