The evaluation of the rational algebraic expression are presented as follows;
1. [tex]\dfrac{1}{3} +\dfrac{2}{5} = \dfrac{11}{15}[/tex]
2. [tex]\dfrac{x + y}{x} + \dfrac{x + y}{y} = \dfrac{x^2 + 2\cdot x \cdot y + y^2}{x \cdot y}[/tex]
3. [tex]\dfrac{3 \cdot x + 1}{x^2+2\cdot x +1} +\dfrac{5}{2\cdot x + 8} =\dfrac{11\cdot x^2 +36\cdot x +13}{2\cdot x^3 + 12\cdot x^2 + 18\cdot x+ 8}[/tex]
What is a rational algebraic expression?
A rational algebraic expression is an algebraic expression that consists of a quotient and divisor that consists of variables and numbers.
1. [tex]\dfrac{1}{3} + \dfrac{2}{5}[/tex]
[tex]\dfrac{1}{3} + \dfrac{2}{5} = \dfrac{5\times 1 + 2 \times 3}{3\times 5} =\dfrac{5 + 6}{15}[/tex]
[tex]\dfrac{5 + 6}{15} = \dfrac{11}{15}[/tex]
Therefore, we get;
[tex]\dfrac{1}{3} +\dfrac{2}{5} = \dfrac{11}{15}[/tex]
2. [tex]\dfrac{x + y}{x} + \dfrac{x + y}{y}[/tex]
[tex]\dfrac{x + y}{x} + \dfrac{x + y}{y} = \dfrac{y\times (x + y) + x\times (x+ y)}{x\cdot y}[/tex]
[tex]\dfrac{y\times (x + y) + x\times (x+ y)}{x\cdot y}= \dfrac{x^2+ 2\cdot y \cdot x +y^2 }{x \cdot y}[/tex]
Therefore;
[tex]\dfrac{x + y}{x} + \dfrac{x + y}{y} = \dfrac{x^2+ 2\cdot y \cdot x +y^2 }{x \cdot y}[/tex]
3. [tex]\dfrac{3 \cdot x + 1}{x^2 + 2\cdot x + 1} + \dfrac{5}{2 \cdot x + 8}[/tex]
[tex]\dfrac{3 \cdot x + 1}{x^2 + 2\cdot x + 1} + \dfrac{5}{2 \cdot x + 8} = \dfrac{(3 \cdot x + 1) \times (2\cdot x + 8) + 5 \times (x^2 + 2\cdot x + 1) }{(x^2 + 2\cdot x + 1) \times (2\cdot x + 8)}[/tex]
[tex]\dfrac{(3 \cdot x + 1) \times (2\cdot x + 8) + 5 \times (x^2 + 2\cdot x + 1) }{(x^2 + 2\cdot x + 1) \times (2\cdot x + 8)} = \dfrac{11\cdot x^2+ 36\cdot x+ 13}{2\cdot x^3 + 12\cdot x^2+18\cdot x+ 8}[/tex]
[tex]\dfrac{3 \cdot x + 1}{x^2 + 2\cdot x + 1} + \dfrac{5}{2 \cdot x + 8}=\dfrac{11\cdot x^2+ 36\cdot x+ 13}{2\cdot x^3 + 12\cdot x^2+18\cdot x+ 8}[/tex]
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Find the measurement of V.
Answer: 60 degrees
Step-by-step explanation: Because all sides are equilateral, and in an equilateral triangle all angles are 60 degrees, hope that helps.
can somone help will mark u brainliest
Sathish is going on a 210021002100-kilometer road trip with 222 friends, whom he will pick up 150150150 kilometers after he begins the trip and drop off when there are 150150150 kilometers remaining. the car consumes 666 liters of gas for every 100100100 kilometers, and gas costs \$1.20$1.20dollar sign, 1, point, 20 per liter.
Sathish will pay $64.8
When Satish is alone, kilometres:
Beginning at 150 kilometres and ending at 150 kilometres will be travelled 300 kilometres in total
When Satish is with friends, the total kilometres travelled is 2100 km:
And when Satish went alone he travelled 300 km
When Satish is with friends, total kilometres travelled: 2100-300 = 1800 km
Gas consumed in litres when Satish is alone: 100 kilometres use 6 litres of gas.
