Can someone answer this????????????????????????

The various answers to the question are:

a)

A number of extension lines needed to accommodate $90 in calls immediately:

Use the calculation for busy k servers.

\($$P_{j}=\frac{\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}}{\sum_{i=0}^{k} \frac{\left(\frac{\lambda}{\mu}\right)^{t}}{i !}}$$\)

The probability that 2 servers are busy:

The likelihood that 2 servers will be busy may be calculated using the formula below.

\(P_{2}=\frac{\frac{\left(\frac{20}{12}\right)^{2}}{2 !}}{\sum_{i=0}^{2} \frac{\left(\frac{20}{12}\right)^{t}}{i !}}$$\approx 0.3425$\)

Hence, two lines are insufficient.

The probability that 3 servers are busy:

Assuming 3 lines, the likelihood that 3 servers are busy may be calculated using the formula below.

\(P_{j}=\frac{\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}}{\sum_{i=0}^{2} \frac{\left(\frac{\lambda}{\mu}\right)^{i}}{i !}}$ \\\\$P_{3}=\frac{\frac{\left(\frac{20}{12}\right)^{3}}{3 !}}{\sum_{i=0}^{3} \frac{\left(\frac{20}{12}\right)^{1}}{i !}}$$\approx 0.1598$\)

Thus, three lines are insufficient.

The probability that 4 servers are busy:

Assuming 4 lines, the likelihood that 4 of 4 servers are busy may be calculated using the formula below.

\(P_{j}=\frac{\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}}{\sum_{i=0}^{k} \frac{\left(\frac{\lambda}{\mu}\right)^{t}}{i !}}$ \\\\$P_{4}=\frac{\frac{\left(\frac{20}{12}\right)^{4}}{4 !}}{\sum_{i=0}^{4} \frac{\left(\frac{20}{12}\right)^{7}}{i !}}$\)

Generally, the equation for is  mathematically given as

To answer 90% of calls instantly, the organization needs four extension lines.

b)

The probability that a call will receive a busy signal if four extensions lines are used is,

\(P_{4}=\frac{\left(\frac{20}{12}\right)^{4}}{\sum_{i=0}^{4} \frac{\left(\frac{20}{12}\right)^{1}}{i !}} $\approx 0.0624$\)

Therefore, the average number of extension lines that will be busy is Four

c)

In conclusion, the Percentage of busy calls for a phone system with two extensions:

The likelihood that 2 servers will be busy may be calculated using the formula below.

\(P_{j}=\frac{\left(\frac{\lambda}{\mu}\right)^{j}}{j !}$$\\\\$P_{2}=\frac{\left(\frac{20}{12}\right)^{2}}{\sum_{i=0}^{2 !} \frac{\left(\frac{20}{12}\right)^{t}}{i !}}$$\approx 0.3425$\)

For the existing phone system with two extension lines, 34.25 % of calls get a busy signal.

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Answer:

20/27

Step-by-step explanation:

Probability is simply the likelihood of a specific event occurring.

Usually, we define probability as equaling the number of favorable outcomes over the total number of possible outcomes.

Here, we are given that there are 27 tokens in a bag.

The number of tokens with there corresponding color is seen as following  

Given this, we want to find the probability of picking a blue or green token without looking.

So here, the favorable outcome (the outcome we are looking for) is the number of blue tokens while the number of possible outcomes is simply the total number of tokens.

So the number of blue and green tokens = 17 + 3 = 20

And total number of tokens = 27

Therefore, probability of picking a blue or green token is 20/27

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Answer:

10 cups

Step-by-step explanation:

6 divided by 4 is 1.5 and if you take 15 divided by 1.5 it'd be 10

Answer:

10 cups of sugar

Step-by-step explanation:

you can easily make it into a ratio.... ( the amountof sugar needed to make 15 batches of cookies is x)

x/15 = 4/6

when you multiply you get 6x = 4 × 15

6x = 60, then you divide by 6

giving you x=10

Elaine needs tο buy 350 inches οf fabric fοr her windοws.

