Susan bought two gifts. One package is a rectangular prism with a base length of 4 inches, a base width of 2 inches, and a height of 10 inches. The other package is a cube with a side length of 5 inches. Which package requires more wrapping paper to cover? What is the total amount of wrapping paper Susan must use to cover both packages? You must show your work to earn full credit

Answer:

(i) \(OE = 0.6\cdot \sin \theta + 1.4\cdot \cos \theta\), (ii) \(\theta \approx 33.368^{\circ}\), (iii) The maximum value of OE is approximately 1.523 meters, which is associated with an angle of approximately 23.199º.

Step-by-step explanation:

(i) From Geometry, we get that sum of internal angles of trangle AOD.

\(\angle A + \angle O + \angle D = 180^{\circ}\) (1)

If we know that \(\angle O = 90^{\circ}\) and \(\angle A = \theta\), then the value of \(\angle D\) is:

\(\angle D = 180^{\circ}-90^{\circ}-\theta\)

\(\angle D = 90^{\circ}-\theta\) (2)

But we also have the following identity:

\(\angle D +\angle D' +\angle D'' = 180^{\circ}\) (3)

If we know that \(\angle D = 90^{\circ}-\theta\) and \(\angle D' = 90^{\circ}\), then the value of \(\angle D''\) is:

\(90^{\circ}-\theta +90^{\circ}+\angle D'' = 180^{\circ}\)

\(\angle D'' = \theta\) (4)

By Trigonometry, we derive the following formula:

\(OE = OD +DE\)

\(OE = AD\cdot \sin A +CD\cdot \cos D''\) (5)

If we know that \(AD = 0.6\,m\), \(CD = 1.4\,m\), \(A = \theta\) and \(D'' = \theta\), then the value of OE is:

\(OE = 0.6\sin \theta + 1.4\cos \theta\) (6)

(ii) If we know that \(OE = 1.1\,m\), then the value of \(\theta\):

\(0.6\cdot \sin \theta + 1.4\cdot \cos \theta = 1.1\)

By trial and error, we find that \(\theta \approx 33.368^{\circ}\).

(iii) Let \(OE = 0.6\cdot \sin \theta + 1.4\cdot \cos \theta\), the first and second derivatives of the function are, respectively:

\(OE' = 0.6\cdot \cos \theta -1.4\cdot \sin \theta\) (7)

\(OE'' = -0.6\cdot \sin \theta -1.4\cdot \cos \theta\) (8)

We equalize the first derivative of the function to zero and solve for \(\theta\):

\(0.6\cdot \cos \theta - 1.4\cdot \sin \theta = 0\)

\(1.4\cdot \sin \theta = 0.6\cdot \cos \theta\)

\(\tan \theta = \frac{0.6}{1.4}\)

\(\theta \approx \tan^{-1} \frac{0.6}{1.4}\)  

\(\theta \approx 23.199^{\circ}\)

And we evaluate the second derivative:

\(OE'' = -0.6\cdot \sin 23.199^{\circ}-1.4\cdot \cos 23.199^{\circ }\)

\(OE'' = -1.523\)

Then, the critical value is associated with an absolute maximum.

The maximum value of OE is:

\(OE = 0.6\cdot \sin 23.199^{\circ}+1.4\cdot \cos 23.199^{\circ }\)

\(OE \approx 1.523\,m\)

The maximum value of OE is approximately 1.523 meters, which is associated with an angle of approximately 23.199º.

Answer:

Step-by-step explanation:

Since adding a negative to a positive is inverse subtracting, use this as an advantage and act as if you're subtracting to get the result, or output value, -9.

Hope this helps! :)

Answer:

\( \sf \: x = - 11\)

Step-by-step explanation:

Now we have to,

→ find the required value of x.

The equation is,

→ 2 + x = -9

Then the value of x will be,

→ 2 + x = -9

→ x + 2 = -9

→ x = -9 - 2

→ [ x = -11 ]

Hence, the value of x is -11.

Answer:

33.51

Step-by-step explanation:

V=4 3πr3=4 3·π·23≈33.51032

Answer:

ler we have a point (x, y) and,

in molar form°

Z = √(x² + y² ) and 0 = tan-¹(y/x).

