three sides of a triangle are 3, radical7, and 4. Is the triangle acute, right or obtuse?

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Explanation:

The original expression is of the pattern cos cos + sin sin. This pattern matches the second identity in the hint. Specifically, we'll say the following:

cos(A - B) = cos(A)cos(B) + sin(A)sin(B)

cos(A)cos(B) + sin(A)sin(B) = cos(A - B)

cos(94)cos(18) + sin(94)sin(18) = cos(94 - 18)

cos(94)cos(18) + sin(94)sin(18) = cos(76)

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We can verify this by use of a calculator. Make sure your calculator is in degree mode.

Both expressions give the same decimal approximation, so this helps confirm the two expressions are equal. You could also use the idea that if x = y, then x-y = 0. Through this method, you'll subtract the left and right hand sides and you should get (very close to) zero.

it is true that  0.5% of 200 is 10.

True.

To find 0.5% of a number, we need to multiply the number by 0.5/100, which can be simplified to 5/100 or 1/20. This is because "percent" means "per hundred", so 0.5% is equivalent to 0.5 per 100 or 0.5/100.

Multiplying the number by 5/100 is the same as multiplying it by 0.5/100, so it will give us the correct result.

For example, if we want to find 0.5% of 200, we can multiply 200 by 5/100 or 0.5/100:

\(0.5% of 200 = 200 \times 5/100 = 10\)

Therefore, it is true that  0.5% of 200 is 10.

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The statement "Linear programming can be used to find the optimal solution for profit, but cannot be used for nonprofit organizations" is False.

Linear programming can be used to find the optimal solution for profit as well as for non-profit organizations. Linear programming is a method of optimization that aids in determining the best outcome in a mathematical model where the model's requirements can be expressed as linear relationships. Linear programming can be used to solve optimization problems that require maximizing or minimizing a linear objective function, subject to a set of linear constraints.

Linear programming can be used in a variety of applications, including finance, engineering, manufacturing, transportation, and resource allocation. Linear programming is concerned with determining the values of decision variables that will maximize or minimize the objective function while meeting all of the constraints. It is used to find the optimal solution that maximizes profits for for-profit organizations or minimizes costs for non-profit organizations.

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The perimeter of the triangle is determined as 14.33 units.

The perimeter of the triangle is calculated by applying the following formula as follows;

Perimeter = distance round the shape

The length of the side of the triangle is calculated as follows;

A = √[ (3 - 1)² + (-3 - 3)² ]

A = 6.33 units

B = √[ (1 - 3)² + (-3 + 3)² ]

B = 2 units

C = √[ (1 - 1)² + (-3 - 3)² ]

C = 6 units

The perimeter of the triangle is calculated as;

P = 6.33 units + 2 units + 6 units

P = 14.33 units

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The approximate proportion of lightbulb replacement requests numbering between 37 and 47 can be determined using the empirical rule. The proportion is approximately 0.3413.

The empirical rule, also known as the 68-95-99.7 rule, states that for a normal distribution:

- Approximately 68% of the data falls within one standard deviation of the mean.

- Approximately 95% of the data falls within two standard deviations of the mean.

- Approximately 99.7% of the data falls within three standard deviations of the mean.

In this case, the mean is 37 and the standard deviation is 10. To find the proportion of lightbulb replacement requests between 37 and 47, we can use the empirical rule:

Proportion = P(37 ≤ X ≤ 47) ≈ P(mean - 1 standard deviation ≤ X ≤ mean + 1 standard deviation)

Proportion ≈ P(37 ≤ X ≤ 47) ≈ P(27 ≤ X ≤ 47)

Using the empirical rule, we know that approximately 68% of the data falls within one standard deviation of the mean. Therefore, the proportion of requests between 27 and 47 is approximately 68%.

However, we need to find the proportion between 37 and 47, so we subtract the proportion of requests below 37. Since the distribution is symmetric, this proportion is the same as the proportion above 47.

Proportion = 68% - (100% - 68%)

Proportion ≈ 0.68 - 0.32

Proportion ≈ 0.36

Rounding the proportion to four decimal places, we get approximately 0.3413.

The approximate proportion of lightbulb replacement requests numbering between 37 and 47, based on the empirical rule, is 0.3413. This means that around 34.13% of the daily requests fall within this range.

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This forest can support approximately 5 people based on its oxygen production.

To find out how many people the forest can support based on the amount of oxygen produced, we will use the given information:

1. The forest produces 970 kg of oxygen per metric ton of wood.
2. The average person breathes 165 kg of oxygen per year.

We'll first calculate the total amount of oxygen the forest produces, and then divide that by the oxygen consumption of one person to find out how many people the forest can support.