300 kilometres at 6 x 3 equals 18 litres.
So, when Satish is with friends, litres of gas are consumed: 100 kilometres use 6 litres of gas.
So, 6 × 18 for 1800 kilometres is equal to 108 litres.
Gas prices when Satish is on his own:
$1.2 per litre
18 x $1.2 = $21.6
Gas prices when Satish is travelling with friends
$1.2 per litre
108 x 1.2 = $129.6
Cost for each friend = $129.6/3 = $43.2
Satish will pay: Cost when travelling with friends + Cost when travelling alone
=$43.2+ $21.6
=$64.8
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please solve the problem
The value of x in the remote angles of the triangle is 22.
How to find external angle of a triangle?The exterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.
In other words the sum of the remote interior angle is equals to the external angle.
Therefore,
110 = 3x + 2x
110 = 5x
divide both sides by 5
110 / 5 = 5x / 5
x = 22
Therefore, using exterior angle theorem, the value of x is 22.
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A parabola can be drawn given a focus of (−3,−3) and a directrix of x=5. Write the equation of the parabola in any form.
Equation of the parabola with focus (-3,-3) and a directrix x=5 is given by x = (-1/16)(y² +6y -7).
As given in the question,
Focus of the parabola is equal to (-3, -3)
Directrix of the parabola is given by x = 5
Let (x, y) be the point on the parabola.
Distance between the (-3,-3) and (x, y) = Distance between (x, y) and x=5
⇒√(x +3)² + (y +3)² = | x -5|
⇒(x² +6x +9) +(y² + 6y +9) = (x-5)²
⇒x² +6x +y² +6y +18 = x² -10x +25
⇒y² +6y -7 = -16x
⇒x = (-1/16) (y² +6y -7) represents the equation of the parabola.
Therefore, equation of the parabola with focus (-3,-3) and a directrix x=5 is given by x = (-1/16)(y² +6y -7).
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List all factors of the numerator and denominator. Use gcf method to simplify Creduce) each fraction. You must show work
The reduced fraction is 7 using GCF method.The GCF is also known as the Highest Common Factor (HCF)
What is GCF method?The largest number, which is the factor of two or more number is called the Greatest Common Factor (GCF). It is the largest number (factor) that divide them resulting in a Natural number. Once all the factors of the number are found, there are few factors which are common in both. The largest number that is found in the common factors is called the greatest common factor. The GCF is also known as the Highest Common Factor (HCF)
The fraction = 14/66
The factors of 14 = 2×2×2×3
The factors of 28 = 11*3*2
The gcf is 2 × 2 = 4
Divide the denominator and numerator by 4
14 ÷2 = 7
14÷ 2 = 7
We get,
The fraction = 14/2 =7
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Shipping Company A charges $14 plus $2.25 a pound to ship overnight
packages. Shipping Company B charges $20 plus $1.50 a pound to ship
an overnight package. For what weight is the charge the same for the two
companies?
For 8 pounds of weight, the charges be the same for both the companies.
Given, that To ship an overnight package
Shipping Company A charges $14 plus $2.25 per pound
Shipping Company B charges $20 plus $1.50 per pound
Let, the weight be w
And the cost of shipment by company A & B be A(w) & B(w) respectively.
According to the question,
A(w) = 14 + 2.25w
B(w) = 20 + 1.50w
Now, when charges be the same
A(w) = B(w)
14 + 2.25w = 20 + 1.50w
On subtracting 1.50w on both the sides, we get
14 + 2.25w - 1.50w = 20 + 1.50w - 1.50w
14 + 0.75w = 20
Now on subtracting 14 on both the sides, we get
14 + 0.75w - 14 = 20 - 14
0.75w = 6
On dividing both the sides by 0.75, we get
0.75w/0.75 = 6/0.75
w = 8
Hence, weight = 8 pounds.
For 8 pounds of weight, the charges be the same for both the companies.
