Math Problem...can you help? (Functions)

The equation of Q(n) is [tex]Q(n) = \frac89 * (88n + 23)[/tex]

The functions are given as:

[tex]R(d) = \frac89 d[/tex]

[tex]P(n) = 88n + 23[/tex]

From the question, we understand that:

d = P(n)

This means that:

d = 88n + 23

Substitute d = 88n + 23 in R(d)

[tex]R(n) = \frac89 * (88n + 23)[/tex]

Also, from the question

Q(n) = R(n)

So, we have:

[tex]Q(n) = \frac89 * (88n + 23)[/tex]

Hence, the equation of Q(n) is [tex]Q(n) = \frac89 * (88n + 23)[/tex]

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Answer: C) Age Group Number of People:

18–24 20

25–31 40

32–38 120

39–45 80

Have a good day/night! I hoped this helped. :D

Answer:

  A:

Step-by-step explanation:

You want to know the table that accurately reflects the data in the described graph.

As presented here, this is a reading comprehension problem.

The problem statement tells you the first bin is labeled 18–24, and the graph there extends to 80. This eliminates tables C and D. Tables A and B show 80 people in the 18–24 age group.

The second bin is labeled 25–31, and the graph there extends to 120. This matches the entry in Table A.

Table A matches the graph.

<95141404393>

Total: 48

DIning Hall: 48(3/8)=18

so theres 30 left for the classes

30/5(#of classes)=6 per class

Since AC, MN and DB intersect at O, ∠AOM ≅ NOC and ∠MOD ≅ ∠BON by the vertical angles theorem. It is given that ∠BON ≅ ∠NOC, so by the transitive property of congruence, ∠AOM ≅ ∠MOD

An equation is an expression that shows the relationship between two or more numbers and variables.

An angle is formed from the intersection of two or more lines. Types of angles are acute, obtuse and right.

Since AC, MN and DB intersect at O, ∠AOM ≅ NOC and ∠MOD ≅ ∠BON by the vertical angles theorem. It is given that ∠BON ≅ ∠NOC, so by the transitive property of congruence, ∠AOM ≅ ∠MOD

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The missing value of x will be 9.6 mL.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

The equation is given below.

12.5 mg : 5 mL = 24 mg : x mL

Then the value of x will be

12.5 / 5 = 24 / x

          x = (24 × 5) / 12.5

          x = 9.6 mL

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32 pints of each of the two existing types of drink must be used to make 40 pints of a mixture that is 45% pure fruit juice.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Let x be the pints of 60% pure fruit juice

0.60x + 0.35(40 - x) = 0.40(40)

x = 8

= 40 - 8 (pints of 35% juice)

= 32

Thus, 32 pints and 8 pints of each of the two existing types of drink must be used to make 40 pints of a mixture that is 45% pure fruit juice.

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Answer:

$1710

Step-by-step explanation:

let me know if you want an explanation :))

Answer:

6n+1

Step-by-step explanation:

Eliminate the parenthesis by changing the symbol of each term inside

3+[5n-2+n]

Eliminate the bracket and group similar terms

5n+n+3-2

Simplify terms

6n+1

These [tex]N[/tex] outcomes make up the entire sample space, so

[tex]\displaystyle \sum_{k=1}^N P(e_k) = P(e_1) + P(e_2) + P(e_3) + \cdots + P(e_N) = 1[/tex]

We're given that [tex]P(e_{j+1}) = 2 P(e_j)[/tex] for all [tex]j\in\{1,2,\ldots,N-1\}[/tex], so

[tex]P(e_1) + 2 P(e_1) + 2^2 P(e_1) + \cdots + 2^{N-1} P(e_1) = 1 \\\\ \implies P(e_1) = \dfrac1{1 + 2 + 2^2 + \cdots + 2^{N-1}} = \dfrac1{2^N - 1}[/tex]

Then we can solve the recurrence relation to get the probability of the [tex]j[/tex]-th outcome,

[tex]P(e_{j+1}) = 2 P(e_j) = 2^2 P(e_{j-1}) = 2^3 P(e_{j-2}) = \cdots \\\\ \implies P(e_{j+1}) = 2^j P(e_1) \\\\ \implies P(e_j) = 2^{j-1} P(e_1) = \dfrac{2^{j-1}}{2^N - 1}[/tex]

The probability of getting this sequence of [tex]k[/tex] outcomes is then

[tex]\displaystyle P(E_k) = P(e_1) + P(e_2) + \cdots + P(e_k) = \sum_{j=1}^k \frac{2^{j-1}}{2^N-1} = \frac{2^k-1}{2^N-1}[/tex]

as required.

Some preliminary results: If [tex]S[/tex] is the sum of the first [tex]n[/tex] terms of a geometric series with first term [tex]a[/tex] and common ratio [tex]r[/tex], then

[tex]S = a + ar + ar^2 + \cdots + ar^{n-1}[/tex]

[tex]\implies rS = ar + ar^2 + ar^3 + \cdots + ar^n[/tex]

[tex]\implies S - rS = a(1 - r^n)[/tex]

[tex]\implies S = \dfrac{a(1 - r^n)}{1 - r}[/tex]

which gives us, for instance,

[tex]1 + 2 + 2^2 + \cdots + 2^{N-1} = \dfrac{1 - 2^N}{1 - 2} = 2^N-1[/tex]

No, your paycheck is incorrect. The gross salary will be 342.25.

The amount of money paid to any employee without any deductions of the taxes or anything is called as gross salary.

The gross salary will be calculated as follows:-

40x 7.25= $290.00 (base salary)

5x  7.25 = 36.25  (overtime)

.02x 800= 16.00 (commission)

Gross salary will be = 36.25 + 16  + 290 = $324.25

Therefore your paycheck is incorrect. The gross salary will be 342.25.

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Answer:

-4.5

Step-by-step explanation:

You arrange the numbers from lowest to highest value:

-17, -12, -11, -10, -7, -2, 7, 10, 16, 20

Then you find the one in the middle:

-7, -2

Because there are two in the middle, you add them and divide them by two:

(-7 + -2)/2 = -4.5

Your answer is -4.5.

Step-by-step explanation:

firstly arrange it increasingly

-2,-7,-10,-11,-17, 7,10,16,20

n=9 it is odd so we use (n+1/2 )th formula

9+1/2

10/2=5th

os it is -17

The value of x is 15° and the type of quadrilateral is a rhombus.

Here, we are given,

m∠A = (7x)◦, m∠B = (4x + 5)◦, m∠C =(6x + 15)◦, m∠D = (6x −5)◦

So, we will have

7x+4x+5+6x+15+6x-5=360°

23x+15°=360°

23x=345°

x=345°/23°

x=15°

Hence, the angles of the quadrilateral are:

m∠A = (7x)◦=105°,

m∠B = (4x + 5)◦ =65°

m∠C =105°

m∠D = (6x −5)◦ =85°

Since the diagonal bisects ∠B and ∠D, we get that the quadrilateral is a rhombus.

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Answer:

{x∈R | [tex]\frac{2x}{3\pi } +\frac{1}{2}[/tex], x∉Z}

Step-by-step explanation:

Given the function y=3tan(2/3x)

We know that tangent is a function that's continuous within it's domain but not continuous on all real numbers

Also, the roots of y=3tan(2/3x) is [tex]3\pi n/2[/tex] where n is an integer

Note that the domain of the function cannot be within [tex]3\pi n/2[/tex]

Therefore, {x∈R | [tex]\frac{2x}{3\pi } +\frac{1}{2}[/tex], x∉Z}

[tex](5x + 7)(8x + 7) \\ \\ 5x + 7 = 0 \\ \\ 5x = - 7 \\ \\ x = \frac{ - 7}{5} \\ \\ 8x + 7 = 0 \\ \\ 8x = - 7 \\ \\ x = \frac{ - 7}{8} .[/tex]

the values of x are -7/5 and -7/8 .

Hi!

___________________________________________________________

[tex]\rightsquigarrow\circ\boldsymbol{Answer.}\circ\leftharpoonup[/tex]

[tex]\rightsquigarrow\circ\boldsymbol{Explanation}\circ\leftharpoonup[/tex]

Set each factor equal to 0.

[tex]\twoheadrightarrow\sf 5x+7=0[/tex]

[tex]\twoheadrightarrow\sf 8x+7=0[/tex]

[tex]\bullet[/tex] Solve each equation

[tex]\twoheadrightarrow\sf 5x+7=0[/tex]

[tex]\bullet[/tex] Subtract 7 from both sides

[tex]\twoheadrightarrow\sf 5x=-7[/tex]

[tex]\bullet[/tex] Divide both sides by 5

[tex]\underline{\twoheadrightarrow\sf x=-\cfrac{7}{5}}[/tex]

[tex]\bullet[/tex] Now let's solve the second equation

[tex]\twoheadrightarrow\sf 8x+7=0[/tex]

[tex]\bullet[/tex] Subtract 7 from both sides

[tex]\twoheadrightarrow\sf 8x=-7[/tex]

[tex]\bullet[/tex] Divide both sides by 8

[tex]\underline{\twoheadrightarrow\sf x=-\cfrac{7}{8}}[/tex]

[tex]\bullet[/tex] Great job, we found the two possible values

--

Hope that this helped! Best wishes.

[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]

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Answer:

y≤x²+4x-1.

Step-by-step explanation:

1) to define the equation of the given graph; it is y=x²+4x-1 (its vertex is (-2;-5));

2) to define inequation accorging to the given graph (the area outside of the parabola means ≤).

Answer:

It is arithmetic progression

Step-by-step explanation:

If wwe see, the numbers are going down by 3 each time, therfore the common difference is 3

Hii!

_________________________________________________________

[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Answer}\circ\leftharpoonup}}[/tex]

1. This sequence is arithmetic

2. The common ratio is 3.

[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Explanation.}}}\circ\leftharpoonup[/tex]

[tex]\bullet[/tex] Difference between arithmetic and geometric sequences

[tex]\twoheadrightarrow\sf Arithmetic\quad sequences[/tex] - In arithmetic sequences, we add the same amount to obtain the next term.

[tex]\twoheadrightarrow\sf Geometric\quad sequences[/tex] - In geometric sequences we multiply times the same amount to obtain the next term.

[tex]\bullet[/tex] Since we add the same amount to get the next term, the given sequence is arithmetic

[tex]\twoheadrightarrow\sf Common\;difference:-3[/tex]

[tex]\bullet[/tex] In the given sequence we add -3, or subtract 3, to obtain the next term

--

Hope that this helped! Best wishes.

[tex]\stackrel\ast{\textsl{Reach far. Aim high. Dream big.}}[/tex]

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The attached graph represents the graph of the parallel lines

The equation of the lines are linear equation

A linear equation is represented as:

y = mx + b

Where b represents the y-intercept.

Using the above form of linear equation as a guide, the equations of the lines are

y = -x + 5

y = -x + 2

y = -x - 3

y = -x - 2

Where -5, 2, -3 and -2 are the given y-intercepts and y = -x is the base equation.

Next, we plot the equations on a coordinate grid

See attachment

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Using the normal distribution, it is found that the girl's score of 10 is higher than 99.62% of the population.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 6, \sigma = 1.5[/tex].

Her z-score is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{10 - 6}{1.5}[/tex]

Z = 2.67

Z = 2.67 has a p-value of 0.9962.

Hence her score is higher than 99.62% of the population.

