On average, 28 percent of 18 to 34 year olds check their social media profiles before getting out of bed in the morning. Suppose this percentage follows a normal distribution with a random variable X, which has a standard deviation of five percent. Find the probability that the percent of 18 to 34 year olds who check social media before getting out of bed in the morning is, at most, 32.

Answer:

The actual dimensions of the kitchen are  12 feet by 14  feet

Step-by-step explanation:

The kitchen's real measurements are 12 feet by 14 feet.

Detailed explanation:

4 / 0.8 = 5, 7 / 1.4 = 5. The actual drawing ratio is a 5:1 ratio.

Consequently, 2.4 inches multiplied by 5 is 12 feet and 2.8 inches multiplied by 5 equals 14 feet.

12 ft. x 14 ft.

Find the scale of the drawing

\(\frac{0.8}{4} \frac{in}{ft.} = \frac{1.4}{7} = 0.2 \frac{in}{ft.}\)

To determine the precise dimensions subtract 0.2 from the measurements on the scale illustration to get 12 feet (2.4/0.2).

2.8/0.2 = 14 ft

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Answer:

About 25 yards.

Step-by-step explanation:

Length of actual park is 60 yards

Scale factor = 1 inch : 10 yards

Length of drawing = 6 inches

Length of actual park

Length of actual park = Scale factor × Length of drawing

Length of actual park = 10 × 6

Length of actual park = 60 yards

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SOLUTIION

The given equations are

This further gives

Therefore the solutions are:

From the option considering the value q=8, it follows

And

Therefore the solution is

Answer:

see below

Step-by-step explanation:

-(5)² = -1 * 5² = -1 * 25 = -25

List ascending order:

  -5.3 x 10² = -5.3 x 100 = -530

  -50

  \(\frac{1}{2} = 0.5\)

  \(\sqrt{25} = 5\)

  {-5.3 x 10², -50, \(\frac{1}{2}\), \(\sqrt{25}\)}

Describe \(\sqrt{8}\): Real, Irrational

List descending order:

  \(\sqrt{72} = 8.485\)

  6

  \(\pi = 3.14159\)

  \(-\frac{3}{4} = -0.75\)

  {\(\sqrt{72}\), 6, \(\pi\), \(-\frac{3}{4}\) }

George loan:

  Principal * rate * time = Interest

  2000 * .034 * 2 = 136

  Principal + Interest = Payback

  2000 + 136 = $2,136

Toy:

  100% - 15% = 85%

  .85 * 4.99 = $4.24

30ft high above the ground is the lamp.

What is an angle?

An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

Here, we have

BC⊥AD and DE⊥AD

∠ABC = ∠ADE(=90°)

Also,∠A=∠A

ΔABC ΔADE (AA similarity)

AB/AD = BC/DE

40/(200 + 40) = 5ft/DE

DE = 5ft×6 = 30ft

Hence, 30ft high above the ground is the lamp.

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The constants α, β, and k are all zero, and the solution to the IVP is y(t) = e²{-2t}, with t = -0.5ln(7)  the condition limt→∞y(t) = 7,t = -0.5ln(7)

Using the method of undetermined coefficients to find the general solution of the differential equation:

y'' + 3y' + 2y = 0

The characteristic equation is:

r²2 + 3r + 2 = 0

Factoring this equation, we get:

(r + 2)(r + 1) = 0

So the roots are r1 = -2 and r2 = -1. Therefore, the general solution is:

y(t) = c1e^{-2t} + c2e^{-t}

Next, we use the information that y1(t) = e²{-3t} is a solution to the differential equation. Substituting this into the general solution, we get:

e²{-3t} = c1e²{-2t} + c2e²{-t}

equation to solve for c1 and c2. Multiplying both sides by e^{2t}, we get:

e²{-t} = c1 + c2e²t

Taking the limit as t approaches infinity,  that c1 must be zero in order for the right-hand side to converge to a finite value. Therefore, we have:

c1 = 0

Substituting this into the previous equation,

e²{-t} = c2e²t

Dividing both sides by e²t,

e²{-2t} = c2

Therefore, we have:

c2 = e²{-2t}

Substituting these values into the general solution,

y(t) = c1e²{-2t} + c2e²{-t} = e²{-2t}

So α = β = 0 and k = -2. Finally,  the information that limt→∞y(t) = 7. Since y(t) = e²{-2t}, we have:

limt→∞e²{-2t} = 7

Taking the natural logarithm of both sides,

-2t = ln(7)Solving for t,

t = -0.5ln(7)

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Product of (x+3)(x-4) is x² - x - 12.  

