1) If a bookshelf is 28 inches long, how many 1 inch books will fit on the bookshelf?
​

Answer:

[tex]\left(x-1+3y\right)\left(x-1-3y\right)[/tex]

Step-by-step explanation:

[tex]x^2-2x+1-9y^2\\\\factor(skip for time)\\\\\left(x-1\right)^2-9y^2\\\\[/tex]

A little algebra process later...

you got the answer

Hoped this helped ya

<3

Answer:

(x-1-3y) x (x-1+3y)

Step-by-step explanation:

x^2-2x+1-9y^2

Using a^2 - 2ab + b^2 = (a-b)^2 (factor the expression) = (x-1)^2 - 9y^2

(x-1)^2 - 9y^2 = (x-1-3y) x (x-1+3y)  should be the answer :)

Answer:

a

  [tex] P(X = 0) =  0.6065 [/tex]

b

[tex]P(x <  25 ) =   1.18 *10^{-33} [/tex]

c

 [tex]  P(x \le 5 ) =  0.9994 [/tex]    

Step-by-step explanation:

From the question we are told that

  The rate  is [tex]\lambda =  \frac{1}{2}\   hr^{-1}[/tex]    =  0.5 / hr

  Generally  Poisson distribution formula is mathematically represented as

       [tex]P(X = x) =  \frac{(\lambda t) ^x e^{-\lambda t }}{x!}[/tex]

Generally the probability that no error occurred during a day is mathematically represented as  

Here  t =  1  hour according to question a

So

   [tex]P(X = x) =  \frac{\lambda^x e^{-\lambda}}{x!}[/tex]

Hence

   [tex][tex]P(X = 0) =  \frac{\frac{1}{2} ^0 e^{-\frac{1}{2}}}{0!}[/tex]

=>  [tex] P(X = 0) =  0.6065 [/tex]

Generally the probability that  a critical error occurs since the start of a day is mathematically represented as

Here  t =  1  hour according to question a

So

   [tex]P(X = x) =  \frac{\lambda^x e^{-\lambda}}{x!}[/tex]

Hence

      [tex]P(x \ge 25 ) =  1 - P(x <  25 )[/tex]

Here

     [tex]P(x <  25 ) = \sum_{x=0}^{24} \frac{e^{-\lambda} * \lambda^{x}}{x!}[/tex]

=>   [tex]P(x <  25 ) =  \frac{e^{-0.5} *0.5^{0}}{0!} + \cdots + \frac{e^{-0.5} *0.5^{24}}{24!}[/tex]

[tex]P(x <  25 ) =  0.6065 + \cdots + \frac{e^{-0.5} *0.5^{24}}{6.204484 * 10^{23}}[/tex]

[tex]P(x <  25 ) =  0.6065 + \cdots + 6.0*10^{-32}[/tex]

[tex]P(x <  25 ) =   1.18 *10^{-33} [/tex]

Considering question c

Here  t =  2  

Gnerally given that the  system just started up and an error occurred  the probability the next reset will occur within 2 hours

[tex]P(x \le 5 ) =  \sum_{n=0}^{5}  \frac{(\lambda t) ^x e^{-\lambda t }}{x!}[/tex]

=> [tex]P(x \le 5 ) =   \frac{(0.5 *  2) ^ 0 e^{- 0.5  * 2 }}{0!} + \cdots  +   \frac{(0.5 *  2) ^ 5  e^{- 0.5  * 2 }}{5!}[/tex]

=> [tex]P(x \le 5 ) =   \frac{1* 2.7183 }{1 } + \cdots  +   \frac{1  *2.7183 }{120}[/tex]

=>  [tex]P(x \le 5 ) =   2.7183 + \cdots  +   0.0226525[/tex]

 [tex]  P(x \le 5 ) =  0.9994 [/tex]    

Answer:

x = 9°

y = 119°

Step-by-step explanation:

Given,

y° = 61°+58° { the exterior angle formed by producing the side of triangle is equal to two non-adjacent angle}

or, y° = 119°

therefore, y° = 119°

Now,

52°+y°+x° = 180°{the sum of angle if triangle is 180°}

or, 52°+119°+x°= 180°

or, 171°+x° = 180°

or, x° = 180°-171°

or, x° = 9°

therefore, x° = 9°

Answer:

Step-by-step explanation:

5.234

Slope: 1/2

y-intercept(s): (0, 7/3)

x: 0, 7

y: 7/3, 0

Step-by-step explanation:

y=-3 -1/3(1+2)=2/3.3=1.3=3

y=3

Answer:

2034

Step-by-step explanation:

Answer:hbjnhbgfvrdfghjhgfdfghjhgfghjkl

Answer:

elsa's interval width will be greater than that of frank

Step-by-step explanation:

first of all we are told that both Elsa and Frank have the same sample proportion so their midpoint is also going to be the same.

now as the confidence level goes higher, so also would the margin of error increase. then the width of the confidence interval would rise so it can be more confident.

from this question elsa has a larger confidence level therefore her intervals width will be greater than franks own.

Answer:

-15, -9, -3, 3

Step-by-step explanation:

First One:

y =3(-4)-3 is -15

Second:

y= 3(-2)-3 is -9

Third:

y= 3(0)-3 is -3

Last One:

y= 3(2)-3 is 3

Answer:

You're right!

Step-by-step explanation:

Answer:

Were you right?

Step-by-step explanation:

Answer:

10%

Step-by-step explanation:

(a) What percentage of meals had less than 10 grams of fat?

(b) Round your answer to the nearest tenth of a percent.

To find the percentage of meals with less than 10 grams of fat, count the number of meals with less than 10 grams of fat and divide by the total number of meals; multiply this figure by a hundred.

(A) Total number of meals = 550

Number of meals having less than 10 grams of fat = 77

Percentage of meals having less than 10 grams of fat = 77/550 × 100

= 0.14 × 100 = 14%

(B) Rounding the answer to the nearest tenth of a percent means approximating it to the nearest multiple of 10 that is not more than 100 (where 100 here represents a full cent or 'percent').

The multiples of 10 that are close to 14 are 10 and 20. The closest being 10, your answer becomes 10%

Answer:

26.31

Step-by-step explanation:

You just have to count up the shapes in each place.

Answer:

$11.20

Step-by-step explanation:

you just double the cost of 2.5 pounds because 2.5 +2.5 is 5

Answer:20.16

Step-by-step explanation:

That is we want the price of

9

pounds (lets call it

$

x

) to be such that

$

5.60

:

2.5

pounds

is the same as

$

x

:

9

pounds

or written as fractions, we want

$

5.60

2.5

pounds

=

$

x

9

pounds

That is

XXX

$

x

=

$

5.60

2.5

pounds

×

9

pounds

XXXXX

=

$

50.40

2.5

=

$

20.16

Answer:

answer is 5

Step-by-step explanation:

f(5)= -5×5^2+26×5

= -125+130

= 5

Answer:

hi to what. good bye???????

Answer:

[tex]95 \frac{3}{4} \: inch \leqslant x \leqslant 96 \frac{1}{4} \: inch[/tex]

Step-by-step explanation:

Given that a lumber supplier sells 96 inch Pieces of oak which must be within 1/4 of an inch.

This situation can be represented by the following absolute value inequality:

[tex]|x \: - 96| \: \leqslant \: \frac{1}{4} [/tex].

The absolute value can be thought of as the size of something because length cannot be negative. The length must be no more than 1/4 away from 96.

To simplify this, pretend this is a standard equality, |x-96| = 1/4. 1/4 is the range of acceptable length, 96 is the median of the range, and x is the size of the wood.