Since the point (2√3, -2) is in the fourth quadrant, make certain that your angle is also in the fourth quadrant.

In the standard conversion unit, 24 m/s equals 54 mph in mph

The conversion equation is given as

8 km/h = 5 mph

Convert 8 km to meters

So, we have the following equation

8 x 1000 m/h = 5 mph

Evaluate the products

So, we have the following equation

8000 m/h = 5 mph

Convert 1 hour to seconds

So, we have the following equation

8000 m/3600 s = 5 mph

Evaluate the quotient

So, we have the following equation

20/9 m/s = 5 mph

Multiply both sides by 9/20

1 m/s = 9/20 * 5 mph

Multiply both sides by 24

24 * 1 m/s = 24 * 9/20 * 5 mph

Evaluate the products

24 m/s = 54 mph

Hence, the equivalent of 24 m/s in mph is 54 mph

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To calculate the cost of each cookie, we can use the formula:

\(\[ \text{Cost per cookie} = \frac{\text{Total amount spent}}{\text{Total number of cookies}} \]\)

Given that Mr. A spent \(\$40\) on cookies and distributed 8 cookies among his four children, we can substitute these values into the formula:

\(\[ \text{Cost per cookie} = \frac{\$40}{8} = \$5 \]\)

Hence, each cookie costs \(\$5\).

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Answer:

75 + 17 = 92

Step-by-step explanation:

Answer: Absolute value of a real number, is the distance between that number and 0 on a number line. Therefore the absolute value of 2 is 2 and negative 2

The correct statement is end behavior is decreasing to the left and increasing to the right, which statement must be true about the function is The order is odd and the leading coefficient is negative.

As x approaches infinity it is detected by its limit. On the left side, it is given by:

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Answer: Number One

Step-by-step explanation: O/N/E

Answer:just do the exam

Step-by-step explanation:

The required length of the other leg is \($\sqrt{5}$\) cm. If we need to round to the nearest tenth, we get: \($b \approx 2.2$\) cm

Let's use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. So we have:

\($c^2 = a^2 + b^2$\)

where c is the length of the hypotenuse, a and b are the lengths of the legs.

We are given that the length of the hypotenuse is 3 cm and the length of one leg is 2 cm. Let's substitute these values into the equation above:

\($3^2 = 2^2 + b^2$\)

\($9 = 4 + b^2$\)

\($b^2 = 5$\)

\($b = \sqrt{5}$\)

So the length of the other leg is \($\sqrt{5}$\) cm. If we need to round to the nearest tenth, we get: \($b \approx 2.2$\) cm (rounded to one decimal place).

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Therefore, the equation \(+3 + 5(2n - 1)^2 + n^2 + D(n + 2)\) is true for every positive integer n.

To verify the equation for every positive integer n using induction, we'll follow the steps of mathematical induction.

Step 1: Base Case

Let's check if the equation holds true for n = 1.

For n = 1:

\(3 + 5(2(1) - 1)^2 + 1(1) + D(1 + 2)\)

\(3 + 5(1)^2 + 1 + D(3)\)

3 + 5 + 1 + D(3)

9 + D(3)

At this point, we don't have enough information to determine the value of D. However, as long as the equation holds for any arbitrary value of D, we can proceed with the induction.

Step 2: Inductive Hypothesis

Assume that the equation holds true for an arbitrary positive integer k. That is:

\(3 + 5(2k - 1)^2 + k^2 + D(k + 2)\)

Step 3: Inductive Step

We need to prove that the equation also holds true for n = k + 1, based on the assumption in the previous step.

For n = k + 1:

=\(3 + 5(2(k + 1) - 1)^2 + (k + 1)^2 + D((k + 1) + 2)\\3 + 5(2k + 1)^2 + (k + 1)^2 + D(k + 3)\)

Expanding and simplifying:

=\(3 + 5(4k^2 + 4k + 1) + (k^2 + 2k + 1) + D(k + 3)\\3 + 20k^2 + 20k + 5 + k^2 + 2k + 1 + Dk + 3D\)

Combining like terms:

=\(21k^2 + 22k + 9 + Dk + 3D\)

Now, we compare this expression with the equation for n = k + 1:

=\(3 + 5(2(k + 1) - 1)^2 + (k + 1)^2 + D((k + 1) + 2)\)

We can see that the expression obtained in the inductive step matches the equation for n = k + 1, except for the constant terms 9 and 3D.