The process of multiplying two or more polynomials with others is known as polynomial multiplication.

To obtain the final polynomial, the terms of the first and second polynomials are multiplied.

We can multiply polynomials in a variety of ways depending on the kinds we are using.

Here we have

Multiply: (x+3)(x-4)  

=> x(x) + x(-4) + 3(x) + 3(-4)

=> x² - 4x + 3x - 12

=> x² - x - 12  

Therefore,

Product of (x+3)(x-4) is x² - x - 12.  

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Answer:

Domain: -9, -6, 0, 9  I put them in ascending order

Range: -7, -6, 0, 3  I put them in ascending order.

Step-by-step explanation:

The domain is the inputs or the x values.

The range is the outputs or the y values.

Both y(t) = 0 and y(t) = (1/16)t^4 are solutions to the initial value problem y' = t * y^(1/2), where y(0) = 0.

To verify if a function is a solution to a differential equation, we need to substitute it into the equation and check if it satisfies both the equation and the initial condition.

For y(t) = 0:
y'(t) = t * (0)^(1/2) = 0
Since y'(t) = 0, this satisfies the differential equation. Additionally, y(0) = 0 satisfies the initial condition.

For y(t) = (1/16)t^4:
y'(t) = t * [(1/16)t^4]^(1/2) = t * [(1/16)^(1/2) * t^2] = (1/16)t^3
This also satisfies the differential equation. And y(0) = 0 is satisfied as well.

The fact that both y(t) = 0 and y(t) = (1/16)t^4 are solutions to the initial value problem does not contradict any theorem. It simply means that there are multiple solutions to the differential equation.

The existence of multiple solutions is possible and consistent with the nature of certain differential equations, and it is not contradictory as long as each solution satisfies the equation and the initial condition.

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Answer:

100

Step-by-step explanation:

The two angles form a straight line which is 180 degrees

5+x  +75 = 180

Combine like terms

x+80 = 180

Subtract 80 from each side

x +80-80=180-80

x = 100

Answer:

x=100°

Step-by-step explanation:

(5+x)°+75°=180°(being a straight line)

x=100°

Answer:

Step-by-step explanation:

f(x) = 0

then x =

-2 and +2

f(x) = 5

then x = +3 and -3

The total number of visitors to the zoo that day=3980.

Given:

cost of each ticket for an adult=$25

cost of each ticket for an adult=$10

Total ticket sales one day=$47,750.

⇒$25+$10=47,750

⇒25+10=47,750-----(1)

Also,

c=6a+270

6a-c=-270------(2)

multiplying eq(2) with 10 we get:

60a-10c=-2700----(3)

Adding eq(1) and eq(3) we get

25a+10c=47,750

60a-10c=-2700

--------------------------

85a=45050

--------------------

To calculate a value just divide 45050 by 85 we get

a=45050/85

a=530

Now to get the value of c substitutes a value.

c=60(530)+270

c=3450

Number of Adult visitors=530

Number of children visitors=3450

Total Number of visitors=3980.

Therefore, the total number of visitors to the zoo that day=3980.

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Answer: 60°C

Step-by-step explanation:

Because you would find the absolute number of the negative so it would be 13 instead of -13 and then you add it to 47..... 13+47=60

No, there is not sufficient evidence to substantiate the claim at the 0.10 level. Null Hypothesis (H0): p ≤ 0.69; Alternative Hypothesis (H1): p > 0.69

A newsletter publisher believes that under 69% of their readers own a Rolls Royce.

No, there is not sufficient evidence to substantiate the claim at the 0.10 level. In order to substantiate the claim at the 0.10 level, the publisher would need to collect data from their readers and perform a hypothesis test to compare the observed percentage of readers with the claimed percentage.

Null Hypothesis: The proportion of the newsletter readers that own a Rolls Royce is less than or equal to 69%.

Null Hypothesis (H0): p ≤ 0.69

Alternative Hypothesis: The proportion of the newsletter readers that own a Rolls Royce is greater than 69%.

Alternative Hypothesis (H1): p > 0.69

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The profit per bag is approximately $2.50  and the total profit is approximately is $36 , the correct option is (c) .

In the question ,

a graph of relation of price and quantity is given .

Under the perfect competition , the profit maximization condition is where price is equal to the marginal cost

that means P = MC .

price is given as = $8 ,

Form the graph ATC = $5.5

per unit profit can be calculated using the formula ,

Per unit profit = Price - ATC

per unit profit = 8 - 5.5

= $2.5

From the graph , the quantity is Q = 14.4 (approximately)

Total profit is calculated using the formula

Total Profit = (profit per unit) × (quantity)

Total Profit = 2.5 × 14.4

= $36

Therefore , The profit per bag is approximately $2.50  and the total profit is approximately is $36 .

The given question is incomplete , the complete question is

This figure is the market for bags of coffee roaster . At a price of $8 per bag . Profit per bag is approximately is      and the total profit is       .

(a) $5.50 , $78

(b) $5.00 , $60

(c) $2.50 , $36

(d) $8.00 , $114

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Answer:

1/7

Step-by-step explanation:

Answer:

1/7

Step-by-step explanation:

\(213 -12x = -23\\\\\implies 12x = 213 +23 = 236\\\\\implies x = \dfrac{236}{12}= \dfrac{59}3 = 19.67\)

The value of x from the given equation is \(19\frac{2}{3}\).

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

The given equation is 213-12x=-23.

Now, 213+23=12x

⇒ 12x=236

⇒ x=236/12

⇒ x=59/3

⇒ x=\(19\frac{2}{3}\)

Therefore, the value of x is \(19\frac{2}{3}\).

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Three iterations are performed here to solve the system of equations using the Successive Over-Relaxation (SOR) method.

To solve the system of equations using the Successive Over-Relaxation (SOR) method, we need to iterate through the equations until convergence is achieved within the given tolerance.

The system of equations is:

- x + 10y - 2z = 8    (Equation 1)

y - 52 = -4           (Equation 2)

1 + 3x - y = 0        (Equation 3)

We start with the initial guesses:

x₀ = 0

y₀ = 0.9

z₀ = 1.1

Using the SOR method, the iteration formula is:

xₖ⁺¹ = (1 - ω)xₖ + (ω/a₁₁)(b₁ - a₁₂yₖ - a₁₃zₖ)

yₖ⁺¹ = (1 - ω)yₖ + (ω/a₂₂)(b₂ - a₂₁xₖ - a₂₃zₖ)

zₖ⁺¹ = (1 - ω)zₖ + (ω/a₃₃)(b₃ - a₃₁xₖ - a₃₂yₖ)

where ω is the relaxation factor, a₁₁, a₂₂, and a₃₃ are the diagonal elements of the coefficient matrix, b₁, b₂, and b₃ are the right-hand side values, and the subscripts k and k+1 represent the iteration steps.

Given:

tol = 0.05       (tolerance)

a₁₁ = 3

a₂₂ = 10

a₃₃ = 5

ω = 0.9

Let's proceed with the calculations using the SOR method:

Iteration 1:

x₁ = (1 - 0.9)(0) + (0.9/3)(8 - 10(0.9) - 2(1.1)) = 0.6

y₁ = (1 - 0.9)(0.9) + (0.9/10)(-4 - 3(0) - 5(1.1)) = 0.833

z₁ = (1 - 0.9)(1.1) + (0.9/5)(1 - 3(0) - 10(0.833)) = 1.035

Iteration 2:

x₂ = (1 - 0.9)(0.6) + (0.9/3)(8 - 10(0.833) - 2(1.035)) = 0.610

y₂ = (1 - 0.9)(0.833) + (0.9/10)(-4 - 3(0.6) - 5(1.035)) = 0.841

z₂ = (1 - 0.9)(1.035) + (0.9/5)(1 - 3(0.6) - 10(0.841)) = 1.012

Iteration 3:

x₃ = (1 - 0.9)(0.610) + (0.9/3)(8 - 10(0.841) - 2(1.012)) = 0.620

y₃ = (1 - 0.9)(0.841) + (0.9/10)(-4 - 3(0.610) - 5(1.012)) = 0.842

z₃ = (1 - 0.9)(

1.012) + (0.9/5)(1 - 3(0.610) - 10(0.842)) = 1.008

Continue these iterations until the solution converges within the given tolerance.

