A box is 12 in.​ high, 24 in.​ long, and 6 in. wide. What is the longest poster you could fit in the​ box? Use a pencil and paper. Explain why you can only fit one​ maximum-length poster in the box but you can fit multiple ​26-in. posters in the same box.


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The initial mass (in mg) of the sample is  32 mg

The mass 7 weeks after the start is 0.198 mg

Exponential decay is a process in which a quantity decreases at a rate proportional to its value. This means that the larger the quantity, the faster it will decrease.

Exponential decay is modeled by the following formula:

[tex]A = A_{0} \times (1/2)^{\frac{t}{T} }[/tex]

where A is the amount after time t, A₀ is the initial amount,

T is the half-life, and t is the time elapsed

Here we have

The half-life of Palladium-100 is 4 days. After 16 days a sample of Palladium-100 has been reduced to a mass of 2 mg.

For the first question, we know that after 16 days, the amount is 2 mg, and the half-life is 4 days. We can plug these values into the formula:

[tex]2 = A_{0} \times (1/2)^{\frac{16}{4}}[/tex]

Simplifying, we get:

2 = A₀ × (1/2)⁴

2 = A₀ × (1/16)

A₀ = 2 × 16

A₀ = 32 mg

So the initial mass of the sample was 32 mg.

For the second question, we need to find the mass after 7 weeks, or 49 days. We can use the same formula, but with t = 49:

[tex]A = 32 \times (1/2)^{\frac{49}{4} }[/tex]

A ≈ 0.198 mg

Therefore,

The initial mass (in mg) of the sample is  32 mg

The mass 7 weeks after the start is 0.198 mg

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Therefore, the price that maximizes revenue is $135, and the quantity sold at that price is q0/2.

What is the unit price?

In order to find the unit price of a certain item, we just need to divide the total price paid (or total cost) by the number of items bought.

According to given information

a. Let x be the number of $18 price increases from the original price of $180, and let y be the corresponding decrease in the number of gaming systems sold. Then we have the data point (x, y) = (0, 0) and the slope of the line is -4/18 = -2/9. Using the point-slope form of a linear equation, we have:

y - 0 = (-2/9)x

y = (-2/9)x

Substituting x = 18n, where n is the number of $18 price increases, we have:

y = (-2/9)(18n) = -4n

Let q be the quantity of gaming systems sold at a price of $180. Then the equation for the price of the gaming system as a function of the quantity sold is:

p(q) = 180 + 18n = 180 + 18(q - q0)/4 = 180 + (9/2)(q - q0),

where q0 is the quantity of gaming systems sold at the original price of $180.

b. The revenue equation is given by R(q) = q*p(q). Substituting the expression for p(q) found in part (a), we have:

R(q) = q*(180 + (9/2)(q - q0)) = (9/2)q^2 + (180 - 9q0/2)q

c. To find the price and quantity sold that will maximize revenue, we can differentiate the revenue equation with respect to q, set the derivative equal to zero, and solve for q:

R'(q) = 9q - 9q0/2 = 0

q = q0/2

Substituting q = q0/2 into the revenue equation, we have:

R(q0/2) = (9/2)(q0/2)^2 + (180 - 9q0/2)(q0/2)

R(q0/2) = (9/8)*q0^2 + (45/2)*q0

To find the corresponding price, we can use the expression for p(q) found in part (a):

p(q0/2) = 180 + (9/2)(q0/2 - q0)

p(q0/2) = 135

Therefore, the price that maximizes revenue is $135, and the quantity sold at that price is q0/2.

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Answer:

B

Step-by-step explanation:

THE TWO SMALLER SIDES = THE LARGER SIDE HENCE ITS A TRIANGLE

Answer:

step by step explanation:

1. 9 4. -12

2. -48 5. 0

3. 17 6. 1

Answer:

y=2x

Step-by-step explanation:

equation formula is y=mx+b

m is slope

b is y-intercept

you know that slope is 2

y intercept is 0

so plug it into the equation

y=2x+0 or just y=2x

Answer:

$526.75 i believe

Step-by-step explanation:

The dimensions of the set of shelves should be approximately 4.21 feet in height and 21.05 feet in width.

When plotted on a coordinate plane, an algebraic equation known as a linear equation looks like a straight line. The variable (or variables) in this equation always have a greatest power of 1, making it a constant. In other words, a linear equation simply makes use of the fundamental operations of addition, subtraction, and multiplication of variables to the first power, as well as constants.

