Martha, Lee, Nancy, Paul, and Armando have all been invited to a dinner party. They arrive randomly, and each person arrives at a different time.

a. In how many ways can they arrive?

b. In how many ways can Martha arrive first and Armando last?

c. Find the probability that Martha will arrive first and Armando last.

Show your work

Answer:

21

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp/ adj

tan 60 = x / 7 sqrt(3)

7 sqrt(3)  tan 60 = x

7 sqrt(3) sqrt(3) = x

7*3 = x

21 = x

Tanθ =sin /cos

tan θ = 5/2 / y

tan (30°) = 5/2 /y

[tex]y = \frac{5 \sqrt{3} }{2} [/tex]

y=4.33

Answer:

A one solution

Step-by-step explanation:

4(x - 5) = 3x + 7

Distribute

4x - 20 = 3x+7

Subtract 3x from each side

4x-3x-20 = 3x+7-3x

x -20 = 7

Add 20 to each side

x -20+20 = 7+20

x = 27

There is one solution

Answer:

Step-by-step explanation:

Let's simplify that before we make the decision, shall we? We'll get rid of the parenthesis by distribution and then combine like terms.

4x - 20 = 3x + 7 and combining like terms and getting everything on one side of the equals sign:

1x - 27 = 0. Since that x has a power of 1 on it (linear), that means we have only 1 solution. If that was an x², we would have 2 solutions; if that was an x³, we would have 3 solutions, etc.

Answer:

(-2,2) and (-3,-4)

Step-by-step explanation:

by graphing the line and parabola, you should get this graph

Answer:

Given E(t)=1100(100-t)+580(100-t)^2

Put t = 99.5, we get

E(99.5)=1100(100-99.5)+580(100-99.5)^2

E(99.5)=1100(0.5)+580(0.5)^2

E(99.5)=1100(0.5)+580(0.25)

E(99.5)=550+145

E(99.5)=695m

Step-by-step explanation:

It can be concluded that -

E(99.5) = 695

E(100) = 0

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is the function as follows -

E(t) = 1100(100 - t) + 580(100 - t)²

The given function is -

E(t) = 1100(100 - t) + 580(100 - t)²

At → E(99.5)

E(99.5) = 1100(100 - t) + 580(100 - t)²

E(99.5) = 1100(100 - 99.5) + 580(100 - 99.5)²

E(99.5) = 1100(0.5) + 580(0.5)²

E(99.5) = 550 + 145

E(99.5) = 695

At → E(100)

E(100) = 1100(100 - t) + 580(100 - t)²

E(100) = 1100(100 - 100) + 580(100 - 100)²

E(100) = 0

Therefore, it can be concluded that -

E(99.5) = 695

E(100) = 0

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Answer:

x=60

Step-by-step explanation:

There are different ways to find x but this is what I found easiest.

To solve first note that AOD and CFB are vertical angles; this means that they are congruent. AOD consists of two angles with the measurements of 90 and x. CFB consists of two angles with the measurements of 30 and 2x. So, to find x set add the adjacent angles and set them equal to the other pair of angles. The equation would be [tex]90+x=30+2x[/tex]. First, subtract x from both sides; this makes the equation [tex]90=30+x[/tex]. Then, subtract 30 from both sides. This gives the final answer, x=60.

9514 1404 393

Answer:

Step-by-step explanation:

Put the given numbers in the relevant formula and do the arithmetic.

right cylinder

   V = πr²h = 3.14(4 cm)²(3 cm) = 3.14×48 cm³ = 150.72 cm³

cone

  V = 1/3πr²h = 1/3(3.14)(5 cm)²(12 cm) = 3.14×100 cm³ = 314 cm³

pyramid of unknown shape

  V = 1/3Bh = 1/3(16 cm²)(30 cm) = 160 cm³

square pyramid

  V = 1/3s²h = 1/3(3 cm)²(16 cm) = 48 cm³

qualitative

Step-by-step explanation:

b cos the question is in quality format

Answer:

cutee!

SUP???

Hiii friend :]

cuteee~!

prettyyy

Answer:

y = 3

Step-by-step explanation:

6sin(30) = 3

Answer:

C

Step-by-step explanation:

The graph has asymptotes at x = 2 and x = -1 corresponding to the denominator of option C.

