Two monomials are shown below. 28x²y 34x y What is the greatest common factor (GCF) of these monomials? A
7xy B
4x²y
C2xy
D2x²y
I need an answer asap ​

Farah's team runs a total of 3.2 kilometers in the relay race.

We have,

First, let's start with the number of laps each student runs:

2 laps per student x 4 students

= 8 laps in total

Next, let's convert the number of laps to the total distance:

8 laps x 400 meters per lap = 3200 meters

Finally, let's convert the distance from meters to kilometers:

3200 meters ÷ 1000 meters per kilometer

= 3.2 kilometers

Thus,

Farah's team runs a total of 3.2 kilometers in the relay race.

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1. a. H0: p(Picked Toledo) - p(Picked Nevada) = 0
  b. Ha: p(Picked Toledo) - p(Picked Nevada) > 0
  c. α= 0.05
  d. Pooled proportion = 0.203125

2. The value of the Test Statistic is 2.24.

3. We can reject the null hypothesis.

4. The proportion of people who picked Toledo is greater than those who picked Nevada.

Based on the Minitab output provided, here is the information you're looking for:

1. a. H0: p(Picked Toledo) - p(Picked Nevada) = 0
  b. Ha: p(Picked Toledo) - p(Picked Nevada) > 0
  c. α= 0.05 (typically used in hypothesis tests, not given in the output)
  d. Compute the pooled proportion:
     Pooled proportion = (X1 + X2) / (n1 + n2) = (18 + 8) / (64 + 64) = 26 / 128 = 0.203125

2. Value of the Test Statistic: z = 2.24

3. To answer "What decision can you make?"
  Since the P-value (0.013) is less than the significance level (α=0.05), you can reject the null hypothesis.

4. To answer "What conclusion can you make?"
  Based on the test results, there is significant evidence to conclude that the proportion of people who picked Toledo is greater than the proportion who picked Nevada.

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The exponential function of base e whose derivative at x=3 is 2y=e^(ax-b) is y = e^(4x - 5).

To create an exponential function of base e using the digits 1-6 at most one time each, with the condition that its derivative at x=3 is 2.

Given the function y = e^(ax-b), let's find its derivative:

1. Differentiate the function with respect to x: dy/dx = a * e^(ax-b)
2. Plug in x = 3 and set dy/dx = 2: 2 = a * e^(3a-b)

Now, we need to find the values of a and b using the digits 1-6, at most one time each. Let's use a = 4 and b = 5, as they seem reasonable and satisfy the single-use condition:

2 = 4 * e^(12 - 5)
2 = 4 * e^7

Now divide both sides by 4:
2/4 = e^7
1/2 = e^7

So, our exponential function using the digits 1-6 at most one time each and satisfying the given condition is                    y = e^(4x - 5).

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Based on the inscribed angle theorem and the tangent theorem, the angles that must be right angles are: ∠XLS, ∠LEG, ∠LTG, and ∠XLQ.

Since, The theorem states that an inscribed angle of a semicircle equals 90°.

And, According to the tangent theorem, a tangent is at right angle at the point of tangency with the radius.

Hence, Based on these theorems, the angles that must be right angles are:

∠XLS, ∠LEG, ∠LTG, and ∠XLQ.

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The IQR is more robust to outliers than the standard deviation, which is sensitive to outliers.

Answering your questions:

Question 1:

The Stanford Five-City Project is a study of five moderately sized Northern California towns. Multiple-risk factor intervention strategies were randomly applied to two of the communities, while the other three cities served as controls. The design of this study can be outlined in schematic form as follows:

Random selection of five moderately sized Northern California towns

Two of the towns randomly assigned to receive multiple-risk factor intervention strategies

Three of the towns serve as controls and do not receive any intervention

The health outcomes of the communities are compared after the intervention to evaluate its effectiveness

Question 2:

Population: The population for this study is all employees who used the psychological counseling benefit in the prior year.

Sample: The sample is the 25 employees who completed and returned their questionnaires.

Concern: The fact that only 25 of the 100 questionnaires were completed and returned raises concerns about the representativeness of the sample. The sample may not be representative of the population, and the results of the study may not be generalizable.

Question 3:

If data are really skewed, an appropriate measure of central location would be the median. An appropriate measure of spread for skewed data would be the interquartile range (IQR), which is the difference between the third quartile (Q3) and the first quartile (Q1). The IQR is more robust to outliers than the standard deviation, which is sensitive to California

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Let 0-1 represent students who participate in sports and let 2-9 represent students who do not participate in sports.