Your answer: A forest produces approximately 970 kg of oxygen for every metric ton of wood produced. If the average person breathes about 165 kg of oxygen per year, the number of people this forest can support can be calculated using the following steps:

Step 1: Determine the total amount of oxygen produced by the forest.
Let's assume the forest produces 1 metric ton of wood.
Total oxygen produced = 970 kg of oxygen per metric ton of wood x 1 metric ton of wood = 970 kg of oxygen.

Step 2: Calculate the number of people the forest can support.
\(Number of people =  \frac{Total oxygen produced}{Oxygen consumption per person}\)
\(Number of people =  \frac{ 970 kg of oxygen}{165 kg of oxygen per person}\)
Number of people = 5.88

Since we cannot have a fraction of a person, we round down to the nearest whole number. Therefore, this forest can support approximately 5 people based on its oxygen production.

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The minimum sample size would be 953.

What is the confidence interval?

A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. A confidence interval is calculated at a specified confidence level; the 95% confidence level is most commonly used, but other levels, such as 90% or 99%, are occasionally used.

The given sample space is n = 300.

x = 101 plan to vote

P = x/n = 101/300 = 0.3367

95% confidence = \(P\pm Z_\frac{\alpha}{2}=1.96\)

Confidence Interval:

                         \(CI=P\pm Z_\frac{\alpha}{2}\sqrt{\frac{P(1-P)}{n}}\\\\CI=0.3367\pm 1.96 \times \sqrt{\frac{0.3367(1-0.3367)}{300}}\\\\CI=(0.2832, 0,3902)\)

Margin of error = 3%

The margin of Error = \(Z_\frac{\alpha}{2}\sqrt{\frac{P(1-P)}{n}}\)

                   \(3 \% = P\pm Z_\frac{\alpha}{2}\sqrt{\frac{P(1-P)}{n}}\)

                  \(\frac{1}{\sqrt{n}}=\frac{0.03}{1.96\sqrt{(0.3367)(1-0.3367)}}\\\\\sqrt{n} = 30.875\\\\n = 953\)

Hence the minimum sample size = 953.

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Answer:

x<-1

Step-by-step explanation:

I think and hope it helps

The independent variable for Scenario A is given as follows:

a. The employee benefits package.

In the case of a relation, we have that the independent and dependent variables are defined by the standard presented as follows:

In the context of this problem, we have that the input and the output of the relation are given as follows:

Hence the independent variable for Scenario A is given as follows:

a. The employee benefits package.

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the formula is y=mx+b

m is the slope

b is the y-intercept form

so the -1 is the y-intercept form. so you need to start at that point on the y axis. then the slope which is -1/2 comes into play. in my school we use rise/run. so from the point you marked at -1 you will go down 1 and to the right 2 points then where you stop is your next point (mark it) keep doing that. also go up the other way from the -1 point. go up 1 and to the left 2. then connect all of your points with a line. I hope this helped.

please chose this answer as brainliest

Answer:

5 x 9 = 45 and 5+9= 14

Step-by-step explanation:

brainliest please

Answer: The first box (the 450 g box for $4.69)

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Explanation:

To get the unit cost, we'll divide each price by the weight

The first box has a unit cost of (4.69)/450 = 0.010422 approximately which rounds to 0.01; so this unit cost is approximately $0.01 per gram or 1 cent per gram.

For the second box, its unit cost is (6.49)/600 = 0.0108167 approximately. When we round to the nearest cent, we get the same unit cost as before. Without rounding, we see that the first box has a slightly lower unit cost. Therefore box 1 is the better buy.

The sum of the series 2 + 4 + 6 + 58 can be expressed using sigma notation as Σ(i = 1 to 4) 2i, which simplifies to 20.

The first term of the series is 2, the second term is obtained by adding 2 to the first term (2 + 2 = 4), the third term is obtained by adding 2 to the second term (4 + 2 = 6), and so on. Finally, the last term of the series is 58.

Now, let's express this series using sigma notation:

Σ(i = 1 to n) 2i

In the above notation, the Greek letter sigma (Σ) represents the sum. The variable i is the index of summation, which starts at 1 and goes up to n. In this case, n represents the number of terms in the series.

The expression 2i represents the terms of the series. As i increases from 1 to n, the value of 2i increases accordingly. For example, when i = 1, 2i = 2. When i = 2, 2i = 4, and so on.

To find the sum of the series using sigma notation, we substitute the values of the index of summation into the expression 2i and add up the terms:

Σ(i = 1 to n) 2i = 2(1) + 2(2) + 2(3) + ... + 2(n)

For our specific series, we have:

Σ(i = 1 to 4) 2i = 2(1) + 2(2) + 2(3) + 2(4)

Simplifying this expression, we get:

2 + 4 + 6 + 8 = 20

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Answer: -50

Step-by-step explanation:

-20 + -30 = -50

The total change in temperature that Dana recorded will be -50 or a drop of 50.

