Identify the set of possible values,
a, such that
x-a is a factor of x^5+3x-5
a) (1, 3, 5)
b) (1,5)
c) (1/5, 1, 5)
d) (1, 5)

Answer:

A:

✔ –4 < –1

B:

✔ –2 < –1

C:

✔ 2 > –5

D:

✔ 2 > –1

The inequality symbol is only reversed when dividing by a

✔ negative

number.

Answer:

1. B
2. B

3. A

4. A
5. negative

Step-by-step explanation:

Answer:

-16/3

Step-by-step explanation:

I am not sure if you are aware of this but I am not sure if you are aware of the fact

Answer:

20 + 4y

Step-by-step explanation:

The 4 multiplies the 5 and the y, i.e., it distributes over the terms of the expression in ( ).

Answer:

(-6,0)

Step-by-step explanation:

3x - 7y = -18             -7y = -3x - 18

y = 3/7x + 18/7

4x - 2(3/7x + 18/7) = -24

4x - 6/7x - 36/7 = -24

22/7x = -132/7

x = -6

3(-6) - 7y = -18

-18 - 7y = -18

-7y = 0

y = 0

Answer:

x= -3

Step-by-step explanation:

Solve the following system:

{8 y + 4.2 x = 41.8

y - 4.2 x = 19.4

In the second equation, look to solve for y:

{8 y + 4.2 x = 41.8

y - 4.2 x = 19.4

y - 4.2 x = y - (21 x)/5 and 19.4 = 97/5:

y - (21 x)/5 = 97/5

Add (21 x)/5 to both sides:

{8 y + 4.2 x = 41.8

y = 1/5 (21 x + 97)

Substitute y = 1/5 (21 x + 97) into the first equation:

{4.2 x + 8/5 (21 x + 97) = 41.8

y = 1/5 (21 x + 97)

4.2 x + (8 (21 x + 97))/5 = ((168 x)/5 + 776/5) + 4.2 x = 37.8 x + 776/5:

{(37.8 x + 776/5) = 41.8

y = 1/5 (21 x + 97)

In the first equation, look to solve for x:

{37.8 x + 776/5 = 41.8

y = 1/5 (21 x + 97)

37.8 x + 776/5 = (189 x)/5 + 776/5 and 41.8 = 209/5:

(189 x)/5 + 776/5 = 209/5

Subtract 776/5 from both sides:

{(189 x)/5 = -567/5

y = 1/5 (21 x + 97)

Multiply both sides by 5/189:

{x = -3

y = 1/5 (21 x + 97)

Substitute x = -3 into the second equation:

Answer: {x = -3, y = 34/5

Answer:

A) -3

Step-by-step explanation:

The expression for the number of boy cousins will be f – 4.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Marcella has 4 fewer male cousins than female cousins.

Let f represent the number of female cousins.

Then the expression for the number of boy cousins will be

⇒ f – 4

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Answer:

It would be 6.05m tall.

No, a fraction is not a term. The distributive property can be applied to fractions because it is a general mathematical principle.

A fraction is not considered a term in the traditional sense. It is a mathematical expression that represents division. However, the distributive property can still be applied to fractions because the property itself is a fundamental rule of arithmetic that extends beyond specific types of expressions.

The distributive property states that for any real numbers a, b, and c:

a × (b + c) = (a × b) + (a × c).

When working with fractions, we can apply the distributive property as follows:

Let's consider the expression: a × (b/c).

We can rewrite this as: (a × b)/c.

Now, let's distribute the 'a' to 'b' and 'c':

(a × b)/c = (a/c) × b.

In this step, we applied the distributive property to the fraction (a/c) by treating it as a whole.

Although fractions represent division, we can still use the distributive property because it is a general mathematical principle that allows for manipulating expressions involving addition, subtraction, multiplication, and division.

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Answer: 72cm³

Step-by-step explanation:

lengh x width x base with means 6 x 4 x 3

Mr. Adams divides 183 markers equally among the 24 students in his class. To find the least number of extra markers in the box, divide the total markers (183) by the number of students (24). The result is 7 with a remainder of 15. So, the least number of extra markers in the box is 15.

Mr. Adams divides 183 markers equally among the 24 students in his class, which means each student gets 7 markers. However, since 7 does not divide evenly into 183, there will be some markers left over. To determine the least number of extra markers in a box, we need to find the remainder when 183 is divided by 24.
Using long division, we get:

   24 | 183
       -----
         7  6
         -----          
This means that there are 6 markers left over that Mr. Adams puts in a box. Therefore, the least number of extra markers in a box is 6.
Mr. Adams divides 183 markers equally among the 24 students in his class. To find the least number of extra markers in the box, divide the total markers (183) by the number of students (24). The result is 7 with a remainder of 15. So, the least number of extra markers in the box is 15.

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From the distribution/ probability table,

A The percentage scores are between 60 and 75. is roughly 49.8%

B. The percent of scores that are less than 65 or above 80 is 18.5%

C. The percent of scores between 60 and 80 is 83.85%

D. The Z score for someone who score 52 is -4.6

E. A student with a z-score of 2.33 has 86.65 test score

F. Mari's Z score is  2.2

The easiest way is to map out the spread of the distribution table.

60       65              70           75          80          85           90

Lets share the percentage evenly in the distribution table using the 68, 95 and 99.7 rule.

   68%                       95%                    99.7%                       100%                        

70 -75 = 34%      65-70 = 13.5%      60-65 = 2.35%        below 60= 0.15%

75 - 80 = 34%     80 - 85 = 13.5%     85-90 = 2.35%       Above 90 = 0.15%    

A. For percentage between 60 - 75 we have

60-65 = 2.35%

65-70 = 13.5%
70 -75 = 34%

2.35 + 34% + 13.5% = 49.85%

B. For percentage less than 65 or above 80  we have

 below 60= 0.15%

60-65 = 2.35%

85-90 = 2.35%

80 - 85 = 13.5%

Above 90 = 0.15%

0.15 + 0.15 + 2.35+ 2.35 + 13.5 = 18.5%

C. The percent of scores between 60 and 80

60-65 = 2.35%

 65-70 = 13.5%

70 -75 = 34%

75 - 80 = 34%

2.35 + 13.5 + 34 + 34 = 83.85%

D. Z score = Z = (X - μ) / σ

Z is the Z-score

X is the value of the element

μ is the population mean

σ is the standard deviation

Z = (52 - 75) / 5 = -23 / 5 = -4.6

E. A student has a z-score of 2.33. What was his test score? We rearrange the  formula

X = μ + Zσ = 75 + 2.335 = 86.65

F. Mari scored an 86. What was her z-score?

Z = (86 - 75) / 5 = 11 / 5 = 2.2

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Answer:

CD is equal to 3.2 m

Perimeter is equal to 37.5 m

The workers would need 3.71 weeks to repair the road.

A generalization of arithmetic in which letters representing numbers are combined using arithmetic rules

Given that the total length of the road is 13km. Workers can repair 3.50 roads per week.

To determine the number of weeks required to repair the road, divide the total by per week. The equation would be:

13 ÷ 3.5

= (13 x 10)/35

= 130/ 35

= 3.71

Therefore the workers would need 3.71 weeks to repair the road.

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When the graph is decreasing, the rectangles give an underestimate and when the graph is increasing, they give an overestimate. These trends are accentuated to a greater extent by areas of the graph that are steeper.

We only need to add up the areas of all the rectangles to determine the area beneath the graph of f. It is known as a Riemann sum. The area underneath the graph of f is only roughly represented by the Riemann sum. The subinterval width x=(ba)/n decreases as the number of subintervals n increases, improving the approximation. Increased sections result in an underestimation while decreasing sections result in an overestimation. We now arrive at the middle rule. The height of the rectangle is equal to the height of its right edges for a right Riemann sum and its left edges for a left Riemann sum. The rectangle height is the height of the top edge's midpoint according to the midpoint rule, a third form of the Riemann sum.

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Answer:

x=50

Step-by-step explanation:

1. multiply the numbers

48x25=24x

1200=24x

2. Divide both sides by the same factor

1200/24 = 24/24x

simplify the expression

x=50

The degree is -6

To simplify, you have to combine the degrees, and you multiply the degree values to get the final degree

Answer:

27.1 mi / h; N 53° E

Step-by-step explanation:

Begin by finding the component form of the two vectors.

The balloon's vector has a magnitude of 20 mi/h and makes an angle of 54° with the x-axis.

The figure shows a vector of balloon speed on a Cartesian plane. The initial point of the vector is the origin. The vector of balloon speed has a length of 20 units. The angle between the vector and the positive direction of the x axis measures 54 degrees.

The balloon's vector components can be determined from the length of the hypotenuse and the angle made with the x-axis.

cos54°=x20

Multiply both sides by 20.

20(cos54°)=x

Calculate and round to the nearest tenth.

11.7≈x

sin54°=y20

Multiply both sides by 20

20(sin54°)=y

Calculate and round to the nearest tenth.

16.2≈y

The balloon's vector is <11.7,16.2>.

Since the wind blows 10 mi/h in the direction of the positive x-axis, it has a horizontal component of 10, and a vertical component of 0.

The figure shows a vector of wind speed on a Cartesian plane. The initial point of the vector is the origin. The vector of wind speed is directed along the positive x axis and has a length of 10 units.

The wind's vector is <10,0>.

To combine the vectors, add the components of the balloon's vector and the wind's vector .

<11.7,16.2>+<10,0>=<21.7,16.2>

The resultant vector in component form is <21.7,16.2>.

The magnitude of the resultant vector is the balloon's actual speed. To find the magnitude of the resultant vector, use the Distance Formula.

∣∣<21.7,16.2>∣∣=(21.7)2+(16.2)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√

Simplify.

∣∣<21.7,16.2>∣∣=470.89+262.44‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√

Simplify again.

∣∣<21.7,16.2>∣∣=733.33‾‾‾‾‾‾‾√

Simplify the square root and round to the nearest tenth.

∣∣<21.7,16.2>∣∣≈27.1 mi/h

The figure shows a vector of balloon speed, a vector of wind speed and a resultant vector on a Cartesian plane. The initial point of the vector of balloon speed is the origin. The initial point of the vector of wind speed is the terminal point of the vector of balloon speed. The initial point of the resultant vector is the origin. The terminal point of the resultant vector is the terminal point of the vector of wind speed. The angle between the resultant vector and the positive direction of x axis is labeled as A.

The angle A is formed by the resultant vector and the x-axis and gives the balloon's actual direction. The tangent of the angle formed with the x-axis is the y component over the x component.

tanA=16.221.7

Solve for m∠A

m∠A=tan−1(16.221.7)

Round to the nearest degree.

m∠A≈37°

This is equivalent to the direction N 53°E, the angle formed by the resultant vector and the y-axis.

Therefore, the balloon's actual speed is 27.1 mi/h, and actual direction is N 53°E.

Answer:

dude... I have fallen in love with your profile picture

Answer: 2 minutes

Step-by-step explanation:

Given the following :

Plane A's descent :

y = -2,500x + 14,000

Plane B's Ascent :

y = 4,000x + 1,000

where y = altitude x = minute

Time to be at the same altitude :

Being at the same altitude means ;

Plane A's descent = Plane B's Ascent

-2,500x + 14,000 = 4,000x + 1,000

-2500x - 4000x = 1000 - 14000

-6500x = - 13000

x = 13000 / 6500

x = 2

x = 2minutes.

Do you know the adjustments for the graph to show the intersecting lines.

Two-tailed because there is no predicted direction of the difference. The correct answer is D.

In hypothesis testing, a one-tailed test is used when the researcher has a specific prediction about the direction of the effect. They expect the results to be either greater than or less than a certain value. However, in this scenario, the researcher simply wants to investigate whether the new type of exercise improves people's health without any specific directional prediction.

A two-tailed test is appropriate when the researcher wants to determine if there is a significant difference between the groups being compared, but without specifying the direction of the difference. In this case, the researcher wants to examine if the new exercise has any effect on health, whether it improves or worsens it. Therefore, a two-tailed test is suitable as it allows for the possibility of observing a significant difference in either direction.

Therefore, considering these factors, the researcher should conduct a two-tailed test to assess the potential impact of the new exercise on people's health. The correct answer is D.

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Once you have followed these steps, you should be able to help the virologist conclusively decide what quantities a and b model by analyzing the given differential equations.

It seems that the specific functions a and b, as well as the differential equations, are not provided in your question. However, I can guide you on how to approach this problem using the given terms and general concepts.

A virologist studies the dynamics of infectious disease using mathematical models. The three quantities of interest are infected people (I), susceptible people (S), and immune people (R). Functions a and b will represent two of these three quantities. To determine which quantities a and b model, we can analyze the given differential equations and follow these steps:

Step 1: Identify the variables and their relationships
Look for the variables (S, I, and R) in the differential equations and analyze how they are related to each other. Determine if there are any rate constants or parameters that link the variables.

Step 2: Analyze the equations' behavior
Study the differential equations' behavior over time, considering different initial conditions. Observe if the equations exhibit any trends, such as an increase or decrease in the quantities.

Step 3: Compare the equations with known epidemic models
Compare the given differential equations with known epidemic models, such as the SIR model or the SEIR model. These models have well-defined equations that describe the rates of change for susceptible, infected, and immune individuals.

Step 4: Rule out alternatives
Based on your analysis, eliminate the alternatives that don't match the behavior exhibited by the differential equations. Ensure that your conclusion is supported by a logical argument.

Once you have followed these steps, you should be able to help the virologist conclusively decide what quantities a and b model by analyzing the given differential equations.

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To find the value of j - i, we need to determine the relationship between the surface areas (An) and volumes (Vn) of the unit ball in Rn for different positive integers n.

For the unit ball in Rn, the formula for surface area (An) and volume (Vn) are given by:

An = (2 * π^(n/2)) / Γ(n/2)

Vn = (π^(n/2)) / Γ((n/2) + 1)

where Γ denotes the gamma function.

To find the value of j - i, we need to identify the positive integers i and j such that Ai > Ak for all k not equal to i, and Vj > Vk for all k not equal to j.

First, let's analyze the relationship between An and Vn. By comparing the formulas, we can see that:

An / Vn = [(2 * π^(n/2)) / Γ(n/2)] / [(π^(n/2)) / Γ((n/2) + 1)]

      = 2 / [n * (n-1)]

From this equation, we can deduce that An / Vn > 1 if and only if 2 > n * (n-1).

To find the positive integer i, we need to identify the highest positive integer n for which 2 > n * (n-1) holds true. We can observe that this condition is satisfied for n = 2. Therefore, i = 2.

Now, let's find the positive integer j. We need to identify the lowest positive integer n for which 2 > n * (n-1) does not hold true. We can observe that this condition is no longer satisfied for n = 3. Therefore, j = 3.

Finally, we can calculate j - i as follows:

j - i = 3 - 2 = 1

Therefore, j - i equals 1.

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Answer:

A. $608 B. $76

Hope this helps

Answer:

\(y=5w+2w=228\)

Step-by-step explanation:

47.5% between 38 and 52 requests for new lightbulbs have been made.

Given,

The physical plant at the main campus of a large state university receives daily requests to replace fluorescent light bulbs.

The mean of the distribution, μ = 52

Standard deviation, σ = 7

We have to find the  approximate percentage of lightbulb replacement requests numbering between 38 and 52 using empirical rule;

Here,

z score corresponding to 38 and 52

z score = (x - μ) / σ = (38 - 52) / 7 = -2

Now,

z score corresponding to 52

z score = 52 -52 / 7 = 0/7 = 0

We are aware that, in accordance with the empirical rule, 68% of the data are within one standard deviation of the mean and 95% are within two.

By comparing the z-scores of data point 38 and 52, we can observe that data point 38 is at the mean. 38 is therefore -2 standard deviations above the mean. That is -2σ to 2σ

The center of the normal distribution curve is known to be the mean. Therefore, we will divide 95% by 2 to obtain the percentage of data points 2 SD above the mean.

95/2 = 47.5%

As a result, 47.5% between 38 and 52 requests for new lightbulbs have been made.

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Answer:

y=13

Step-by-step explanation:

Simplifying y + 10 = 2y + -3 Reorder the terms: 10 + y = 2y + -3 Reorder the terms: 10 + y = -3 + 2y Solving 10 + y = -3 + 2y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2y' to each side of the equation. 10 + y + -2y = -3 + 2y + -2y Combine like terms: y + -2y = -1y 10 + -1y = -3 + 2y + -2y Combine like terms: 2y + -2y = 0 10 + -1y = -3 + 0 10 + -1y = -3 Add '-10' to each side of the equation. 10 + -10 + -1y = -3 + -10 Combine like terms: 10 + -10 = 0 0 + -1y = -3 + -10 -1y = -3 + -10 Combine like terms: -3 + -10 = -13 -1y = -13 Divide each side by '-1'. y = 13 Simplifying y = 13

Answer:

60 km

Step-by-step explanation:

Given that :

Location of emergency telephone = every 10km

Location of water well = Every 15 km

Location of gas station = every 20 km

To obtain how often an emergency telephone, water well and gas station coincide, we obtain the lowest common multiple of 10, 15 and 20

Multiples of ;

10 : 10, 20, 30, 40, 50, 60, 70

15 : 15, 30, 45, 60, 75, 90, 105

20 : 20, 40, 60, 80, 100

Hence, the lowest common multiple of 10, 15 and 20 is 60, thus, an emergency telephone line, gas station and water well will coincide every 60km

We can conclude that they form a right triangle

So GF = FH

OF^2 = GF^2 + OG^2

OF^2 = 8.4^2 + 8^2

OF^2 = 70.56 + 64

OF^2 = 134.56

OF = 11.6

Based on the given clues, we can determine the person, drink, and price paid for each individual:

Calvin: Root Beer, $4.99

Dean: Lemonade, $7.99

Kelli: Water, $6.99

Lee: Iced Tea, $5.99

From clue 1, we know that either Calvin or the person who got the Root Beer paid $4.99. Since Calvin paid more than Lee according to clue 4, Calvin cannot be the one who got the Root Beer. Therefore, Calvin paid $4.99.

From clue 2, Kelli paid $6.99.

From clue 3, the person who got the water paid $1 less than Dean. Since Dean paid the highest price, the person who got the water paid $1 less, which means Lee paid $5.99.

From clue 5, the person who got the Root Beer paid $1 less than the person who got the Iced Tea. Since Calvin got the Root Beer, Lee must have gotten the Iced Tea.

Therefore, the final assignments are:

Calvin: Root Beer, $4.99

Dean: Lemonade, $7.99

Kelli: Water, $6.99

Lee: Iced Tea, $5.99

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