Three boxes are stacked one on top of the other. One box is 3 feet 5 inches tall, one is 5 feet 11 inches tall, and one is 4 feet 9 inches tall. How high is the stack?
Write your answer in feet and inches. Use a number less than 12 for inches.

Using relations in a right triangle, it is found that the length of AC is of 6.43 inches.

The relations in a right triangle are given as follows:

In this problem, the length of side AC is b, which is opposite to the angle of 40º, while the hypotenuse is of 10 in, hence:

\(\sin{40^\circ} = \frac{b}{10}\)

\(b = 10 \times \sin{40^\circ}\)

Using a calculator:

\(b = 6.43\)

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Answer:

It's false! because 2 3 and 6 do not sum up to each side!

Step-by-step explanation:

If α is an ordinal and β ∈ α, then β satisfies all three properties of an ordinal. Therefore, β is also an ordinal.

To prove the statement "If α is an ordinal and β ∈ α, then β is an ordinal," we need to demonstrate that if α is an ordinal and β is an element of α, then β satisfies the three properties of an ordinal:

Well-Ordering: Every element of β is strictly well-ordered by the membership relation ∈. This property holds because α is an ordinal and satisfies the well-ordering property, and β being an element of α inherits this property.

Transitivity: For any two elements γ and δ in β, if γ ∈ δ and δ ∈ β, then γ ∈ β. Since β is an element of α and α is transitive, the transitivity property carries over to β.

Trichotomy: For any two elements γ and δ in β, either γ ∈ δ, δ ∈ γ, or γ = δ. Again, this property is inherited from α, as β is an element of α.

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Answer:

1

Step-by-step explanation:

1.  One way to do this is converting both into improper fractions.  To do this, multiply the whole number by the denominator and add that to the numerator.

2 3/5 --> 2*5 is 10 --> 10+3 is 13.  --> 13/5

2.  This leaves us with 13/5 - 8/5

3.  Subtract the numerators

13/5 - 8/5 = 5/5

4.  Simplify.  If the numerator is the same number as the denominator, it's a whole number.

5/5 = 1

Answer: 480

Step-by-step explanation:

To solve this, you need to set up a proportion: 200/2.5 x/6

The 200 represents the km, and the 2.5 and 6 represent the hours. You can either solve this by multiplying 200 by 6 and setting it equal to 2.5 by x then solving for x, or you can find the rate the car travels in km in one hour. To do that, you divide 200 by 2.5 and get 80: this is your km per hour. Then you multiply that to 6 to see how far the car will go in 6 miles if it continues at the speed of 80 km per hour.

Answer:

Answer: 480 km

Step-by-step explanation:

As we know that if we keep speed or velocity constant, distance is directly proportional to time.

• In the first case:

\({ \rm{d_{1} = kt _{1}}}\)

• Substitute the variables with their respective values to find the value of constant, k

\({ \rm{200 = (k \times 2.5)}} \\ \\ { \rm{k = \frac{200}{2.5} }} \\ \\ { \underline{ \rm{ \: \: k = 80 \: km {h}^{ - 1} \: \: }}}\)

• In the second case

\({ \rm{d _{2} = kt _{2} }}\)

\({ \rm{d _{2} = (80 \times 6)}} \\ \\ { \boxed{ \boxed{ \rm{ \: \: d _{2} = 480 \: km \: \: }}}}\)

To determine when the total cost of each health club will be the same, we can set up an equation and solve for the number of months.

Let's assume the number of months is represented by 'x'.

For Club A, the total cost is given by:

Total cost of Club A = $13 (one-time fee) + $28x (monthly fee)

For Club B, the total cost is given by:

Total cost of Club B = $19 (one-time fee) + $27x (monthly fee)

To find the number of months when the total cost is the same, we set the two equations equal to each other:

$13 + $28x = $19 + $27x

Simplifying the equation, we get:

$28x - $27x = $19 - $13

$x = 6

Therefore, after 6 months, the total cost of each health club will be the same.

To find the total cost for each club after 6 months, we substitute the value of 'x' back into the equations:

Total cost of Club A after 6 months = $13 + $28(6) = $13 + $168 = $181

Total cost of Club B after 6 months = $19 + $27(6) = $19 + $162 = $181

So, the total cost for both Club A and Club B will be $181 after 6 months.

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The area of the unshaded part is 2464 cm²

The diameter of 56 cm, which means the radius is half of that: 56/2 = 28 cm.

The area of a circle is given by the formula: A = πr², where r is the radius.

= π(28)²

= π(784)

= 2464 cm².

The two semicircles form a complete circle with a diameter of 56 cm, so each semicircle has a radius of 28 cm.

The area of a semicircle is half the area of a full circle.

So, the combined area of the two semicircles is:

A₂ = 0.5π(28)²

= 0.5π(784)

= 1232 cm².

The total area of the entire figure is:

total = A₁ + A₂

= 2464 cm² + 1232 cm² = 3696 cm².

Area of the shaded regions:

The shaded regions are the two semicircles, which have a combined area of A₂

= 1232 cm².

unshaded = A total - A₂

= 3696 cm² - 1232 cm²

= 2464 cm²

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Answer:

Step-by-step explanation:

Answer:

$26.25

Step-by-step explanation:

35×.25=8.75

35-8.75= 26.25

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The previous year's total revenue for the small business was approximately $25,130.43.

The total revenue of the small business the previous year can be calculated by finding the value that is 15% more than the revenue of $28,900 this year.

To determine the previous year's revenue, we can set up the equation:

Previous Year's Revenue + 15% of Previous Year's Revenue = $28,900

Let's solve the equation to find the previous year's revenue:

Let x be the previous year's revenue.

x + 0.15x = $28,900

Combining like terms, we have:

1.15x = $28,900

Dividing both sides by 1.15, we get:

x = $28,900 / 1.15 ≈ $25,130.43

Therefore, the previous year's total revenue for the small business was approximately $25,130.43.

We set up the equation by adding 15% of the previous year's revenue to the previous year's revenue. This is done to find the total revenue that is 15% more than the previous year's revenue. By solving the equation, we find that the previous year's revenue was approximately $25,130.43.

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Answer:

9/14

Step-by-step explanation:

3/7 + 50%×3/7 =

= 3/7 + 1/2×3/7

= 3/7 + 3/14

= 6/14 + 3/14

= 9/14

The required fraction which 50% grater than 3/7 is 9/14.

Fraction to determine that 50% grater than 3/7.

Fraction of the values is number represent in form of Numerator and denominator.

Here, fraction = 50% grater than 3/7
                     = 1.5 x 3/7
                    = 4.5/7
                     =  45/70
                     = 9/14

Thus, The required fraction which 50% grater than 3/7 is 9/14.

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Answer:

x/6=12+7

x/6=19

x=19*6

x=114

Answer:

h=23

Step-by-step explanation:

triangle equals 180 degrees

180-40=140

140/4=35

Answer:

20 m/s

Step-by-step explanation:

560 m/25 s

=22.4 m/s

≈ 20 m/s ( nearest tenth of m/s )

Answer:

22.4

Step-by-step explanation:

Just divide 560 by 25 .

Answer:

22

Step-by-step explanation:

Answer:

B. 50

Step-by-step explanation:

n/5=10

n/5×5=10×5

n=50

Answer:

y = 15 , x = 6

Step-by-step explanation:

you can easily find y from first equation

Move y to the other side of the equation and reverse its sign

so (-11) changes to (+11) and now we have this equation

y = 15

now you must replace 15 instead of y in second equation ,then we have this equation

15 = 2x + 3

now we have to find x

move (+3) to other side of equation and reverse its sign

(+3) changes to (-3)

we have this equation now

15 - 3 = 2x

12 = 2x

x = 12 ÷ 2 = 6

Answer:

\(x\neq 0\)

Step-by-step explanation:

Dividing by 0 is undefined, hence not allowed.

