Will a 12.5-inch x 17-inch rectangular tray fit in
the box shown? Explain.
Please help!!!

Answer: The total surface area of the cylinder is 850π m².

Step-by-step explanation:

The cylinder has a curved surface area of 408π m², which is the area of the lateral surface of the cylinder. The lateral surface of a cylinder is the curved surface that connects the top and bottom bases of the cylinder.

The formula for the lateral surface area of a cylinder is given by: Lateral Surface Area = 2πrh, where r is the radius of the cylinder and h is the height (or length) of the cylinder.

We are given that the length of the cylinder is 17 m. Since the length of a cylinder is the same as its height, we can substitute h = 17 m into the formula for the lateral surface area to get:

408π m² = 2πr(17 m)

Simplifying this equation, we get:

r = 12 m

Now that we know the radius of the cylinder, we can find the total surface area of the cylinder. The formula for the total surface area of a cylinder is given by:

Total Surface Area = 2πr(r + h)

Substituting r = 12 m and h = 17 m into this formula, we get:

Total Surface Area = 2π(12 m)(12 m + 17 m) = 850π m²

Therefore, the total surface area of the cylinder is 850π m².

The expressions that have values less than 0 are a) and b)

According to the question

Here's how you can use a number line to solve this problem:

For example in expression a) -5 + 3, start at zero and move 5 units to the left (because of the negative sign on 5), and then move 3 units to the right. The final position is at -2, which is to the left of zero. Therefore, expression a) has a value that is less than zero.

Similarly expression b) has a value that is less than zero.

Also expressions c) and d) can be solved in the same way. If the final position is to the right of zero, the expression does not have a value that is less than zero.

In conclusion, expressions a) and b) have a value that is less than zero, while expressions c) and d) do not.

What is a number line?

A number line is a visual representation of real numbers arranged in a straight line used to compare, add, and subtract numbers.

What is meant by expressions?

An expression is a combination of numbers, variables, and mathematical operations used to represent a quantity or a mathematical statement.

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The rate at which the surface area of the balloon is increasing at the instant the area is 153.24 square inches and the volume is 178.37 cubic inches is 4.96 square inches per second.

The surface area of a spherical balloon and the volume of the balloon are related by the equation [tex]A³ - 36πV²[/tex], where A is in square inches and V is in cubic inches. To find the rate at which the surface area of the balloon is increasing, we can use derivatives. We start by taking the derivative of the equation [tex]A³ - 36πV²[/tex] with respect to time (t).

[tex]d/dt[A³ - 36πV²] = 3A²dA/dt - 72πVdV/dt[/tex]

Given the rate at which the balloon is being inflated with gas (dV/dt) and the area and volume of the balloon (A, V) at the given instant, we can solve for the rate at which the area is increasing (dA/dt).

[tex]dA/dt = (3A² - 72πV)dV/dt / 36πV[/tex]

Plugging in the given values for A, V, and [tex]dV/dt,[/tex]we can calculate dA/dt:

[tex]dA/dt = (3(153.24)² - 72π(178.37))(18)/(36π(178.37)) ≈ 4.96[/tex]

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The probability of rolling two 1's is 1/18. This concludes the answer.

Why it is and what does probability mean?

Probability =  No. of favorable outcomes/Total Outcomes

Here the no of favorable outcomes = 2{(2,1), (1,2) }

Total outcomes = 36

P (1 and 2) = 2/36 = 1/18

Therefore, the solution is 1/18

Probability is a branch of mathematics that deals with the study of random events or outcomes. It is used to quantify the likelihood of an event occurring, which ranges from 0 (impossible) to 1 (certain). Probability is expressed as a ratio, fraction, or percentage. The concept of probability is used in various fields such as science, economics, finance, and statistics to make informed decisions and predictions.

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Answer:

Step-by-step explanation:

27/9a

= 3^3/3^2 a

= 3/a

Answer:

The midpoint of the diameter is (4, 1)

This is the center of the circle

=====================================================

Explanation:

Add up the x coordinates and divide in half

(-1+9)/2 = 8/2 = 4

The x coordinate of the midpoint is x = 4

Repeat for the y coordinates

(4 + (-2))/2 = (4-2)/2 = 2/2 = 1

The y coordinate of the midpoint is y = 1

The midpoint is located at (x,y) = (4,1)

The midpoint of any diameter is the center of the circle. This is because all diameters go through the center.

