the pediatrician writes an order for robinul injection 35 mcg iv now. how many milliliters will the nurse administer? round the answer to the nearest hundredth.

Answers

Answer 1

The pediatrician writes an order for robinul injection 35 mcg iv now. The nurse will administer 0.035 ml of Robinul injection for 35 mcg of medication.

The question is about calculating the number of milliliters a nurse should administer for a 35 mcg Robinul injection. Let's first understand the meaning of Robinul.Robinul is a medication used to treat excess sweating or salivation in the human body. It reduces the secretion of fluids by blocking the chemicals that stimulate their production. It is available in the form of tablets, injection, or solution.

The nurse is instructed to administer 35 mcg of Robinul injection now.Let's calculate the number of milliliters of Robinul injection to be administered by the nurse.

Now, 1 ml = 1000 mcg35 mcg = (35/1000) ml= 0.035 ml (rounded to the nearest hundredth).

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Related Questions

Help please, not sure how to solve this!!!

Answers

The exponential function for the Greenville's population so that the yearly growth rate is visible is given as follows:

G(t) = 24000(1.00124)^t.

How to define an exponential function?

An increasing exponential function is modeled according to the rule presented as follows:

y = a(1 + r)^t.

In which:

a is the initial amount.r is the growth rate, as a decimal.

The function for Greenville's population is given as follows:

G(t) = 24000(1.00496)^4t.

Which means that the population grows at a rate of 0.00496 = 0.496% every four years, hence the yearly growth rate is given as follows:

r = 0.00496/4

r = 0.00124.

Then the function is given as follows:

G(t) = 24000(1.00124)^t.

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What is the length of one side of the fenced-in garden? 12 ft 15 ft 21 ft 108 ft

Answers

Answer:

B. 15

Step-by-step explanation:

its right on edge

make x the subject of the formula

y = 7x + 4

Answers

Answer: x = (y-4)/7

Hope this helps

A right rectangular prism is 3 in by 4.75 in by 20.5 in. what is the total surface area of the prism? 151.5 in2 173.125 in2 317.75 in2 346.25 in2

Answers

The rectangular prism is 3 inches by 4.75 inches by 20.5 inches, has a total surface area of 346.25 in².

We need to find the surface area of an object, the surface area of a solid three-dimensional object is the area of the boundary surface of the object and its surroundings, therefore:

The dimensions of the rectangular prism will be as follows:

Let the length of the rectangular prism = 3 inches

Let the width of the prism = 4.75 inches

Let the height of the prism = 20.5 inches

Therefore, the surface area, A, of a rectangular prism can be found using the formula:

A = 2 × Length × Width + 2 × Length × Height + 2 × Height × Width

Therefore, the surface area of the rectangular prism in the question is found as follows:

Area, A = 2 × 3 × 4.75 + 2 × 3 × 20.5 + 2 × 20.5 × 4.75 = 346.25

The total surface area of the rectangular prism is 346.25 in².

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Answer:

346.25

Step-by-step explanation:

took the test :)

in a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests, brad has scored 87 , 89 , and 78 on the first three. what range of scores on the fourth test will give brad a c for the semester (an average between 70 and 79 , inclusive)?

Answers

Brad needs to score between 72 and 79 on the fourth test in order to get a C for the semester.

To explain why this is so, we need to first understand how the grade for the semester is calculated.Since the final course grade depends entirely on the average of four equally weighted 100-point tests, this means that each test will count for 25% of Brad’s final grade. Therefore, Brad needs to get an average score of 70-79 (inclusive) on the four tests combined in order to get a C for the semester.



In order to calculate what range of scores Brad needs to get on the fourth test in order to get a C for the semester, we need to look at the scores he has already obtained on the first three tests. Brad has scored 87, 89 and 78 on the first three tests. This gives him a total score of 254 (87+89+78=254). This means that Brad needs to get a score of between 70 and 79 on the fourth test in order to reach a total score of between 280-309 (inclusive), which will result in an average score of between 70-79 (inclusive), and give Brad a C for the semester.

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the amount of time it takes john to wait in line at the bank is continuous and uniformly distributed between 7 minutes and 17 minutes. what is the probability that it takes john between 9 and 12 minutes to wait in line at the bank?

Answers

The probability of John waiting is

0.333.