The number system is a way to represent or express numbers.

A decimal number is a very common number that we use frequently.

Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.

As per the given,

First temperature drop = -20

Second temperature drop = -20

Total drop = -20 - 20 = -40

Hence "The total change in temperature that Dana recorded will be -50 or a drop of 50".

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80.49% of Brookland voters support increasing funding for mental health services.

To estimate the number of voters in favor of increased funding for mental health services in Brookland, one can use the percentage of voters who participated in the survey and apply it to the total number of voters in the city.

The percentage of supporters of the financial increase is calculated by dividing the number of supporters by the total number of survey respondents:

Ratio = (482 / 600) = 0.8033

To estimate the number of voters, we multiply the proportion by the total number of voters in the city:

Estimated number of voters = 0.8033 * 19,310 = 15,541

An estimated 15,541 voters in Brookland support increasing funding for the city's mental health services.

To calculate the percentage of voters, we divide the estimated number of voters by the total number of voters in the city and multiply by 100:

Percentage of voters = (15,541 / 19,310) * 100 = 80.49%

Therefore, approximately 80.49% of Brookland voters support increased funding for mental health services.

If you increase the number of randomly selected voters to 1200, the margin of error decreases. A larger sample size usually provides a more accurate representation of the population.

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Answer:

The name of the solid with 20 faces that are congruent equilateral triangles is icosahedron.

The solid you are referring to is called an icosahedron. An icosahedron is a specific type of convex polyhedron that has 20 faces. In this case, all 20 faces are congruent equilateral triangles. Option d is correct answer.

To understand why this solid is called an icosahedron, let's break down the term. "Icosa-" comes from the Greek word for twenty, while "-hedron" means face. Therefore, an icosahedron is a polyhedron with twenty faces.

Each face of an icosahedron is an equilateral triangle, meaning that all three sides of the triangle are equal in length, and all three angles are equal to 60 degrees. Since all 20 faces are congruent, they have the same side lengths and angles.

The icosahedron has a total of 12 vertices and 30 edges. The vertices are the points where three edges meet, and the edges are the line segments connecting the vertices. The icosahedron has a symmetrical and regular structure, making it one of the five Platonic solids.

An icosahedron is a convex polyhedron with 20 congruent equilateral triangle faces, 12 vertices, and 30 edges.

Option d is correct answer.

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The graph shows the different combinations of loaves of bread and rolls that the baker can sell in order to reach a total revenue of $27.

What is the slope-intercept form?

The slope-intercept form is a way of expressing a linear equation in the form of y = mx + b, where m is the slope of the line and b is the y-intercept. The y-intercept is the point at which the line crosses the y-axis, meaning the point at which the line intersects the y-axis when x = 0.

The given equation is in the form of y = mx + b where y =27, m = 3 and b = 1, is a linear equation and it can be represented as a straight line in a coordinate plane.

To graph this equation, we can use the following steps:

The graph shows the different combinations of loaves of bread and rolls that the baker can sell in order to reach a total revenue of $27.

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Answer:

answer is 20

Step-by-step explanation:

5/7 of 28

5/7×28= 20

hope it helps

The solution of the given differential equation is y(x) = c₁(x^(-1)) + c₂(x) + u(x)[ln|x| + c₃/x²], where c₁, c₂, and c₃ are arbitrary constants.

Given the equation:x^2y″+xy′−y=3x

The general solution of the given differential equation can be obtained by following these steps:

Step 1: Characteristic equation: The characteristic equation of the differential equation is given by the auxiliary equation:x²m² + xm - 1 = 0,

which can be factorized as follows:(xm - 1)(x m + 1) = 0

Hence, m = 1/x and m = -1/x are the roots of the characteristic equation.

Step 2: Complementary function: Using the roots of the characteristic equation, the complementary function can be given as:Y_c(x) = c₁(x ^ (-1)) + c₂(x)

Step 3: Particular integral: To find the particular integral of the given differential equation, we assume that y_p(x) = u(x) v(x).Now, y′ = u′v + uv′, and y″ = u″v + 2u′v′ + uv″

Substituting these values in the given differential equation, we get:x²(u″v + 2u′v′ + uv″) + x(u′v + uv′) − uv = 3x

Simplifying the above expression, we get:u(x) (xv″ + v′) = 3xTherefore, (xv″ + v′) = 3/x

Integrating both sides of the above equation, we get:v(x) = ln|x| + c₃/x²where c₃ is an arbitrary constant.

Substituting v(x) in y_p(x) = u(x) v(x), we get:y_p(x) = u(x)[ln|x| + c₃/x²]

Step 4: General solution: The general solution of the given differential equation is given by the sum of the complementary function and the particular integral:

Therefore, y(x) = y_c(x) + y_p(x)y(x) = c₁(x^(-1)) + c₂(x) + u(x)[ln|x| + c₃/x²]

Hence, the solution of the given differential equation is y(x) = c₁(x^(-1)) + c₂(x) + u(x)[ln|x| + c₃/x²], where c₁, c₂, and c₃ are arbitrary constants.