First apply the rule |x| = y → x = [tex]\pm[/tex]y

|x-96| = 1/4

x - 96 = [tex]\pm[/tex]1/4

x = [tex]96 \pm 1/4[/tex]

(These are just the minimum, and maximum sizes)

Now with a less than or equal to, the solutions are now everything included between these two values.

Therefore:

[tex]96 - 1/4 \: \leqslant x [/tex] [tex]\leqslant \: 96 + 1/4 [/tex]

With less than inequalities, you must have the lower value on the left, and the higher value on the right.

If x represents the size of the pieces, then the acceptable lengths are represented by this following inequality:

[tex]95 \frac{3}{4} \: inch \leqslant x \leqslant 96 \frac{1}{4} \: inch[/tex]

This is interpreted as x (being the size of the oak) is greater than or equal to 95 3/4, and less than or equal to 96 1/4 in inches.

Answer:

Step-by-step explanation:

The maximum profit will be found in the vertex of the parabola, which is what your equation is. You could do this by completing the square, but it is way easier to just solve for h and k using the following formulas:

[tex]h=\frac{-b}{2a}[/tex] for the x coordinate of the vertex, and

[tex]k=c-\frac{b^2}{4a}[/tex] for the y coordinate of the vertex.

x will be the selling price of each widget and y will be the profit. Usually, x is the number of the items sold, but I'm going off your info here for what the vertex means in the context of this problem.

Our variables for the quadratic are as follows:

a = -10

b = 600

c = -3588. Therefore,

[tex]h=\frac{-600}{2(-10)}=30[/tex] so the cost of each widget is $30. Now for the profit:

[tex]k=-3588-(\frac{(600)^2}{4(-10)})[/tex] This one is worth the simplification step by step:

[tex]k=-3588-(\frac{360000}{-40})[/tex] and

k = -3588 - (-9000) and

k = -3588 + 9000 so

k = 5412

That means that the profit made by selling the widgets at $30 apiece is $5412.

Hence,the profit made by selling the widgets at $[tex]30[/tex] apiece is $[tex]5412[/tex].

What is the maximum profit?

Maximum profit, or profit maximisation, is the process of finding the right price for your products or services to produce the best profit.

Here given that,

A company sells widgets. The amount of profit, [tex]y[/tex], made by the company, is related to the selling price of each widget, [tex]x[/tex], by the given equation.

As the maximum profit found in the vertex of the parabola,

Here, [tex]x[/tex] will be the selling price of each widget and [tex]y[/tex] will be the profit.

The number of items sold is [tex]x[/tex].

So, the quadratic equation is:-

[tex]a = -10b = 600c = -3588.[/tex]

Therefore, so the cost of each widget is $[tex]30[/tex].

For the profit:-

[tex]k = -3588 - (-9000) andk = -3588 + 9000 sok = 5412[/tex]

Hence,the profit made by selling the widgets at $[tex]30[/tex] apiece is $[tex]5412[/tex].

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Answer:

The number of tickets sold at the gate is [tex] G = 211.25[/tex]

The number of tickets sold in advance is  [tex]  A = 311.25 [/tex]

Step-by-step explanation:

From the question we are told that

 The cost of a tickets at the gate is [tex]a =  \$ 5[/tex]  

  The cost of a ticket in advance is  [tex]b =  \$ 3[/tex]

Let the number of ticket sold in the gate be G

Let the number of ticket sold in advance  be   A

From the question we are told that

  One hundred more tickets were sold in advance than at the gate and this can be mathematically represented as

       [tex]G  +  100 =  A[/tex]

From the question we are told that

  The total revenue from ticket sales was $1990  and this can be mathematically represented as

    [tex]5 G  +  3A  =  1990[/tex]

substituting for  A in the equation above

    [tex]5 G  +  3[G  +  100]=  1990[/tex]    

    [tex]5 G  +  3G  +  300=  1990[/tex]    

    [tex] 8G  +  300=  1990[/tex]  

    [tex] 8G  =  1690[/tex]

