The ages of people in a movie theater are normally distributed with a mean of 32 years and a standard deviation of 6.2 years. What is the age of a movie attendee with a z-score of -1.2?

enter the answer, rounded to the nearest tenth.

Answer: It has to be between 0.1 to 0.3

Step-by-step explanation:

1 . For the two-variable linear equation, produce three points » ordered pair solutions (x, y).

2 . Put each point on a coordinate plane and plot it.

3 . Draw an arrow at each end of a line that passes through the indicated spots.

When two equations are given and we are supposed to draw a graph.

We first have to take any random value of x preferably a small number like 1, 2 etc. and put this value in the equation and get the value of y .

Similarly, do the same for the second equation and get atleast three to four values of both x and y and plot them in a graph .

To cross check whether the graph plotted is correct ; HINT : they should form a straight line .

The graph is given below :

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Answer:

225

Step-by-step explanation:

(- 15)² = - 15 × - 15 = 225

Step-by-step explanation:

it is simple, really.

the interception angles of parallel lines with another, intersecting line are the same for every parallel line.

so, the angle at the intersection point are the same for the lines m and n.

that means the angle on the right side of (x - 3) is (8x + 3).

and the angle on the left side of (8x + 3) is (x - 3).

now, the sum of all angles around a single point on one side of a line is always 180°.

therefore,

(x - 3) + (8x + 3) = 180

x - 3 + 8x + 3 = 180

9x = 180

x = 180/9 = 20

Answer:

No! Brendan has totally got the wrong idea.

Step-by-step explanation:

Numbers on the right hand side of zero are said to be positive, while, the numbers on the opposite side are said to be negative.

That means Brendan's correct in saying that -1/3 lies on the opposite side of 3, since negative numbers lie on the opposite side of the positives.

But,

Negative "of" a number is the same number with opposite sign.

That is, if a number is 3 units away from the zero, it's negative will also be 3 units away from zero, but on the opposite side.

-1/3 and 3 do not lie at the same distance from zero.

-1/3 would be approached before -1 by walking in the negative direction whereas 3 would be approached after 1.

Therefore, Brendan is wrong as the negative of a number has opposite sign but same "magnitude".

The number of edges of a polyhedron with 4 faces and 4 vertices will be 6.

The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.

Using Euler's formula, the number of the edges does a polyhedron with 4 faces and 4 vertices have

We know the formula for the edges of the polyhedron will be

F + V = E + 2

The number of faces, vertices, and edges of a polyhedron are denoted by the letters F, V, and E.

Then we have

4 + 4 = E + 2

     E = 8 - 2

     E = 6

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Answer: 25.5%

Step-by-step explanation:

Answer:

1000

Step-by-step explanation:

l=PRT/100

I=5000*4*5/100

I=1000

Answer:

Step-by-step explanation:

so by "exact" they mean leave in the \(\sqrt{x}\) parts.... sooo

they tell us the Hypotenuse  ( Hyp) and one  angle and want that side Opposite ( Opp)  of the angle... sooo use the mnemonic

SOH CAH TOA  

to help remember how the sin , cos, and tan functions fit on a triangle

there problems b/c easy A's when you get this.  :P so learn it, know it, live it  :D

Sin = Opp / Hyp

Cos = Adj / Hyp

Tan = Opp / Adj

now look at which one of the above formulas have the things we know and want to find

Sin looks like a good choice b/c it's got  Opp, which we want to find, and Hyp which we know and also an angle which we can plug into the function

Sin(45) = Opp / 6

see how I got that?

\(\sqrt{2}\) / 2 = Opp / 6

6 ( \(\sqrt{2}\) / 2 ) = Opp

3\(\sqrt{2}\)  = Opp

the problem says leave it exact.. so don't try to reduce \(\sqrt{2}\)  just leave it

there is  your answer

X  = 3\(\sqrt{2}\)

Answer:  Elaine is 135cm tall

Step-by-step explanation:

Elaine's height is 75% of her father's height.

We can calculate Elaine's height by multiplying her father's height by 75% or 0.75.