Given:

Width of the set of shelves = 5 times the height of the set of shelves

Number of shelves = 3

Total amount of wood available = 80 feet

Let's denote the height of the set of shelves as "h" and the width of the set of shelves as "w".

Using the first given information, we can write the equation:

Width (w) = 5 times the height (h) ==> w = 5h

Next, we know that the set of shelves has 3 shelves, so the number of shelves is fixed at 3.

Finally, we are given that we have 80 feet of wood available to build the shelves.

Using these equations, we can substitute w = 5h into the equation for the total amount of wood:

3w + 4h = 80

Substituting w = 5h, we get:

3(5h) + 4h = 80

15h + 4h = 80

19h = 80

h = 80/19

So, the height of the set of shelves is approximately 4.21 feet.

Now, substituting this value of h back into w = 5h, we get:

w = 5(4.21)

w = 21.05

So, the width of the set of shelves is approximately 21.05 feet.

Therefore, the dimensions of the set of shelves should be approximately 4.21 feet in height and 21.05 feet in width.

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the new length of AB after a dilation by a scale factor of 3 with (0,0) as the center would be 3 times the original length of AB.

How to solve the question?

To find the new length of AB after a dilation by a scale factor of 3 with (0,0) as the center, we can use the following formula:

AB' = AB x 3

where AB' is the length of AB after the dilation, and AB is the original length of AB.

However, we need to first determine the length of AB in the original right triangle ABC. To do this, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

Let's assume that AB is the hypotenuse of the right triangle ABC, and that AC and BC are the other two sides. Then we have:

AB²= AC²+ BC²

Without more information about the lengths of AC and BC, we cannot determine the value of AB. However, once we have determined the length of AB, we can use the formula above to find the new length of AB after dilation.

Assuming we know the length of AB in the original right triangle ABC, we can now use the formula for dilation to find the new length of AB:

AB' = AB x 3

For example, if AB is 5 units long in the original triangle, then after dilation, AB' would be:

AB' = 5 x 3 = 15 units

Therefore, the new length of AB after a dilation by a scale factor of 3 with (0,0) as the center would be 3 times the original length of AB.

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Check the picture below.

[tex]\sin(38^o )=\cfrac{\stackrel{opposite}{x}}{\underset{hypotenuse}{7}}\implies 7\sin(38^o)=x\implies 4.31\approx x \\\\[-0.35em] ~\dotfill\\\\ \cos(38^o )=\cfrac{\stackrel{adjacent}{y}}{\underset{hypotenuse}{7}}\implies 7\cos(38^o)=y\implies 5.52\approx y[/tex]

Make sure your calculator is in Degree mode.

Answer:

Step-by-step explanation:

You want the leg measures in a right triangle with a hypotenuse of 7 inches and an angle of 38°.

The mnemonic SOH CAH TOA reminds you of the relations between side lengths and trig functions:

  Sin = Opposite/Hypotenuse   ⇒   Opposite = Hypotenuse×Sin

  Cos = Adjacent/Hypotenuse   ⇒   Adjacent = Hypotenuse×Cos

The given triangle will have opposite and adjacent sides of ...

  opposite = (7 in)sin(38°) ≈ 4.31 in

  adjacent = (7 in)cos(38°) = 5.52 in

The leg lengths of the triangle are 4.31 inches and 5.52 inches.

Answer:

Let m be the mass of the object and w be the weight of the object. According to the problem, weight varies directly with mass, so we can write:

w = k * m

where k is the constant of proportionality.

To find k, we can use the information given in the problem. We know that when m = 2 kg, w = 4 N. Substituting these values into the equation above, we get:

4 N = k * 2 kg

Solving for k, we get:

k = 4 N / 2 kg = 2 N/kg

Now we can use this value of k to find the mass of an object that weighs 18 N. We can rearrange the equation above to solve for m:

m = w / k

Substituting w = 18 N and k = 2 N/kg, we get:

m = 18 N / 2 N/kg = 9 kg

Therefore, the mass of the object that weighs 18 N is 9 kg.

Answer:

The amount of persons who have heard in 30mins would be:

45 persons

Answer: To find the circumference of a circle, there are 2 formulas.

Step-by-step explanation:

The first formula is 2πr and the second formula is πd when solving any math problem. You can use either one but you would use which one is the most helpful to answer your question. Hope this helps!

The area of the shaded region in the specified figure of the square containing a circle is 21.5 m², which is the first option

A square is a quadrilateral with all sides of the same length and four interior angles which are right angles.

The figure is a composite figure comprising of a square and a circle

The radius of the circle, r = 5 meters

The side length of the square = 10 meters

The value of π = 3.14

The area of the square = 10 m × 10 m = 100 m²

The area of the circle = π × (5 m)² = 25·π m²

The area of the shaded region is the difference between the area of the square and the area of the circle, therefore;

The area of the shaded region = (100 - 25·π) m²

The area of the shaded region is therefore; (100 - 25 × 3.14) m² = 21.5 m²

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Therefore, the correct answer is: The slope of g(x) is less than the slope of f(x).

The origin is the location where the two axes meet. On both the x- and y-axes, the origin is at 0. The coordinate plane is divided into four portions by the intersection of the x- and y-axes. The term "quadrant" refers to these four divisions.

We can use the slope formula to get the slopes of the lines f(x) and g(x):

slope of f(x) = (change in y)/(change in x) = (1 - (-2))/(1 - 0) = 3/1 = 3

slope of g(x) = (change in y)/(change in x) = (2 - 0)/(0 - (-4)) = 2/4 = 1/2

The slope of g(x) is 1/2, which is less than the slope of f(x), which is 3.

Therefore, the correct answer is: The slope of g(x) is less than the slope of f(x).

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The number of years it would take is approximately equal to 53 years.

In Mathematics, a population that increases at a specific period of time represent an exponential growth. This ultimately implies that, a mathematical model for any population that increases by r percent per unit of time is an exponential function of this form:

P(t) = I(1 + r)^t

Where:

By substituting given parameters, we have the following:

96627 = 11211(1 + 0.0418)^t

8.61894567835 = (1.0418)^t

By taking the ln of both sides, we have:

Time, t = ln(8.61894567835)/ln(1.0418)

Time, t = 52.60 ≈ 53 years.

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Step-by-step explanation:

Find the LCM of 9 and 15

West   9    18     27    36     45  

East       15             30         45                   In 45 minutes

Answer:

To find the median cost of these boxes of cereal, we need to order the prices from least to greatest:

$1.90, $2.30, $2.40, $2.50, $2.50, $2.70, $2.90, $3.20, $3.50, $3.90

There are 10 numbers, so the median is the average of the 5th and 6th numbers:

Median = ($2.50 + $2.70) / 2 = $2.60

Therefore, the median cost of these boxes of cereal is $2.60.

Answer:

What is the median cost of these boxes of cereal?

$3.50, $2.30, $2.50, $3.90, $2.90, $2.40, $1.90, $2.50, $3.20, $2.70

Let's put it in order first:

$1.90, $2.30, $2.40, $2.50, $2.50, $2.70, $2.90, $3.20, $3.50, $3.90

Now find the middle number (s):

$1.90, $2.30, $2.40, $2.50, $2.50, $2.70, $2.90, $3.20, $3.50, $3.90

In this case, there are 2 middle numbers so do this:

$2.50 + $2.70

= $5.20

5.20 ÷ 2

So the median cost of those cereal boxes would be $2.60.

Step-by-step explanation:

You're welcome.

Answer:  1st one

Step-by-step explanation:

Answer: a. Yes, this is a statistical question since it includes collecting information from a test of 6th graders and utilizing factual strategies to analyze the comes about and draw a conclusion approximately the inclinations for Sweet Grove and Bushels apple juice.

b. Draw a conclusion based on the results of the experiment, and report any limitations or assumptions made during the experiment.

Step-by-step explanation:

The range of the relation whose graph is shown include the following: C. -1 ≤ y ≤ 1.

In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = {-4, 4} or -4 ≤ x ≤ 4.

Range = {-1, 1} or -1 ≤ y ≤ 1.

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Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.

To close the expansionary gap, the government would need to decrease spending by $100 billion.

The formula to calculate the change in equilibrium output due to a change in government spending is:

∆Y = (∆G / (1 - MPC))

Where:

∆Y = change in equilibrium output

∆G = change in government spending

MPC = marginal propensity to consume

Here, the output is $400 billion above its natural level, and the central bank agrees to adjust the money supply to hold the interest rate constant, so there is no crowding out. Therefore, we can assume that the change in government spending (∆G) would have a one-to-one effect on the equilibrium output (∆Y).

Given that MPC = 3/4, we can plug in the values into the formula:

400 = (∆G / (1 - 3/4))

∆G = (1 - 3/4) * 400

∆G = (1/4) * 400

∆G = 100

Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.