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Answer:

I think its 20, hope this helps.

Answer:

one-hundred six-thousand four-hundred fifty-one

Step-by-step explanation:

To find the length of the diagonal fence that stretches from one corner to the opposite corner of a rectangle, we can use the Pythagorean theorem, which states that the square of the length of the diagonal (hypotenuse) is equal to the sum of the squares of the lengths of the two other sides (legs) of the rectangle.

In this case, the rectangle has dimensions 24 meters by 45 meters. Therefore, the length of the diagonal fence is:

Diagonal fence = √(24^2 + 45^2) meters

Simplifying the equation, we get:

Diagonal fence = √(576 + 2025) meters

Diagonal fence = √2601 meters

Diagonal fence = 51 meters

So Steve will need 51 meters of fencing to stretch diagonally from one corner to the opposite corner of his backyard.

we have the following:

solving for x:

the missing denominator is 60

Answer:

(D) 1+0.06m

Step-by-step explanation:

Let's say that m=$120

(A)= $127.2

(B)= $127.2

(C)= $127.2

(D)= $8.2

As you can see after I substituted in 120 for (m) and solved, D is the only equation that did not represent her current balance.

I hope this helps!

Answer:

D

Step-by-step explanation:

edge

The number of  children bought meal tickets =  700

The number of adult  bought meal tickets = 950

A linear equation is one that can be written as display style a 1x 1+ldots +a nx n+b=0, where x 1, ldots, x n are the variables and display style b, a 1, ldots, a n are the coefficients, which are frequently real integers.

Let x and y be the quantity of kid and adult tickets sold, respectively. 1650 tickets were sold in total, as far as we know.

x + y = 1650

x = 1650 - y

At $12 for adults and $4 for children, the total revenue from tickets is $14200. There are

4x + 12y = 14200

substituting the value of x in the equation:

4(1650 - y) + 12y = 14200

6600 - 4y + 12y = 14200

6600 + 8y = 14200

8y = 14200 - 6600 = 7600

y = 7600 / 8

= 950 adult tickets

x = 1650 - 950

= 700 children tickets

The number of  children bought meal tickets =  700

The number of adult  bought meal tickets = 950

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Answer:

what is the question?

Step-by-step explanation:

Answer: neither

Explanation:

y=1/5+2/5x

y=-1/5-2/5x

For it to be perpendicular the slopes have to be opposite reciprocals and they are not. For it to be parallel the slopes have to be the same and they too are not.

Step-by-step explanation:

y = f(x)

this has the same meaning. y is just the variable for the functional result value. while x is usually used as variable for the input value.

so (I recommend to use the brackets to make sure that people understand it is meant that x gets multilevel by 3 in the numerator, and not by 4 in the denominator),

y = 12 + (3/4)x

is the same as

f(x) = 12 + (3/4)x

you could also write it as

f(x) = 12 + 3x/4

don't skip things, always think about the rules of the sequence of the operations in an expression, and how a reader could understand it. always be as precise, complete and consistent as possible.

Answer:

a, c, e

Step-by-step explanation:

Answer:

C and E

Step-by-step explanation:

The graph's range is only between and including 0 and 1.

C and E are the only options between this range

Answer:

Holly = £510

Step-by-step explanation:

Wei-Kong = 3x

Holly = 2(3x) = 6x and

Wilfred = x

3x + 6x + x = 850

10x = 850

x = 850/10

x = 85

Holly = 6(85)= 510

Answer:

Holly receives £510.

Step-by-step explanation:

Assuming you made a typo and meant "Wei-Kong works for three times as many hours AS Wilfred:

Wilfred= x

Wei-Kong= 3x (because he works three times as long as Wilfred)

Holly= 6x (because she works twice as long as Wei-Kong)

The question asks for the total of their wages.

x + 3x + 6x = 850

10x = 850

x = 85

This is not the final answer. Substitute this value for X into the equation above for Holly:

Holly = 6x

Holly = (6)(85)

Holly = £510 (final answer)