A fractiοn represents a part οf a number οr any number οf equal parts. There is a fractiοn, cοntaining numeratοr(upper value) and denοminatοr(lοwer value).

If each windοw is 35 inches wide, then the tοtal width οf fabric Elaine needs is:

Tοtal width = 4 windοws x 35 inches per windοw

Tοtal width = 140 inches

Fabric = 2 1/2 x Tοtal width

Tο simplify this, we can first cοnvert the mixed number tο an imprοper fractiοn: 2 1/2 = 5/2

Then, we can multiply this fractiοn by the tοtal width:

Fabric = 5/2 x Tοtal width

Substituting the value οf Tοtal width, we get:

Fabric = 5/2 x 140 inches

Fabric = 350 inches

Therefοre, Elaine needs tο buy 350 inches οf fabric fοr her windοws.

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Answer:

The circle graph does not represent a function because it doesn't pass the vertical line test.

Step-by-step explanation:

Answer:

$25

Step-by-step explanation:

Simply by using long division, this can be solved. Change 60% into its decimal form (0.6,) and divide 15 by 0.6.

Answer:

x = 17

Step-by-step explanation:

all three expressions should be added together and set equal to 180 degrees

6x - 15 + 2x - 2 + 4x - 7 = 180

now combine like terms

12x - 24 = 180

add 24

12x = 204

x = 204/12

x = 17

The constant term of the binomial expansion is 3.9344626e+22

From the question, we have the following binomial expression that can be used in our computation:

(-3x⁷ + -2/x)⁴⁸

This expression can be rewritten

So, we have the following representation

(-3x⁷ + (-2/x))⁴⁸

The nth term of a binomial expression (a + b)ⁿ is represented as

(a + b)ⁿ ⇒ ⁿCₓaⁿ⁻ˣbˣ

This means that

a = -3x⁷

b = (-2/x)

n = a

So, we have the following representation:

ⁿCₐaⁿ⁻ᵃbˣ = ⁴⁸Cₐ(-3x⁷)ⁿ⁻ᵃ(-2/x)ᵃ

Expand

ⁿCₐaⁿ⁻ᵃbˣ = ⁴⁸Cₐ * (-3)ⁿ⁻ᵃ * (x⁷)ⁿ⁻ᵃ * (-2)ᵃ * (-1/x)ᵃ

By comparing both sides of the equation, we have the following equations"

Coefficient = ⁴⁸Cₐ * (-3)ⁿ⁻ᵃ * (-2)ᵃ * (-1)ᵃ

Like factors = (x⁷)ⁿ⁻ᵃ  * (1/x)ᵃ

This gives

Like factors = (x⁷)ⁿ⁻ᵃ  * (x⁻¹)ᵃ

Like factors = (x⁷)ⁿ⁻ᵃ  * (x⁻ᵃ)

Apply the law of indices

Like factors = (x)⁷ⁿ ⁻ ⁷ᵃ ⁻ ᵃ

This gives

Like factors = (x)⁷ⁿ ⁻ ⁸ᵃ

So, we have

7n - 8a = 0

Where

n = 48 i.e. the number of terms

So, we have

7 * 48 - 8a = 0

This gives

8a = 7 * 48

Divide by 8

a = 42

Recall that:

Coefficient = ⁴⁸Cₐ * (-3)ⁿ⁻ᵃ * (-2)ᵃ * (-1)ᵃ

So, we have

Coefficient = ⁴⁸C₄₂ * (-3)⁴⁸⁻⁴² * (-2)⁴² * (-1)⁴²

This gives

Coefficient = 12271512 * (-3)⁶ * (-2)⁴²

Evaluate the products

Coefficient = 3.9344626e+22

So, the constant term is 3.9344626e+22

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Answer:

just graph 5 like usual.....

Step-by-step explanation:

Answer:

You have the right answer selected (139°)

Step-by-step explanation:

Similar means that their angles are the same.

