Enter the values for the highlighted variables that show how to subtract the rational expressions correctly:

StartFraction 2 Over x squared minus 36 EndFraction minus StartFraction 1 Over x squared + 6 x EndFraction = StartFraction 2 Over (x + 6) (x minus 6) EndFraction minus StartFraction 1 Over x (x + a) EndFraction. = StartFraction b x Over (x + 6) (x minus 6) x EndFraction minus StartFraction x minus c Over (x + 6) (x minus 6) x EndFraction. = StartFraction d x minus x + e Over (x + 6) (x minus 6) x EndFraction. = StartFraction x + f Over (x + 6) (x minus 6) x EndFraction. = StartFraction g Over x (x minus 6) EndFraction

a =

b =

c =

d =

e =

f =

g =

The number of revolutions made by the wheel is 5.24 ≅ 5.  

One complete revolution is equal to 360 degrees, so to find the number of complete revolutions the wheel has made, we can divide the total number of degrees rotated by 360.    

Here we have

A wheel rotated by 1888°  

As we know One complete revolution is equal to 360 degrees

Hence, the angle can be rotated by the wheel in 1 rotate = 360°  

Let the wheel make 'x' revolution to make 1888°  

=> 360(x) = 1888

=> x = 1888/360

=> x = 5.24

Therefore,

The number of revolutions made by the wheel is 5.24 ≅ 5.    

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Answer:

(4- x)(x - 4) = 16 - x2 help me sir please

Answer:

The first two equations.

Step-by-step explanation:

The first equation:

x² - 100 = 0

x² = 100

√x² = √100

x = ±10

x = 10 or -10

Second equation:

(x - 6)² = 25

√(x - 6)² = √25

x - 6 = ±5

x - 6 = 5 or x - 6 = -5

x = 11 or 1

It seems that for the other two equations, you have to complete the square and factor them out.

9514 1404 393

Answer:

  B.  F(-9/2, 0), x = 9/2

Step-by-step explanation:

One definition of a parabola is that it is all of the points that are equidistant from the focus and the directrix. Among other things, this means the parabola "wraps around" the focus, and opens away from the directrix.

The focus is on the axis of symmetry, so shares a coordinate with the vertex. Since the vertex is a point on the parabola, it is equidistant from the focus and directrix—halfway between them.

The given equation has x get more negative as y increases, so the parabola opens to the left. This means the focus will be a point on the -x axis. Only one answer choice meets that requirement:

  focus: (-9/2, 0), directrix: x = 9/2

__

The equation of a parabola with its vertex at the origin can be written as ...

  x = 1/(4p)y^2

In this case, we have 4p = -18, so p = -9/2. This is the distance from the vertex to the focus. The negative sign means the focus is to the left of the vertex, and its x-coordinate is -9/2 (as noted above).

By increasing the number of wire turns, using a thicker wire, increasing the battery voltage, and using a soft iron core, the student can enhance the electromagnet's strength, allowing it to pick up more paper clips.

To increase the number of paper clips the electromagnet will pick up, the student should take the following actions:

1. Increase the number of wire turns: By wrapping the wire around the iron nail more times, the student will create a stronger magnetic field. This is because each wire turn generates a magnetic field, and when the turns are in close proximity, their fields add up, creating a stronger overall field.

2. Use a thicker wire: A thicker wire will allow more current to flow through it, which will result in a stronger magnetic field. The higher the current, the more powerful the electromagnet becomes.

3. Increase the voltage of the battery: By increasing the voltage of the battery, the student can cause more current to flow through the wire. This will enhance the magnetic field, making the electromagnet more effective at picking up paper clips.

4. Use a soft iron core: Soft iron materials have higher magnetic permeability than other materials, meaning they can easily be magnetized and demagnetized. When the wire is wrapped around a soft iron nail, the resulting electromagnet will have a stronger magnetic field, thus improving its ability to pick up paper clips.

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a) To find the average life of the ten batteries, we need to calculate the mean, which is the sum of all the values divided by the number of values.Sum of all values = 10.8 + 10.6 + 11.4 + 8.9 + 10.1 + 10.6 + 9.9 + 12.6 + 10.5 + 11.9 = 106.2

Number of values = 10

Average life = Sum of all values / Number of values = 106.3 / 10 ≈ 10.63

Therefore, the average life of the ten batteries, rounded to the nearest tenth of an hour, is approximately 10.6 hours.

b) Comparing the two advertisements:

i) The first advertisement claims that Atlas batteries are guaranteed to last 10 hours. This means that all Atlas batteries are expected to last at least 10 hours. However, based on the data provided, we can see that the average life of the batteries is approximately 10.6 hours, which is higher than the guaranteed 10-hour minimum

ii) The second advertisement claims that Atlas batteries have an average life of over 10 hours. This statement aligns with the data we have, as the average life of the batteries is indeed over 10 hours.