Let 0-9 represent students selected for the sample, with digits 0-8 representing students who participate in sports and digit 9 representing a student who does not participate in sports.

So, an appropriate assignment of digits for this simulation would be: Let 0-1 represent students who participate in sports and let 2-9 represent students who do not participate in sports.

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The rate of increase in water pressure in  atmospheres 0.000992 atm/km.

To find the rate of increase in water pressure in atm/km, we need to convert the given rate of increase from atm/m to atm/km.

[tex]1 km = 1000 m[/tex]

So, we can convert the given rate of increase as follows:

[tex]0.992 atm/m = (0.992 atm/m)[/tex] × [tex](1000 m/km)[/tex]

[tex]= 992 atm/km[/tex]

Therefore, the rate of increase in water pressure in atm/km is 992 atm/km.

We must convert the stated rate of increase in water pressure from atm/m to atm/km in order to determine the rate of increase in atm/km.

We are aware that 1000 metres make up 1 kilometre. As a result, we can translate the supplied water pressure rise rate from atm/m to atm/km as follows:

[tex]0.000992 atm/km = 0.992 atm/m[/tex] × [tex](1 km/1000 m)[/tex]

0.000992 atm/km is the rate of rise in water pressure as a result.

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Complete Question:

The water pressure on Mustafa as he dives is increasing at a rate of

0. 992, atmospheres left parenthesis, start text, a, t, m, end text, right parenthesis per meter left parenthesis, start text, m, end text, right parenthesis. What is the rate of increase in water pressure in  atmospheres?

The experimental probability of landing on a number greater than 4 is 18/60

The experimental probability will be given by the number of times that the outcome was greater than 4 (so a 5 or a 6) over the total number of trials.

We can see that the total number of trials is 60, and we have:

The outcome 5 a total of 10 times.

The outomce 6 a total of 8 times.

Adding these values we will get 10 + 8 = 18

Then the experimental probability of a number greater than 4 is:

E = 18/60

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To solve this problem :
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (the initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, we have:
P = $46,950.00
r = 6.78% = 0.0678
n = 2 (since the interest is compounded semi-annually)
t = 12 (since we are investing for 12 years and withdrawing at the end of every three months)

To find the amount that can be withdrawn, we need to solve for A when t = 12/4 = 3 (since we are withdrawing every three months):
A = P(1 + r/n)^(nt)
A = $46,950.00(1 + 0.0678/2)^(2*3)
A = $46,950.00(1.0339)^6
A = $46,950.00(1.2307)
A = $57,789.27
So the sum of money that can be withdrawn from the fund is $57,789.27.

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The proof that of the above expression on the condition of a/b = c/d = e/f is given below.

Given: a/b = c/d = e/f

Let e/b = e/c = k

Then, a/b = k and c/d = k, so a = kb and c = kd

Now we have:

√((a⁴ +  c⁴)/  (b⁴ + d⁴))   = √(((k b) ⁴ + ( kd )⁴ )/(b ⁴ + d ⁴)  )

= √ (k ⁴ *  (b⁴ + d⁴ ) / (b⁴ + d⁴))

= k²

Let p = 1 and q = k², then:

(p  a² + q * c²)/(p * b² + q * d²) = (a² + k² * c²)/(b² + k⁴ * d²)

= (k² *   b² + k² *    d ²)/(b ² +   k ⁴ * d ²)

= k ²

Therefore, we have shown that √ ((a ⁴ + c ⁴)/(b ⁴ + d ⁴))   = (p x a ² + q * c ²) / (p * b ² + q * d² )

if a/b =  c/ d =  e/f.

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The 8 measures that can be used to calculate the distance across a circle through its center is known as the diameter.

The 8 measures include diameter, radius, chord, tangent, secant, circumference, arc length, and central angle. The diameter is the longest measure and extends from one side of the circle through its center to the opposite side. The radius is half the length of the diameter and extends from the center to the circumference.

A chord is a straight line segment that connects two points on the circumference. A tangent is a straight line that touches the circumference at only one point. A secant is a line that intersects the circumference at two points.

The circumference is the distance around the circle, while the arc length is the distance along a portion of the circumference. A central angle is an angle whose vertex is at the center of the circle, and its rays extend to the circumference.