77 + 62 = 139

You have to add 180, but then you have to subtract it.

Answer:

D. 0° to 90°

Step-by-step explanation:

If we see curve of sin(o) on coordinate,  we will notice that value of sin curve increases from 0 to 90 degrees and then decreases from 90 to 180 degrees.

Hence option D is correct.

Alternatively

we see that

sin 0 = 0

sin 30 = 1/2

sin 45 = 1/\(\sqrt{2}\)

sin 60 = \(\sqrt{3} /2\)

sin 90 = 1

Thus, we see  that value of sin is increasing from 0 to 90

now lets see value of sin from 90 to 180

sin 90 = 1

sin 120 = \(\sqrt{3} /2\)

sin 135 = 1/\(\sqrt{2}\)

sin 150 = 1/2

sin 180 = 0

Thus, we see  that value of sin is decreasing from 90 to 180.

We are given the following equation :

\({:\implies \quad \sf P=2L+2w}\)

And we need to solve for w, so let's start :

\({:\implies \quad \sf P=2L+2w}\)

Now, transpose 2L to LHS ;

\({:\implies \quad \sf P-2L=2w}\)

\({:\implies \quad \sf 2w=P-2L}\)

\({:\implies \quad \boxed{\bf{w=\dfrac{(P-2L)}{2}}}}\)

Hence, Option a) is correct

The common ratio of the geometric series which satisfies the condition given is; 4.

The given Geometric series has successive terms;

Hence, the common ratio of the geometric series is the quotient of S and C;

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Answer:

A shopper that is at the 95th percentile of this distribution spends $116.125.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of $75 per trip and a standard deviation of $25 per trip.

This means that \(\mu = 75, \sigma = 25\)

How much money does a shopper spend that is at the 95th percentile of this distribution?

This is X when Z has a p-value of 0.95, so X when Z = 1.645.

\(Z = \frac{X - \mu}{\sigma}\)

\(1.645 = \frac{X - 75}{25}\)

\(X - 75 = 1.645*25\)

\(X = 116.125\)

A shopper that is at the 95th percentile of this distribution spends $116.125.

Answer:

700,000

Step-by-step explanation:

0,000,000

0,700,000

so its 700,000

Hope this helps plz hit the crown :D

Answer:

  a) x = 1 ± (3/7)√7

  b) (-∞, -5) ∪ [-2, 5) ∪ [6, ∞)

Step-by-step explanation:

You want solutions to the relations ...

We like to solve these in the form f(x) = 0. It helps avoid extraneous solutions.

  \(7+\dfrac{1}{x} -\dfrac{1}{x-2}=0\\\\\\\dfrac{7x+1}{x}-\dfrac{1}{x-2}=0\\\\\\\dfrac{(7x+1)(x-2)-x}{x(x-2)}=0\\\\\\ \dfrac{7x^2-14x-2}{x(x-2)}=0\)

The roots of the numerator quadratic are found by ...

  x² -2x -2/7 = 0 . . . . . divide by 7

  x² -2x +1 -9/7 = 0 . . . . add and subtract 1

  (x -1)² = 9/7 . . . . . . . . . . write as a square, add 9/7

  x -1 = ±√(9·7/49) = ±(3/7)√7 . . . . take the square root

  x = 1 ± (3/7)√7

Rational inequalities are best solved by identifying the roots of numerator and denominator. These tell you where the function changes sign. The end behavior of the rational function tells you what the signs are changing from.

  \(\dfrac{x^2-4x-12}{x^2-25}\ge 0\\\\\\\dfrac{(x+2)(x-6)}{(x+5)(x-5)}\ge0\)

This has a horizontal asymptote at y=1 for |x|→∞. It has vertical asymptotes at x=±5.

The sign changes occur at x ∈ {-5, -2, 5, 6}. The rational expression is positive (approaching +1) for x < -5 and for x > 6. It is negative in the adjacent intervals, so positive again for -2 < x < 5.

