The product of 2.5 and a number is 10. First write an equation to describe the situation.

The gross death rate is 8.38%.

What is a Rate?

A rate is a measure of the frequency of an event or occurrence in relation to a specific population or time period. Rates are often expressed in terms of units per time or per population, such as cases per 100,000 people or births per year.

The gross death rate is the number of deaths in a given time period divided by the total population or, in this case, the total number of discharges.

To calculate the gross death rate for City Hospital in June, we need to subtract the eight deaths that occurred within 48 hours of admission from the total number of deaths:

Total deaths = 49 - 8 = 41

Then, we divide the total number of deaths (41) by the total number of discharges (489) and multiply by 100 to get the rate per 100 discharges:

Gross death rate = (41 ÷ 489) x 100 = 8.38%

Therefore, the gross death rate for City Hospital in June is 8.38%.

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The graph of the exponential function is on the image at the end.

Here we want to graph the function:

f(x) = 0.5*(4)ˣ

To graph this (or any function) we can find some points on the function, and to do so, we need to evaluate it.

when x = 0:

f(0) =   0.5*(4)⁰ = 0.5

Then the point is (0, 0.5)

when x = 1

f(1) =   0.5*(4)¹ = 2

So we have the point (1, 2)

if x = 2

f(2) =   0.5*(4)² = 8

So we have the point (2, 8)

Now we can graph these points and connect them with a general exponential curve.

The graph of the exponential function is shown below.

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Answer:

Option 2

Step-by-step explanation:

The length is unknown, so it is l for now. A rectangle has 2 lengths and widths, so the values are 2w and 2l. The sum of 2w and 2l have to be greater than or equal to 776, so the answer is option 2. If you solve the inequality, the length is equal to or greater than 355

Answer:

y = 80

x = 5

Hope this helped :)

Step-by-step explanation:

Lets say x + 5 so,

y = 8(5) + 12

y = 40 + 12

y = 52 so now we go back to the top equation which would be,

16(5) - 2(52) = -24

80 - 2(52) = -24

80 - 104 = -24, true

Therefore, any number you put in will still get you -24 so your answer is correct if you do substitution right.

Answer:

y = 80

x = 5

Hope this helped :)

Step-by-step explanation:

Lets say x + 5 so,

y = 8(5) + 12

y = 40 + 12

y = 52 so now we go back to the top equation which would be,

16(5) - 2(52) = -24

80 - 2(52) = -24

80 - 104 = -24, true

Therefore, any number you put in will still get you -24 so your answer is correct if you do substitution right.

The probability that the sum of the numbers rolled on the dice is even =1/2.

For the given question,

A fair dice is rolled twice.

Six different results are available with a single roll of the dice (1,2,3,4,5,6)

Therefore, if two dice are rolled, there are a total of 36 possible results, or 6².

Sample space for the sum of even = [(1,1), (1,3), (1,5), (2,2), (2, 4),(2,6), (3, 1), (3,3),(3,5),(4,2),(4,4),(4,6), (5, 1), (5,3),(5,5),(6,2),(6,4),(6,6)]

Total sample space for sum of even = 18

For the probability that the sum of the numbers rolled is even is -

probability (sum is even) = 18 / 36 = 1/2

Thus, the probability that the sum of the numbers rolled is even is 1/2.

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The correct system of equations that has (8,−3) as a solution is option B.

Let's substitute the values x = 8 and y = −3 into the equations of each option to check if they satisfy the system of equations.

a. {4x−3y=23

  2x+5y=31

Substituting x = 8 and y = −3 into the first equation:

4(8) − 3(-3) = 23

32 + 9 = 23 (not true)

Substituting x = 8 and y = −3 into the second equation:

2(8) + 5(-3) = 31

16 - 15 = 31 (not true)

b. {4x+3y=23

  2x−5y=−31

Substituting x = 8 and y = −3 into the first equation:

4(8) + 3(-3) = 23

32 - 9 = 23 (true)

Substituting x = 8 and y = −3 into the second equation:

2(8) − 5(-3) = -31

16 + 15 = -31 (true)

c. {3x+4y=−23

  2x+5y=−31

Substituting x = 8 and y = −3 into the first equation:

3(8) + 4(-3) = -23

24 - 12 = -23 (not true)

Substituting x = 8 and y = −3 into the second equation:

2(8) + 5(-3) = -31

16 - 15 = -31 (not true)

d. {4x+3y=23

  2x−5y=31

Substituting x = 8 and y = −3 into the first equation:

4(8) + 3(-3) = 23

32 - 9 = 23 (true)

Substituting x = 8 and y = −3 into the second equation:

2(8) - 5(-3) = 31

16 + 15 = 31 (true)

Therefore, option B {4x+3y=23 and 2x−5y=−31} is the correct system of equations that has (8,−3) as a solution.

To determine which system of equations has (8,−3) as a solution, we need to substitute these values into each equation of the given options and check if they satisfy the equations.

Starting with option A, when we substitute x = 8 and y = −3 into the first equation, we get 4(8) − 3(-3) = 32 + 9 = 41, which is not equal to 23. Similarly, substituting these values into the second equation, we get 2(8) + 5(-3) = 16 - 15 = 1, which is not equal to 31. Hence, option A is not the correct system.

Moving on to option B, substituting x = 8 and y = −3 into the first equation, we get 4(8) + 3(-3) = 32 - 9 = 23, which matches the value on the right-hand side of the equation. Substituting the values into the second equation, we get 2(8) - 5(-3) = 16 + 15 = 31, which also matches the value on the right-hand side. Therefore, option B is the correct system of equations with (8,−3) as a solution.

Next, in option C, substituting x = 8 and y = −3 into the first equation yields 3(8) + 4(-3) = 24 - 12 = 12, which is not equal to −23. Similarly, substituting the values into the second equation gives us 2(8) + 5(-3) = 16 - 15 = 1, which is not equal to −31. Hence, option C is not the correct system.

Lastly, in option D, when we substitute x = 8 and y = −3 into the first equation, we get 4(8) + 3(-3) = 32 - 9 = 23, matching the right-hand side. Substituting the values into the second equation, we get 2(8) - 5(-3) = 16 + 15 = 31, which is equal to the value on the right-hand side. Thus, option D is also a correct system of equations with (8,−3) as a solution.

In conclusion, option B {4x+3y=23 and 2x−5y=−31} is the correct system of equations that has (8,−3) as a solution.

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The correct system of equations that has (8,−3) as a solution is option B.

Let's substitute the values x = 8 and y = −3 into the equations of each option to check if they satisfy the system of equations.

a. {4x−3y=23

 2x+5y=31

Substituting x = 8 and y = −3 into the first equation:

4(8) − 3(-3) = 23

32 + 9 = 23 (not true)

Substituting x = 8 and y = −3 into the second equation:

2(8) + 5(-3) = 31

16 - 15 = 31 (not true)

b. {4x+3y=23

 2x−5y=−31

Substituting x = 8 and y = −3 into the first equation:

4(8) + 3(-3) = 23

32 - 9 = 23 (true)

Substituting x = 8 and y = −3 into the second equation:

2(8) − 5(-3) = -31

16 + 15 = -31 (true)

c. {3x+4y=−23

 2x+5y=−31

Substituting x = 8 and y = −3 into the first equation:

3(8) + 4(-3) = -23

24 - 12 = -23 (not true)

Substituting x = 8 and y = −3 into the second equation:

2(8) + 5(-3) = -31

16 - 15 = -31 (not true)

d. {4x+3y=23

 2x−5y=31

Substituting x = 8 and y = −3 into the first equation:

4(8) + 3(-3) = 23

32 - 9 = 23 (true)

Substituting x = 8 and y = −3 into the second equation:

2(8) - 5(-3) = 31

16 + 15 = 31 (true)

Therefore, option B {4x+3y=23 and 2x−5y=−31} is the correct system of equations that has (8,−3) as a solution.