The denominator of the first term contains x^2.

Hence 0 is not allowed.

Answer:

i) 20

ii) 50

iii) 96

iv) 400

v) 200

Step-by-step explanation:

Given equations, for which we have to solve for the variable.

i)

\(X+$10\% of X $=22\\\Rightarrow X + \dfrac{10}{100}X =22\\\Rightarrow \dfrac{11}{10}X=22\\\Rightarrow X = 20\)

ii)

\(x+$20\% of x = Rs.\ 60 $\\\Rightarrow x+\dfrac{20}{100}x =60\\\Rightarrow \dfrac{6}{5}x = 60\\\Rightarrow x = 50\)

iii)

\(x+$25\% of x = Rs. 120$\\\Rightarrow x + \dfrac{25}{100}x = 120\\\Rightarrow \dfrac{5}{4}x = 120\\\Rightarrow x = 96\)

iv)

\(X= $ Rs. 200+50\% of X$\\\Rightarrow \dfrac{50}{100}X = 200\\\Rightarrow X = 400\)

v)

\(X=180+$10\% of X$\\\Rightarrow X - \dfrac{10}{100}X = 180\\\Rightarrow \dfrac{9}{10}X = 180\\\Rightarrow X = 200\)​

The required demand function and revenue per ticket are p(x) = -0.4 * (x - 21000) + $9 and  $9.

a) To find the demand function p(x), we can use the two data points: (21000, $9) and (26000, $7). To find the slope of the demand function, we can use the formula:

slope = (change in price) / (change in attendance)

Plugging in the two data points, we get:

slope = ($9 - $7) / (26000 - 21000) = -$2 / 5000 = -0.4

To find the y-intercept, we can use either data point and the slope we just found. Let's use the first data point:

p(x) = slope * (x - 21000) + $9

Now we have our demand function:

p(x) = -0.4 * (x - 21000) + $9

b) To maximize revenue, we need to find the price that will result in the maximum number of tickets sold. This is equal to the price that corresponds to the peak of the demand function, or the maximum value of x for which p(x) is decreasing. To find this, we can take the derivative of the demand function and set it equal to zero:

dp/dx = -0.4 = 0

x = 21000

So the maximum revenue is obtained by selling 21000 tickets at the price of $9 each, for a total revenue of $189,000. To maximize revenue, the ticket price should be set at $9.

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The percent of the bags of chips weigh less than 176 grams is b 16%

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

Mean = 180

Standard deviation = 4

Bags of chips weigh less than 176 grams

This means that

x = 176

So, the z-score is

z = (176 - 180)/4

Evaluate

z = -1

The percent of the bags of chips weigh less than 176 grams is represented as

P = P(z < -1)

Using a graphing calculator, we have

Percentage = 0.15866

So, we have

Percentage = 16%

Hence , the percentage is 16%

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*Answer*

15:47

Step-by-step explanation:

He left; 15:03

Walk for; 12mins

Spends extra;4min

So by my side,

I'll sum up those values we're having to find the total time that was spent

12+4= 16mins

So, at that time when he reached at the station it was 15:19 when we add those extra mins

And so I think it'll 15:47

My thought told me so though

Graph 1 and 3 will represent the cost of raspberries and blueberries perfectly.

The general equation of a straight line is

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of straight line also represents direct proportionality as y = mx

m = y/x    

[m] is constant of proportionality.

We have Raspberries (R) cost twice as much as blueberries (B). The prices of blueberries and raspberries represent proportional relationships. In this case, 1 and 2 Illustrates this perfectly.

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Complete question

Raspberries cost twice as much as blueberries. A B The prices of blueberries and raspberries represent proportional relationships. Cost (dollars) Raspberries Weight (lb.) Raspberries Select all of the graphs that could represent the cost of raspberries and blueberries. (Select all that apply.)