Choose all options that apply . Which of the following are steps necessary to ensure patient safety ? a) Make sure that the medication is dispensed in the same units in which it was prescribed. b ) Review any calculation questions with the pharmacist . Check to see if there's a better medication for the patient's problem. d) Dispense an extra dose to save the patient from having to return in case of loss or damage to one of the doses. Oe ) Compare the label on the medication with the order from the physician .

Answer:

The 99% confidence interval for the proportion of GSU Juniors who believe that they will, immediately, be employed after graduation is (0.7987, 0.8307).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the z-score that has a p-value of \(1 - \frac{\alpha}{2}\).

Suppose we take a poll (random sample) of 3923 students classified as Juniors and find that 3196 of them believe that they will find a job immediately after graduation.

This means that \(n = 3923, \pi = \frac{3196}{3923} = 0.8147\)

99% confidence level

So \(\alpha = 0.01\), z is the value of Z that has a p-value of \(1 - \frac{0.01}{2} = 0.995\), so \(Z = 2.575\).  

The lower limit of this interval is:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.8147 - 2.575\sqrt{\frac{0.8147*0.1853}{3923}} = 0.7987\)

The upper limit of this interval is:

\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.8147 + 2.575\sqrt{\frac{0.8147*0.1853}{3923}} = 0.8307\)

The 99% confidence interval for the proportion of GSU Juniors who believe that they will, immediately, be employed after graduation is (0.7987, 0.8307).

Answer:

1/2 feet per second.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

D goes thru positive 4 and negative 3

Answer:

38.9 degrees C

Step-by-step explanation:

Use the equation:

\(C=\frac{5}{9} (F-32)\)

to convert degrees Fahrenheit  to degrees Celsius. So replace the value for the Fahrenheit with 102 and solve for C:

\(C=\frac{5}{9} (F-32)\\C=\frac{5}{9} (102-32)\\C=\frac{5}{9} (70)\\C=\frac{350}{9} \approx38.89\,^oC\)

which to the nearest tenth can be written as: 38.9 degrees C

Answer:

0.375

Step-by-step explanation:

3/2 equals 1 and a half, and 1 and a half divided by 4 will get you 0.325

Answer:

4x - 2 = 3x + 1. Solution We substitute the value 3 for x in the equation and see if the left-hand member equals the right-hand member. 4(3) - 2 = 3(3) + 1.

If the test statistic is higher than 1.645, reject H0. If the test statistic is higher than 2.33, reject H0.

Conjectures used in statistical tests, which are formal techniques for drawing conclusions or making judgments based on data, include the null hypothesis and the alternative hypothesis.

The hypotheses, which are based on a sample of the population, are suppositions regarding a statistical model of the population.

The tests are essential components of statistical inference and are frequently used to distinguish between statistical noise and scientific claims when interpreting experimental data in science.

"The null hypothesis is the proposition under investigation in a statistical significance test.

The significance test is intended to determine how strong the evidence is against the null hypothesis. The null hypothesis is typically a claim that there is "no effect" or "no difference.

H0 is a common way to represent it.

Hence, If the test statistic is higher than 1.645, reject H0. If the test statistic is higher than 2.33, reject H0.

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Answer: 7x + 1

Step-by-step explanation:

(6x-4)+(x+5)

Step 1: Remove Parentheses:

              6x-4+x+5

Step 2: Combine Like Terms:

             7x +1

The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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1) The lower limit of the confidence Interval is: 1489.77.

The upper limit of the confidence Interval is: 1530.23

2) The lower limit of the confidence Interval is: 1478.32

The upper limit of the confidence Interval is: 15411.68

The formula to find the confidence interval is:

CI = x' ± z(σ/√n)

where:

CI is confidence interval

x' is sample mean

z is z-score at confidence level

σ is standard deviation

n is sample size

1) The parameters are:

σ = $234

x' = $1510

n = 362

z at 90% CL = 1.645

Thus:

CI = 1510 ± 1.645((234/√362)

CI = 1510 ± 20.23

CI = (1489.77, 1530.23)

2) The parameters are:

σ = $234

x' = $1510

n = 362

z at 99% CL = 2.576

Thus:

CI = 1510 ± 2.576((234/√362)

CI = 1510 ± 31.68

CI = (1478.32, 15411.68)

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Answer:

It's B (1÷13=3) for Part a

1 whole is equal to 3/3. One batch of brownies uses up to 1/3 of butter. So 1 ÷ 1/3 = 3.