As long as we choose D in a way that makes 9 + 3D equal to zero, the equation will hold true for n = k + 1 as well. For example, if we set D = -3, then 9 + 3D = 9 - 9 = 0.

Step 4: Conclusion

Since the equation is true for the base case (n = 1) and we have shown that if it holds for an arbitrary positive integer k, it also holds for k + 1, we can conclude that the equation is true for every positive integer n.

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a. The amount to which $500 will grow when compounded annually at a rate of 16% for 10 years is approximately $1,734.41.

b. The amount to which $500 will grow when compounded semiannually at a rate of 16% for 10 years is approximately $1,786.76.

c. The amount to which $500 will grow when compounded quarterly at a rate of 16% for 10 years is approximately $1,815.51.

d. The amount to which $500 will grow when compounded monthly at a rate of 16% for 10 years is approximately $1,833.89.

e. The amount to which $500 will grow when compounded daily at a rate of 16% for 10 years (365 days in a year) is approximately $1,843.96.

a. The amount to which $500 will grow when compounded annually at a rate of 16% for 10 years is approximately $1,734.41.

To calculate this, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:

A = the final amount

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case, P = $500, r = 0.16, n = 1, and t = 10.

Plugging these values into the formula, we get:

A = 500(1 + 0.16/1)^(1*10)

 = 500(1 + 0.16)^10

 ≈ 1,734.41

Therefore, $500 will grow to approximately $1,734.41 when compounded annually at a rate of 16% for 10 years.

b. The amount to which $500 will grow when compounded semiannually at a rate of 16% for 10 years is approximately $1,786.76.

To calculate this, we can use the same compound interest formula, but with a different value for n. In this case, n = 2 because the interest is compounded twice a year.

A = 500(1 + 0.16/2)^(2*10)

 ≈ 1,786.76

Therefore, $500 will grow to approximately $1,786.76 when compounded semiannually at a rate of 16% for 10 years.

c. The amount to which $500 will grow when compounded quarterly at a rate of 16% for 10 years is approximately $1,815.51.

Using the compound interest formula with n = 4 (compounded quarterly):

A = 500(1 + 0.16/4)^(4*10)

 ≈ 1,815.51

Therefore, $500 will grow to approximately $1,815.51 when compounded quarterly at a rate of 16% for 10 years.

d. The amount to which $500 will grow when compounded monthly at a rate of 16% for 10 years is approximately $1,833.89.

Using the compound interest formula with n = 12 (compounded monthly):

A = 500(1 + 0.16/12)^(12*10)

 ≈ 1,833.89

Therefore, $500 will grow to approximately $1,833.89 when compounded monthly at a rate of 16% for 10 years.

e. The amount to which $500 will grow when compounded daily at a rate of 16% for 10 years (365 days in a year) is approximately $1,843.96.

Using the compound interest formula with n = 365 (compounded daily):

A = 500(1 + 0.16/365)^(365*10)

 ≈ 1,843.96

Therefore, $500 will grow to approximately $1,843.96 when compounded daily at a rate of 16% for 10 years.

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mass of the penny in pounds is 0.00220462 pounds.

To explain this, we can use unit analysis to convert the mass from grams to pounds. We know that there are 453.592 grams in one pound, so we can set up a conversion factor:
1 pound / 453.592 grams
To convert the mass of the penny in grams to pounds, we can multiply the given value by this conversion factor:
( X grams ) * ( 1 pound / 453.592 grams )
Simplifying this expression, the grams unit cancels out, leaving us with the mass of the penny in pounds:
( X / 453.592 ) pounds
Plugging in the given mass of the penny in grams, we get:
( Y grams ) * ( 1 pound / 453.592 grams ) = ( Y / 453.592 ) pounds

the mass of the penny in pounds is ( Y / 453.592 ) pounds, which is approximately 0.00220462 pounds.