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Jackson is on point. Of all fish, catfish make up one-third of the total.

The United States of America, Great Britain, and other English-speaking countries predominately utilise the pound as a unit of weight.

Any quantity associated with something is assumed to contain one pound if it does. The pound is the most widely used weight unit in the English-speaking world, including Britain, America, and other nations.

Zebra danios make up half of all the fish.

More fancy guppies than catfish, by a factor of two.

x = guppies

2x = catfish

x + 2x = 1/2 of the fish population

3x = 1/2 of the fish population

3x * 2 = 6x

x = 1/6 number of fancy guppies

catfish:

2x = 2(1/6) = 2/6 = 1/3 catfish.

Jackson is on point. Of all fish, catfish make up one-third of the total.

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The complete question is,

Alberto puts 3 kinds of fish in his fish tank: zebra danios, fancy guppies, and cat fish. Half of Alberto's fish are zebra danios. He has 2 times as many catfish as he has fancy guppies. Alberto's friend Jackson says 1/3 of Alberto's fish are catfish. Is Jackson correct?

Thus, Number of hours must pass for the hands to form a straight angle is 5 hours.

To read the time on an analogue clock, look in the direction its hands are pointing. The current hour is indicated by the smallest hand, the current minute by the largest hand, and the current second by the thinnest hand.

There are 24 hours in a day, and the hour hand completes two full rotations of the clock because the numbers on the dial only go up to 12. once, from noon to midnight, and once, from midnight to noon.

Given data:

Current time on clock = 1:00

Hour hand at 1 .

Minute hand at 12.

Number of hours must pass for the hands to form a straight angle:

When

minute hand is at 12 and hour hand will be at 6.

Number of hours = 6: 00 - 1: 00

Number of hours = 5 hours

Thus, Number of hours must pass for the hands to form a straight angle is 5 hours.

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Answer: 3/4

Step-by-step explanation:

Any number as the denominator of the fraction that is less than 8 (the denominator) will give you a fraction greater than 3/8.

Another different answer could be 3/5 or 3/6.

A fraction that has a value greater than 3/8 using 3 as the numerator is 3/6, 3/4, 3/2 and so on.

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

The given fraction is 3/8.

Here, 3/8 = 0.375

We need write the fraction which is greater than 3/8 using 3 as the numerator is 3/6 = 0.5

Therefore, a fraction that has a value greater than 3/8 using 3 as the numerator is 3/6, 3/4, 3/2 and so on.

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Answer: To find the P-value, we first need to determine the direction of the alternative hypothesis. Since the alternative hypothesis is two-tailed, we need to divide the significance level (α) by 2 before finding the critical values and the rejection region. Therefore, we have:

H0: p = 0.06

Ha: p ≠ 0.06

α = 0.05/2 = 0.025

The test statistic is z = 1.79, which represents the number of standard errors that the sample proportion is from the hypothesized population proportion under the null hypothesis. We can find the P-value by looking up the area in the standard normal distribution table beyond the test statistic in both tails:

P-value = P(Z ≤ -1.79 or Z ≥ 1.79)

= P(Z ≤ -1.79) + P(Z ≥ 1.79)

= 0.0364 + 0.0364

= 0.0728

Therefore, the approximate P-value for Elliot's significance test is 0.0728. Since the P-value is greater than the significance level of 0.05, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the proportion of adults who bike to work in Elliot's city has changed significantly from the previous year.

Step-by-step explanation:

The simplified exponential expression is given as follows:

[tex]21^6[/tex]

The exponential expression in the context of this problem is defined as follows:

[tex]\frac{21^3 \times 21^5}{21^2}[/tex]

First we look at the numerator, when we have two terms with the same base and different exponents multiplying, we keep the base and add the exponents, hence:

21^3 x 21^5 = 21^8

Now we have the following division operation:

21^8/21^2.

When we have two terms with the same base and different exponents dividing themselves, we keep the base and subtract the exponents, hence:

21^(8 - 2) = 21^6.

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Answer:

mAngleABC = 76°

Step-by-step explanation:

AD is a diameter. So arcAD is half of the circle, that's 180°.

arcCD = 28°

arcAC + arcCD = 180°

arcAC + 28° = 180°

subtract 28°

arcAC = 152°

AngleABC is an inscribed angle (vertex is on the circle) so AngleABC is half of arcAC.

AngleABC

= 152 ÷ 2

= 76

AngleABC = 76°