These measures are useful in many areas, such as in geometry, trigonometry, and physics. They can be used to calculate various properties of circles, such as the area, perimeter, and volume of circular objects. Understanding these measures is essential in solving problems related to circles and circular motion.

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Answer: x=67    x=70    x=61

Step-by-step explanation:

see image for explanaton

The product of the expression is 2x⁶ + 23x³ + 63

First, we should note that algebraic expressions are described as expressions that are composed of coefficients, terms, constants, variables and factors.

These algebraic expressions are also made up of mathematical operations, such as;

From the information given, we have that;

2x3 +9 and x3 +7?

Then,

(2x³ + 9)(x³ + 7)

expand the bracket

2x⁶ + 14x³ + 9x³ + 63

add like terms

2x⁶ + 23x³ + 63

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The solution to the initial value problem is: y = (-1/9)e^(-3/2 t) + (1/3)(t – 4) + 10/9

To solve this initial value problem, we first need to find the homogeneous solution by setting H(t – 4) to 0. So we have:

2y' + 3y = 0

This is a first-order linear homogeneous differential equation, which we can solve using the separation of variables:

2y' = -3y

dy/y = -3/2 dt

ln|y| = -3/2 t + C

y = Ce^(-3/2 t)

Now we need to find the particular solution for H(t – 4) = 1. We can use the method of undetermined coefficients, guessing that the particular solution has the form y_p = A(t – 4) + B. Substituting this into the differential equation, we get:

2A + 3(A(t – 4) + B) = 1

Simplifying and equating coefficients, we get:

3A = 1

A = 1/3

Plugging this back into the equation and solving for B, we get:

2(1/3) + 3(1/3)(-4) + B = 0

B = 10/9

So the particular solution is y_p = (1/3)(t – 4) + 10/9.

The general solution is the sum of the homogeneous and particular solutions:

y = Ce^(-3/2 t) + (1/3)(t – 4) + 10/9

To find the value of C, we use the initial condition y(0) = 1:

1 = C + 10/9

C = -1/9

Therefore, the solution to the initial value problem is:

y = (-1/9)e^(-3/2 t) + (1/3)(t – 4) + 10/9

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Answer:5

Step-by-step explanation:

135/27 = 5

5 buses of 27 people will equal to 135 students being transported

Answer:A."The theoretical probability, P(gold), is 25%

explanation:It's realy simple

The shortcut that can be used to prove ΔAET ≅ ΔFRP is ASA (option d).

The given information includes the measure of some angles and the fact that two sides of the triangles are congruent. To prove that two triangles are congruent, you need to show that all their corresponding sides and angles are congruent.

To determine which shortcut can be used to prove that ΔAET ≅ ΔFRP, we need to check which postulate applies to the given information.

We know that angle AET is congruent to angle FRP (given), AE is congruent to FR (given), and angle T and angle P are congruent (given).

Therefore, the shortcut that applies to this situation is the ASA postulate, which states that two angles and the included side of the triangles are congruent. Thus, we can conclude that ΔAET ≅ ΔFRP by the ASA postulate.

Hence the correct option is (d).

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To determine the probability that the power supply will be inadequate on any given day, we need to find the probability that the daily consumption of electric power exceeds 12 million kilowatt-hours. We have a gamma distribution with α = 3 and β = 2.

Step 1: Identify the parameters of the gamma distribution.
α = 3 (shape parameter)
β = 2 (scale parameter)

Step 2: Set up the problem.
We want to find the probability P(X > 12), where X is the random variable representing daily power consumption in millions of kilowatt-hours.

Step 3: Calculate the cumulative distribution function (CDF) for the given parameters at X = 12.
We can use a gamma CDF calculator or software to find the CDF. For example, using the R programming language, you can use the "pgamma" function:

pgamma(12, shape = 3, scale = 2)

Step 4: Calculate the probability of power supply being inadequate.
Since we want the probability of X > 12, we can subtract the CDF from 1 to obtain the probability:

P(X > 12) = 1 - CDF(12)

After calculating the CDF with the given parameters, you'll obtain the probability that the power supply will be inadequate on any given day.

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The solution is, the probability that exactly two of the dice show an even number is 0.3125.