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By writing Z in polar form, we will see that:

[tex]z^3 = C[/tex]

First, we can see that:

z = (-1 - i)

If we write it in polar form, we get:

[tex]z = \sqrt{2} *e^{i(\pi + \pi/4)[/tex]

If we apply the power 3, we get:

[tex]z^3 = (\sqrt{2} *e^{i(\pi + \pi/4)})^3\\\\z^3 = 2^{3/2}*e^{i*(3\pi + 3\pi/4)}\\\\z^3 = 2^{3/2}*e^{i*15\pi/4}[/tex]

Notice that:

[tex]\frac{15\pi}{4}[/tex]

Is an angle equivalent to:

[tex]\frac{15\pi}{4} - 2\pi = \frac{15\pi}{4} - \frac{8\pi}{4} = \frac{7\pi}{4} = 1.75\pi[/tex]

Because the angle is measured from the positive x-axis, this means that we will have:

[tex]z^3 = C[/tex]

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Answer:

C

Step-by-step explanation:

y = 3x - 4

4y = 12x - 4

divide the bottom equation by 4

y = 3x - 4

y = 3x - 1

y = -3

3x - 1 = -3

3x = -2

x = -2/3

(-2/3, -3) is the answer. by this logic, there is a splution so can't be a, the answer is not (0, 4) so not b so it must be c

Answer:

answer is 5

Step-by-step explanation:

I think so

if yes L I k e

Answer:

  it saves 2.5 minutes

Step-by-step explanation:

The expected value of a random variable is the sum of products of possibilities and the probability of each.

Here, you have a probability of 0.9 of saving 5 minutes, and a probability of 0.1 of adding 20 minutes.

__

The expected value of the shortcut is ...

  0.9(-5) +0.1(20) = -4.5 +2.0 = -2.5

The shortcut is expected to save 2.5 minutes on average.

_____

Additional comment

The probability of 0.9 comes from the 9 of 10 trips that result in a time saving.

Answer:

Step-by-step explanation:

2 ( x + 3 ) / 4 ( x + 1 )

2 (x + 3) ÷4 (x + 1)

2 (x + 3) ÷ 2×2(x+1)

cancel out the 2 in the numerator with the 2 in the denominator

(x + 3) ÷ 2(x + 1)

x+3 / 2(x+1)

Answer:

40600 = 4.06 × 104.

Step-by-step explanation:

Answer:

B) 10 cm

Step-by-step explanation:

Hello!

We can use the Pythagorean theorem to solve for the hypotenuse.

Formula: [tex]a^2 + b^2 = c^2[/tex]

We can plug in the values for each leg to solve for the hypotenuse.

The answer is Option B: 10 cm

Volume is a three-dimensional scalar quantity. As per the Cavaleri's principle the volume of both the figures will be the same.

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

According to Cavalieri's principle, if two figures have the same height and cross-sectional area throughout each point along that height, they have the same volume.

The height of both the objects is 16 cm, also the base area of both the objects is 96 cm². As it can be observed that for both the object there base area is the same through out their height.

Hence, as per the Cavaleri's principle the volume of both the figures will be the same.

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After taking into consideration the advantages in tax management, it will not be beneficial for Raphael and Martina to get married and avail tax benefits.

The individual taxable incomes of Raphael and Martina after availing the standard deductions will be $33,000 and $3,400 respectively. Now the computation of taxation liabilities will be computed as,

For Raphael, 10% of $33,000= $3,300;

For Martina, 10% of $3,400 = $340.

However, the joint income will be $61,200 and taxation liabilities of Raphael and Martina will be,

[tex]\rm Taxable\ Income = Total\ Income - Standard\ Deduction\\\\\rm Taxable\ Income =61200-24800\\\\\rm Taxable\ Income =\$36400[/tex]

Solving further,

[tex]\rm Joint\ Taxation = (\frac{10}{100}\ x\ 19750) + (\frac{12}{100}\ x\ 16650)\\\\\rm Joint\ Taxation = 1975+1998\\\\\rm Joint\ Taxation = \$3973[/tex]

Now, it can be compared that the joint taxation is higher than the summation of individual taxation of Raphael and Martina, and thus, tax benefits are not enough for Raphael and Martina to get married.

Hence, the tax benefits of Raphael and Martina after getting married are given as above.

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