To determine which system of equations has (8,−3) as a solution, we need to substitute these values into each equation of the given options and check if they satisfy the equations.

Starting with option A, when we substitute x = 8 and y = −3 into the first equation, we get 4(8) − 3(-3) = 32 + 9 = 41, which is not equal to 23. Similarly, substituting these values into the second equation, we get 2(8) + 5(-3) = 16 - 15 = 1, which is not equal to 31. Hence, option A is not the correct system.

Moving on to option B, substituting x = 8 and y = −3 into the first equation, we get 4(8) + 3(-3) = 32 - 9 = 23, which matches the value on the right-hand side of the equation. Substituting the values into the second equation, we get 2(8) - 5(-3) = 16 + 15 = 31, which also matches the value on the right-hand side. Therefore, option B is the correct system of equations with (8,−3) as a solution.

Next, in option C, substituting x = 8 and y = −3 into the first equation yields 3(8) + 4(-3) = 24 - 12 = 12, which is not equal to −23. Similarly, substituting the values into the second equation gives us 2(8) + 5(-3) = 16 - 15 = 1, which is not equal to −31. Hence, option C is not the correct system.

Lastly, in option D, when we substitute x = 8 and y = −3 into the first equation, we get 4(8) + 3(-3) = 32 - 9 = 23, matching the right-hand side. Substituting the values into the second equation, we get 2(8) - 5(-3) = 16 + 15 = 31, which is equal to the value on the right-hand side. Thus, option D is also a correct system of equations with (8,−3) as a solution.

In conclusion, option B {4x+3y=23 and 2x−5y=−31} is the correct system of equations that has (8,−3) as a solution.

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Answer:

8n+7

Step-by-step explanation:

The statements which are true among the answer choices are as follows;

Since, it follows from the task content that; A 5 1/2 ounce raw hamburger patty has 27 1/2 grams of protein, it follows that the protein content per ounce is;

P(hamburger) = 55/2 ÷ 11/2

= 5g per ounce.

Also, A 6 ounce piece of raw chicken breast has 48grams of protein, hence we have;

P(chicken breast) = 48/6 = 8 grams per ounce.

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Answer:

(2)(6)+3

?

=

15

15=15

True

Step-by-step explanation:

help

The declaration states that the value of Arc EFC = 253°.

A measure is indeed a quantitative concept used to express how large a collection is. Each unique measure represents a different method for determining how large a collection is. It would initially appear that a set's cardinality is the only logical way to determine its number.

We can tell we are working with a circular that has 360 degrees because of the connection.

We can infer that we have it if we look at that file.

Arc EFC

Arc CD

Arc DE

And everything together give us 360,

Arc EFC + Arc CD + Arc DE = 360

If we examine the figure again, we can see that the central angle of an intercepted arc is identical to the arc's measure.

Arc CD is 90 degrees since the central angle is 90 degrees given

Arc DE is 17 degrees

Arc EFC + Arc CD + Arc DE = 360

If we input all the figures

Arc EFC + 90 + 17 = 360

Arc EFC + 107 = 360

Arc EFC = 360 - 107

Arc EFC = 253

Therefore, Arc EFC = 253°

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The correct questions is:

Circle O, and are diameters. Arc ED measures 17°. Circle O is shown. Line segments F C and A E are diameters. Line segments C O and B O are radii. Point B is between points A and C, and point C is between points E and C. Angle D C is a right angle. What is the measure of Arc E F C? 107° 180° 253° 270°

Alex's statement that it is more likely to roll an even number on the second number cube if he rolls an odd number on the first number cube is not correct.

The probability of rolling an even number on the second number cube is the same regardless of whether an odd or even number is rolled on the first number cube.

Each number cube has 6 faces, and 3 of those faces are even numbers (2, 4, and 6).

So the probability of rolling an even number on a single number cube is 3/6 or 1/2.

This probability does not change based on the result of the roll on the other number cube.

Hence, No, Alex is not correct.

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The expectation value of the position squared when the particle in the box is in its third excited state is equal to \(\frac{9l^2}{8}\), where l is the length of the box. This is equal to nine-eighths of the length of the box squared.