Elaine's height = 0.75 * 180 cm

                        = 135 cm

Therefore, Elaine is 135 cm tall.

The total number of ways/ permutation that A occupies first position is 24 ,  A occupies the first position, and B the second is 6 and a appears before b is 10 ways.

What is permutation ?

Permutation is a meeting of objects in an exceedingly definite order. The members or components of sets square measure organized here in an exceedingly sequence or linear order.

Main body:

A) a occupies the first position-

As A is first, and arrange the remaining letters.  letters (B,C,D,E,F) can be arranged as-

4*3*2*1 = 24 ways

B) a occupies the first position, and b the second

As A is first and b is just after it , there are 5 position out of which 2 are taken by A, B in order , so number of ways they can be arranged is

3*2*1 = 6 ways

C) a appears before b

in this part there is no  condition that a appears just before b , so b can be places anywhere after A.

after fixing A at first place , B can be placed at 4 places.

after fixing A at 2nd place , B can be placed at 3 places.

after fixing A at 3rd place , B can be placed at 2 places.

after fixing A at 4th  place , B can be placed at 1 places.

total ways = 4+3+2+1 = 10

Hence the answer to these parts are 24, 6,10

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The male literacy rate in chile is 97%.

The proportion of adults aged 15 and older with literacy, expressed as a percentage of the corresponding population generally or for a particular sex, in a given nation, territory, or geographic area at a specific time, usually in the middle of the year.

Reading and writing help develop abilities and support "lifelong learning."

A foundational requirement for a larger education is literacy and numeracy. Children who have trouble reading are more likely to leave school before finishing their basic education (sometimes as a result of linguistic challenges in the classroom).

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The male literacy rate in chile is 97%.

The definition of literacy rate

The proportion of adults aged 15 and older with literacy, expressed as a percentage of the corresponding population generally or for a particular sex, in a given nation, territory, or geographic area at a specific time, usually in the middle of the year.

What makes literacy crucial?

Reading and writing help develop abilities and support "lifelong learning."

A foundational requirement for a larger education is literacy and numeracy. Children who have trouble reading are more likely to leave school before finishing their basic education (sometimes as a result of linguistic challenges in the classroom).

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What is the male literacy rate in chile?

A. 85% B. 92% C. 97% D. 100%

The function y=10x(x+1) is already in factored form, with a=10, r=0, and s=-1.

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The set X is termed the domain of the function and the set Y is called the codomain of the function. Initially, functions represented the idealized relationship between varied quantities and other variables.

To see this, we can rewrite the function as f(x)=10(x-0)(x-(-1)), which matches the form f(x)=a(x-r)(x-s). Therefore, the values of a, r, and s are:

a = 10
r = 0
s = -1

It is important to note that the values of r and s are the x-intercepts of the function, or the values of x that make the function equal to zero. In this case, the x-intercepts are 0 and -1, which correspond to the values of r and s.

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Answer:

the two numbers are 62 and 26

Step-by-step explanation:

the product of these numbers is 1612

and sum is 88

please mark me as Branliest. I really need please

The two numbers are 26 and 62

Let the two numbers be x and y

If the sum of the numbers is 88, then;

If the product of the numbers is 1612, then;

From equation 2;

x = 1612/y

Substitute into 1:

1612/y + y = 88

1612 + y² = 88y

y² - 88y + 1612 = 0

Factorize the result to have y = 26 and 62

Since x = 1612/y, the value of y is 26 and 62

Hence the two numbers are 26 and 62

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Answer:

Step-by-step explanation:

80 - 48q - 21q - 6

-48q - 21q + 80 - 6

-69q + 74

\( \bold \red{ \: Ur \: Query}\)

\( \bold \red{ \: Answer}\)

⟹ 74 - 69q

\( \bold \red { \: Step \: by \: Step \: Explanation}\)

⟹ 8(10−6q)+3(−7q−2)

⟹ 80-48q - 21q-6

⟹ 74 - 69q

⟹ -69q + 74

\( \huge \bold \blue {Hope \: It \: Helps \: u}\)

Answer:

9 2/5

Step-by-step explanation:

6 38/45 + 2 5/9 ​

6 38/45 + 2 25/45 = 8 63/45 = 9 18/45 = 9 2/5

—The inscribed angle theorem states that an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle.