Step-by-step explanation:

Answer:

nominal ordinal interval ratio

Step-by-step explanation:

there

Answer:

-2x-3

Step-by-step explanation:

See the image below:) you can use the app photo math, you just take a picture of the problem and it gives you the answer and explains the steps.

Answer:

632.83mm²

Step-by-step explanation:

Applying Pythagorean theorem to triangle SOH

SH² = SO² + OH²

SH = \(\sqrt{(15.4)^2+(7.2)^2}=17mm\)

Since the base of the pyramid is a regular pentagon, angle OAH
is 108°/2 = 54°.

AH = 7.2/tan 54° = 5.23mm

So AB = 2AH = 10.46mm

The area of triangle SAB is:

A1 = 1/2 × SH × AB = 1/2 × 17 × 10.46 = 88.91mm²

The area of all triangles is

A2 = 5 × A1 = 5 × 88.91 = 444.55mm²

The area of the base is:

A3 = (perimeter × apothem)/2 = (5 × 10.46 × 7.2)/2 = 188.28mm²

The surface area of the pyramid is:

A2 + A3 = 444.55 + 188.28 = 632.83mm²

Step-by-step explanation:

the surface area is the sum of the base area (pentagon) and the 5 side triangles (we only need to calculate one and then multiply by 5, as they are all equal).

these side triangles are isoceles triangles (the legs are equally long).

the usual area formula for a pentagon is

1/2 × perimeter × apothem

the apothem is the minimum distance from the center of the pentagon to each of its sides.

in our case this is 7.2 mm.

how to get the perimeter or the length of an individual side of the pentagon ?

if the apothem of a pentagon is given, the side length can be calculated with the formula

side length = 2 × apothem length × tan(180/n)

where 'n' is the number of sides (5 in our case). After getting the side length, the perimeter of the pentagon can be calculated with the formula

perimeter = 5 × side length.

so, in our case

side length = 2 × 7.2 × tan(180/5) = 14.4 × tan(36) =

= 10.4622124... mm

perimeter = 5 × 10.4622124... = 52.31106202... mm

area of the pentagon = 1/2 × perimeter × apothem =

= 1/2 × 52.31106202... × 7.2 = 188.3198233... mm²

now for the side triangles.

the area of such a triangle is

1/2 × baseline × height

baseline = pentagon side length

height we get via Pythagoras from the inner pyramid height and the apothem :

height² = 7.2² + 15.4² = 51.84 + 273.16 = 289

height = 17 mm

area of one side triangle =

1/2 × 10.4622124... × 17 = 88.92880543... mm²

all 5 side triangles are then

444.6440271... mm²

and the total surface area is then

444.6440271... + 188.3198233... = 632.9638504... mm²

≈ 632.96 mm²

Answer:

Below

Step-by-step explanation:

At  B   (  40 mins)  and  D (30 mins)   he is not moving....visiting .

The width of A is the time it took to get to first house = 20 mins

The width of C is t the time to get to second house = 60 to 70 = 10 mins

Riding toward home at C and E  ( the distance...the y-value....is getting less)