The distance from the center to either endpoint represents the radius of the circle (aka half the diameter).

Answer:

-14ab + 31b -4a

Step-by-step explanation:

(20ab + 16 b + 4a) - (34ab - 15b +8a)

20 ab +16b + 4a -34ab + 15b -8a

-14ab + 31b -4a

[tex]3[/tex] days [tex]0[/tex] hours. The answer is three because the function [tex]W[/tex] that solves the differential equation gives the number of weeds in a large garden.

A number is calculated and represented using a decimal, which is an algebra quantity. In handwriting, numerical symbols like "3" are used to represent numbers. A counting system is a logical way of expressing numbers that uses digits or symbols to represent them.

Vets Day and Memorial Day are commonly celebrated on November 11 in the United States and overseas, respectively. The history, mythology, and mathematical importance of this particular time and date are all explained here.

[tex]\frac{dw}{dt}=\frac{1}{12}(-318+24W)[/tex]

[tex]\frac{d^{2}W }{dt^{2} }=\frac{d}{dt}[\frac{1}{12} (-318+24W)][/tex]

When [tex]W=14, \frac{dW}{dt}[/tex]

[tex]=\frac{1}{12}(-318+24*14)[/tex]

[tex]=\frac{18}{12}=1.5[/tex]

[tex]=2\frac{dW}{dt}=2*1.5[/tex]

[tex]=3[/tex]

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The formula for f(t) as a sum of Heaviside functions is f(t) = tuc(t) - tuc(t-3) + (2t-3)uc(t-3) - (2t-3)uc(t-4) + 5uc(t-4).

To express f(t) as a sum of Heaviside functions, we break down the function into its respective intervals and use the unit step function or Heaviside function to represent the function in each interval.

f(t) = t, 0 ≤ t ≤ 3

f(t) = 2t - 3, 3 < t ≤ 4

f(t) = 5, 4 < t

Using the Heaviside function uc for the jump at c, we can represent each interval as follows:

f(t) = tuc(t) - tuc(t-3), 0 ≤ t ≤ 3

f(t) = (2t-3)uc(t-3) - (2t-3)uc(t-4), 3 < t ≤ 4

f(t) = 5uc(t-4), 4 < t

Therefore, the formula is f(t) = tuc(t) - tuc(t-3) + (2t-3)uc(t-3) - (2t-3)uc(t-4) + 5uc(t-4)

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Answer:

The answer is letter D.

Step-by-step explanation:

Ye

Answer:

The answer is C

x -10 < -20

x < -20 + 10

x< -10

The sign won't change to the other side because the variable we were asked to find is in the positive form.

The value of X is 42.5 and Y is 90.98.

How to solve equations?

To solve an equation, you need to perform the same operation on both sides of the equation until you isolate the variable on one side and have a numerical value on the other side. The process of solving an equation generally involves the following steps:

Simplify both sides of the equation by combining like terms and following the order of operations.

Add or subtract the same value from both sides of the equation to isolate the variable term.

Multiply or divide both sides of the equation by the same non-zero value to isolate the variable term.

Check your solution by plugging it back into the original equation and verifying that it satisfies the equation.

Solving the given equations :
To solve for X, we can use inverse operations to isolate the variable. Since 10 is multiplied by X, we can use the inverse operation of division by 10 to isolate X. So, dividing both sides of the equation by 10 gives:

[tex]10x/10 = 425/10[/tex]

Simplifying the left side of the equation gives:

[tex]x = 42.5[/tex]

Therefore, X is 42.5.

To solve for Y, we can use similar steps. Since 81729 is divided by Y, we can use the inverse operation of multiplication by Y to isolate Y. So, multiplying both sides of the equation by Y gives:

[tex]81729 = 898.12 \times Y[/tex]

Simplifying the right side of the equation gives:

[tex]Y = 81729 / 898.12[/tex]

[tex]Y = 90.98[/tex]

Therefore, Y is 90.98.

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Answer: 6

Step-by-step explanation:

Average rate of change is the same as slope.

To find the average rate of change between two points, use the formula y2 - y1 / x2 - x1

Plug in the (0, 7) and (6, 43) coordinates.

43 - 7 / 6 - 0 = 6

we can use the notation P(A) and apply the definition of probability: P(A) = P(B), P (A ∩ B), and P (A ∪ B) if we have the necessary information.

I believe you meant to say, "Venn diagram". A Venn diagram is a type of graphical representation used to illustrate relationships between sets or groups of objects, concepts, or ideas. It consists of a series of overlapping circles or other closed shapes, with each circle representing a set or group and the overlapping areas representing the relationships or intersections between them.

by the question.

Let A be the event that a student is a cast member of Seussical, and let B be the event that a student is a cast member of Wizard of Oz. Then, we can define the following:

A ∩ B: The event that a student is a cast member of both Seussical and Wizard of Oz.

A ∪ B: The event that a student is a cast member of either Seussical, Wizard of Oz, or both.

A': The event that a student is not a cast member of Seussical.

B': The event that a student is not a cast member of Wizard of Oz.

Based on the information given, we do not know how many students are in each of these events, but we can still make some general observations. For example:

If A and B have no students in common (i.e., A ∩ B = ∅), then the number of students in A ∪ B is equal to the sum of the number of students in A and the number of students in B.

If some students are in both A and B (i.e., A ∩ B is not empty), then the number of students in A ∪ B is equal to the sum of the number of students in A, the number of students in B, and the number of students in A ∩ B. In other words, some students are counted twice when we add up the number of students in A and the number of students in B, so we need to subtract the number of students in A ∩ B to avoid double-counting.

We do not know whether the events A and B are mutually exclusive (i.e., whether A ∩ B = ∅) or not. If they are mutually exclusive, then P(A ∩ B) = 0, and we can use the addition rule of probability to find P (A ∪ B) = P(A) + P(B). If they are not mutually exclusive, then we need to use the general addition rule of probability: P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

Finally, if we want to find the probability that a student chosen at random is a cast member of Seussical,

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The simplified polynomial, with each term written in standard form, is: 36a^3b - 6a^2b^3 + 11a^2b

To simplify the given polynomial, we need to expand and combine like terms.

First, we can distribute the coefficients of the first term:

12a^2 · 3ba = 36a^3b

Next, we can simplify the second term by multiplying the coefficients and adding the exponents:

-2ab · 3ab^2 = -6a^2b^3

Finally, we can combine the like terms:

36a^3b - 6a^2b^3 + 11a^2b

To write each term in standard form, we arrange the terms in decreasing order of exponents of 'a' and 'b':

36a^3b - 6a^2b^3 + 11a^2b

So, the simplified polynomial, with each term written in standard form, is:

36a^3b - 6a^2b^3 + 11a^2b

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Answer:28

Step-by-step explanation:

Answer: 28

Explanation:  Look for a pattern or reason for the following number in the sequence. In this case 3+1=4, 4+3=7, 7+5=12, 12+7=19, so the probable answer is to add the following odd number to the last one in the line to get the next. (19+9=28)

Answer: 8 mangoes

Step-by-step explanation:

1. To find the total number of mangoes Peter had, add 8 and 24 which gives you 32. 8 + 24 = 32.

2. If Peter had an equal number of mangoes in each bag, and a total number of 32 mangoes, then you must divide the total number of mangoes by the number of bags, which is 4. 32 ÷ 4 = 8. Therefore, there were 8 mangoes in each bag.

Answer:

The answer  is 8 mangoes

Answer:49

Step-by-step explanation:

The equation m = 12 + 2Y1 gives the slope of the line through the points P1=(-1.5, Y1) and P2=(-2, -6)

To find a point's coordinates in a coordinate system, you perform the opposite. Starting at the point, move vertically up or down until you reach the x-axis. Your x-coordinate is shown there. Afterwards, you'll be able to get a better understanding of how to use it.

It is assumed that the formula you supplied would be used to determine the slope (m) of the line connecting the two specified points, P1 and P2.