The probability that it takes John between 9 and 12 minutes to wait in line at the bank is 0.333.

This is because the continuous and uniformly distributed time between 7 and 17 minutes is divided into 10 minutes, meaning each unit is equal to 0.1. Therefore,

the probability of John waiting between 9 and 12 minutes is 3 units of 0.1 which is 0.333.

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A little help :) Appreciated - 30 points (Reupload)

Answers

Answer:

See below!

Step-by-step explanation:

a) 1, 2, 3, 4, 5

The possible outcomes are all the options that there are on the spinner

b) 2

There are only 2 even numbers!

c) [tex]\frac{2}{5}[/tex] or 0.4

There are 2 out of 5 numbers are even on the spinner so that must be the solution!

d) 1

The spinner has only one multiple of 3, so the possible outcome should also be 1.

e) [tex]\frac{1}{5}[/tex] or 0.2

There are only 1 out of 5 options which are multiples of 3, so that would be our solution

f) 4

There are 4 prime numbers in the spinner (1, 2, 3, 5), so that would be a possible outcome.

g) [tex]\frac{4}{5}[/tex] or 0.8

The spinner has 4 out of 5 prime numbers, so our answer would be that!

Hope this helps, have a lovely day! :)

scientists tagged 770 pike for a research project about a local lake. later, they trapped 270 pike, of which 21 had tags. to the nearest whole number, what is the best estimate for the pike population?

Answers

The best estimate for the pike population is 9860, rounded to the nearest whole number.

The best estimate for the pike population can be calculated using the mark and recapture method, also known as the Lincoln-Petersen index. According to this method, the population estimate is given by:

N = (M * C) / R

Where:

N = Population estimate

M = Number of individuals in the first sample

C = Number of individuals in the second sample

R = Number of individuals in the second sample that were tagged in the first sample

Substituting the given values, we get:

N = (770 * 270) / 21

N = 9860

The method used to estimate the pike population is the mark and recapture method, also known as the Lincoln-Petersen index. This method is commonly used in ecology and wildlife management to estimate the size of a population of animals based on samples taken from the population.

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in the same room with a floor area that measures 15' x 10', how many feet of rubber wall base is required to cover the length of all four (4) walls, minus 3' for the door opening?

Answers

To cover the length of all four walls in a room that measures 15' x 10', minus 3' for the door opening, it would require 50 feet of rubber wall base.

A rubber wall base is a type of molding that is installed at the base of walls to protect the wall and add aesthetic appeal to the room. To calculate the amount of rubber wall base required for a room, we need to determine the perimeter of the room, which is the sum of the length of all four walls.

In this case, the room measures 15' x 10', which means that the length of the four walls would be (2 x 15) + (2 x 10) = 30 + 20 = 50 feet.

However, we need to subtract 3 feet for the door opening because the rubber wall base does not need to cover the area where the door is located. Therefore, the total amount of rubber wall base required for the room would be 50 - 3 = 47 feet.

But, we need to add some extra footage for corner pieces and cuts. Typically, it is recommended to add an extra 5% to 10% of the total length of the wall base to account for these additional pieces. So, adding 5% of 47 feet, we get an additional 2.35 feet, which we can round up to 3 feet.

Therefore, the final answer is 47 + 3 = 50 feet.

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suppose the process mean shifts to 702.00 while the standard deviation remains constant. what is the probability of an out-of-control signal occurring on the first sample following the shift?

Answers

The probability of an out-of-control signal occurring on the first sample following the shift is approximately 0.0026 or 0.26%.

To determine the probability of an out-of-control signal occurring on the first sample following the shift, we need to calculate the probability of observing a sample mean or range value that falls outside the control limits.

For the X-bar chart:

New process mean (after the shift) = 702.00

Standard deviation (constant) = 1.738

Sample size (n) = 6

We can calculate the standard error (SE) for the X-bar chart using the formula:

SE = Standard deviation / √(sample size)

SE = 1.738 / √(6) ≈ 0.709

Next, we calculate the control limits for the X-bar chart based on the new process mean:

New UCL = New process mean + 3 × SE

= 702.00 + 3 × 0.709

= 704.127

New LCL = New process mean - 3 × SE

= 702.00 - 3 × 0.709

= 699.873

Now, we need to determine the probability of observing a sample mean outside the control limits, given that the process mean has shifted to 702.00. We can assume a normal distribution for the sample means.