Based on the information provided, the second advertisement claiming that Atlas batteries have an average life of over 10 hours is more accurate, as the average life calculated from the given data is 10.6 hours.

In summary, the average life of the ten batteries is approximately 10.6 hours, and the second advertisement stating an average life of over 10 hours is more accurate based on the data provided.

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Answer:

Step-by-step explanation:

It can be determined that the function is:

So missing x is:

Missing y is:

Missing numbers are:

Correct choice is d.

                                           FIRST METHOD

Answer:

Step-by-step explanation:

Given the table

x                                         y

7                                        16

9                                        17

Missing x                          18

13                                        Missing y

From the table, it is clear that y-values are incremented by 1 unit and the x-values are incremented by 2 units.

i.e.

y = 17-16 = 1

y = 18-17 = 1

as 19-18 = 1

Thus,

Thus, the value of Missing y = 19

also the x-values increment by 2.

i.e.

x  = 9-7 = 2

as x = 11 - 9 = 2

Thus, Missing x = 11

Therefore,

                                                2ND METHOD

Given that the table represents a  linear function, so the function is a straight line.

Taking two points

Finding the slope between (7, 16) and (9, 17)

\(\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\)

\(\left(x_1,\:y_1\right)=\left(7,\:16\right),\:\left(x_2,\:y_2\right)=\left(9,\:17\right)\)

\(m=\frac{17-16}{9-7}\)

\(m=\frac{1}{2}\)

Using the point-slope form to determine the linear equation

\(y-y_1=m\left(x-x_1\right)\)

where m is the slope of the line and (x₁, y₁) is the point

substituting the values m = 1/2 and the point (7, 16)

\(y-y_1=m\left(x-x_1\right)\)

\(y-16=\frac{1}{2}\left(x-7\right)\)

Add 16 to both sides

\(y-16+16=\frac{1}{2}\left(x-7\right)+16\)

\(y=\frac{1}{2}x+\frac{25}{2}\)

Thus, the equation of the linear equation is:

\(y=\frac{1}{2}x+\frac{25}{2}\)

Now substituting y = 18 in the equation

\(18=\frac{1}{2}x+\frac{25}{2}\)

Switch sides

\(\frac{1}{2}x+\frac{25}{2}=18\)

subtract 25/2 from both sides

\(\frac{1}{2}x+\frac{25}{2}-\frac{25}{2}=18-\frac{25}{2}\)

\(\frac{1}{2}x=\frac{11}{2}\)

\(x=11\)

Thus, the value of missing x = 11 when y = 18

Now substituting x = 13 in the equation

\(y=\frac{1}{2}\left(13\right)+\frac{25}{2}\)

\(y=\frac{13}{2}+\frac{25}{2}\)

\(y=\frac{13+25}{2}\)

\(y=\frac{38}{2}\)

\(y = 19\)

Thus, the value of missing y = 19 when x = 13

Hence, we conclude that:

Hence, option D is true.

Answer:

40

Step-by-step explanation:

Honestly, I was stuck and so I guessed. It was right

Answer:

associative property of multiplication

Answer:

1. Clark

2. 3211

3. 100

Step-by-step explanation:

Answer:

33/55

Step-by-step explanation:

Total applicants, n(T) = 350

Female applicants, n(F) = 158

Female and Graduate applicants, n(FnG) = 66

Graduates, n(G) = 110

Probability of female Given that applicant has graduate degree; this is a conditional probability problem;

Recall :

P(A given B) = P(A|B) = P(AnB) / P(B)

Therefore ;

P(F|G) = P(FnG) / P(G) = 66 / 110 = 33/55

Angle WZY is 50 degrees, angle WZX is also 50 degrees, and angle XZW is 160 degrees.

What is the inscribed angle theorem?

The inscribed angle theorem, also known as the central angle theorem, states that an angle formed by two chords in a circle is half the measure of the arc they intersect, or subtend, inside the circle.

To find all other angles in the circle with quadrilateral WXYZ inscribed in it and WY going through the center Q:

Since WY goes through the center, angle WYZ and angle WXY are both right angles (90 degrees)

By the inscribed angle theorem, angle WZY is equal to half the measure of the arc WX.

Since angle XYZ is given as 50 degrees, the measure of the arc WX is 2 times 50 degrees, which is 100 degrees.

Therefore, angle WZY is 50 degrees.

By the same logic, angle WZX is also 50 degrees.

Since angles WYZ and WXY are right angles, angles XZY and WZX are also right angles.