We may use the following formula to find the slope (m) of the line passing through the coordinates P1=(X1, Y1) and P2=(X2, Y2):m = (Y2 - Y1) / (X2 - X1) (X2 - X1)

Using the values provided:

P1 = (-1.5, Y1) (-1.5, Y1)

P2 = (-2, -6) (-2, -6)

These values can be used as substitutes in the formula:

m = (-6 - Y1) / (-2 - (-1.5))

Making the denominator simpler:

m = (-6 - Y1) / (-2 + 1.5)

m = (-6 - Y1) / (-0.5)

m = 12 + 2Y1

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Question:

Formula: m=;

X₂-X1

P₁ = (X₁, Y₁) P₂ = (X2, Y₂)

1) P₁=(-1.5) and P₂=(-2,-6)

How to solve this exercise of linear equations of two points.

According to the given image, with the help of a protractor, we can conclude that ∠NCD represents an angle of 50°.

An instrument for measuring angles is a protractor, which is often made of transparent plastic or glass.

Protractors might be straightforward half-discs or complete circles. Protractors with more complex features, like the bevel protractor, include one or two swinging arms that can be used to measure angles.

Most protractors use degrees (°) to express angles.

Protractors with radian scales calculate angles.

The majority of protractors have 180 equal segments.

Degrees are further subdivided into arcminutes by some precision protractors.

They are employed in geometry, engineering, and mechanics.

So, in the given image the proctor is measuring the angle of 50°.

Therefore, according to the given image, with the help of a protractor, we can conclude that ∠NCD represents an angle of 50°.

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Ann has 60 $1 bills, 5 $10 bills, and 20 $20 bills.

Let's assume Ann has $1x, $10y, and $20z bills.

From the given information, we can write two equations based on the relationships between the numbers of bills:

z = 4y (Ann has four times as many $20 bills as $10 bills)

x = 3z (Ann has three times as many $1 bills as $20 bills)

We know that the total amount of money Ann has is $204, so we can write a third equation:

x + 10y + 20z = 204

Now we can use substitution method here, substitute equation 2 into equation 1 to get:

z = 4y

x = 3z

x = 3(4y) = 12y

Substituting these equations into equation 3, we get:

12y + 10y + 20(4y) = 204

42y = 204

y = 4.86

Since y must be a whole number (representing the number of $10 bills), we can round up to y = 5.

Using equation 1, we can find that z = 4y = 20 (representing the number of $20 bills).

Using equation 2, we can find that x = 3z = 60 (representing the number of $1 bills).

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The given question is incomplete, the complete question is:

Ann has $ 1, $10, and $20 bills. She has 4 times as many $20 bills as $10 bills. She has 3 times as many $1 bills as $20 bills. She has a total of $204 .What is the number of $1, $10, and $ 20 bills she has

Step-by-step explanation:

x = +1

x = -2

x = -3

x = -4

Use number line to find the value and fit equation

Answer:1st one

Step-by-step explanation:

The z-score for Keenan is 0.71, rounded up to the hundredth.

The Z-score determines the standard deviations by which the measure deviates from the mean. After calculating the Z-score, we look at the z-score table to ascertain the p-value associated with it. This p-value represents the percentile of X or the probability that the measure's value is smaller than X. You may get the likelihood that the value of the measure is greater than X by subtracting 1 from the p-value.

The formula for calculating the z-score is as follows: The z-score is the number of standard deviations an individual's score deviates from the mean.

z = (x - μ) / σ

where the mean score is, the standard deviation is, and x is the individual's score.

About Keenan's test:

z = (80 - 77) / 4.2

z = 0.71

Keenan's z-score is 0.71 as a result, rounded to the nearest hundredth.

Any decimal number is rounded to the nearest hundredth value when it is expressed as a fraction. A hundredth is 1/100 or 0.01 in decimal form. For instance, 2.17 is the result of rounding 2.167 to the nearest tenth.

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If it is true that 60 percent of the trees in a forested region are classified as softwood, 0.015 is the probability of obtaining a sample proportion as large as or larger than the one obtained by the botanist.The correct answer is option C

The P-value is the probability of obtaining an outcome as extreme or more extreme than the one actually observed given that the null hypothesis is true. In this case, the null hypothesis is that the proportion of trees classified as softwood is 0.60. The P-value of 0.015 indicates that the probability of obtaining a sample proportion as large as or larger than the one obtained by the botanist is 0.015 if the null hypothesis is true.