To calculate the probability, we need to determine the z-scores for the new UCL and LCL using the formula:

z = (X - μ) / SE

where X is the value of interest (UCL or LCL), μ is the process mean, and SE is the standard error.

For the UCL:

z = (New UCL - μ) / SE

= (704.127 - 702.00) / 0.709

= 2.999

For the LCL:

z = (New LCL - μ) / SE

= (699.873 - 702.00) / 0.709

= -2.999

We can use a standard normal distribution table or a statistical calculator to find the probabilities associated with these z-scores.

Using a standard normal distribution table, the probability of observing a sample mean greater than the new UCL (2.999 z-score) is approximately 0.0013 (or 0.13%), and the probability of observing a sample mean lower than the new LCL (-2.999 z-score) is also approximately 0.0013 (or 0.13%). Since we are interested in either of these cases (an out-of-control signal), we add the probabilities:

Probability of an out-of-control signal = 0.0013 + 0.0013 ≈ 0.0026 (or 0.26%)

Therefore, the probability of an out-of-control signal occurring on the first sample following the shift is approximately 0.0026 or 0.26%.

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Complete question =

Control charts for x-bar and s have been maintained on a proces and have exhibited statistical control. The sample size is n=6. The control chart parameters are as follows:

X-bar: UCL = 708.20, Center line = 706.00, LCL = 703.80

R chart: UCL = 3.420, Center line = 1.738, LCL = 0.052

natural tolerance limits for the process are ±5.214.

the estimated standard deviation is 1.738.

d) Suppose the process mean shifts to 702.00 while the standard deviation remains constant. What is the probability of an out-of-control signal occuring on the first sample following the shift?

Fred is a plant manager at Salem Construction Company. He has been employed there for 28
years and will be retiring at the end of this year. His pension is calculated on the average of
his last four years' salaries. In those years, he earned $82,000, $96,000, $105,000, and
$109,000. His employer will credit him 1.8% of that average for each year he worked.
a) Calculate Fred's annual pension.
B) Find his monthly p
ension.

Answers

Fred's Annual pension will be $603.

How to calculate Fred's annual pension, we first need to find the average of his last four years' salaries?

Average salary = (82000 + 96000 + 105000 + 109000) / 4 = $100,500

Fred's employer will credit him 1.8% of that average for each year he worked, so we can calculate his annual pension as follows:

Annual pension = 0.018 * 4 * 100500 = $7,236

Therefore, Fred's annual pension will be $7,236.

How to find his Annual  pension?

We can simply divide his annual pension by 12:

Annual pension = 7236 / 12 = $603

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This figure consists of a rectangle and a quarter circle.

What is the perimeter of this figure?

Use 3.14 for π.

SOMEONE PLEASE HELP ME!! 40 POINTS

Answers

Answer:

61.27

Step-by-step explanation:

Circle perimeter formula: C=2πr

Quarter circle=2πr/4. Given r=11cm

                     2x3.14x11/4=17.27

Rectangle perimeter: C=2(a+b)

                                    =2(2+20)=44

so, total: 17.27+44=61.27

The expression the quantity secant of x plus 1 end quantity over tangent of x was simplified with the following steps:


Step 1: secant x over tangent x plus 1 over tangent x

Step 2: the quantity 1 over cosine x end quantity over tangent x plus 1 over tangent x

Step 3: the quantity 1 over cosine x end quantity over the quantity sine x over cosine x end quantity plus cosine x over sine x

Step 4: 1 over sine x plus cosine x over sine x

Step 5: cosecant x plus cosine x over sine x

Step 6: cosecant x plus cotangent x

Which identity/formula was used to simplify from step 2 to step 3?

Answers

The identity used to simplify from step 4 to step 5 is the definition of the cosecant function cosecant x = 1/sine x.

What is a mathematical expression?

A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. This mathematical operation may be addition, subtraction, multiplication, or division. An expression's structure is as follows: Expression is (Number/Variable, Arithmetic Operator, Number/Variable).

                                For instance, the expression x + y is an expression where x and y are terms with an addition operator between them. Mathematical expressions can be divided into two categories: algebraic expressions, which include both numbers and variables, and numerical expressions, which solely contain numbers.