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Help asap please
I don’t underddd
a sanitation supervisor is interested in testing to see if the mean amount of garbage per bin is different from 50. in a random sample of 36 bins, the sample mean amount was 50.67 pounds and the sample standard deviation was 3.9 pounds. conduct the appropriate hypothesis test using a 0.01 level of significance. a) what are the appropriate null and alternative hypotheses?
We accept the null hypothesis, according to which the average amount of trash per bin is equal to 50.
Hypothesis.Though there is not so much information, but the fact that $700 is an average. We can work with two hypothesis at first, he first Hypothesis before the downturn the rent are over $700. And the second one, the bedroom rent are under $700.Graphically, the shaded area before the downturn, represents the set of values for Rents greater than $700. So, rent (y) > 700) Graphically, the shaded area after the downturn, represents the set of values for Rents lesser than $700. So, rent 700 <y<0A hypothesis is an educated prediction regarding the solution to a scientific question that is supported by sound reasoning. It is the expected result of the experiment, however it is not proof in an experiment.Depending on the information received, it might be supported or might not be supported at all.acc to our question-
A sanitation supervisor is interested in testing o see if the mean amount of garbage per bin is different from 50.This means that the null hypothesis is:And the alternate hypothesis is:The test statistic is:In which X is the sample mean, is the value tested at the null hypothesis, is the standard deviation and n is the size of the sample.50 tested at the null hypothesis:This means that In a random sample of 36 bins, the sample mean amount was 50.67 pounds and the sample standard deviation was 3.9 pounds.This means that Value of the test statistic:p-value:Since we are testing if the mean is differente from a value and the z-score is positive, the pvalue is 2 multipled by 1 subtracted by the pvalue of z = 1.03z = 1.03 has a pvalue of 0.84851 - 0.8485 = 0.15152*0.1515 = 0.30300.3030 > 0.01, which means that we accept the null hypothesis, that is, the the mean amount of garbage per bin is not different from 50.learn more about hypothesis click here:
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The price of a pair of Nike Panda's
increases from $52 to $64. What is the
percent increase to the nearest
percent?
Answer: 23%
PLEASE GIVE BRAINLIEST THANK YOU VERY MUCH!!
Ruth has 36 vases of flowers. Some of the vases contain 3 daisies. The other vases contain 4 lilacs. There are 125 flowers in the vases in total. How many vases of each type of flower does Ruth have?
Answer:
13 vases of lilacs23 vases of daisiesStep-by-step explanation:
You want to know the number of vases of each type of flower if there are 36 vases containing 125 flowers, with 3 daisies or 4 lilacs in a vase.
SetupLet x and y represent daisy and lilac vases, respectively. The problem statement gives two relations:
x +y = 36 . . . . . total number of vases
3x +4y = 125 . . . total number of flowers
SolutionSubstituting for x, we have ...
x = 36 -y
3(36 -y) +4y = 125
108 +y = 125
y = 13
x = 36 -13 = 23
There are 23 vases of daisies and 13 vases of lilacs.
need help please I cant find the answer
Answer:
6
1/3
Step-by-step explanation:
Similar triangles
The corresponding side on triangle A is 18 units
18 * 1/3 = 6
The side length of the missing side on B is 6 units
Side B 5
------ = ----------- = 1/3
Side A 15
The ratio is 1/3
Answers:
question one: 6
question two: 1/3
==========================================
Explanation:
The side 12 from triangle A corresponds to the side 4 from triangle B.
The scale factor is A/B = 4/12 = 1/3 which tells us that sides in triangle B are 1/3 as long compared to sides in triangle A. This takes care of the second question.
We'll use this scale factor to determine the missing side of triangle B.
The side 18 in triangle A corresponds to this missing side in triangle B.
Take 1/3 of 18 to get (1/3)*18 = 6 which is that missing side.
--------------
Another way to look at it: Take any side of triangle B, triple it, and you'll get a corresponding side of triangle A.
Example: The jump from 5 to 15 is "times 3".
Triangle QRS and its dimensions are shown.
s,. 6 centimeters,. 12 centimeters,. q,. 15 centimeters,. r,.
Which measurements in centimeters represent the dimensions of a triangle that is similar to triangle QRS?
The dimensions that represent a similar triangle to triangle QRS are given as follows:
B. 10 cm, 20 cm, 25 cm.
What are similar triangles?Similar triangles are two triangles that have the same angle measures.
These triangles will also have proportional side lengths, because of the sine/cosine/tangent relations in a right triangle and the law of sines for non-right triangles.
In this problem, we want a triangle that is similar to a triangle with the dimensions presented as follows:
s,. 6 centimeters,. 12 centimeters,. q,. 15 centimeters,. r,.
Hence all these dimensions have to be multiplied by the same scale factor.
Then, option B is correct, as the ratios between the lengths are given as follows:
10/6 = 20/12 = 25/15 = 5/3.
Meaning that all sides were multiplied by 5/3.
Missing InformationThe problem is given by the image at the end of the answer.
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Answer Answer is B, thank you, I just love to help.
Step-by-step explanation:
ASAP!! Brainliest to first answer
3x - 2/3x = 14
Answer:
x = 6
Step-by-step explanation:
Given equation,
→ 3x - (2/3)x = 14
Now the value of x will be,
→ 3x - (2/3)x = 14
→ (9/3)x - (2/3)x = 14
→ ((9 - 2)/3)x = 14
→ (7/3)x = 14
→ 7x = 14 × 3
→ x = 42/7
→ [ x = 6 ]
Hence, the value of x is 6.
Add 7w-12 and -15w+60
Show your work
Answer:
Step-by-step explanation: 7w-12+(-15w+60)= 7w-12-15w-60= -8w-72
-8w-72 is the answer or -8(w+9) if you take out a -8
The required simplified solution of the sum of the expressions is -8w + 48
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
To add 7w-12 and -15w+60
According to the question,
= 7w - 12 - 15w + 60
= 7w - 15w + 60 - 12
= -8w + 48
Thus, the required simplified solution of the sum of the expressions is -8w + 48
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Please help as I am confused
The region common to both the graphs as shown is the solution set.
What are the system of equations?A system of equations is a collection of two or more equations with a same set of unknowns
Given are the following quadratic inequalities -
x² - 6x - 7 < 0
3x² - 28x + 32 ≤ 0
We have the following quadratic inequalities -
x² - 6x - 7 < 0
3x² - 28x + 32 ≤ 0
We will plot both of them. The common region be the possible set of solutions to the given inequalities. Refer to the graph attached. The region common to both the graphs is the solution set.
Therefore, the region common to both the graphs as shown is the solution set.
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cual es el interes que genera $600, colocados al 8% anual durante 1 año 4 meses?
The simple interest on the loan of $600 at rate of 8% over a time period of 16 months is $664 and the interest generated is $64
Simple InterestThe formula for simple interest helps you find the interest amount if the principal amount, rate of interest and time periods are given.
Simple interest formula is given as:
S.I = P(1 + rt)
S.I = Simple InterestP = principalr = rate t = timeSubstituting the values into the formula
S.I = 600(1 + 0.08 * 16)
S.I = 664
The interest generated is $64
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Translation: What is the interest generated by $600, placed at 8% per year for 1 year 4 months?
Solve using method of elimination (full working out step by step)
-4x + 3y = 31
4x- y = -21
Answer:
answer in the picture step by step
A 145-ft tower is located on the side of a mountain that is inclined 32° to the horizontal. A guy wire is to be attached to the top of the tower and anchored at a point 55 ft downhill from the base of the tower. Find the shortest length of wire needed. (Round your answer to the nearest foot.)
By apply the law of cosine, the shortest length of wire needed is 180 feet.
How to determine the shortest length of wire needed?In order to determine the shortest length of wire needed, we would apply the law of cosine because a mental image of the scenario described produces a right-angled triangle.
In Trigonometry, law of cosine (cos) is given by this mathematical expression:
C² = A² + D² - 2(A)(D)cosD
Note: Angle D = 90° + 32° = 122°
Substituting the given parameters into the formula, we have;
C² = 55² + 145² - 2(55)(145)cos122°
C² = 3,025 + 21,025 - 2(7,975)(-0.5299)
C² = 24,050 - (-8,451.905)
C² = 24,050 + 8,451.905
C² = 32,501.905
C = √32,501.905
C = 180.28 ≈ 180 feet.
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new york city is the most expensive city in the united states for lodging. the mean hotel room rate is $204 per night. assume that the room rates are normally distributed with a standard deviation of $55. answers to 3 decimals. what is the probability of more than $225?
The probability of more than $225 is 0.35197.
Here we need to find the probability of more than $225.
We need to calculate the z-score associated with x = $225
Z(score) = 225 - 204 / 55
= 0.381818
z(score) = 0.38
For z = 0.38 the corresponding probability is P(z < 0.38) = 0.64803.
Here we have to find the values greater than this value:
P(z > 0.38) = 1 - P (z < 0.38)
P( z > 0.38) = 0.35197
So the probability that a hotel room costs 225 or more per night is P (x > 225) = 0.35197 and the percentage is 35.197%.
Therefore the probability is 0.35197.
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help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The time taken to reach the maximum height is 1.25 seconds.
The maximum height is 32 feet.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
h(t) = -16t² + 40t + 7
Differentiating with respect to t.
h'(t) = -16 x 2t + 40
0 = -32t + 40
32t = 40
t = 40/32
t = 1.25
The maximum height.
h(t) = -16t² + 40t + 7
h(1.25):
= -16 x 1.25 x 1.25 + 40 x 1.25 + 7
= -25 + 50 + 7
= 32 feet
Thus,
The time taken to reach the maximum height is 1.25 seconds.
The maximum height is 32 feet.
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Help Please!
Solve the inequality and graph it’s solution.
Answer:
A) n > 0
Step-by-step explanation:
You want the solution and graph for -8n +18 > -6(3n -3).
SolutionEliminating parentheses, we have ...
-8n +18 > -18n +18
Subtracting 18 gives ...
-8n > -18n
Adding 18n, we have ...
10n > 0
Finally, dividing by 10 gives ...
n > 0
The graph is attached.
The PlentyofFish dating site company is designing a marketing campaign with the objective of reducing the purchase risk of its dating service in the customer's mind. PlentyofFish is offering a limited free 30-day trial to test out the site. Which stage has the smallest percentage of prospects associated with the AIDA model is PlentyofFish implementing for its campaign ?
The stage that has the smallest percentage of prospects associated with the AIDA model is PlentyofFish implementing for its campaign is the action stage.
What is the AIDA Model?The AIDA Model (Attention, Interest, Desire, and Action) is an advertising effect model that identifies the stages that an individual goes through when purchasing a product or service.
The AIDA model is one of several models known as hierarchy of effects models or hierarchical models, all of which imply that when making a purchase decision, consumers go through a series of steps or stages.
An AIDA model entails the following steps:
Attention: The first step in marketing or advertising is to think about how to get consumers' attention.
Interest: Once a consumer is aware that a product or service exists, the company must work to increase the potential customer's level of interest.
Desire: Once the consumer is interested in the product or service, the goal is to make them want it.
Action: The ultimate goal of a marketing campaign is to motivate the recipient to take action and buy the product or service.
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help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeee!!!!!!!!!!!!!!!!!!!!!
Answer:
see the attachment photo!
Find the solution(s) of the system of equations:
y = x2 + 6x + 9
y = 2x + 6
Answer:
(-1,4) (-3,0)
picture below (im assuming you meant x^2.)
if you meant x2, please look at the second image
FIRST PHOTO = y=x^2 + 6x + 9 & y=2x+6
SECOND PHOTO = y=x2 + 6x + 9 & y=2x+6
Sylvia Okumbe is trying to break her national record of 14 minutes 35 seconds
for running 5000 m (12 1/2 laps of the track). Her average time per lap for the
first 5 laps is 1 minute 13 seconds. What average lap time does she need for
the remaining 7 1/2 laps?
Enter your answer as a number in seconds. Only type the number of seconds -
no spaces or words
Sylvia needs tο cοmplete the remaining 7.5 laps in an average time οf 68 secοnds οr less tο break the natiοnal recοrd.