Finally, we can find angle WZY + angle XYZ + angle XZW + angle WZX = 360 degrees (sum of angles in a quadrilateral), and we can solve for angle XZW which is 160 degrees.

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Answer:

4 times = 1 mile

1 time = 1/4 of a mile

She wants to ride 3/4 of a mile

3/4 is 3 times 1/4

She has to ride her bike 3 times around the track

3 times <<<<<===== answer

hope this helps tell me if im wrong plz

Step-by-step explanation:

im not sure have a good day stay safe and get a good grade

Answer:

44, 45, and 46

Step-by-step explanation:

135-(x+1)=x+(x+2)

135-(x+1)=2x+2

135=3x+3

132=3x

x=44

So the first number is 44

Then just add 1 and 2 to get 45 and 46 as the second and third number.

For each customer, there are only two possible outcomes. Either they will order an alcoholic beverage, or they will not. The probability of a customer ordering an alcoholic beverage is independent of any other customer, which means that the binomial probability distribution is used to solve this question..

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

At a Noodles & Company restaurant, the probability that a customer will order a nonalcoholic beverage is .50

This means that \(p = 0.5\)

Sample of 14 customers

This means that \(n = 14\)

Probability that at least 7 will order a nonalcoholic beverage

This is:

\(P(X \geq 7) = 1 - P(X < 7)\)

In which

\(P(X < 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)\)

Then

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{14,0}.(0.5)^{0}.(0.5)^{14} = 0.0001\)

\(P(X = 1) = C_{14,1}.(0.5)^{1}.(0.5)^{13} = 0.0009\)

\(P(X = 2) = C_{14,2}.(0.5)^{2}.(0.5)^{12} = 0.0056\)

\(P(X = 3) = C_{14,3}.(0.5)^{3}.(0.5)^{11} = 0.0222\)

\(P(X = 4) = C_{14,4}.(0.5)^{4}.(0.5)^{10} = 0.0611\)

\(P(X = 5) = C_{14,5}.(0.5)^{5}.(0.5)^{9} = 0.1222\)

\(P(X = 6) = C_{14,6}.(0.5)^{6}.(0.5)^{8} = 0.1833\)

So

\(P(X < 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) = 0.0001 + 0.0009 + 0.0056 + 0.0222 + 0.0611 + 0.1222 + 0.1833 = 0.3954\)

\(P(X \geq 7) = 1 - P(X < 7) = 1 - 0.3954 = 0.6046\)

0.6046 = 60.46% probability that at least 7 will order a nonalcoholic beverage.

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Step-by-step explanation:

Let x be the length of rectangle and y its width.

P is the perimeter.

So it is given that length is 5 less than twice its width

x=2y-5 so 2y=x+5

also P=2x+2y=26

lets find x

we know 2y=x+5 we replace 2y on P=2x+2y=26

so 26=2x+(x+5)

26=3x+5

21=3x

x=7

so we have that 2y=x+5 so 2y=7+5=12

y=6

we found

length=7

and

width=6

Answer:

No entiendo que es lo que hay qué hacer

To find the height of the cylinder when the volume is given as 1500 in³ and the radius is 7 inches, we can use the formula for the volume of a cylinder:

Volume = π * r² * h

Substituting the given values, we have:

\(1500 = 3.14 * 7^2 * h1500 = 3.14 * 49 * h1500 = 153.86 * h\)

To solve for h, we divide both sides of the equation by 153.86:

h = 1500 / 153.86

h ≈ 9.75

Rounding the answer to the nearest hundredth, the height of the cylinder is approximately 9.75 inches.

Therefore, the height of the cylinder is 9.75 inches.

Note: It is important to use the accurate value of π, which is approximately 3.14159, for precise calculations. However, in this case, since you specified to use 3.14 for π, I have used that approximation to calculate the height.

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a.) m = -1

b.) m = 0

c.) m = undefined

d.) m = 1/2

Answer (bolded part is slope):

a.) y = -x + 2 (slope = -1)

b.) y = -2 (slope = 0)

c.) x = 3 (slope = undefined)

d.) y = \(\frac{2}{3}\)x + \(\frac{3}{2}\) (slope = 2/3)

we refer to this as standardized survey questionnaire.

A standardised questionnaire is one that is written and administered so all participants are asked precisely the same questions in an identical format and responses recorded in a uniform manner. Standardizing a measure increases its reliability.Just because a questionnaire has been piloted on a few of your colleagues, used in previous studies, or published in a peer reviewed journal does not mean it is either valid or reliable. The detailed techniques for achieving validity, reliability, and standardisation are beyond the scope of this series. If you plan to develop or modify a questionnaire yourself, you must consult a specialist text on these issues.