 =  the expression 1/sine x

 = 1/sine x + cosine x/sine x

 =  cosecant x + cosine x/sine x

  = cosecant x + cotangent x.

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a family trip to washington d.c considers the following scenarios: transportation (plane, car, train) and weather conditions (sunny, windy, rainy, cloudy). how many different combinations are possible?

Answers

There are 12 different combinations of transportation and weather conditions for the family trip to Washington D.C.

To find the total number of different combinations of transportation and weather conditions for the family trip to Washington D.C, we can use the multiplication rule of counting, which states that if there are m ways to do one thing and n ways to do another, then there are m x n ways to do both.

There are three different transportation options: plane, car, and train, and four different weather conditions: sunny, windy, rainy, and cloudy. To find the total number of different combinations, we simply need to multiply the number of transportation options by the number of weather conditions:

Total number of combinations = number of transportation options x number of weather conditions

Total number of combinations = 3 x 4

Total number of combinations = 12

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in a regression analysis, the coefficient of determination measures goodness of fit. independence of variables. economic plausibility. independence of residuals.

Answers

The coefficient of determination measures goodness of fit.

The coefficient of determination, often referred to as R-squared, measures the goodness of fit in a regression analysis. It does not measure the independence of variables, economic plausibility, or independence of residuals.

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What is the equation of the line of reflection that reflects shape P into shape Q

Answers

The equation of the line of reflection that reflects shape P into shape Q is y = −2x + 12.

To find the equation of the line of reflection that reflects shape P into shape Q, we need to follow some steps:

Step 1: Draw the mirror line. To reflect a point or shape, we must have a mirror line. The mirror line is the line that passes through the reflection and is perpendicular to the reflecting surface. It serves as a reference for reflecting points or shapes.

Step 2: Find the midpoint of PQ. The midpoint of PQ is the point that lies exactly halfway between P and Q.

Step 3: Find the slope of PQ. The slope of PQ is the rise over run or the difference of the y-coordinates over the difference of the x-coordinates.

The slope formula is given by m = (y2 − y1) / (x2 − x1).

Step 4: Find the perpendicular slope of PQ. The perpendicular slope of PQ is the negative reciprocal of the slope of PQ. It is given by m⊥ = −1/m.

Step 5: Write the equation of the line of reflection. The equation of the line of reflection is given by y − y1 = m⊥(x − x1) or y = m⊥x + b, where m⊥ is the perpendicular slope of PQ and b is the y-intercept of the line. To find b, we substitute the coordinates of the midpoint of PQ into the equation and solve for b. Then we substitute m⊥ and b into the equation to get the final answer.

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what is the modular inverse of $11$, modulo $1000$? express your answer as an integer from $0$ to $999$, inclusive.

Answers

The modular inverse of 11, modulo 1000 is 901. Expressing the answer in integer form.

To find the modular inverse of 11  modulo 1000, we need to find an integer x such that [tex]$11x\equiv1\pmod{1000}$[/tex].

One way to find the modular inverse is to use the extended Euclidean algorithm. Using this algorithm, we can find the greatest common divisor of 11 and 1000 and express it as a linear combination of 11 and 1000.

We can then use the coefficients of this linear combination to express 1 as a linear combination of 11 and 1000.

Applying the extended Euclidean algorithm, we have:

1000= 11 *90 + 10

11 = 10 *1 + 1

Working backward, we can express 1 as a linear combination of 11 and 1000:

1 =11 - 10* 1

= 11 - (1000 - 11*90)

= 901 * 11 - 1 *1000

Therefore, the modular inverse of 11 modulo 1000 is 901, since

11*901=1 mod{1000}.

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In the diagram below, what is the measure of angle x?

Answers

Answer: C - 105

Step-by-step explanation:

75+75=150

360-150=210

210/2=105

Describe some common or unique formulas that you use in your life.

Answers

Quadratic Fοrmula: This fοrmula is used tο find the rοοts οf a quadratic equatiοn. It is calculated as:

[tex]$ \rm x = \frac{(-b \pm \sqrt{(b^2 - 4ac)}}{ 2a}[/tex]

What is quadratic equatiοn?

it's a secοnd-degree quadratic equatiοn which is an algebraic equatiοn in x. Ax² + bx + c = 0, where a and b are the cοefficients, x is the variable, and c is the cοnstant term, is the quadratic equatiοn in its standard fοrm.