The expectation value of the position squared when the particle in the box is in its third excited state can be calculated using the formula\(\langle x^2 \rangle = \frac{l^2}{8} \left( 2n^2 + 6n + 3 \right)\),

where n is the quantum number of the state and l is the length of the box. Here, n is 3, so the expectation value is equal to

\(\frac{l^2}{8} \left( 2 \times 3^2 + 6 \times 3 + 3 \right) = \frac{9l^2}{8}\).

This can be written as nine-eighths of the length of the box squared.

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The formula to be used to calculate the 95% confidence interval bounding both sides of the population mean of a normal distribution with known standard deviation (sigma) is given by

X ± Z * σ/\(\sqrt{n}\).

We have to find out the formula that is to be used to calculate the 95% confidence interval bounding both sides of the population mean of a normal distribution with known standard deviation (sigma).

We have to first understand what is meant by 95% confidence interval. Considering any normal distribution, approximately 85% of the values are within two standard deviations of the mean. Standard Deviations of the mean is the range of numbers that we believe contains.

It is also known to us that "n" is the sample size. If the sample size is greater than 30 then we can use the formula to determine the 95% confidence interval.

The sample means, the sample standard deviation, the sample size, and the z-value are represented in the formula.

Therefore, the formula to be used to calculate the 95% confidence interval bounding both sides of the population mean of a normal distribution with known standard deviation (sigma) is given by

X ± Z * σ/\(\sqrt{n}\).

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We will have that Sarah's function is the correct one, since each hour she will get $9, then when we multiply will give us the amount of money she makes in the number of hours.

H = 9h

Answer:

X-4=30

Step-by-step explanation:

Difference means subtraction

X represents the unknown variable because its says "Of a number" of which we do not know

If you are still confused let me know

Explanation:

Points are locations in space or on a 2D flat plane. Think of an address to a house or perhaps longitude/latitude coordinates. Such locations do not have any width, length or height. There are no dimensions a point. Points are infinitely small. The only reason they appear to have a size is because otherwise we wouldn't be able to see the point locations.

This is why choices A B and D can be ruled out. Only choice C is true.

Answer:

z=500

Step-by-step explanation:

since we know that the whole equation is equal to 250, we can substitute values in.

250=150/1/5 -z

250=750-z

-500=-z

z=500

The value of z for the function f(x)=150/x-z is z=500.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the function f is defined by f(x)=150/x-z where z is a constant. The value of the function at x = 1/5 is 250.

The value of the constant z will be calculated as,

The whole equation is equal to 250, we can substitute values in.

250=150/1/5 -z

Simplify the equation and solve for the value of z,

250=750-z

-500=-z

z=500

Therefore, the value of z for the function f(x)=150/x-z is z=500.

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The coordinates of A'' are \(A''(x,y) = (3-x, y-5)\).

Let be \(A(x,y) = (x,y)\), we apply the following operations to get the coordinates of A'':

Reflection over x = 2

\(A'(x,y) = (x,y) + 2\cdot [(2,y)-(x,y)]\)

\(A'(x,y) = (x,y) +2\cdot (2-x, 0)\)

\(A'(x,y) = (x,y) +(4-2\cdot x, 0)\)

\(A'(x,y) = (4-x, y)\)

Translation

\(A''(x,y) = (4-x, y) +(-1, -5)\)

\(A''(x,y) = (3-x, y-5)\)

The coordinates of A'' are \(A''(x,y) = (3-x, y-5)\).

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Answer:

6u - 10

Step-by-step explanation:

Given

6(u - 2) + 2 ← distribute parenthesis

= 6u - 12 + 2 ← collect like terms

= 6u - 10

Answer:

x=(3e+2d)/(2g-ef)

Step-by-step explanation:

d=e(3+fx)/(2+gx)

or, 2d+2gx=3e+efx

or, 2gx-efx=3e+2d

or, x(2g-ef)=3e+2d

or, x=(3e+2d)/(2g-ef)

Answer:

x = (-2d + 3e) / (dg - fe)

Step-by-step explanation:

We solve it by using algebra.