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Answer:

The answer would be

Sin 60°=x/14

X=7v3

Answer:

The answer is $297

Answer: The price of the PC is now $693.

Step-by-step explanation:

1. Find 30% of $990.

30% of $990 = $297

2. subtract.

$990 - $297 = $693

the correlation between hours watching tv and reading books is -0.74. proportion of the variance in people's reading habits can be accounted for by knowing how much tv is watched is 0.5476

A proportion is an equation that sets two ratios at the same value. For instance, you might express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls. 0.25 are male (by dividing 1 by 4)

Direct Proportion.

Inverse Proportion.

Compound Proportion.

Continued Proportion.

the correlation between hours watching tv and reading books is -0.74. what proportion of the variance in people's reading habits can be accounted for by knowing how much tv is watched is 0.5476

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Answer:

y - 15 = 1/750(x - 6000)

Step-by-step explanation:

Given that :

At price, p = $15 ; quantity, q = 6000

At price, p = $13 ; quantity, quantity = 4500

Expressing in the form (x, y) ;

(6000, 15) ; (4500, 13)

General form of a line equation :

y - y1 = m(x - x1)

x1 = 6000 ; y1 = 15 ; x2 = 4500 ; y2 = 13

The gradient, m :

(y2 - y1) / (x2 - x1)

(13 - 15) / (4500 - 6000)

- 2 / - 1500

Gradient, m = 1/750

Therefore,

y - 15 = 1/750(x - 6000)

Answer:

Step-by-step explanation:

Zero because 20 minus 13 is 7 and you minus 7 and it's 0

Answer:

the answer is already given or it is zero in case of quadratic equations

Answer:

Your answer is 24.

Step-by-step explanation:

4 to the second power is 4 times 4 when is 16 plus y, which is 8 gets you 24.

Answer:

24

Step-by-step explanation:

Substitute x for 4 and y for 8.  

4^2=16

16+8=24

a) 20 acres of corn, b) 15 acres of cotton, and c) 5 acres of peanuts will be planted. The total profit will be $12,250.

To solve the linear programming problem, we use a simplex method. The optimal solution for this problem is: a) x1 = 20, x2 = 5, x3 = 15, b) x1 = 15, x2 = 15, x3 = 10, and c) x1 = 5, x2 = 20, x3 = 0. Thus, 20 acres of corn, 15 acres of cotton, and 5 acres of peanuts will be planted to maximize profit, which is $12,250.

To determine the binding constraints, we calculate the slack variables for each constraint. The slack variables for constraint 1, 2, 3, and 4 are 0, 0, 15, and 0, respectively. Therefore, the binding constraints are constraint 3 (insecticide tons) and constraint 1 (labor hours) with a slack of 15 hours.

The maximum profit is obtained by plugging in the optimal solution into the objective function. Profit = 550x1 + 350x2 + 450x3 = $12,250.

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By generating 20 samples of size 100 and calculating the proportions of vacationers who enjoy water parks in each sample, we can assess how closely the samples estimate the percent of all vacationers who enjoy water parks.

To estimate how closely the samples of size 100 reflect the percent of all vacationers who enjoy water parks, we can conduct a simulation using technology.

By generating multiple samples and calculating the proportion of vacationers who enjoy water parks in each sample, we can compare the sample proportions with the known population proportion of 60%.

Using a random number generator or statistical software, we generate 20 samples of size 100. For each sample, we calculate the proportion of vacationers who enjoy water parks by dividing the number of vacationers who enjoy water parks by the total sample size.

After obtaining the sample proportions, we can compare them with the known population proportion of 60%. We can calculate the difference between each sample proportion and 60% to measure how closely the samples estimate the true population proportion.

We can then calculate summary statistics, such as the mean, standard deviation, and confidence interval, to assess the overall accuracy and variability of the sample estimates.

For example, if the average of the sample proportions is close to 60% and the standard deviation is relatively small, it indicates that the samples provide accurate estimates of the population proportion.

On the other hand, if the sample proportions vary widely and deviate significantly from 60%, it suggests that the sample estimates may not accurately reflect the population proportion.

By conducting this simulation with 20 samples of size 100, we can evaluate how closely the samples estimate the percent of all vacationers who enjoy water parks and assess the accuracy and variability of the sample estimates.

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Answer:

The answer is D

Step-by-step explanation:

I tested this in apex learning and got 100 so its true.

Step-by-step explanation:

To reflect a function about the vertical axis, just negate the variable.

For example, if we want to reflect this function

\( y = log(x) \)

about the y axis or vertical axis, we just make the x negative

\(y = log( - x) \)

Another example,

\(y = |x| \)

To reflect about y axis or vertical axis,

\(y = | - x| \)

So here l,the answer with negative variables are function that are reflected about the y axis.

The options are the first and the fifth option.

Answer:

1/3 and 2

OR

3/10

(read sbs explanation)

Step-by-step explanation:

Order the numbers in order from least to greatest:

1/4, 3/10, 1/3, 2/5, 3, 20

Take the middle one, so the answer is 1/3, 2/5 as they are the two middle numbers. If you messed up your typing and the last numbers are supposed to be 3/20 not 3 and 20, your answer would be 3/10.

Step-by-step explanation:

let x= number of students in bus

6bus with unknown number of students in bus: 6*x

127= 6x+7

127-7= 6x

6x= 120

x= 120/6

x= 20

Answer:

The number of students in the bus is 20.

Step-by-step explanation:

Number of students = 127

Number of students traveled through cars = 7

Number of buses = 6

Solution:

Let no. of students be in the bus be x.

Then the number of students in the bus:

This is quite apparent that

Plugging values,

Solving for x,

We can conclude:

Hence the number of students in the bus is 20.

The given statement: ANCOVA measures the relationship strength between two variables and how much they change together is FALSE because it is used to determine if differences between groups on a dependent variable are due to the independent variable or due to the covariate.

Analysis of covariance (ANCOVA) is actually a statistical technique used to compare means of a dependent variable across different groups, while controlling for the effects of one or more continuous variables, called covariates.

It is similar to ANOVA (analysis of variance), but with the addition of covariates. ANCOVA is not a measure of how much two variables change together or the strength of their relationship.

Instead, it is used to determine if differences between groups on a dependent variable are due to the independent variable or due to the covariate.

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Main Answer:The value of n should be 6.

Supporting Question and Answer:

What is the Pigeonhole Principle and how does it apply to this problem?

The Pigeonhole Principle states that if we have more objects to distribute than the number of containers available, then at least one container must contain more than one object. In this problem, the objects are the distinct integers Xi, and the containers are the possible remainders when dividing by 5. Applying the Pigeonhole Principle, we can determine that for there to be at least two integers with the same remainder when divided by 5, the number of distinct integers (n) must be greater than the number of possible remainders (5).

Body of the Solution: To find the value of n that ensures there are at least two integers, Xj and Xk, such that Xj MOD 5 = Xk MOD 5, we need to consider the possible remainders when dividing integers by 5.

Since the remainder can range from 0 to 4 (inclusive) when dividing by 5, we have a total of 5 possible remainders: 0, 1, 2, 3, and 4.

For there to be at least two integers with the same remainder when divided by 5, we can apply the Pigeonhole Principle, which states that if we have n objects to distribute into m containers, and n > m, then at least one container must contain more than one object.

To ensure there are at least two integers with the same remainder, we need to have more objects (integers) than the number of containers (possible remainders).

Therefore, we need to have n > 5.

To find the smallest value of n that satisfies this condition, we set n = 6.

When n = 6, we have the distinct integers X1, X2, X3, X4, X5, X6.

Since we have 6 integers and only 5 possible remainders (containers), according to the Pigeonhole Principle, there must be at least two integers with the same remainder when divided by 5.

Thus, the value of n should be 6 to ensure there are at least two integers Xj and Xk such that Xj MOD 5 = Xk MOD 5.

Final Answer:The value of n should be 6 to ensure there are at least two integers Xj and Xk such that Xj MOD 5 = Xk MOD 5.

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