Answer:

[tex]\displaystyle 51[/tex]

General Formulas and Concepts:

Algebra I

Algebra II

Calculus

Limits

Limit Rule [Variable Direct Substitution]:                                                             [tex]\displaystyle \lim_{x \to c} x = c[/tex]

Limit Property [Addition/Subtraction]:                                                                   [tex]\displaystyle \lim_{x \to c} [f(x) \pm g(x)] = \lim_{x \to c} f(x) \pm \lim_{x \to c} g(x)[/tex]

Limit Property [Multiplied Constant]:                                                                     [tex]\displaystyle \lim_{x \to c} bf(x) = b \lim_{x \to c} f(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle f(x) = \left \{ {{3\sqrt{2x - 1}, \ x \leq 2} \atop {6(2x - 1)^2 - 3, \ x > 2}} \right.[/tex]

Step 2: Solve

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

Book: College Calculus 10e

Answer:

[tex]\angle P[/tex]

Step-by-step explanation:

Given

[tex]\triangle PRQ = \triangle TSU = 90^o[/tex]

[tex]PQ = 20[/tex]     [tex]QR = 16[/tex]    [tex]PR = 12[/tex]

[tex]ST = 30[/tex]       [tex]TU = 34[/tex]    [tex]SU = 16[/tex]

See attachment

Required

Which sine of angle is equivalent to [tex]\frac{4}{5}[/tex]

Considering [tex]\triangle PQR[/tex]

We have:

[tex]\sin(P) = \frac{QR}{PQ}[/tex] --- i.e. opposite/hypotenuse

So, we have:

[tex]\sin(P) = \frac{16}{20}[/tex]

Divide by 4

[tex]\sin(P) = \frac{4}{5}[/tex]

Hence:

[tex]\angle P[/tex] is correct

Answer:

A or <P

Step-by-step explanation:

on edge 2021

Answer:

[tex]a = 4, -4[/tex]

Step-by-step explanation:

Step 1:  Plug in -4 for c

[tex]-a^{2} + c^{2}[/tex]

[tex]-a^{2} + (-4)^{2}[/tex]

[tex]-a^{2} + 16[/tex]

Step 2:  Solve for a

[tex]-a^{2}+16-16=0-16[/tex]

[tex]-a^{2}/-1 = -16/-1[/tex]

[tex]a^{2} = 16[/tex]

[tex]\sqrt{a^{2}} = \sqrt{16}[/tex]

[tex]a = 4, -4[/tex]

Answer:  [tex]a = 4, -4[/tex]

Where are the statements?

Answer:

5 bags of cement are required.

Step-by-step explanation:

Since to make concrete, the ratio of cement to sand is 1: 3, if cement and sand are sold in bags of equal mass, to determine how many bags of cement are required to make concrete using 15 bags of sand the following calculation must be done:

Cement = 1

Sand = 3

3 = 15

1 = X

15/3 = X

5 = X

Therefore, 5 bags of cement are required.

Answer:

6

Step-by-step explanation:

236/10 = 23 remainder 6, so 6 crayons is the answer

Answer:

[tex]{ \bf{f(x) = \tan x + 9 \sin x }}[/tex]

For gradient, differentiate f(x):

[tex]{ \tt{ \frac{dy}{dx} = { \sec }^{2}x + 9 \cos x }}[/tex]

Substitute for x as π:

[tex]{ \tt{gradient = { \sec }^{2} \pi + 9 \cos(\pi ) }} \\ { \tt{gradient = - 8 }}[/tex]

Gradient of tangent = -8

[tex]{ \bf{y =mx + b }} \\ { \tt{0 = ( - 8\pi) + b}} \\ { \tt{b = 8\pi}} \\ y - intercept = 8\pi[/tex]

Equation of tangent:

[tex]{ \boxed{ \bf{y = - 8x + 8\pi}}}[/tex]

9514 1404 393

Answer:

  x - 5,682,953

Step-by-step explanation:

If x is the number of women, and the number of men is 5,682,953 less, then the number of men is x -5,682,953

Answer:

The slope is undefined.

Step-by-step explanation:

The line must pass through the points (10,-3) and (10,-8), meaning that it must be vertical. The slope of a line is undefined if the line is vertical.

Answer:

Relationship exists between price and overall score

Step-by-step explanation:

Given the data:

Brand Price Score

Bose 180 76

Scullcandy 160 76

Koss 95 69

Phillips/O'Neill 70 58

Denon 80 50

JVC 35 26

Using the correlation Coefficient calculator ; the correlation Coefficient, R = 0.875

H0 : no relationship exists

H1 : relationship exists

Using the R Coefficient ;

The test statistic :

T = r / √(1 - r²) / (n - 2)

n = 6

The test statistic :

T = 0.875 / √(1 - 0.875²) / (4)

T =0.875 / 0.05859375

T = 0.9333

The Pvalue from test statistic :

df = n - 2 ; 6 - 2 = 4

Pvalue(0.933, 4) = 0.02246

At α = 0.05

Pvalue < α ; We reject H0 ; and conclude that relationship exists between price and overall score

Answer: $40 / $80

Step-by-step explanation: 40$ if it's $8 for BOTH per hour, or if it's $8 for ONE per hour it's $80

If y (0) = -1/3, then

-1/3 = 1 / (1 + C e ⁻⁰)

Solve for C :

-1/3 = 1 / (1 + C )

-3 = 1 + C

C = -4

So the particular solution to the DE that satisfies the given initial condition is

[tex]\boxed{y=\dfrac1{1-4e^{-x}}}[/tex]

Answer:

0.26684

Step-by-step explanation:

Given that :

Mean, μ = 62.5

Standard deviation, σ = 1.96

P(Z ≥ 63.72)

The Zscore = (x - μ) / σ

P(Z ≥ (x - μ) / σ)

P(Z ≥ (63.72 - 62.5) / 1. 96) = P(Z ≥ 0.6224)

P(Z ≥ 0.6224) = 1 - P(Z < 0.6224)

1 - P(Z < 0.6224) = 1 - 0.73316 = 0.26684

Answer:

It is a ray because there are two points with a line passing through them which is extenging on one side but not on the other.

Answer:

jhshejwjabsgsgshshsnsjs

Answer:

Step-by-step explanation:

Put the equation into center-radius form.

x² + y² + 8x - 12y + 24 = 0

x² + y² + 8x - 12y = -24

(x²+8x) + (y²-12y) = -24

(x²+8x+4²) + (y²-12y+6²) = 4²+6²-24

(x+4)² + (y-6)² = 28

Center: (-4,6)

radius: √28

Answer:

5:12

Step-by-step explanation:

125:300 simplified = 5:12

I hope this helps

Answer:

dC=3.5

DC is between 3.475 and 3.525

Step-by-step explanation:

So let dx=1 since the change there is a change in 1 unit.

Find dC/dx by differentiating the expression named C.

dC/dx=0.05x+3

So dC=(0.05x+3) dx

Plug in x=10 and dx=1:

dC=(0.05×10+3)(1)

dC=(0.5+3)

dC=3.5

Let D be the change in cost-the triangle thing.

Since dx=1 we only want the change in unit to be within 1 in difference.

So this means we want it to be from x=9 to x=1] ot from x=10 to x=11.

Let's do from x=9 to x=10 first:

DC=C(10)-C(9)

DC=[0.025×10^2+3×10+4]-[0.025×9^2+3×9+4]

DC=[2.5+30+4]-[0.025×81+27+4]

DC=[36.5]-[2.025+31]

DC=[36.5]-[33.025]

DC=3.475

Now let's do from x=10 to x=11

DC=[0.025×11^2+3×11+4]-[0.025×10^2+3×10+4]

DC=[0.025×121+33+4]-[36.5]

DC=[3.025+37]-[36.5]

DC=[40.025]-[36.5]

DC=3.525

So DC, the change in cost where the change in unit is 1, is between 3.475 and 3.525.

Answer:

Storage solution;  deionized water; stabilizes

Step-by-step explanation:

A pH scale measures the concentration of hydrogen ions in acidic and alkaline solutions.

In chemistry, pH literally means the power of hydrogen ions and it is a measure of the molar concentration of hydrogen ions in a particular solution; thus, specifying the acidity, neutrality or basicity of any chemical solution.

Mathematically, the pH of a solution is given by the formula;

[tex] pH = -log_{10}(H^{+}) [/tex]

On a pH scale, a solution with a pH of 7 is neutral, a solution with a pH below 7 is acidic and it's basic (alkaline) when it's pH is above 7.

A pH meter can be defined as a scientific instrument or device designed and developed for the measurement of the hydrogen-ion concentration in water-based solutions, in order to determine their level of acidity or alkanility.

As a general rule, when using a pH meter to take a measurement, you should keep it in a storage solution until it is needed. Also, a deionized water should be used to rinse the pH meter and gently pat dry.

Furthermore, the pH meter should be placed in a given sample solution and a reading of the measurement taken when the pH of the solution stabilizes

When taking a measurement with a pH meter, keep the instrument in the storage solution until it is needed. Rinse the pH meter with distilled water and gently pat dry.

The pH meter has been the instrument used for the measurement of the hydrogen ion concentration in a sample. The instrument has consisted of a probe that has been placed in the storage medium when it is not in use.

The working procedure of the pH meter has required the washing of pH meter with the distilled water and properly removing the excess water from the probe by pat dry.

The probe has been immersed in the sample and the pH has been recorded. After the experiment, the instrument has been again washed with the distilled water and get stored in the storage solution.

For more information about pH meter, refer to the link:

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Answer:

D: Start at the origin. Move 3 and one-half units left because the x-coordinate is Negative 3 and one-half. Negative 3 and one-half is between -3 and -4. Move 2 units down because the y-coordinate is -2.