We will use the Binomial Probability formula to find the answer

The formula is given by ⁿCₓ (p)ˣ (1-p)ⁿ⁻ˣ

Where:

n, the number of trials = 5

x, the number of success that we aim = 2

p, the probability of success = 0.5 ⇒ there are six out of twelve numbers on the dice that are even

Substitute these values into the formula, we have

P(2) = ⁵C₂ (0.5)² (1-0.5)⁵⁻²

P(2) = ⁵C₂ (0.5)² (0.5)³

P(2) = 0.3125

The solution is, the probability that exactly two of the dice show an even number is 0.3125.

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complete question:

Ben rolls 5 fair 12-sided dice. the 12 faces of each die are numbered from 1 to 12. what is the probability that exactly two of the dice show an even number?

Since we know that the heptagon is convex, all of its interior angles are less than 180 degrees. Let's call the smallest angle x degrees.

According to the problem, the other six angles are each 1 degree larger than the angle just smaller than it. This means the second angle is x+1, the third angle is x+2, and so on, until we get to the seventh angle which is x+6.

We know that the sum of the interior angles of a heptagon is (7-2) * 180 = 900 degrees. So we can set up an equation:

x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6) = 900

Simplifying this equation, we get:

7x + 21 = 900

Subtracting 21 from both sides:

7x = 879

Dividing both sides by 7:

x = 125.57

So the smallest angle is approximately 125.57 degrees.

To find the fourth largest angle, we need to find the value of x+3.

x+3 = 125.57 + 3 = 128.57

So the fourth largest angle is approximately 128.57 degrees.

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The value of the unknown angle is 40⁰

A chord of a circle is a straight line segment whose endpoints both lie on a circular arc. If a chord were to be extended infinitely on both directions into a line, the object is a secant line. More generally, a chord is a line segment joining two points on any curve

In geometry, a circular segment (symbol:  also known as a disk segment, is a region of a disk which is "cut off" from the rest of the disk by a secant or a chord.

Circle theorems are properties that show relationships between angles within the geometry of a circle. We can use these theorems along with prior knowledge of other angle properties to calculate missing angles, without the use of a protractor. This has very useful applications within design and engineering.

Angles in the same segment are equal

The two angles marked are seen to be in the same segment and as such they are equal angles

The value of each of the angles is 40⁰

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The value of A such that the binary number is 35, must be A = 1.

We want to find the value of A such that:

1000A1 represents the number 35.

Remember that each of these numbers are the coefficient of the correspondent powers of 2, then we can write:

1000A1 = 1*2⁰ + A*2¹ + 0*2² + 0*2³ + 0*2⁴ + 1*2⁵

Solving that we will get:

1*2⁰ + A*2¹ + 0*2² + 0*2³ + 0*2⁴ + 1*2⁵ = 1 + 2A + 32

And that must be equal to 35, then:

1 + 2A + 32 = 35

2A = 35 - 33

2A = 2

A = 2/2 = 1

That is the value of A.

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The balance point of the data, given the number of hours rehearsed and the score would be (5, 50).

The balance point on the graph is simply the average of the x vertices and the y vertices.

The average of the x vertices is:

= ( 1 + 3 + 4 + 8 + 9 )  / 5

= 25 / 5

= 5

The average of the y vertices is:

= ( 30 + 50 + 20 + 90 + 60 ) / 5

= 250 / 5

= 50

This then means that the balance point would be ( 5, 50 ).

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The measure of a central angle of a regular polygon with 7 sides is approximately 51.4 degrees.

A polygon is a geometric object with two dimensions and a finite number of sides. A polygon's sides are made up of segments of straight lines that are joined end to end. As a result, a polygon's line segments are referred to as its sides or edges. Vertex or corners refer to the intersection of two line segments, where an angle is created.

To find the measure of a central angle of a regular polygon with 7 sides, we can use the formula:

central angle = 360 degrees/number of sides

Plugging in 7 for the number of sides, we get:

central angle = 360 degrees / 7
central angle ≈ 51.4 degrees

Therefore, the measure of a central angle of a regular polygon with 7 sides is approximately 51.4 degrees.

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The measure of the selected angles from the attached figure of coordinate plane equals to 44° are ∠2 and ∠4.

In the figure of the coordinate plane,

Measure of angle ABD = 90 degrees

measure of angle ABD = 44° + measure of angle 1

⇒  measure of angle 1 =  measure of angle ABD - 44°

⇒  measure of angle 1 =  90° - 44°

⇒  measure of angle 1 =  46°

Angles formed in the second quadrant.

measure of angle 1 + measure of angle 2 = 90°

⇒measure of angle 2 = 90° - 46°

⇒measure of angle 2 = 44°

From the figure,

Measure of ∠ABC = 44°

Using the result of vertically opposite angle we have,

Measure of angle 4 =Measure of ∠ABC

⇒Measure of angle 4 =  44°

Therefore, the measure of the angles in the figure equals to 44° are ∠2 and ∠4.

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According to the given box plot:

Most of the response times were under 13 minutes is true

Fewer than 30 of the response times were over 13 minutes is true

More than half of the response times were 11 minutes or greater is true

About 75% of the response times were 13 minutes or less is true

In box plot the difference between a dataset's first and third quartiles is used to determine the interquartile range (IQR), a measure of variability.

The interquartile range (IQR) depicts the range of values centred on the data's median. Because it is more resistant to outliers than other measures of variability like the range or the standard deviation, it is valuable in statistics.

Observations that are more than 1.5 times the IQR from the adjacent quartile are considered probable outliers and can be located using the IQR.

Box plots and the IQR are frequently combined to compare and summarise data from several groups or samples.

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The probability that a tire is from plant A, given that the owner finds that it is defective, is 0.67 or 67%.

Let A be the event that the tire comes from plant A, and D be the event that the tire is defective. We want to find P(A|D), the probability that the tire comes from plant A, given that it is defective.

Using Bayes' theorem, we have:

P(A|D) = P(D|A) * P(A) / P(D)

We know that P(D|A) = 0.20, the probability that a tire from plant A is defective, and P(D|B) = 0.10, the probability that a tire from plant B is defective.

We also know that P(A) = P(B) = 0.50, the probability that an order consists of tires from plant A or plant B.

To find P(D), we use the law of total probability:

P(D) = P(D|A) * P(A) + P(D|B) * P(B)

= 0.20 * 0.50 + 0.10 * 0.50

= 0.15

Now we can substitute these values into Bayes' theorem:

P(A|D) = P(D|A) * P(A) / P(D)

= 0.20 * 0.50 / 0.15

= 2/3

= 0.67 (rounded to two decimal places)

Therefore, the probability that a tire is from plant A, given that the owner finds that it is defective, is 0.67 or 67%.

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To turn on light 1, switches A, B, C, and D must all be on.

To determine which switches must be on for light 1 to function, we need to trace the path of the circuit from the battery to light 1 and see which switches need to be closed to complete the circuit.

Since this is a parallel circuit, the current can flow through multiple paths, and each light can have its own path to the battery. So, we need to identify the path that leads to light 1.

Starting at the battery, there are two paths that branch off, one leading to switch A and the other leading to switch B. Both switches must be closed for the current to flow through their respective paths.

From switch A, the current flows through light 2 and then to switch C. If switch C is open, then the current cannot flow to light 1. Therefore, switch C must be closed for light 1 to function.

From switch B, the current flows through light 3 and then to switch D. If switch D is open, then the current cannot flow to light 1. Therefore, switch D must be closed for light 1 to function.

Therefore, to turn on light 1, switches A, B, C, and D must all be on.

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The solution to the equation -5(x + 2) = 5 is x = -3.

Given the equation in the question:

-5( x + 2 ) = 5

First, we distribute the -5 to the expression inside the parenthesis:

-5×x + 2×-5= 5

-5x - 10 = 5

Next, let's isolate the variable x by adding 10 to both sides:

-5x - 10 + 10 = 5 + 10

-5x = 5 + 10

Simplifying the left side:

-5x = 5 + 10

-5x = 15

Finally, we can solve for x by dividing both sides by -5:

-5x / -5 = 15 / -5

x = -3

Therefore, the value of x is -3.

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The numbers that are at a distance of 3 from the number 10 are 7 and 13.

To describe all numbers x that are at a distance of 3 from the number 10, we can use the absolute value notation. The distance between two numbers is given by the absolute value of their difference. So, the numbers x that are 3 units away from 10 can be expressed as:

| x - 10 | = 3

This means that the absolute value of the difference between x and 10 is equal to 3. To find the values of x that satisfy this equation, we can solve for x as follows:

x - 10 = 3 or x - 10 = -3

Adding 10 to both sides of each equation, we get:

x = 13 or x = 7

Therefore, the numbers that are at a distance of 3 from the number 10 are 7 and 13.

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