Therefore, the P-value is an indicator of how well the sample data supports the null hypothesis. In this case, the P-value of 0.015 is lower than the commonly accepted significance level of 0.05, which indicates that the sample data does not support the null hypothesis and suggests that the proportion of trees classified as softwood is actually greater than 0.60.

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Denote by X the arrival time of the first guest. The time of arrival of the first guest at a bank is modeled by the Poisson distribution, where the arrival rate is λ. Thus, the number of arrivals during time t is Poisson(λt).

Therefore, the distribution of X is Exponential(λ), which means that its probability density function is

f(x) = λe−λx, x > 0.

The expected value of X is E[X] = 1/λ and the variance is Var(X) = 1/λ².

b. Denote by Y the arrival time of the second guest.

The number of arrivals during time t is Poisson(λt). The first guest arrived at time X, so the number of arrivals from time X to time t is Poisson(λ(t - X)).

Thus, the arrival time of the second guest has the conditional probability density function:

f(y | X) = λe^(−λ(y−x)), y > x

Therefore, the unconditional probability density function of Y is obtained through the law of total probability:

f(y) = ∫f(y | x)f(x)dx

= ∫λe^(−λ(y−x))λe^(−λx)dx

= λ²e^(−λy), y > 0

Therefore, the distribution of Y is Exponential(λ), which is the same as that of X.

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Answer:

Step-by-step explanation:

see diagram

The inverse of the function g(x) is g⁻¹(x) = 0.5 + √(1.25 - x) and the value for x for which f(g(x)) = g(f(x))​ is 1

Given that

f(x) = 3 - 2x

Rewrite as

g(x) = -x² + x + 1

Express as vertex form

g(x) = -(x - 0.5)² + 1.25

Express as equation and swap x & y

x = -(y - 0.5)² + 1.25

Make y the subject

y = 0.5 + √(1.25 - x)

So, the inverse is

g⁻¹(x) = 0.5 + √(1.25 - x)

Here, we have

f(g(x)) = g(f(x))​

This means that

f(g(x)) = 3 - 2(-x² + x + 1)

g(f(x)) = -(3 - 2x)² + (3 - 2x) + 1

Using a graphing tool, we have

f(g(x)) = g(f(x))​ when x = 1

Hence, the value of x is 1

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Complete question

f(x) = 3 - 2x and g(x) = x - x² + 1 where x is an element of f have set of numbers

Find the inverse of G and the value for x for which f(g(x)) = g(f(x))​.

Answer:

actual length = 15 feet

Step-by-step explanation:

using the conversion

12 inches = 1 foot

the actual length  = 40 × scale length = 40 × 4.5 = 180 inches = 180 ÷ 12 = 15 feet

Answer:

40.4026226 aka 40.403

Step-by-step explanation:

tan 22 degrees = h/100

The standard deviation of the sampling distribution of pCheck to see if the 10% condition is 0.44.

If a large candy machine has 45% orange candies, and an SRS of 25 candies is taken from it, then the 10% condition can be checked to see if it is met. To do this, it is necessary to calculate the sample proportion p. To calculate p, the number of orange candies in the sample (let's call it x) is divided by the total number of candies in the sample (25). Thus, p = x/25. The 10% condition is met if the value of p is less than or equal to 0.1 (10%).

Since the value of p is unknown, the number of orange candies in the sample must first be determined. To find this number, the proportion of orange candies in the entire candy machine must be used. The proportion of orange candies is 45%, or 0.45.

This means that for every 100 candies in the candy machine, 45 are orange. Since there are 25 candies in the sample, 0.45*25 = 11.25 orange candies are expected in the sample. Since this is a sample proportion, the exact value of x must be rounded to the nearest whole number. This gives a value of 11 orange candies in the sample.

Now that the value of x is known, the value of p can be calculated. This gives p = 11/25 = 0.44.

Since 0.44 is greater than 0.1 (10%), the 10% condition is not met in this case.

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