A standardised questionnaire is one that is written and administered so all participants are asked the precisely the same questions in an identical format and responses recorded in a uniform manner. Standardizing a measure increases its reliability.

Thus option (d) standardized survey questionnaire is correct.

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The  volume of the sphere is calculated as  8,788 cm³.

The volume of the sphere is calculated using the following formulas as shown below;

V = ⁴/₃πr³

where;

The radius of the sphere is given as 13 cm

π is given as 3

The  volume of the sphere is calculated as follows;

V =  ⁴/₃πr³

V = ⁴/₃ x 3 x 13 x 13 x 13

V = 8,788 cm³

Thus, The  volume of the sphere is calculated by using the formula for volume of sphere.

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Answer:

2.56

Step-by-step explanation:

100%->23.86

15%-> 3.579

3.579+23.86=27.439(how much he needs to pay including tip)

30-27.439=2.561

                ≈2.56 (since we dont usually pay up to 3 d.p.)

You would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample between approximately 264.0 days and 274.1 days.

To find the range in which you would expect to find the middle 98% of most pregnancies, you can use the concept of z-scores and the standard normal distribution.

For the given data:

Mean (μ) = 269 days

Standard deviation (σ) = 17 days

To find the range, we need to find the z-scores corresponding to the 1% and 99% percentiles. Since the normal distribution is symmetric, we can find the z-scores by subtracting and adding the respective values from the mean.

To find the z-score for the 1% percentile (lower bound):

z1 = Φ^(-1)(0.01)

Similarly, to find the z-score for the 99% percentile (upper bound):

z2 = Φ^(-1)(0.99)

Now, we can calculate the z-scores:

z1 = Φ^(-1)(0.01) ≈ -2.33

z2 = Φ^(-1)(0.99) ≈ 2.33

To find the corresponding values in terms of days, we multiply the z-scores by the standard deviation and add/subtract them from the mean:

lower bound = μ + (z1 * σ) = 269 + (-2.33 * 17) ≈ 229.4 days

upper bound = μ + (z2 * σ) = 269 + (2.33 * 17) ≈ 308.6 days

Therefore, you would expect to find the middle 98% of most pregnancies between approximately 229.4 days and 308.6 days.

Now, let's consider drawing samples of size 58 from this population. The mean and standard deviation of the sample means can be calculated as follows:

Mean of sample means (μ') = μ = 269 days

Standard deviation of sample means (σ') = σ / sqrt(n) = 17 / sqrt(58) ≈ 2.229

To find the range in which you would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample, we repeat the previous steps using the mean of the sample means (μ') and the standard deviation of the sample means (σ').

Now, calculate the z-scores:

z1 = Φ^(-1)(0.01) ≈ -2.33

z2 = Φ^(-1)(0.99) ≈ 2.33

Multiply the z-scores by the standard deviation of the sample means and add/subtract them from the mean of the sample means:

lower bound = μ' + (z1 * σ') = 269 + (-2.33 * 2.229) ≈ 264.0 days

upper bound = μ' + (z2 * σ') = 269 + (2.33 * 2.229) ≈ 274.1 days

Therefore, you would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample between approximately 264.0 days and 274.1 days.

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Answer:

x = 6

Step-by-step explanation:

3(2x-6) = 18

6x - 18 = 18

6x = 36

x = 6

Answer:

he makes $112.50

Step-by-step explanation:

first you have to find out how much he makes before tax is taken out. all you do is multiply 12.50 by 30, which gives you $375.00. then, you can either put in the calculator 30%375 or 0.3×375(both are the same thing) and you should get $112.50

Algebra transformation

for  Graph1 f(x)=f(x)+4

for  Graph2 f(x)=-f(x-4)

for  Graph3 f(x)=f(x-7)

for  Graph4 f(x)=f(x-2)-5

In mathematics, the reflection of a graph is a transformation that produces a mirror image of the original graph across a specific line or point. The line or point across which the reflection occurs is called the axis of reflection.

Graph1

Transform the graph by +4 units in y direction.

f(x)=f(x)+4

Graph2

Transform the graph by +4 units in x direction.

f(x)=f(x-4)

Now take the reflection of graph about x axis

f(x)=-f(x-4)

Graph3

Transform the graph by +7 units in x direction.

f(x)=f(x-7)

Graph5

Transform the graph by -5 units in y direction.

f(x)=f(x)-5

Now Transform the graph by -2 units in x direction.

f(x)=f(x-2)-5

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Answer:

for me the picture is blurry sorry

Step-by-step explanation:

Answer:

-23

Step-by-step explanation:

Answer:

10c-4+11d Welcome :D

Step-by-step explanation: