The surface area of a box is 160 square inches. The length of the box is twice its width, and is 4 inches less than its height. What is the height of the box, in inches?

Answer:

107%

Step-by-step explanation:

Multiply 1.07 by hundred: 1.07*100= 107

Answer:

Step-by-step explanation:

12.8/2 = 96 / 2 = 48

the answer is the first one

Step 1

Write the equation

sin(7x + 1) = cos(x + 33)

Step 2

From the complementary angle theorem

sinx = cos(90 - x)

Therefore

sin(7x + 1) = cos(x + 33)

cos(90 -[7x + 1]) = cos(x + 33)

cos(90 - 1 - 7x) = cos(x + 33)

cos(89 - 7x) = cos(x + 33)

89 - 7x = x + 33

89 - 33 = x + 7x

56 = 8x

x = 56/8

x = 7

sin(7x + 1)

sin(7x7 + 1)

sin(49 + 1)

sin50

cos(x + 33)

cos(7+33)

cos40

Angle 1 = 50

Angle 2 = 40

Answer:

get a calculator and do 28 - 25%

Step-by-step explanation:

The number of sick students in a class is 7.

Given that, Martin's class has 28 students in it.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Number of sick students is

25% of 28

= 25/100 × 28

= 0.25 × 28

= 7

Therefore, the number of sick students in a class is 7.

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Probability that the mother in this sample had a premature baby given that the mother admitted to smoking is 50 percent.

Likelihood is the part of science concerning mathematical depictions of how likely an occasion is to happen, or how likely it is that a suggestion is valid. The likelihood of an occasion is a number somewhere in the range of 0 and 1, where, generally talking, 0 demonstrates difficulty of the occasion and 1 shows conviction.

P (A) is the probability of an event “A”

n (A) is the number of favorable outcomes

n (S) is the total number of events in the sample space

The higher the likelihood of an occasion, the more probable it is that the occasion will happen. A straightforward model is the throwing of a fair coin. Since the coin is fair, the two results are both similarly likely; the likelihood of "heads" approaches the likelihood of "tails"; and since no different results are conceivable, the likelihood of by the same token "heads" or "tails" is 1/2.

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The standard deviation of the given data can be calculated using the formula for the population standard deviation:

Standard deviation = √[∑(X - μ)² * f / N]

where X is the data value, μ is the mean, f is the frequency, and N is the total number of observations.

Given the data:

X: 3 4 5 6 7 8 9

f: 37 8 10 12 4 3 2

Assumed mean (μ) = 6

To calculate the standard deviation, we need to calculate the squared difference between each data value and the mean, multiply it by the frequency, and sum up these values. Then divide the sum by the total number of observations (N) and take the square root of the result.

Let's calculate it step by step:

(X - μ)² * f:

(3 - 6)² * 37 = 111

(4 - 6)² * 8 = 32

(5 - 6)² * 10 = 10

(6 - 6)² * 12 = 0

(7 - 6)² * 4 = 4

(8 - 6)² * 3 = 12

(9 - 6)² * 2 = 18

Sum of (X - μ)² * f = 187

Now divide the sum by the total number of observations (N = 37 + 8 + 10 + 12 + 4 + 3 + 2 = 76) and take the square root of the result:

Standard deviation = √(187 / 76) ≈ 1.82

Therefore, the standard deviation of the given data is approximately 1.82.

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Let the event D be that a person has the disease.

Now Let T be positive test and T' be a negative test result.

So the probability that the person has the disease given that the test is positive is given by:

So only 0.46% of the people who tested positive will have the disease.

a. There are 9 outcomes : 4-1, 4-2, 4-3, 4-4, 3-1, 3-2, 3-3, 2-1, 2-2

b. 32 times ( as there are 3 outcomes out of 9 that has a difference of 1, she should get a 50% odds)

c. 32 times ( as there are also 3 outcomes out of 9 that has a difference of 0)

The 3 combinations of coins with the value of 30% of a dollar are 2 dimes + 1 Nickel + 5 Pennies, 1 dime + 2 Nickels + 10 Pennies, 3 Nickels + 1 dime + 5 Pennies.

How many types of coins are there?

There are 4 types of coins. They are Quarter, Nickel, dime, and Penny.

1 Quarter = 25 cent

1 dime = 10 cents

1 Nickel = 5 cents

1 penny = 1 cent

Now calculate 30 percentage of a dollar.

1 dollar = 100 cents.

30% of 100 cents = (30/100) × 100 = 30 cents.

2 dimes + 1 Nickel + 5 Pennies = 20 cents + 5 cents + 5 cents = 30 cents

1 dime + 2 Nickels + 10 Pennies = 10 cents + 10 cents + 10 cents = 30 cents

3 Nickels + 1 dime + 5 Pennies = 15 cents + 10 cents + 5 cents = 30 cents

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Answer:

The last option

Step-by-step explanation:

There are 42 species in the sample

the proportions are:

frogs = 18/42 = 3/7

lizards = 18/42 = 3/7

worms = 6/42 = 1/7

The number of frogs and lizards is the same and exceeds that of worms

The only option that meets these proportions is the last

Hope this helps

Answer:

should be 48

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

Apply rule- a * (-b) = -a * b

4 * (-6)

= -24(-2)

= 48

Hope this helps:)

Using the Pythagorean theorem:

6^2 = 5^2 + x^2

Simplify:

36 = 25 +x^2

Subtract 25 from both sides:

11 = x^2

Square root of both sides:

x = sqrt(11) (exact) or 3.316625 as a decimal

Answer:

It depends

Step-by-step explanation:

If you are given a right triangle, you use Pythagorean Theorem: a² + b² = c²

If you are given an angle but its not a right triangle, you can use either Law of Sines: \(\frac{A}{sin(a)} = \frac{B}{sin(B)} = \frac{C}{sin(C)}\) or Law of Cosines: \(c^2 = a^2 + b^2 -2abcosC\).

Answer:

Sample Response: Create and label a diagram. Then, using the Pythagorean theorem, substitute the values for corresponding variables into the theorem and solve by applying inverse operations.

Step-by-step explanation:

Edge 2021

The total cost of power generation for a specific load demand can be calculated by optimally allocating the load demand to each unit based on their power output limits. The allocation is done in a way that minimizes the overall cost while meeting the load demand.

In the given power system depicted in Figure 1, there are three units that are always running. Each unit has specific characteristics regarding their minimum power output (Pmin), maximum power output (Pmax), and incremental cost (Ci). Let's discuss the characteristics of each unit and calculate the total cost of power generation for a given load demand.

Unit 1:

Pmin = 200 MW

Pmax = 500 MW

Ci = $50/MWh

Unit 2:

Pmin = 150 MW

Pmax = 400 MW

Ci = $40/MWh

Unit 3:

Pmin = 100 MW

Pmax = 300 MW

Ci = $30/MWh

To calculate the total cost of power generation for a given load demand, we need to determine the optimal power output for each unit. We start by considering the units with the lowest incremental cost first.

Suppose the load demand is D MW. We allocate the load demand to the units as follows:

Step 1: Check if Unit 1 can meet the load demand within its power range. If yes, allocate the load demand to Unit 1 and calculate the cost:

Cost1 = Ci * P1, where P1 is the power output of Unit 1.

Step 2: If there is still remaining load demand, allocate it to Unit 2:

Cost2 = Ci * P2, where P2 is the power output of Unit 2.

Step 3: If there is still remaining load demand, allocate it to Unit 3:

Cost3 = Ci * P3, where P3 is the power output of Unit 3.

Finally, the total cost of power generation, Cost_total, is the sum of Cost1, Cost2, and Cost3:

Cost_total = Cost1 + Cost2 + Cost3

To find the optimal power output for each unit, we consider the load demand and compare it to the minimum and maximum power output limits for each unit. The power allocation is based on meeting the load demand while minimizing the overall cost of power generation.

In summary, given the characteristics of the three units in the power system (Pmin, Pmax, and Ci), the total cost of power generation for a specific load demand can be calculated by optimally allocating the load demand to each unit based on their power output limits. The allocation is done in a way that minimizes the overall cost while meeting the load demand.

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To conduct the study on the curriculum change for 5th graders in math, the statistical test that should be used is the t-test.

This test is appropriate when there are two groups to compare. The null hypothesis of the t-test is that the means of the two groups are equal while the alternative hypothesis is that they are not equal. To conduct the t-test, the mean and standard deviation of each group will be calculated. The t-test compares the means of the two groups to determine whether the difference between them is statistically significant.

Reporting of the findings of the t-test will be done through the use of graphs and charts. The results will be presented in a clear and concise manner, highlighting the key findings and their implications for the curriculum change. Any potential ethical dilemmas should also be addressed in the report. These may include issues such as informed consent, confidentiality, and potential biases in the data. It is important to ensure that all ethical guidelines are followed throughout the study to ensure the validity and reliability of the findings.

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After printing the long pdf Document of 47 pages , the remained balance in Fathi's printing account is -$4.90 ..

In mathematics, a basic algebraic operation is any of the common arithmetic operations, including addition, subtraction, multiplication, division, raising integers to powers, and taking square roots.

We have given that,

Total or initial balance of fathi's printing account

= $1.10

Each sheet of paper reduce his balance by $0.25..

Total number of pages in pdf document

= 47

He wants to print this pdf document.

When he print both sides of paper then it reduce the counts of paper used for printing the pdf.

That's if he print only one side then he will print 47 pages but now, he print on both sides .

so, total pages used to print pdf Document= 47/2

= 23 both sided printed + 1 one side printed = 24 pages

Using all provided details, we get

After Fathi print, the balance in his printing account = Initial balance - 24 × balance reduce by each page print

= $1.10 - 24 × $0.25 = $1.10 - $ 6

= - $4.90

Hence, - $4.90 balance in his printing account.

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The expression that can be used to find the volume of the sphere in the composite figure is: V= 4/3 π(5)³

The formula provides us with the means to determine the volume of a sphere

V = 4/3 πr³, where r is the radius of the sphere.

In this case, the radius is 5 millimeters.

So, the expression that can be used to find the volume of the sphere in the composite figure is:

V = 4/3 πr³

V= 4/3 π(5)³

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Answer:

For every 3 tablespoons of cocoa, Nate uses 1 tablespoon of sugar.

Step-by-step explanation:

Since the sugar is halved, the cocoa should be halved as well. 6/2 is 3.

Answer:

-by-step explanation:

for the flip the inequality symbol I think it would go in the third one. That’s all I got right now.

The total capacity of the tank is 272.675 cubic meters.

Given that,

A storage tank consist of a hemisphere and a cylinder which share a common base.

The base of both hemisphere and cylinder will be the same circle with the same radius.

Also, we have,

Height of the tank = 16.5 m

Base diameter of the cylinder = 4.7 m

Radius of the base of the cylinder = 4.7 / 2 = 2.35 m

Radius of the hemisphere = 2.35 m

Height of the cylinder = Total height of the tank - Height or radius of the hemisphere

Total capacity of the tank = Volume of hemisphere + Volume of cylinder

                                          = 2/3 π r³ + π r² h

                                          = 2/3 π (2.35)³ + π (2.35)² (16.5 - 2.35)

                                          = 8.652π + 78.143π

                                          = 272.675 cubic meters

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Given that cot(0) = 4/3 and theta is in Quadrant I, what is sin(theta)?

we have that

If angle theta is in quadrant I , then the value of sin(theta) is positive

Remember that

tan(theta)=1/cot(theta)

so

tan(theta)=3/4

substitute in the expression above

is positive because is quadrant I

remember that

sec(theta)=1/cos(theta)

so

cos(theta)=4/5

tan(theta)=3/4

tan(theta)=sin(theta)/cos(theta)

substitute given values

3/4=sin(theta)/(4/5)

sin(theta)=(3/4)*(4/5)=3/5

the answer is

The roof of the garage is a right triangle if it satisfies the Pythagorean theorem.

The Pythagorean theorem states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, we have two sides that are "feet" in length each and a base of length "feet".

To determine if it is a right triangle, we need to check if the Pythagorean theorem holds true.

Let's denote the two sides as A and B, and the base as C. According to the Pythagorean theorem, A^2 + B^2 = C^2.

In this case, we have A = B = "feet", and C = "feet". Plugging these values into the equation, we get (feet)^2 + (feet)^2 = (feet)^2.

Simplifying this equation, we have 2*(feet)^2 = (feet)^2.

Since the equation does not hold true, it means that the roof of the garage is not a right triangle.
Therefore, the roof of the garage is not a right triangle.

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Answer:

(5,4)

Step-by-step explanation:

that is directly between the two points

The correct entry to remove the outstanding balance would be option c) Debit allowance for doubtful accounts, credit accounts receivable.

When a customer goes out of business and is unable to make payment, it is considered a doubtful collection.

The company has already adjusted for this doubtful collection by creating an allowance for doubtful accounts,

which represents an estimated amount of accounts receivable that may not be collected.

To remove the outstanding balance from the company's books,

Decrease the accounts receivable and reduce the allowance for doubtful accounts.

Achieved by debiting allowance for doubtful accounts to reduce it and crediting accounts receivable to decrease the outstanding balance.

Therefore, the entry which is correct to debit allowance for doubtful accounts and credit accounts receivable.

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To create a parallelogram, just think of 2 different pairs of parallel lines that never intersect.

A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. To create a parallelogram, we need to visualize two different pairs of lines that never intersect. The pairs of lines must be parallel to each other, meaning they have the same slope and will never converge or cross each other. By ensuring that these pairs of lines remain parallel, we can form a quadrilateral with opposite sides that are parallel and equal in length, defining a parallelogram.

Understanding the concept of parallel lines is fundamental for constructing a parallelogram. This knowledge enables us to identify and visualize the appropriate lines that can form a parallelogram. By ensuring the parallelism of these lines, we guarantee the creation of a quadrilateral with specific geometric properties.

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When diameter is 60 mm, the volume increases at a rate of 22,620 mm³/s.

Step 1: Create an equation that connects a sphere's volume to radius as the first step.

V = 4/3*π*r³

Step 2: Calculate each side's derivative in respect to time (Let the time be "t").

(d/dt)V = (d/dt)(4/3*π*r³)

dV/dt = 4πr²*dr/dt

Step 3: The problem description informs us that the diameter is 600 m, hence r must be 30 mm.

Additionally, it is stated that now the radius of a sphere is expanding at a rate of 2 mm/s; as a result, dr/dt must equal 2 mm/s.

We are interested in dV/dt, or the rate of change of the sphere's volume.

dV/dt = 4π(30mm)²*(2mm/s)

dV/dt = 22,620 mm³/s

So, when diameter is 60 mm, the volume increases at a rate of 22,620 mm³/s.

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To calculate the concentrations of all species present in a 0.72 M NH3 solution (Kb=1.8×10−5), we can use the principles of the equilibrium expression for the dissociation of NH3 in water.

NH3 (ammonia) is a weak base that reacts with water to form NH4+ (ammonium) and OH- (hydroxide) ions. The equilibrium expression for this reaction can be written as:

NH3 + H2O ⇌ NH4+ + OH-

Since the initial concentration of NH3 is 0.72 M, we can assume that x mol/L of NH3 will dissociate to form x mol/L of NH4+ and OH-. Therefore, the concentrations of NH4+ and OH- will also be x mol/L.

To calculate the value of x, we can use the Kb expression, which relates the equilibrium constant to the concentrations of the species. In this case, Kb = [NH4+][OH-]/[NH3]. Substituting the known values, we have:

1.8×10−5 = x * x / (0.72 - x)

Solving this equation will give us the value of x, which represents the concentration of NH4+ and OH-. Finally, we can express the concentrations of NH3, NH4+, and OH- using two significant figures, separated by commas, based on the calculated value of x.

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Step-by-step explanation:

both (1,11)and (_1,_5)

No, the fact that the slope of the "best fit" line is less than 1 does not necessarily tell us whether the mean of the spreads was higher than the mean of the outcomes.

The slope only tells us about the relationship between the two variables, not their individual means. The slope indicates the change in the outcome variable for every unit increase in the spread variable. Therefore, a slope less than 1 suggests that the change in outcomes is smaller for each unit increase in spread. However, to determine which variable has a higher mean, we need to calculate the mean for each variable separately. Additionally, we should consider the variability of each variable to get a complete understanding of the relationship between them.

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