What is Time, Speed and Distance?Time is the duratiοn between twο events, speed is the rate at which distance is cοvered per unit time, and distance is the amοunt οf space between twο οbjects οr pοints.
Sylvia has cοmpleted the first 5 laps in a tοtal time οf 5 x 73 secοnds = 365 secοnds.
Tο break the natiοnal recοrd οf 14 minutes 35 secοnds (οr 875 secοnds) fοr running 5000m, Sylvia has 5000m - 5 laps (οf 400m each) = 3000m remaining tο run, which is equivalent tο 7.5 laps (since each lap is 400m).
Let's say Sylvia needs tο cοmplete the remaining 7.5 laps in x secοnds.
Tο break the natiοnal recοrd, the tοtal time fοr running 12.5 laps (οr 5000m) shοuld be 875 secοnds οr less. Sο, we can set up the fοllοwing equatiοn tο find the required average lap time fοr the remaining 7.5 laps:
365 secοnds + 7.5x secοnds ≤ 875 secοnds
Subtracting 365 secοnds frοm bοth sides gives:
7.5x secοnds ≤ 510 secοnds
Dividing bοth sides by 7.5 gives:
x secοnds ≤ 68 secοnds
Sο, Sylvia needs tο cοmplete the remaining 7.5 laps in an average time οf 68 secοnds οr less tο break the natiοnal recοrd.
Therefοre, the answer is 68 secοnds.
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1. The distance between the points (5, 7) and (8,-5) is
a) √153
b) √154
c) √13
d) √53
The distance between the points (5, 7) and (8,-5) is √13.
Define distance between points.The length of the path joining two points determines their distance from one another. It's crucial to know how to calculate the distance between two points when working with graphs. This makes it possible for a learner to estimate how long the line is, which is useful in a variety of circumstances. Using the distance formula is the most typical method of determining the distance.
Points (5, 7) and (8,-5)
Formula:
AB² = (x₂ - x₁)² + (y₂ + y₁)²
AB² = (8 - 5)² + (-5+7)²
AB² = (3)² +(2)²
AB² = 9 + 4
AB² = 13
AB = √13
The distance between the points (5, 7) and (8,-5) is √13.
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in developing patient appointment schedules, a medical center wants to estimate the mean time that a staff member spends with each patient. use a planning value for the population standard deviation of seven minutes. (round your answers up to the nearest integer.) how large a sample should be taken if the desired margin of error is two minutes at a 95% level of confidence?
A sample should be 47 to be taken if the desired margin of error is two minutes at a 95% level of confidence
Given information:
A medical facility wants to determine the average amount of time each patient spends with a staff member while creating patient appointment schedules. utilize a planned value of seven minutes for the population's standard deviation.
б=7, ME=2
95% Confidence (to the nearest whole number):
For 95% confidence interval z-critical value is z_{c}=1.96. So
n = (z * б /ME )² = (1.96* 7/ 2)= 47.05
The Requried sample size is 47
If the acceptable margin of error is two minutes at a 95% level of confidence, then a sample of 47 should be taken.
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Help me plss!!!
Solve for x.
Question 6 options:
1)
32
2)
6
3)
63
4)
3
The value of angle with x, given the equation on the circle, is 4) 3.
How to find the value of x?The angle is given by the expression:
31x + 3
The same angle is shown to be a right angle with the line EF being straight and therefore a right angle. Right angles have a total measure of 90 degrees.
The value of x can therefore be found by equating the expression to 90 degrees:
31x + 3 = 90
31 x = 90 - 3
x = 87 / 31
x = 2.8
x = 3
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3X + 2Y) (6X + 6Y) what is the answer
Answer:
18X^2 + 18XY + 12YX + 12Y^2
Step-by-step explanation:
you have to moltiplicate the first term with the other two and the same thing for the second term of the first moltiplication
Step-by-step explanation:
what is the question you need an answer for ?
I assume you only need the result of the multiplication of both terms.
remember, when multiplying summary terms, we need to multiply every part of one term with every part of the other term.
(3x + 2y)(6x + 6y) = 18x² + 18xy + 12xy + 12y² =
= 18x² + 30xy + 12y²