The inequality is satisfied for ...

The relationship of the graph g(x) = (x − 2)^3 + 6 compare to the parent function of f(x) = x^3 is that g(x) is shifted 2 units to the right and 6 units up.

Translations is a transformation technique that changes the position of an object from one point on the plane to another.

Given the function below

g(x) = (x − 2)^3 + 6

The function compared to f(x) = x^3, shows a translation of f(x) by 2 unit to the right along the horizontal and vertical translation of the function 6 units up

Hence the relationship of the graph g(x) = (x − 2)^3 + 6 compare to the parent function of f(x) = x^3 is that g(x) is shifted 2 units to the right and 6 units up.

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Answer:

g(x) is shifted 6 units to the left and 2 units down.

Step-by-step explanation:

took the test

Answer:

a.) only E occurs :

E((FUG)')

b.) both E and G but not F

EG(F')

C.) Atleast one of the events :

(E U G U F)

d.) Atleast two of the events

(EG U EF U GF)

E.) all three occurs

(EGF)

F.) none of the events occur :

(E U G U F)'

G.) At most one of the events occur

(EG U EF U GF)'

H.) at most two of them occur

(E' U G' U F')

I.) exactly two of them occur;

(EG U EF U GF) * (EGF)'

j. at most three of them occur.

EFG U (EFG)'

Step-by-step explanation:

Events = {E, F, G}

a.) only E occurs :

E((FUG)') ; E and not F or G

b.) both E and G but not F

EG(F') ; both E and G and not F

C.) Atleast one of the events :

(E U G U F) ; Either E or F or G

d.) Atleast two of the events

(EG U EF U GF) ; Either EG or EF or GF occurs

E.) all three occurs

(EGF) ; All three events, E, G and F occurs

F.) none of the events occur :

(E U G U F)' ; Neither E, G nor F occurs

G.) At most one of the events occur

(EG U EF U GF)' ; complement of atleast two) at most one

H.) at most two of them occur

(E' U G' U F') ; Either E , F or G does not occur

I.) exactly two of them occur;

(EG U EF U GF) * (EGF)' ; Exactly two events occurs and all three events Do not occur

j. at most three of them occur.

EFG U (EFG)' ; All three events occur union all three events do not occur

The length of the arc CD is 14.13 centimeters.

Remember that for an arc defined by an angle a in a circle of radius R, the length of the arc is given by:

L  = (a/360°)*2*pi*R

Where pi = 3.14

Here the angle is a = 45°

And R = 18cm, so we can replace that in the formula above to find the length.

L = (45°/360°)*2*3.14*18cm = 14.13cm

That is the length of the arc CD.

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Answer:

1/12

Step-by-step explanation:

1/2 multiplied by 1/6 equals 1/12

The corresponding height of similar rectangular prism m is 9 centimeter.

Given that, the volume of rectangular prism m is 17 cm³ and the volume of rectangular prism n is 136 cm³.

If two solids are similar, then the ratio of their volumes is equal to the cube of the ratio of their corresponding linear measures.

The height of n is 18 cm.

Here, m³/n³ = 17/136

m³/18³ = 17/136

m³/18³ = 17/136

(m/18)³ = 1/8

(m/18)³ = (1/2)³

m/18 = 1/2

m=9 cm

Therefore, the corresponding height of similar rectangular prism m is 9 centimeter.

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Answer:

y = -3x/4 + 4

Step-by-step explanation:

slope m = -3/4

-2=(-3/4)×8+b

or, b = 4

y = mx + b

y = -3x/4 + 4

Answered by GAUTHMATH

i just want a badge don't mind me ok

Answer:

the answer is px and at ako

The prove of the given trigonometric function is given below.

The given trigonometric function is,

(sin⁴(x) - cos⁴(x))/(sin²(x) - cos²(x))

Now proceed left hand side of the given expression:

We can write the expression  as,

⇒[(sin²(x))² - (cos²(x))²]/(sin²(x) - cos²(x))

Since we know that ,

Algebraic identity:

a² - b²  = (a-b)(a+b)

Therefore the above expression be

⇒(sin²(x) - cos²(x))(sin²(x) + cos²(x))/(sin²(x) - cos²(x))

⇒(sin²(x) + cos²(x))

Since we know that,

Trigonometric Identities come in handy when trigonometric functions are used in an expression or equation. Trigonometric identities hold for all values of variables on both sides of an equation. Geometrically, these identities include one or more trigonometric functions (such as sine, cosine, and tangent).

Then,

sin²(x) + cos²(x)² = 1 is an trigonometric identity

Hence,

(sin⁴(x) - cos⁴(x))/(sin²(x) - cos²(x)) = 1

Hence proved.

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Answer:

  y = 3x +8

Step-by-step explanation:

Solve for y, simplify.

  y -5 = 3(x +1)

  y -5 = 3x +3 . . . . eliminate parentheses

  y = 3x +8 . . . . . . add 5

The loaded die appears to behave differently from a fair die.Based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

To test the claim that the outcomes of the loaded die are not equally likely, we can use the chi-square goodness-of-fit test. The null hypothesis (H₀) assumes that the outcomes are equally likely, while the alternative hypothesis (H₁) assumes that they are not equally likely.

Step 1: Set up hypotheses

H₀: The outcomes of the die are equally likely.

H₁: The outcomes of the die are not equally likely.

Step 2: Select the significance level

The significance level is given as 0.025, which means we have a two-tailed test and an alpha level of 0.025 for each tail.

Step 3: Compute the test statistic

We calculate the chi-square test statistic using the observed frequencies and the expected frequencies assuming equal probabilities for each outcome.

Expected frequencies (fair die):

1: 200/6 = 33.33

2: 200/6 = 33.33

3: 200/6 = 33.33

4: 200/6 = 33.33

5: 200/6 = 33.33

6: 200/6 = 33.33

Applying the chi-square formula, we get the test statistic:

χ² = ∑((observed - expected)² / expected)

Calculating this value, we get χ² ≈ 13.97.

Step 4: Determine the critical value

Since the significance level is 0.025 and the test is two-tailed, we divide the significance level by 2 to find the critical value associated with each tail. With 5 degrees of freedom (6 categories - 1), the critical value is approximately 11.07.

Step 5: Make a decision

The test statistic (13.97) is greater than the critical value (11.07), which leads us to reject the null hypothesis. Thus, we have evidence to suggest that the outcomes of the loaded die are not equally likely.

The loaded die appears to behave differently from a fair die.

In conclusion, based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

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Therefore, the expression (7-3i) + (x - 2i)² - (4i + 2x²) in the simplest a + bi form is: -2x² - 1 - (4x + 7i)

Linear Equation                   General Form                    Example

Slope intercept form             y = mx + b                            y + 2x = 3

Point–slope form                   y – y1 = m(x – x1 )              y – 3 = 6(x – 2)

General Form                            Ax + By + C = 0               2x + 3y – 6 = 0

Intercept form                        x/a + y/b = 1                 x/2 + y/3 = 1

As a Function f(x) instead of y      f(x) = x + C                         f(x) = x + 3

The Identity Function                      f(x) = x                     f(x) = 3x

Constant Functions                      f(x) = C                       f(x) = 6

Let's start by expanding the square term (x - 2i)² using the formula for (a + b)²:

(x - 2i)² = x² - 4xi + 4i²

Note that i² = -1, so we can simplify this expression to:

(x - 2i)² = x² - 4xi - 4

Substituting this expression and the given values into the original expression, we get:

(7 - 3i) + (x² - 4xi - 4) - (4i + 2x²)

Grouping the real and imaginary terms, we get:

(7 - 4 - 2x²) + (-3i - 4i - 4x) + (x²)

Simplifying the real part, we get:

-2x² - 1

Simplifying the imaginary part, we get:

-7i - 4x

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