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Chance is a term used to represent the percentage of time a specific result is expected to occur when the same basic procedure is repeated over and over again, where each repetition is independent.

Chance is a term that is used to describe the probability that a certain outcome will occur given a set of fundamental instructions repeated again with each repetition being independent.

Ultimately, this means the number of times a result of an event occurs when repeated over a number of times is chance.

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Answer:185 guests

Step-by-step explanation: it can only hold 185 guests no more.

Answer:

210

Step-by-step explanation:

Multiply by the total amount by the decimal equivalent of 70% (0.7) to get your answer.

The matrix transformation of triangle XYZ with coordinates

When dilated by a factor of 2.5 now becomes;

ANSWER:

The correct vertices of the image now becomes;

1.The total cost would be:50 cash registers x 450 AED per cash register = 22,500 AED

2.the cost of one new cash register at the end of 8 years would be approximately 661.39 AED.

3. the value of one old cash register after 8 years would be approximately 222.19 AED.

4.It is not possible to determine whether the money from selling the old cash registers is enough to pay for the new ones without knowing the selling price of the old cash registers.

5.It would take approximately 19 years for the value of the cash registers to reach 95 AED.

1. The company needs to buy at least 50 cash registers, each costing 450 AED. Therefore, the total cost would be:

50 cash registers x 450 AED per cash register = 22,500 AED

 2. The continuous compounding formula is A = \(Pe^(^r^t^)\), where A is the resulting amount, P is the initial amount, e is Euler's number, r is the annual interest rate, and t is the time in years. We can apply this formula here by setting P = 450 AED, r = 6%, t = 8 years and solving for A:

A = 450*e^(0.06*8) = 661.39 AED (rounded to two decimal places)

 3. The value of each old cash register decreases at a rate of 7.5% per year. We can use the formula for exponential decay, P = , where P is the resulting amount, P is the initial amount, e is Euler's number, r is the rate of change, and t is the time in years. Setting P to 450 AED, r to -7.5%, and t to 8 years, we can solve for the resulting value:

P = 450*e^(-0.075*8) = 222.19 AED (rounded to two decimal places)

 4. If the selling price is greater than the value of the old cash registers after 8 years (i.e., 222.19 AED), then the company would make a profit on each old cash register sold to help pay for the new ones; if the selling price is less than 222.19 AED, then the company would incur a loss on each old cash register sold.

 5. To find when the value of the cash register will be approximately 95 AED, we can use the formula from part (3).

95 = 450*e^(-0.075t)

Dividing both sides by 450 and taking the natural logarithm of both sides, we get:

ln(95/450) = -0.075t

Solving for t, we get:

t = -(1/0.075) * ln(95/450) ≈ 19.01 years

With a lifespan of only 8 years, it is not a realistic scenario for the cash registers to depreciate to such a low value. Therefore, it is important for the company to properly maintain and replace the cash registers on a regular cycle to ensure that their value remains close to the original purchase price.

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Answer:

c

Step-by-step explanation:

Answer: The expected value of V can be calculated as the sum of the products of the possible values of V and their corresponding probabilities. Let's consider the three possible scenarios:

Using the utility function, we can see that the expected value of V is:

E[V] = 0 * 0.2 + (1/2) * (0.8 * 9/10) + 10 * (0.8 * 1/10)

E[V] = 0 + 0.36 + 0.8

E[V] = 1.16

Therefore, the expected value of V is 1.16. However, since V represents the number of healthy vacation days, it must be a non-negative integer. So, the closest integer to 1.16 is 1. Therefore, the answer is c. 2.

Given that Lucy had 72 dollars, which is nine times as much as Xavier had, we can select the right method which represents Xavier's money in the steps below.

Let Xavier's money be x. Since Lucy has nine times more money than Xavier we can say that Lucy's money is;

Since Lucy also had 72 dollars we can say;

Therefore, the right answer would be;

Answer: Option C

Answer:

The initial number of video views was more than the initial number of site visits, and the number of video views grew by  a smaller factor than  the number of site visits.  The difference between the total number of site visits and the video views after 5 weeks is  20,825

Step-by-step explanation:

the initial video view was 5120 and the initial number of site visits were 4800, so the initial video view was more than.

The video views grew by 5/4 and the number of site visits grew by 3/2, and since 3/2 is > 5/4, the video views grew by a smaller factor than the number of site visits.

the result for the video views after 5 weeks is 15,625 and the site visits after 5 weeks is 36450, so 36450-15,625=20,825

Answer:

Step-by-step explanation:

Here's proof of the answer correcto

happy earth day 2 years hehe