what is the probability that a random sample of 20 second grade students from the city results in a mean reading rate of more than 97 words per minute

Answer:

a) p(X =2) = 0.261

b) P(x>2) = 0.566

c) P(2<x<5)  = 0.334

Step-by-step explanation:

Given 24% of U.S. adults say they are more likely to make purchases during a sales tax holiday

Probability 0f U.S. adults say they are more likely to make purchases during a sales tax holiday (p) = 0.24

                           n = 10

By using Poisson distribution

mean number of make purchases during a sales tax holiday

λ = np = 10 X 0.24 = 2.4

a)

The probability of getting exactly '2'

The probability

b) The probability of getting more than '2'

             = 0.090 + 0.2177+0.261 = 0.566

P(x>2) = 0.566

c) The probability of getting between  two and five

P( 2<x<5) = P(x=3)+p(x=4) =P(2<x<5) = 0.2090 + 0.125 = 0.334

hope this helps

Answer:

yes yes ...................

Answer:

B: (4, 2)

D: (-4, -1)

E: (3, -3)

F: (0, 4)

Step-by-step explanation:

(x-coordinate, y-coordinate)

Answer:

B: (4, 2)

D: (-4, -1)

E: (3, -3)

F: (0, 4)

Step-by-step explanation:

(x-coordinate, y-coordinate)

Answer: 3274 cookies

Step-by-step explanation:

She sold : 2016 ÷ 8 = 252 ( bags )

The remaining cookies : 12 × 252 = 3024 ( cookies )

She baked : 3024 + 250 = 3274 ( cookies )

Answer:

1/4

Step-by-step explanation:

rise/run                                          you can count it but it doesn't always work

If you want to know the mathematical way of doing it it's:

m(slope) = y2-y1/x2-x1                 Choose any two points I chose (-4,5) & (0,6)

m = 6-5/0-(-4)                               Then subtract 6 - 5 and 0-(-4)  

m = 1/4

Using the given information, we can write the compound inequality for the variable n:

45 ≤ n ≤ 120

Here we know that Liz spends at least 45 minutes and no more than 120 minutes on her phone.

So if we define the variable n as:

n = number of minutes that Liz spends on her phone.

We know that n must be larger than or equal to 45, so we can write the first inequality:

45 ≤ n

And we also know that it must be smaller than or equal to 120, then the other inequality is:

n ≤ 120

Combining the two we can write the compound inequality:

45 ≤ n ≤ 120

That is what we wanted to get.

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Cassidy and Calvin have the same amount of money in 11 months.

The amount is $370.

Cassidy has $425 in her savings account, and she has to pay $5 each month to her parents for her cell phone. This will be:

= 425 - 5m

Calvin has $95 and he saves $25 each month from his job walking dogs for his neighbor. This will be:

= 95 + 25m

where m = number of months

The equation will be:

425 - 5m = 95 + 25m

Collect like terms

425 - 95 = 25m + 5m

330 = 30m

Divide

m= 330/30

m = 11

The number of months is 11.

The amount will be:

= 425 - 5m

= 425 - 5(11)

= 425 - 55.

= 370

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Answer:

5 coffees will cost $9.25

Step-by-step explanation:

If you divide $5.55 by the 3 coffees, you get $1.85 which is the price per coffee. Multiply $1.85 by 5 to get $9.25 which is the cost for 5 coffees

Answer:

See below

Step-by-step explanation:

The area (triangle) marked 'x' in the diagram below

Answer: $38,125

Step-by-step explanation:

1/8*305000

Answer:

$336

Step-by-step explanation:

[tex]\frac{280}{35} \times 42 \\ \\ =\frac{56}{7} \times 42 \\ \\ =8 \times 42 \\ \\ =\$336[/tex]

Answer:

C (the one which starts with x = -2 and y = -1)

Step-by-step explanation:

because for every x value there is only an y value

The distance from Kano to Lagos is 1200 km

The problem involves addition of fractions

The fraction required are:

let the distance form kano to Lagos be x

it was discovered that a driver has travelled 3/8 = 3x/8

another driver had travelled 3/10 of that distance = 3x/10

The drivers are still 390 km apart

total distance, x

x = 390 + 3x/8 + 3x/10

x - 3x/8 - 3x/10 = 390

0.325x = 390

x = 390 / 0.325

x = 1200 km

From the driving distance information 1200 km is the distance from Kano to Lagos

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Answer: Circumference equals = 27.004
              Area equals = 58.0586

We can write the area and circumferance of the given circle as 18.49π square units and 8.6π units.