=>  [tex] G = 211.25[/tex]

Substituting this for G in the above equation

     [tex]5 [211.25]  +  3A  =  1990[/tex]

=>    [tex]  3A  =  1990 - 1056.25[/tex]

=>    [tex]  A = 311.25 [/tex]

Answer:

2 plus 3

Step-by-step explanation:

Answer:

that what

Step-by-step explanation:

Answer:

97.65

Step-by-step explanation:

97.65

Step-by-step explanation

Answer:

-5/6,-1/4,-0.11,0.567

Step-by-step explanation:

A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. The probability of at most 2 red cards is 0.5.

A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,

P(x) = ⁿCₓ (pˣ) (q⁽ⁿ⁻ˣ⁾)

Where,

x is the number of successes needed,

n is the number of trials or sample size,

p is the probability of a single success, and

q is the probability of a single failure.

Using the given information the number of cards is 24 out of which 12 are red. Therefore, the probability of getting a red card is 0.5.

A) All red cards.

P(X=5) = ⁵C₅ (0.5⁵) (0.5⁰)

            = 0.03125

B.) at least two red cards.

P(X≥2) = 1 - ⁵C₀ (0.5⁰) (0.5⁵) - ⁵C₁ (0.5¹) (0.5⁴)

= 0.8125

C.)  At most 2 red cards.

P(X≤2) = ⁵C₀ (0.5⁰) (0.5⁵) + ⁵C₁ (0.5¹) (0.5⁴) + ⁵C₂ (0.5²) (0.5³)

           = 0.5

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Answer:

99.7%

Step-by-step explanation:

Empirical rule formula states that:

• 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ.

• 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ.

• 99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.

From the question, we have mean of 98.18 F and a standard deviation of 0.65 F

The approximate percentage of healthy adults with body temperatures between 96.23 F and100.13 ​F is

μ - 3σ

= 98.18 - 3(0.65)

= 98.18 - 1.95

= 96.23 F

μ + 3σ.

98.18 + 3(0.65)

= 98.18 + 1.95

= 100.13 F

Therefore, the approximate percentage of healthy adults with body temperatures between 96.23 F and 100.13 ​F which is within 3 standard deviations of the mean is 99.7%

Answer:

Option C: an outline of a pine tree

Step-by-step explanation:

Artists usually use two main types of shapes when drawing. One is geometric shape and the other is bimorphic shape.

A geometric shape simply refers to common regular and precise shapes like triangles, rectangles, squares which are commonly found in man made objects. Whereas, a bimorphic shape is one that is basically rounded or irregular and depicts natural things or living organisms.

Now, from the question, the only thing there that refers to a natural occurring object is "an outline of a pine tree".

Thus, it is a bimorphic shape.

Answer:

C. an outline of a pine tree

Step-by-step explanation:

I just took the test!

Answer:

2 2/3 or 8/3

Step-by-step explanation:

Formula for each side = 2/3 x 2/3

2/3 x 2/3 = 4/9

6 sides

4/9 x 6 or 4/9 + 4/9 + 4/9 + 4/9 + 4/9 + 4/9

=2 2/3 or 8/3

Answer:

2 2/3

Is the answer

Answer:

[tex]9\sqrt{2}[/tex]

Step-by-step explanation:

d = [tex]\sqrt{(5-(-4)^2+(5-(-4)^2 \\[/tex]

d = [tex]\sqrt{(9)^2+(9)^2[/tex]

d = [tex]9\sqrt{2}[/tex]

Answer:

D i think... sry if im not correct i tried my best

Step-by-step explanation:

Answer:

(6,11)

I can confirm that this question is right.

12/2      22/2

(6   ,        11)

Answer:cool

Step-by-step explanation:

Answer:

23

Step-by-step explanation:

let the number be 'a'

-2(a - 19)= -8

open the brackets

-2a + 38 = -8

collect like terms

38 + 8 = 2a

46 = 2a

a = 23