If p is prime, then there exists a field of order p². O True False

Answer:

Part A 70x+50=250

Part B(75x + 35) = 250 - 5x

Step-by-step explanation:

Here to form an equation you must add all the money that she earned and subtract the money that she had to spend We dont know how many car washes she did, so we must represent it with a variable, or x.

Answer:

Step-by-step explanation:

Part A: Rhett washed 3 cars and earned $50 in tips. y=70x+50

Part B: $75 - $5 = $70 (this is the amount charged minus the amount needed to get the job done per car wash)

the +35 is the tips extra/ constant that will be added after the jobs are done.

x is the number of car washes done

y would be the profit received.

so y = 70x + 35 (profit = value of car wash * number of cars washed + tips)

The fraction and ratio that complete the equations in its simplest term is 5/6k and 2 : 9 respectively.

h : k = 5 : 6

h/k = 5/6

cross product

h × 6 = k × 5

6h = 5k

divide both sides by 6

h = 5/6k

Then,

2x = 9y

2/9 = x/y

2 : 9 = x : y

Ultimately, the simplest form of fraction and ratio which completes the equation is 5/6k and 2:9.

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The interest earned increases with higher principal amounts, higher interest rates, and longer time periods.

Principal (P) | Interest Rate (r) | Time Period (t) | Interest Earned (I)

$1,000 | 2% | 1 year | $20

$5,000 | 4% | 2 years | $400

$10,000 | 3.5% | 3 years | $1,050

$2,500 | 1.5% | 6 months | $18.75

$7,000 | 2.25% | 1.5 years | $236.25

To calculate the interest earned (I), we can use the simple interest formula: I = P * r * t.

For the first row, with a principal of $1,000, an interest rate of 2%, and a time period of 1 year, the interest earned is calculated as follows: I = $1,000 * 0.02 * 1 = $20.

For the second row, with a principal of $5,000, an interest rate of 4%, and a time period of 2 years, the interest earned is calculated as follows: I = $5,000 * 0.04 * 2 = $400.

For the third row, with a principal of $10,000, an interest rate of 3.5%, and a time period of 3 years, the interest earned is calculated as follows: I = $10,000 * 0.035 * 3 = $1,050.

For the fourth row, with a principal of $2,500, an interest rate of 1.5%, and a time period of 6 months (0.5 years), the interest earned is calculated as follows: I = $2,500 * 0.015 * 0.5 = $18.75.

For the fifth row, with a principal of $7,000, an interest rate of 2.25%, and a time period of 1.5 years, the interest earned is calculated as follows: I = $7,000 * 0.0225 * 1.5 = $236.25.

These calculations show the interest earned for different savings principals, interest rates, and time periods.

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Answer:

60°

Step-by-step explanation:

360 - ( 80+115+10) = 60°

Answer:

x/2-10=18

Step-by-step explanation:

An equation is formed of two equal expressions. The given statement The quotient of a number and -2, less 10, is -18 can be written as an equation as (x/-2)-10=-18.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the number be represented by x. Therefore, the given statement can be written as,

(x/-2)-10=-18

Hence, the given statement The quotient of a number and -2, less 10, is -18 can be written as an equation as (x/-2)-10=-18.

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Answer:

x= 2

Step-by-step explanation:

In the context of intergroup sources of power, dependencies are activities that other groups depend on to complete their tasks.

Dependencies refer to the specific tasks or activities that one group relies on another group to fulfill. These dependencies create interdependencies between groups, establishing power dynamics and influencing the relationships between them. When one group possesses certain dependencies that are crucial for the functioning or success of other groups, it can leverage these dependencies to gain power and influence within the intergroup dynamics. For example, if Group A is responsible for providing essential raw materials that Group B needs to manufacture their products, Group A holds a dependency advantage over Group B. Group B is reliant on Group A's timely and reliable provision of the raw materials to carry out their production processes. In this scenario, Group A can use their control over the supply of raw materials as a source of power to negotiate favorable terms, pricing, or other concessions from Group B. The dependency of Group B on Group A's resources strengthens the power position of Group A within the intergroup relationship.

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Answer:

14.40 dollars

Step-by-step explanation:

72 divided in 5

Using vertical angles, Maggie made her mistake when combining the like terms of x, which has a result of -3x and not 3x, hence the correct result is of x = 9.

Vertical angles are two angles that are opposite by the same vertex when two lines cross each other, and they are congruent, that is, they have the same measure.

For this problem, the vertical angles are given as follows:

Since they are congruent, we can solve for the variable x as follows:

4x + 2 = 7x - 25.

Moving all the terms with x to the left side of the equality and all the constant terms to the right side, with opposite signal, we have that:

4x - 7x = -25 - 2

Combining the like terms, it is found that:

-3x = -27.

Here happened Maggie's mistake, as 4x - 7x = -3x, hence the correct solution is given by:

3x = 27

x = 27/3

x = 9.

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Answer: Alan would have to sell exactly 180 boxes.

Step-by-step explanation:

Answer:

3 x 3 x 3 x 3 x 3

3x3x3x3x3

=243

UwU your welcome

its the first one or A

Answer:

The answer to that is the first one :)

Differences with in number of volunteers can explain  60.01% of the variation in the amount of trash bags collected.

The coefficient of correlation (r) between both the number of volunteers x and also the number of trash bags collected y is 0.775.