Given is that a circle with a radius of 4.3.

We can write the area of the given circle as -

Area = πr²

Area = π x 4.3 x 4.3

Area = 18.49π square units

We can write the circumferance of the given circle as -

circumferance = 2πr

circumferance = 2 x π x 4.3  

circumferance  = 8.6π units

Therefore, we can write the area and circumferance of the given circle as 18.49π square units and 8.6π units.

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He got 11 vacation days in five years.  If his annual salary is $64,480 he earned during his vacation days $2277

The average nationwide is 10, however it varies a little by industry and area. These days off—generally regarded as vacation time—usually get longer the longer an employee works. For the majority of businesses, an employee can receive an additional three to four days per year every five years based on longevity.

The normal recommendation is to wait three to six months. However, the organization and its culture have a big impact. He continued by saying that many businesses make it very clear what their vacation policy is. Some employers allow you to accumulate additional vacation time the longer you work

64,480/12 =5373.33

5373.33/26 = 207

207 x 11 =2277

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He got 11 vacation days in five years.  If his annual salary is $64,480 he earned during his vacation days $2277

The average across the country is 10, but it varies slightly by region and industry. The length of these vacation days typically increases with an employee's length of service. Based on longevity, most companies allow employees to get an extra three to four days per year every five years.

The usual advice is to hold off for three to six months. The organization and its culture, however, play a significant role. He went on to remark that a lot of companies are quite explicit about their vacation policies. The longer you work for some employers, the more vacation time you can accrue.

64,480/12 =5373.33

5373.33/26 = 207

207 x 11 =2277

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The solution to the given equation is 5.630.

What is a logarithmic equation?

An equation using the logarithm of an expression containing a variable is referred to as a logarithmic equation. Check to verify if you can write both sides of the equation as powers of the same number before attempting to solve an exponential equation.

Here, we have

2^(x+1) = 3^(2x-5)

Taking logarithms on both sides, we get

(x+1)log2 = (2x - 5)log3

xlog2 + log2 = 2xlog3 - 5log3

log2 + log3⁵ = 2xlog3 - xlog2

log 2* 243 = x(log6 - log2)

log486 = x(log6/2)

log486 = xlog3

x = log486/log3

x = 5.630

Hence, the solution to the given logarithmic equation is 5.630.

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The x intercept of y = -2x - 21 is  [tex]\frac{-21}{2}[/tex]

The y intercept of y = -2x - 21 is -21

What is x - intercept and y - intercept of a line?

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

The given equation of line is

y = -2x - 21

For x intercept, we have to put y = 0

[tex]-2x - 21 = 0\\2x = -21\\x = \frac{-21}{2}[/tex]

So the x intercept is [tex]\frac{-21}{2}[/tex]

For y intercept, we put x = 0

[tex]y = -2\times 0 -21\\y = -21[/tex]

The y intercept is -21

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The function which have Domain:{-5, -3, 0, 3, 11} and Range:{4, 0, 2} is  {(3,0), (-3,-4), (11, 2), (0,4), (-5, 0)}.

What is Function?

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.

What is domain?

The domain of a function is the set of values that we are allowed to plug into our function.

What is range?

The collection of potential output values for a function is known as its range. For instance, the range is the non-negative real numbers for the function fn(x)=x2 on the domain of all real numbers (x ∈ R), which may be represented as fn(x)≥0 (or [0,∞] using interval notation).

Given:

Domain: {-5, -3, 0, 3, 11)

Range: {4, 0, 2}

If the input of function is a and output is b then it is defined by (a, b).

a always belong to domain and b from range of function.

∴ By using given domain and range set of our answer is {(3,0), (-3,-4), (11, 2), (0,4), (-5, 0)}

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Answer:our answer is {(3,0), (-3,-4), (11, 2), (0,4), (-5, 0)}

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want the measures of supplementary angles x° and (x-58)°.

Consecutive interior angles where a transversal crosses parallel lines are supplementary.

  x° +(x -58)° = 180°

  2x = 238

  x = 119

  x -58 = 61

The two angles are ...

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The statement that is true about the number of rooms that can be painted using inequality is; D.

The hotel can repaint 2 rooms, but this number is neither the maximum nor the minimum.

We are given;

Budget of hotel to repaint the lobby and some hotel rooms; $63750

Amount spent on painting the lobby = $26700

Cost to paint each room = $4250

Thus, the inequality to represent the given situation is;

26,700 + 4,250n ≤ $63,750

where;

n is number of rooms the hotel can repaint

Subtract 26700 from both sides of the inequality to get;

4250n ≤ 37050

n ≤ 37050/4250

n ≤ 8.717

Since we can't paint only a portion, we leave it as a maximum of 8 rooms

Looking at the given options, the only correct one is option D.

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For the given right angled triangle, the base of the triangle is 10 units and perpendicular side is 9 units then its side length x is equal to 13.45 units (nearest hundredth).

As given in the question,

Given right angled triangle,

Base of the triangle is equal to 10 units

Perpendicular side of a triangle is equal to 9 units

Side length 'x' is the hypotenuse of the right angled triangle.

Using Pythagoras theorem we get,

(Hypotenuse)² = ( Base)² + ( Perpendicular side)²

⇒ x² = (10)² + (9)²

⇒ x² = 100 + 81

⇒ x² = 181

⇒ x = √181

⇒ x = 13.4536...

⇒ x = 13.45 units ( nearest hundredth)  

Therefore, for the given right angled triangle, the base of the triangle is 10 units and perpendicular side is 9 units then its side length x is equal to 13.45 units (nearest hundredth).

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The exact value of the sine of angle 78° sin(78°) is presented as follows;

[tex]sin(78^{\circ}) = \dfrac{\sqrt{5}-1+\sqrt{\sqrt{5}\cdot \left(6+6\cdot \sqrt{5} \right) } }{8}[/tex]

The sine of an angle is found by taking the ratio of the opposite side to the hypotenuse side of a right triangle that has the specified angle.

The sine of angle 78° is found from the sine of the sum of two angles (60° + 18°)  as follows;

sin(78°) = sin(60° + 18°)

sin(A + B) = sin(A)·cos(B) + cos(A)·sin(B)

Therefore, sin(78°) = sin(60° + 18°)  = sin(60)·cos(18°) + cos(60°)·sin(18°)

Where, 18° = A, we have;

5·A = 90°

2·A = 90° - 3·A

sin(2·A) = sin(90° - 3·A) = cos(3·A)

2·sin(A)·cos(A) = 4·cos³(A) - 3·cos(A)

2·sin(A)·cos(A) - (4·cos³(A) - 3·cos(A)) = 0

2·sin(A) - (4·cos²(A) - 3) = 0

2·sin(A) - (4·(1 - sin²(A)) - 3) = 0

4·sin²(A) - 2·sin(A) - 1 = 0

Which gives;

[tex]sin(A) = \dfrac{-1\pm \sqrt{5} }{4}[/tex]

cos²(18°) = 1 - sin²(18°)

cos(18°) = √(1 - sin²(18°))

[tex]cos(18^{\circ}) =\sqrt{1 - \left( \dfrac{\sqrt{5} -1 }{4}\right)^2} = \dfrac{1}{4} \cdot \sqrt{10+2\cdot \sqrt{5} }[/tex]

[tex]cos(18^{\circ}) = \dfrac{1}{4} \cdot \sqrt{10+2\cdot \sqrt{5} }[/tex]

Therefore;

[tex]sin(78^{\circ})=\dfrac{\sqrt{3} }{2} \cdot \left( \dfrac{1}{4} \cdot \sqrt{10+2\cdot \sqrt{5} }\right) +\dfrac{1}{2} \cdot \left( \dfrac{\sqrt{5} -1 }{4}\right)= \dfrac{\sqrt{5}-1+\sqrt{\sqrt{5}\cdot \left(6+6\cdot \sqrt{5} \right) } }{8}[/tex]

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When red is the first one , blue the second and green the third one (and as you can see, all of them share the vertex (-2, 3)).

The vertex of a quadratic equation:

a[tex]x^{2}[/tex]+bx + c = y

is located at :

x = -b/2a.

In this case, x = -2

Then,

-b/2a = -2

And we also have that:

a[tex](-2)^2[/tex] -2b + c = 3

Then we have two equations:

-b/2a = -2

a[tex](-2)^2[/tex] -2b + c = 3

We have only equations and 3 variables, So we can just give the variable c different values and we will find different quadratic equations that are not equivalent.

Let's begin with c = 0 ,Our equations are:

-b/2a = -2

a[tex](-2)^2[/tex] -2b + 0 = 3

In the first equation we can isolate b and get :

b = 4a

Now we can replace this in the other equation and solve this for a.

4a + 4a x -2 = 3

-4a = 3

a = -3/4

then:

b = 4a = 4 x -3/4 = -3

The first quadratic equation is:

(-3/4)[tex]x^{2}[/tex] - 3x = y

Now, To find the second let's use a different value of c.

c = 1

b = 4a

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

Let's solve in the same way as before:

4a + 4a x -2 + 1= 3

-4a = 2

a = 2/-4 = 1/-2

b = 4 x -1/2 = -2

Then our equation is :

(-1/2)[tex]x^{2}[/tex] -2x + 1 = y

For the last equation, let's use c = 2

then our equation are:

b = 4a

a(-2)^2 - 2b +2 = 3

Same as before, replace the first equation in the second

4a + 4a x-2 +2 = 3

-4a +2 = 3

-4a = 1

a = -1/4

Then:

b = 4 x (-1/4) = -1

Our third equation is :

(-1/4)x^2 - x + 2 = y

Now, Below you can see all of them graphed.

When red is the first one , blue the second and green the third one (and as you can see, all of them share the vertex (-2, 3)).

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Step-by-step explanation:

we know the square numbers of the basic integer numbers :

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

6² = 36

7² = 49

8² = 64

9² = 81

10² = 100

so, we see when we square the inequality, the closest numbers are

81 < 91 < 100

and therefore

9 < sqrt(91) < 10

The pounds of trash that Janicka recycle is 3 3/5 pounds.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split.

In this situation, Janicka picked up 5 2/5 lb of trash and 2/3 of what she collected was able to be recycled.

The amount to be recycled will be:

= 2/3 × 5 2/5

= 2/3 × 27/5

= 54 / 15

= 3 9/15

= 3 3/5

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Answer:

The big bang is how astronomers explain the way the universe began. It is the idea that the universe began as just a single point, then expanded and stretched to grow as large as it is right now—and it is still stretching!

Step-by-step explanation:

In 1927, an astronomer named Georges Lemaître had a big idea. He said that a very long time ago, the universe started as just a single point. He said the universe stretched and expanded to get as big as it is now, and that it could keep on stretching The universe is a very big place, and it’s been around for a very long time. Thinking about how it all started is hard to imagine. Some More Information

Just two years later, an astronomer named Edwin Hubble noticed that other galaxies were moving away from us. And that’s not all. The farthest galaxies were moving faster than the ones close to us. This meant that the universe was still expanding, just like Lemaître thought. If things were moving apart, it meant that long ago, everything had been close together.

Everything we can see in our universe today—stars, planets, comets, asteroids—they weren't there at the beginning. Where did they come from?

A Tiny, Hot Beginning

When the universe began, it was just hot, tiny particles mixed with light and energy. It was nothing like what we see now. As everything expanded and took up more space, it cooled down.

The tiny particles grouped together. They formed atoms. Then those atoms grouped together. Over lots of time, atoms came together to form stars and galaxies.

The first stars created bigger atoms and groups of atoms. That led to more stars being born. At the same time, galaxies were crashing and grouping together. As new stars were being born and dying, then things like asteroids, comets, planets, and black holes formed!

The inequality represented by the graph in slope intercept form is

A graph is a pictorial representation of data and the graph presented represents inequality data

The graph shows a linear function written in the slope intercept form  form as

y = mx + c

where slope, m calculated as

c = intercept

x = input variables

y = output variables

calculation of slope

The points used for the slope is gotten from the graph as (2. 0)  (0, -4)

m = (y₂ - y₁) / (x₂ - x₁)

substituting the values

= ( -4 - 0 ) / ( 0 - 2 )

= -4 / -2

= 2

y intercept, c

this is a point where the graph cuts the y axis

c = -4

The graph contains

this gives the idea to use less than or equal to written with the symbol ≤

hence the equation is written using y = mx + c and substituting the values

y ≤ 2x - 4

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