The measure of an inscribed angle is half the measure of the intercepted arc. That is, m∠ABC=12m∠AOC. This leads to the corollary that in a circle any two inscribed angles with the same intercepted arcs are congruent.

The limit as n approaches infinity of [(n^2 - 1)/(n^2 + 1)] is equal to 1. The limit as n approaches infinity of [(n - 1)/(n^2 + 1)] is equal to 0.

(a) The limit as n approaches infinity of [(n^2 - 1)/(n^2 + 1)] is equal to 1.

To see why, note that both the numerator and denominator approach infinity as n goes to infinity. Therefore, we can apply the limit law of rational functions, which states that the limit of a rational function is equal to the limit of its numerator divided by the limit of its denominator (provided the denominator does not approach zero). Applying this law yields:

lim(n→∞) [(n^2 - 1)/(n^2 + 1)] = lim(n→∞) [(n^2 - 1)] / lim(n→∞) [(n^2 + 1)] = ∞ / ∞ = 1.

(b) The limit as n approaches infinity of [(n - 1)/(n^2 + 1)] is equal to 0.

To see why, note that both the numerator and denominator approach infinity as n goes to infinity. However, the numerator grows more slowly than the denominator, since it is a linear function while the denominator is a quadratic function. Therefore, the fraction approaches zero as n approaches infinity. Formally:

lim(n→∞) [(n - 1)/(n^2 + 1)] = lim(n→∞) [n/(n^2 + 1) - 1/(n^2 + 1)] = 0 - 0 = 0.

(c) The limit as x approaches 2 of [x^4 - 2sin(xπ)] is equal to 16 - 2sin(2π).

To see why, note that both x^4 and 2sin(xπ) approach 16 and 0, respectively, as x approaches 2. Therefore, we can apply the limit law of algebraic functions, which states that the limit of a sum or product of functions is equal to the sum or product of their limits (provided each limit exists). Applying this law yields:

lim(x→2) [x^4 - 2sin(xπ)] = lim(x→2) x^4 - lim(x→2) 2sin(xπ) = 16 - 2sin(2π) = 16.

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Answer:

H 4/2

Step-by-step explanation:

The derivative of f(x) = arccos(x^2) is: f'(x) = -2x / √(1-x^4)

The derivative of f(x) = arccos(x^2), we'll use the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function. In this case, the outer function is arccos(u) and the inner function is u = x^2.

First, let's find the derivative of the outer function, arccos(u). The derivative of arccos(u) is -1/√(1-u^2). Next, we'll find the derivative of the inner function, x^2. The derivative of x^2 is 2x.

Now we'll apply the chain rule. We have:

f'(x) = (derivative of outer function) * (derivative of inner function)

f'(x) = (-1/√(1-u^2)) * (2x)

Since u = x^2, we'll substitute that back into our equation:

f'(x) = (-1/√(1-x^4)) * (2x)

So, the derivative of f(x) = arccos(x^2) is:

f'(x) = -2x / √(1-x^4)

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Answer:

$0.31

Step-by-step explanation:

Unit price is measured by dividing the price by the amount of an item, so 3.72/12 = 0.31

Answer: The answer is C

Step-by-step explanation:

The first four terms of an arithmetic sequence are 5, 9, 13, 17 and the nth term formula of this sequence is 4n+1.

To find the expression for the (n-1)th term, we need to substitute (n-1) into the nth term formula.

So, the nth term formula is 4n+1.

Substituting (n-1) for n, we get:

4(n-1)+1 = 4n-3

Therefore, the expression for the (n-1)th term of an arithmetic sequence is 4n-3.

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Answer:

See below

Step-by-step explanation:

Better description of what you want.

D)

3 - 2(s - 1) = 13 + 6s  Distribute the -2

3 -2s + 2 = 13 + 6s  Combine like terms

5 - 2s = 13 + 6s  Add 2s to both sides

5 - 2s + 2s = 13 + 6s + 2s

5 = 13 + 8s  Subtract 13 from both sides

5 - 13 = 13 - 13 + 8s

-8 = 8s  Divide both sides by 8

\(\frac{-8}{8}\) = \(\frac{8s}{8}\)

-1 = s

E)

2(n + 9) = -6 (2n-5) + 8  Distribute the 2 nd the -6

2n + 18 = -12n + 30 + 8  Combine like terms

2n + 18 = -12n + 38  Add 12n to both sides

2n + 12n + 18 = -12n + 12n + 38

14n + 18 = 38  Subtract 18 from both sides

14n + 18 - 18 = 38 - 18

14n = 20  Divide both sides by 14

\(\frac{14n}{14}\) = \(\frac{20}{14}\)

n = \(\frac{20}{14}\)  Divide the numerator and denominator by 2 to simplify

n = \(\frac{10}{7}\)

F)

5(4k -3) -5k = 10 +2(3k + 1)  Distribute the 5 and the 2

20k -15 - 5k = 10 +6k +2  Combine like terms

15k - 15 = 12 + 6k  Subtract 6k from both sides

15k - 6k - 15 = 12 + 6k -6k

9k -15 = 12  Add 15 to both sides

9k - 15 + 15 = 12 + 15

9k = 27  Divide both sides by 9

\(\frac{9k}{9}\) = \(\frac{27}{9}\)

k = 3

Answer:

$2499/20 or $124.95

Step-by-step explanation:

Here the cloth of cost per meter is $147/4

and the cost of 17/5 meters of cloth is (147/4)×(17/5) (147*17)/(4*5)

2499/20 or 124.95

hence the cost of 17/5 meters is $2499/20 or $124.95

Answer:

\(Remainder = 1956\)

\(Quotient = 5\)

Step-by-step explanation:

Given

\(Dividend = n\)

\(Divisor = 10000\)

\(Quotient = 1\)

\(Remainder = 2011\)

Required

Determine the quotient and remainder when the divisor is 2011

First, we need to determine the value of n.

The relationship between the given parameters is:

\(Dividend = Quotient * Divisor + Remainder\)

Substitute values in the above:

\(n = 1 * 10000 + 2011\)

\(n = 10000 + 2011\)

\(n =12011\)

So, we divide 12011 by 2011 and record the quotient and divisor:

\(\frac{12011}{2011} =\)

The integer division of 12011 and 2011 is 5.

The remainder is calculated using:

\(Dividend = Quotient * Divisor + Remainder\)

Where

\(Dividend = 12011\)

\(Quotient = 5\)

\(Divisor = 2011\)

So, Remainder =:

\(Remainder = 12011 - 2011* 5\)

\(Remainder = 12011 - 10055\)

\(Remainder = 1956\)

Hence:

\(\frac{12011}{2011} = 5\ Remainder\ 1956\)

Answer:

B. Robert's sister's sales total $18.00.

E. Robert's sister's sales are represented by x when solving 3.5x = 63 .

Step-by-step explanation:

Let

Robert sister's sales = x

Robert sales = 2.5 * x

= 2.5x

Total sales = Robert sister's sales + Robert sales

63 = x + 2.5x

63 = 3.5x

Divide both sides by 3.5

x = 63 ÷ 3.5

= 18

x = $18.00

Robert sales = 2.5x

= 2.5(18)

= $45.00

A. Robert's sales are represented by x when solving 3.5x=63 .

No

B. Robert's sister's sales total $18.00.

Yes

C. Robert's sales are represented by x when solving 2.6x=63 .

No

D. Robert's sales total $25.20.

No

E. Robert's sister's sales are represented by x when solving 3.5x = 63 .

Yes

The angle of the car's velocity with respect to the floor just before the impact is 0° (i.e., it is directly below the horizontal).

(a) To determine the velocity with which the car left the table, the conservation of energy principle can be applied. Initially, all the energy is potential energy as the car is at rest.

Therefore, the initial energy is equal to the potential energy, and the final energy is equal to the sum of kinetic and potential energies. Equating the two yields:

PE = KEPE

= mghKE

= 1/2mv²

where PE is potential energy,

KE is kinetic energy,

m is the mass of the car,

g is the acceleration due to gravity,

h is the height of the table, and

v is the velocity of the car when it leaves the table.

Substituting the given values,

PE = KE29.0²/2

= 9.81 × 0.01 × h + 0m²/2

where h is the height of the table in meters.

Solving for v, we get:

v = (2gh)1/2

= 6.57 m/s

Therefore, the velocity with which the car left the table is 6.57 m/s.

(b) To find the angle of the car's velocity with respect to the floor just before the impact, the law of conservation of momentum can be applied.

The horizontal and vertical components of the momentum are conserved independently.

Initially, the horizontal momentum is zero as the car is at rest.

Therefore, the final horizontal momentum must also be zero, i.e., the car's velocity has no horizontal component.

The vertical momentum is given by:

p = mv

where m is the mass of the car and v is the velocity of the car when it leaves the table.

Substituting the given values,

p = 0.01 × 6.57

= 0.0657 kg m/s

The angle of the car's velocity with respect to the floor just before the impact is given by:

tanθ = v_vertical/v_horizontal

= p/mv_horizontal

= 0/6.57θ

= tan⁻¹(0/6.57)

= 0°

Therefore, the angle of the car's velocity with respect to the floor just before the impact is 0° (i.e., it is directly below the horizontal).

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A drop of water is denser than a ping-pong ball.

Usually, water is made of particles that are firmly pressed together. In differentiation, plastic (the material ping pong balls are made of) may be a lightweight fabric and the particles are not as firmly stuffed together.

The thickness of a ping pong ball is 0.0840 g/cm³, though water’s thickness is 997 kg/m³. Subsequently, ping pong balls aren’t about as thick as water and will continuously coast and surface greatly quickly.

The ping pong ball appears to oppose gravity and coast within the air.

Ping-pong balls drift within the water since they are amazingly lightweight, empty, and filled with air. Too, the water’s surface pressure makes it simple for the ping pong ball to drift.

In expansion, water is denser than ping pong balls, making them look for the most noteworthy point of water.

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The sound which we hear when the pig pong ball is bounced on the floor

is 19.48 DB

The repeating of sounds, especially in rhyme, is the form of repetition that most people connect with poetry. Alliteration, assonance, and onomatopoeia are other sound patterns in poetry that give additional meaning in addition to rhyme. Every one of these audio elements has a certain purpose in a poem.

a) \(\sum \ log(n)\)

by expanding the series for each value of n is

log (1) + log (2) + log(3) + log (4) + ......... + log ( 96)

simplify the expanded form we get

0 + 0.3010 + 0.4771+0.6020 ......................... + 1.982

=> 149.9963

b) \(\sum_{n=0}\) to infinity \(\sqrt{0.9^n}\)

formula for the sum of number in geometric progression

is  a/1-r

to find the ratio of the successive terms

plugging into the formula

r = \(\frac{a_{n+1}}{a_n}\)

r = \(\frac{\sqrt{0.9^{n+1}} }{\sqrt{0.9^n} }\)

=> r = \(\frac{\sqrt{0.9^n \times 0.9} }{\sqrt{0.9^n} .1}\)

=> r = \(\frac{\sqrt{0.9} }{1}\)

=> r = \(\sqrt{0.9}\)

=> a = \(\sqrt{0.9^0}\)

=> a = \(\sqrt{1}\)

=>  a= 1

by applying the formula having the value a =1 is

\(\frac{1}{1-\sqrt{0.9} }\)

rationalize the denominator by multiplying with \(1+\sqrt{0.9}\)

=> \(\frac{1+\sqrt{0.9} }{(1-\sqrt{0.9} ) (1+\sqrt{0.9}) }\)

=> 19.4868

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