1. Simple Interest Fοrmula: This fοrmula is used tο calculate the interest earned οr paid οn a lοan οr investment. It is calculated as:

[tex]\rm I = P \times r \times t[/tex]

Where I is the interest earned οr paid, P is the principal amοunt, r is the interest rate, and t is the time periοd.

2. Pythagοrean Theοrem: This fοrmula is used tο calculate the length οf οne side οf a right triangle given the lengths οf the οther twο sides. It is calculated as:

[tex]\rm a^2 + b^2 = c^2[/tex]

Where a and b are the lengths οf the twο legs οf the right triangle, and c is the length οf the hypοtenuse.

3. Quadratic Fοrmula: This fοrmula is used tο find the rοοts οf a quadratic equatiοn. It is calculated as:

[tex]$ \rm x = \frac{(-b \pm \sqrt{(b^2 - 4ac)}}{ 2a}[/tex]

Where a, b, and c are cοefficients οf the quadratic equatiοn ax² + bx + c = 0, and x is the sοlutiοn.

4. Bοdy Mass Index (BMI) Fοrmula: This fοrmula is used tο calculate a persοn's bοdy mass index, which is a measure οf bοdy fat based οn height and weight. It is calculated as:

BMI = (weight in kilοgrams) / (height in meters)²

A BMI οf 18.5 tο 24.9 is cοnsidered healthy, while a BMI οf 25 tο 29.9 is cοnsidered οverweight, and a BMI οf 30 οr higher is cοnsidered οbese.

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Complete question:

Describe some common or unique mathematical formulas that you use in your life.

|||
Calculator
Cone X has a diameter of 20 ft and a height of 16 ft. Cone Y is the same height as cone X, but its diameter is twice the diameter of
cone X
What is the difference in the volumes of the two cones?
Use 3.14
05.024 ft
15.072 ft
O 20.096 ft
3.01 Readiness Checkpoint: Volumes of Cylinders and Cones Di
I don't know
2 3
4 Finish

Answers

Answer:

  (a)  5024 ft³

Step-by-step explanation:

You want the difference in volumes of two cones with height 16 ft, where the larger has diameter 40 ft and the smaller has diameter 20 ft.

Volume

The volume of a cone is given in terms of its radius as ...

  V = π/3(r²h) . . . . . . r=radius; h=height

The radius is half the diameter, so the formula with diameter is ...

  V = π/3(d/2)²h = π/12d²h

Difference

The two given cones have the same height, but different diameters. The difference in volumes will be ...

  V2 -V1 = (π/12)((d2)²h) -(π/12)((d1)²h) = (πh/12)((d2)² -(d1)²)

  V2 -V1 = 3.14(16 ft)/12 × ((40 ft)² -(20 ft)²) = 3.14·16/12·1200 ft³

  = 3.14·1600 ft³ = 5024 ft³

The difference in volumes of the two cones is 5025 cubic feet.

Mr. Johnson placed three desks together in his classroom. Each desk measures at 1.5 meters.
How many centimeters are all three desks?

Answers

Answer: 7.62

Step-by-step explanation:

Answer:

350 centimeters

Step-by-step explanation:

1.5 meters x 3 = 3.5 meters

There are 100 centimeters in one meter

So, 3.5 x 100 = 350

Solve 2x2 + 26 = 0 to identify the roots.

Answers

X= - 0/2 ± √ (0/2)^2-13

X= ± √0^2-13

X= ± √-13

X= ± √13 i



Solution:

option B
The answer is B ( the second choice)

2x^2 + 26 = 0

(Divide both sides by 2)

x^2+ 13=0

(Move the 0 and change the sign)

x^2= -13

(Simplify)

x= - 13i and x= 13i

10. 4 out of 5 students are going on the field trip tomorrow. If there are 400 students, how many
are going on the field trip?

Answers

The total students who are going on the field trip are 320 students out of 400 students which has been obtained by using the concept of fractions.

Define Fraction?

A fraction represents a part of a number or any number of equal parts. There is a fraction, containing numerator(upper value) and denominator(lower value).

If 4 out of 5 students are going on the field trip, then the fraction of students going on the field trip is 4/5.

To find out how many students are going on the field trip, we can multiply this fraction by the total number of students:

Number of students going on the field trip = (4/5) x 400

Number of students going on the field trip = 320

Therefore, 320 students are going on the field trip.

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2. The base of a right triangular prism has an area of 98 square units. If the total surface area of
the prism is 466 square units, which of the following are possible areas for the faces of the
prism?
O30, 110, and 190 square units
O 40, 80, and 120 square units
O 50, 100, and 150 square units
O 60, 90, and 120 square units
(1

Answers

Optiοn 2: 40, 80, and 120 square units, is the οnly set οf regiοns fοr the prism's faces that are viable.

Hοw is a triangular prism defined?

A triangular prism is indeed a prism that has three rectangular sides and twο triangular bases. A pentahedrοn, that is. The rectangular base οf the supplied right triangular prism measures b and h and has an area οf bh = 98 square units. Let l stand in fοr the prism's height. The prism's entire surface area is calculated as fοllοws:

2bh + bl + lh

By simplifying and replacing the values οf bh, we οbtain:

2(98) + bl + lh = 466

bl + lh = 135

The areas οf the twο nοn-base sides οf a prism are each (1/2)bl since they are equivalent right triangle with legs b and l. Let's examine each οf the available respοnses tο see if it cοmplies with the requirements:

Optiοn 1: 30, 110, and 190 square units

If the area οf οne οf the nοn-base faces is 110 square units, then (1/2)bl = 110, sο bl = 220. But bl + lh = 135, sο this is nοt pοssible. This grοup οf lοcatiοns is therefοre nοt feasible.

Optiοn 2: 40, 80, and 120 square units

If the area οf οne οf the nοn-base faces is 80 square units, then (1/2)bl = 80, sο bl = 160. This means that lh = 135 - bl = 135 - 160 = -25, which is nοt pοssible. Sο this set οf areas is nοt pοssible.

Therefοre, this set οf areas is nοt pοssible. This grοup οf areas cannοt thus be achieved. If the area οf οne οf the nοn-base faces is 100 square units, then (1/2)bl = 100, sο bl = 200. But bl + lh = 135, sο this is nοt pοssible. Hence, it is impοssible tο cοver this grοup οf areas.

Optiοn 4: 60, 90, and 120 square units

If the area οf οne οf the nοn-base faces is 90 square units, then (1/2)bl = 90, sο bl = 180. This means that lh = 135 - bl = 135 - 180 = -45, which is nοt pοssible. Sο, this set οf areas is nοt pοssible.

Optiοn 2's range οf 40, 80, and 120 square units is the οnly set οf areas fοr the prism's faces that can be cοnsidered.

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The point (−0.5, 4) is reflected across the y-axis and then across the x-axis. What are the coordinates of the reflected point?

Answers

Answer: The coordinates of the reflected point are (0.5, -4)

Step-by-step explanation: When a point is reflected across the y-axis, the x-coordinate changes sign while the y-coordinate remains the same. So the point (-0.5, 4) reflected across the y-axis will be (0.5, 4).When a point is reflected across the x-axis, the y-coordinate changes sign while the x-coordinate remains the same. So the point (0.5, 4) reflected across the x-axis will be (0.5, -4).

Answer:

(5,-4) because if the quadrant one is positive positive quadrant two is negative positive quadrant three is negative negative Quadrant four is positive negative

Step-by-step explanation: Hope this helps!! Mark me brainliest! :))

What is the median for 5, 7, 24, 3, 6, 4, 4, 30, 19

Answers

There is only one middle number because the collection has an odd number of numbers. Since six is the midpoint, six represents the median.

what is median ?

When a dataset is sorted from lowest to highest, the median, a measure of central tendency, reflects the midpoint value of the dataset. The values are first presented from lowest to greatest in order to get the median of a set of data. The median is the middle value when there are an odd number of values. Use the following data set as an example: 5, 7, 24, 3, 6, 4, 4, 30, 19. We first organise the data in order before calculating the median: 3, 4, 4, 5, 6, 7, 19, 24, 30

The dataset contains 9 values, which is strange. The middle value, which is six, is therefore the median.

given

We must first arrange the numbers in ascending order in order to determine the median of the group:

3, 4, 4, 5, 6, 7, 19, 24, 30

The median will be the middle number as there are nine numbers in this collection.

There is only one middle number because the collection has an odd number of numbers. Since six is the midpoint, six represents the median.

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Which expression is equivalent to 0.75a + 10b + a – 2b?

Answers

Answer:

1.75a + 8b

Step-by-step explanation:

0.75a + 10b + a - 2b ← collect like terms

= (0.75 + 1a) + (10b - 2b)

= 1.75a + 8b

Answer:

1.75a+8b

Step-by-step explanation:

Given here, 0.75a + 10b + a – 2b = 0.75a+a+10b-2b

                                                     =1.75a+8b

Hence, The required equivalent expression is 1.75a+8b

the altitude of a triangle is increasing at a rate of centimeters/minute while the area of the triangle is increasing at a rate of square centimeters/minute. at what rate is the base of the triangle changing when the altitude is centimeters and the area is square centimeters?

Answers

The rate of change of the base of the triangle is (20 - 1/12 × base × b) cm/min when the altitude is h cm and the area is a sq cm. And this is solved by the concept of Differentiation.

The problem asks to find the rate of change of the base of a triangle when the altitude and area of the triangle are given.

Let's use the formula for the area of a triangle, which is A = 1/2 × base × altitude. Taking the derivative with respect to time, we get dA/dt = 1/2 × (d/dt)(base) × altitude + 1/2 × base × (d/dt)(altitude).

Now, we are given that dA/dt = the rate of change of the area = a constant value. Also, we know that (d/dt)(altitude) = the rate of change of the altitude = b cm/min.

Therefore, we can substitute these values into the formula above to get:

a = 1/2 × (d/dt)(base) × h + 1/2 × base × b

We want to find (d/dt)(base) when h and a are given. Since h is given, we can solve for (d/dt)(base) by isolating it in the equation above:

(d/dt)(base) = (2/a) × (a - 1/2 × base × b)/h

Substituting the given values of h and a, we get:

(d/dt)(base) = (2/60) × (120 - 1/2 × base × b)/6

where b is given in cm/min. Simplifying this expression, we get:

(d/dt)(base) = (20 - 1/12 × base × b) cm/min

Therefore, the rate of change of the base of the triangle is (20 - 1/12 × base × b) cm/min when the altitude is h cm and the area is a sq cm

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donica works at an electronics store. Her monthly pay is $1950. she also receives 4% commission on all her sales. she had $12,475 in sales last month. Her rent is 30% of her earnings last month.

how much does Donica pay for rent? round to the nearest whole number

Please explain how:)

Answers

Therefore , the solution of the given problem of percentage comes out to be Donica spends $735 in rent.

What exactly does a percentage mean?

A statistic or measure that is stated as a percent of 100 is referred to as "a%" in statistics. The terms "pct," "pct," and "pc" are also uncommon. However, it is commonly denoted by the symbol "%". There are no measurements; the proportion of the total sum is flat. Because the numerator of percentages almost always equals 100, they are genuinely integers. Either the percent sign (%) or the word "fraction" must come before a number to indicate that it represents a percent.

Here,

Sales royalty for Donica is calculated as follows:

=>  $12,475 * commission of 4%

=>  $499 commission

Donica's overall earnings for the previous month after deducting the commission were:

Total income equals monthly salary plus commission.

=>  Total income=  $1950 + $499.

=>  $2449 in total profits

We need to multiply Donica's total income by 30% to determine how much she spends in rent:

=>  Rent is 30% of total income.

=>  Rent = 0.3 * $2449 =  $734.70.

When this is rounded to the closest whole integer, we obtain:

=> Rent = $735

Donica thus spends $735 in rent.

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In an arithmetic sequence, the tenth term is 28. The sum of term 5 and term 7 is 32. Calculate the sum of the first 50 terms

Answers

The sum of the first 50 terms is 3775. Let a be the first term and d be the common difference of the arithmetic sequence.

Then, the tenth term is a + 9d = 28, and the sum of the fifth and seventh terms is 2a + 12d = 32.

Solving these equations simultaneously, we get a = 2 and d = 3.

To find the sum of the first 50 terms, we use the formula for the sum of an arithmetic sequence:

S50 = (50/2)(2a + (50-1)d) = 25(2 + 49(3)) = 3775.

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