1. Multiply each side by 2 + gx:

dgx + 2d = fxe + 3e

2. Subtract fxe on both sides:

dgx − fxe + 2d = 3e

3. Subtract 2d from both sides:

dgx − fxe = −2d + 3e

4. Factor out x:

x (dg − fe) = −2d + 3e

5. Divide dg - fe:

x = (-2d + 3e) / (dg - fe)

I hope this helped! :D

Answer:

256

Step-by-step explanation:

The quotient of the given expression will be 256.

From the given data

\(=\dfrac{2^{4} }{2^{-4} }\)

Now it will become

\(2^{4} \times 2^{4} = 2^{8} =256\)

Thus the quotient of the given expression will be 256

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Answer:

27, 28, 29

Step-by-step explanation:

x +x+1 +x +2 =84

3x+3 +84

3x=84-3

3x=81

x=81 :3

x=27 (the first number

27+1 =28 (the second number

27 +2 =29 (the third number

The union of events A and B, denoted by A∪B, contains all outcomes that are in A or B. Option B

In probability theory, events A and B represent sets of outcomes from a given experiment or sample space. The union of two events A and B is the set of all outcomes that belong to either A or B or both. It is formed by combining the elements from both sets without repetition.

Mathematically, the union of events A and B is defined as:

A∪B = {x : x ∈ A or x ∈ B}

This means that any outcome x that is in event A or event B (or both) will be included in the union of A and B.

To illustrate this concept, consider the following example:

Event A: Rolling an even number on a fair six-sided die

A = {2, 4, 6}

Event B: Rolling a number greater than 4 on a fair six-sided die

B = {5, 6}

The union of A and B, denoted by A∪B, will contain all outcomes that are in A or B:

A∪B = {2, 4, 5, 6}

Therefore, option B is the correct choice. The union of events A and B contains all outcomes that are in A or B.

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Its not must that 3x have to be the one to be subtracted. You could take 8x as well.

But always subtract from the smaller one (in this case 3x) because its easier.

If you are subtracting 3x-3x and 8x-3x, the equation would be like

4 = 5x - 16

5x = 4+16

5x = 20

x = 4

Answer:

Point A' should be 2 units left and 8 units above of Point C.

Point B' should be 10 units right and above Point C.

Point C stays the same.

The percentage for the markup for the wheelbarrow is 40%.

It is important to note that the percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100

In this case, the retailer sells wheelbarrows for $21 that were acquired at a cost of $15. The markup will be:

= Selling price - Cost price

= $21 - $15

= $6

Markup percentage will be:

= Markup / Cost price × 100

= \(\frac{6}{15}\)× 100%

=0.4*100%

= 40%

Therefore, the percentage for the markup is 40%.

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Answer:

0.047619

P.S. do you need to round?

Answer:

\(\frac{1}{21}\)

Step-by-step explanation:

If pipes A and B can fill a storage tank in 8 h and 12 h and pipe A was turned on at noon, and  pipe B was turned on at 1:30 P.M, then the water tank will be full at 5:24 pm

Another type of time- and work-based inquiry is called "pipes and cistern." You could ask questions like how long it takes to fill or empty a tank, how much effort is involved, and other similar inquiries. There are two important points that a candidate should understand about such questions:

An inlet is a conduit that is linked to a tank to allow water to be added to it. This kind of work has been accomplished.

An exit is a conduit that is attached to empty the water from the tank. This shows that the task was done in an unfavourable manner. In the query, it may also be referred to as "leak."

How to solve?

Let t = the "on" time duration of pipe A

(t-1.5) = the "on" time of pipe B

Let the completed job = 1; (a full tank)

3t + 2(t-1.5) = 24(1)

3t + 2t - 3 = 24

5t = 24 + 3

t = 27/5

t = 5.4 hrs, which is 5 hrs + (.4*60) = 5 hrs, 24 min

Therefore, the tank will be full at 5:24 pm

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