He is fastest where the line has greatest slope...where it is steepest =  C

He was away from home the width of the graph = 115 mins

The equations that have the solution x = 5 are 25/x + 4 = 9 and 32 − 4x = 12

From the question, we have the following parameters that can be used in our computation:

x⁵ + 5 = 6

25/x + 4 = 9

32 − 4x = 12

11 + 6x = 22

3x + 1 = 9

18 − 2x = 9

Solving each equation, we have

Equation 1: x⁵ + 5 = 6

Evaluate the like terms

x⁵  = 1

Take the fifth-root

x = 1

Equation 2: 25/x + 4 = 9

Evaluate the like terms

25/x = 5

So, we have

5x = 25

Divide by 5

x = 5

Equation 3: 32 − 4x = 12

Evaluate the like terms

4x = 20

Divide by 4

x = 5

Equation 4: 11 + 6x = 22

Evaluate the like terms

6x = 11

Divide by 4

x = 11/6

Equation 5: 3x + 1 = 9

Evaluate the like terms

3x = 8

Divide by 3

x = 8/4

Equation 6: 18 − 2x = 9

Evaluate the like terms

2x = 9

Divide by 2

x = 9/2

Hence, the equations are 25/x + 4 = 9 and 32 − 4x = 12

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Answer:

2\(\frac{3}{4} + -4\frac{1}{4} = -1\frac{2}{4}\)

Step-by-step explanation:

The initial position of the blue line is 2 and 3/4. The final position (represented by the red line) is -1 and 1/2. 2 and 3/4 - 4 and 1/4 is the only thing you can subtract to get -1 and 2/4.

Answer:

2 3/4 +(-3 1/4)= -1 2/4

Step-by-step explanation:

hope you get it right

The length of the longer wire is 82 feet.

Let's denote the length of the longer wire as L. According to the given information, the shorter wire is attached to the ground 16 feet from the base of the pole, and the longer wire is attached to the ground 32 feet from the base of the pole.

We can form two similar right triangles using the wires. The height of each triangle is the height of the pole, and the base of each triangle is the distance from the base of the pole to where the wire is attached to the ground.

In the first triangle, the shorter wire creates an angle with the ground. Let's denote this angle as θ. Since we are given the cosine of this angle, we can use the cosine function to find the height of the pole in terms of θ and the base of the triangle:

cos(θ) = adjacent/hypotenuse = 16/L

Given that cos(θ) = 8/41, we can substitute this value into the equation:

8/41 = 16/L

To solve for L, we can cross-multiply and solve for L:

8L = 41 * 16

L = (41 * 16)/8

L = 82

Therefore, the length of the longer wire is 82 feet.

In summary, the length of the longer wire is 82 feet, as determined by using the cosine of the angle formed by the shorter wire and the ground, and considering the similarity of the triangles formed by the wires and the pole.

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There are no solutions to the system of inequalities Option (d)

Inequalities are a fundamental concept in mathematics and are commonly used in solving problems that involve ranges of values.

A system of two inequalities is a set of two inequalities that are considered together. In this case, the system of inequalities is

y > 3x + 1

y < 3x - 3

The inequality y > 3x + 1 represents a line on the coordinate plane with a slope of 3 and a y-intercept of 1. The inequality y < 3x - 3 represents another line on the coordinate plane with a slope of 3 and a y-intercept of -3. We can draw these lines on the coordinate plane and shade the regions that satisfy each inequality.

The first line has a positive slope and goes through (negative 2, negative 5) and (0, 1). Everything to the left of the line is shaded. The second line has a positive slope and goes through (0, negative 3) and (1, 0). Everything to the right of the line is shaded.

We can start by analyzing the inequality y > 3x + 1. This inequality represents the region above the line with a slope of 3 and a y-intercept of 1. Therefore, any point that is above this line satisfies this inequality.

Next, we analyze the inequality y < 3x - 3. This inequality represents the region below the line with a slope of 3 and a y-intercept of -3. Therefore, any point that is below this line satisfies this inequality.

To determine which values satisfy both inequalities, we need to find the region that satisfies both inequalities. This region is the intersection of the regions that satisfy each inequality.

When we analyze the regions that satisfy each inequality, we see that there is no region that satisfies both inequalities. Therefore, there are no values that satisfy the system of inequalities shown.

There are no solutions to the system of inequalities y > 3x + 1 and y < 3x - 3 by analyzing the regions that satisfy each inequality on a coordinate plane. The lack of a solution is determined by the fact that there is no region that satisfies both inequalities.

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Complete Question :

Which is true about the solution to the system of inequalities shown?

y > 3x + 1

y < 3x – 3

On a coordinate plane, 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 2, negative 5) and (0, 1). Everything to the left of the line is shaded. The second line has a positive slope and goes through (0, negative 3) and (1, 0). Everything to the right of the line is shaded.

Options:

a)Only values that satisfy y > 3x + 1 are solutions.

b)Only values that satisfy y < 3x – 3 are solutions.

c)Values that satisfy either y > 3x + 1 or y < 3x – 3 are solutions.

d)There are no solutions.

Answer:

D

Step-by-step explanation:

Answer: B

Step-by-step explanation:

The average number of hours that adults spend working each day is 8 hours and Ryan is correct because he got the average of 8 right.

We know that,

The sample mean is a statistic that is computed by taking the arithmetic mean of the values of a variable in a sample. If the sample is taken from probability distributions with a shared expected value, the sample mean is an estimator of that value.

The mean is gotten from the formula;

x' = ∑x/n

Number of hours of work per day are; 6, 7, 8, 9 and 10

Thus; sum up all of it

∑x = 6 + 7 + 8 + 9 + 10

∑x = 40

Mean is; x' = 40/5

x' = 8

Since Ryan concluded that the average is 8 hours,

Therefore,

We can say that Ryan is correct.

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The equation of a parabola that opens up and has a vertex at (7,7) can be written in the form

The focal diameter of the parabola is 16, which means that the distance from the vertex to the focus is 8 (since the focal diameter is the sum of the distances from the vertex to the focus and from the vertex to the directrix).

To find the equation of the parabola, we need to determine the value of a that will give us the correct focal diameter. The distance from the vertex to the focus is given by the equation sqrt(4a(y - 7)), so we can set this equal to 8 and solve for a:

sqrt(4a(y - 7)) = 8

4a(y - 7) = 64

a(y - 7) = 16

a = 16 / (y - 7)

Substituting this value of a back into the equation for the parabola gives us:

y = (16 / (y - 7))(x - 7)^2 + 7

This is the equation of the parabola that opens up, has a vertex at (7,7), and a focal diameter of 16.

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Answer:

0

Step-by-step explanation:

Expected Value = (Probability of winning) x (Amount won) + (Probability of losing) x (Amount lost)

In this case, the probability of winning is 1/6 (since there is only one way to roll a 3 out of six possible outcomes), and the probability of losing is 5/6 (since there are five other outcomes that do not result in a win).

The amount won is $15, and the amount lost (i.e., the cost of playing the game) is $3.

Therefore, the expected value is:

Expected Value = (1/6) x $15 + (5/6) x (-$3)

Expected Value = $2.50 - $2.50

Expected Value = $0

Using word problems and equations, Sarah worked for 10 hours and Penelope worked for 5 hours

This is a word problem and in order to solve this, we need to translate mathematical statements in form of word problems into mathematical equations.

Let's assume that Sarah worked x hours.

Given that Sarah can iron 30 shirts per hour, the total number of shirts she ironed is 30x.

Since Penelope worked half the hours of Sarah, Penelope worked x/2 hours.

Given that Penelope can iron 35 shirts per hour, the total number of shirts she ironed is 35 * (x/2) = (35/2)x.

The total number of shirts ironed by both Sarah and Penelope is 475 shirts.

So, we can write the equation: 30x + (35/2)x = 475.

To solve this equation, we can simplify it: (60/2)x + (35/2)x = 475, which becomes (95/2)x = 475.

Now, we can solve for x: x = (475 * 2) / 95 = 10.

Therefore, Sarah worked 10 hours and Penelope worked half of that, which is 5 hours.

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SOLUTION

The figure given is a sphere, and we want to find the surface area. The diameter of the sphere has been given as 11 cm.

Surface area of a sphere is found using the formula

Putting in the values of pi and radius r into the formula, we have the surface area S.A as

Hence the answer is 380.13 square-centimeter to the nearest hundredth

1. The investment of $2,250 with an absolute change of -$350 is now worth $1,900.

2. The percentage change in the worth of the investment is -15.56%.

A percentage change refers to the percentage difference between the initial value and the current value.

To compute the percentage change, use the absolute change and divide by the initial value, then multiply by 100.

For this investment of $2,250 which is now worth $1,900, there was a percentage change of -15.56%, implying that it has drastically reduced in value.

Initial Investment Cost = $2,250.00

Absolute change in investment value = $350

Current value of investment = $1,900 ($2,250 + $350)

The percentage change = -15.56% (-$350/$2,250 x 100)

Thus, the investment is currently valued at $1,900, having lost $350 in value, which in percentage terms, is -15.56%.

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Answer:

See explanations below

Step-by-step explanation:

Given the functions

f(x) = 12x - 12

g(x) = x/12 - 1

To show they are inverses, we, must show that f(g(x)) = g(f(x))

f(g(x)) = f(x/12 - 1)

Replace x with x/12 - 1 into f(x)

f(g(x)) =12((x-12)/12) - 11

f(g(x)) =  x-1 - 1

f(g(x)) =x - 2

Similarly for g(f(x))

g(f(x)) = g(12x-12)

g(f(x)) =(12x-12)/12 - 1

12(x-1)/12 - 1

x-1 - 1

x - 2

Since f(g(x)) = g(f(x)) = x -2, hence they are inverses of each other

Answer:

a)73

b)27

c)58

d)70

Answer:

the solution to the trigonometric inequality cos(0.65x) > 0.44 over the interval 0 ≤ x < 4.834.

Step-by-step explanation:

The given inequality is:

cos(0.65x) > 0.44

To solve this inequality, we need to isolate the variable x.

First, let's take the inverse cosine (arccos) of both sides to remove the cosine function:

arccos(cos(0.65x)) > arccos(0.44)

Since the range of the inverse cosine function is limited to [0, π], we can rewrite the inequality as:

0 ≤ 0.65x < π

Now, let's solve for x by dividing each part of the inequality by 0.65:

0/0.65 ≤ x < π/0.65

Simplifying, we have:

0 ≤ x < π/0.65

Now, let's calculate the approximate value of π/0.65 to determine the interval for x:

π/0.65 ≈ 4.834

i hope i helped!

The analysis of the distances and angles viewed by Felix are presented as follows;

2. The angle formed is a right angle

3. Please find the drawing of the scenario created with MS Word

4. The distance obtained using Pythagorean Theorem is about 438.53 miles

5. The distance the person travels is about 437.86 miles

6. The central angle Felix is viewing from his altitude is about 6.34°

The Pythagorean Theorem states that the square of the hypotenuse side of a right triangle is equivalent to the sum of the squares of the legs of the right triangle.

2. The angle formed by a tangent to a spherical surface, such as the Earth's approximately spherical surface and the radius of the sphere is a right angle.

Therefore;

3. The possible elevation of Felix above the Earth's surface, obtained from a similar question is; 24.214 miles

Therefore;

The legs of the right triangle are the radius of the Earth and the distance from Felix's to the point on the horizon.

The hypotenuse sum of Felix's altitude and the radius of the Earth

Please find attached the drawing of the scenario created with MS Word

4. Pythagorean Theorem indicates that the distance from Felix to the image on the horizon, d, can be obtained as follows;

d = √((3,959 + 24.214)² - 3,959²) ≈ 438.53

The distance from Felix to the image on the horizon is about 438.53 miles

5. The distance the person has to travel can be found as follows;

The surface of the Earth is assumed to be flat

The distance to the horizon from Felix is about 438.53 miles

The distance, l, the person on the ground has to travel is therefore;

l = √(438.53² - 24.214²) ≈ 437.86

6. The central angle, θ, of the Earth that Felix is viewing, with an arc length of 437.86 miles can be found using the formula for finding the arc length of a sector of a circle as follows;

θ/360 × 2 × π × 3,959 ≈ 437.86

θ ≈ 437.86 × 360/(3,959 × 2 × π) ≈ 6.34°

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