To calculate the percentage of variation for one derivative contract by the other, simply square the correlation coefficient.

Here, r = 0.775

Squaring both side.

r² = 0.775²

r² = 0.600625

Simply multiply with 100 to get the percent.

r² = 60.0625

r² = 60.01

Thus, differences in the number of volunteers can explain 60.01% of the variation in the number of trash bags collected.

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Answer:

b

Step-by-step explanation:

Answer: -3/2

Good luck

(a) The probability that a randomly selected woman's height is less than 64 inches is approximately 55.76%.
(b) The probability that the mean height of 48 randomly selected women is less than 64 inches is approximately 61.03%.


(a) To find the probability for a single woman's height, we standardize the value using the z-score formula. The resulting z-value is 0.148, which corresponds to a cumulative probability of approximately 0.5576 or 55.76%.

This means there is a 55.76% chance that a randomly selected woman's height will be less than 64 inches.

(b) The Central Limit Theorem allows us to approximate the distribution of the sample mean as normal when the sample size is large. By calculating the z-value for the sample mean using the formula, we find a z-value of 0.282. This corresponds to a probability of approximately 0.6103 or 61.03%.

Hence, there is a 61.03% chance that the mean height of 48 randomly selected women will be less than 64 inches.

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There are 32,760 ways in which the teams can finish first, second, third, and fourth in the league.

To determine the number of ways the teams can finish first, second, third, and fourth in a league with 15 teams, we can use the concept of permutations.

For the first position, any of the 15 teams can finish first.

For the second position, there are 14 teams remaining that can finish second.

For the third position, there are 13 teams remaining that can finish third.

For the fourth position, there are 12 teams remaining that can finish fourth.

To calculate the total number of ways, we multiply the number of choices for each position:

Total number of ways = 15 * 14 * 13 * 12 = 32,760

Therefore, there are 32,760 ways in which the teams can finish first, second, third, and fourth in the league.

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The graph of the function f(x) and g(x) are plotted in coordinate plane of the attached graph.

Intersecting point of f(x) and g(x) in the attached graph is (-1.2 , 2.4).

Function are equal to ,

f(x) = 2x

g(x) = 1/2 x+ 3

To graph the functions f(x) = -2x and g(x) = (1/2)x + 3,

Plot points on a coordinate plane and connect them to create the graph.

Here is how all step by step,

Choose a range of x-values to plot. Let us say use -5 to 5.

Substitute various x-values into the function equations to find the corresponding y-values.

For example, for f(x) = -2x,

choose x = -5, -4, -3, ..., 4, 5, and calculate the corresponding y-values.

Similarly, for g(x) = (1/2)x + 3,

substitute the same range of x-values and calculate the corresponding y-values.

Plot the points (x, y) on the coordinate plane based on the calculated values.

For f(x) = -2x, the points will lie on a straight line with a slope of -2.

For g(x) = (1/2)x + 3, the points will also lie on a straight line with a slope of 1/2.

Connect the plotted points for each function with a straight line to create the graph.

Here's a table with some example points for both functions,

x     f(x) = -2x      g(x) = (1/2)x + 3

-5     10              0.5

-4      8                1

-3      6              1.5

-2      4              2

-1      2               2.5

0      0               3

1     -2              3.5

2     -4              4

3      -6              4.5

4     -8              5

5     -10             5.5

Now, plot these points on the coordinate plane and connect them to create the graph of each function.

The graph of f(x) = -2x will be a straight line sloping downward,

and the graph of g(x) = (1/2)x + 3 will be a straight line sloping upward.

Graph is attached.

Intersecting point of f(x) and g(x) is (-1.2 , 2.4).

Therefore, the graph of the given function is attached and its intersecting point is (-1.2 , 2.4).

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Answer:

Step-by-step explanation:

Answer:

x÷2=56

or, X=56×2

or, X= 112

a) Expected number of cars in the facility:

λ=4 cars/hour

µ=1/12=0.0833 hour/car

Utilization factor: ρ=λ/µ=4/0.0833=48

The expected number of cars in the facility is

E[N]=ρ/(1-ρ)=48/(1+48)=0.98 cars

b) Percentage of time the facility is idle:

A = λ/µ

A=4/(1/12)

A=48 hour

A = λ/µ/(λ/µ+1)

A= 48/49

A = 0.9796

Percentage of time the facility is idle:

1 - A = 1 - 0.9796

1 - A = 0.0204 or 2.04%

c) Probability that there are five cars in the facility: Five cars in the facility means 4 cars are getting tested (one is getting service

d).The probability that there are five cars in the facility:

\($P_{5}=\rho^{4} \cdot \frac{\rho}{1-\rho}\)

\(P5=48^{4} \cdot \frac{48}{1+48} \approx 0.149$\)

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a) The bird would fly approximately 4.17 km in a straight line from the starting point to the final point. b) The bird would fly at an angle of approximately 47.46 degrees counterclockwise from the east.

To find the distance and angle that a bird would fly in a straight line from the starting point to the final point, we can use the concept of vector addition.

(a) Distance:

The person's total displacement can be represented as a vector sum of their individual movements: 2.8 km north + 2.9 km west - 5.8 km south.

To simplify this, we can break it down into horizontal (x-axis) and vertical (y-axis) components:

Horizontal displacement = -2.9 km (west)

Vertical displacement = 2.8 km (north) - 5.8 km (south) = -3 km (south)

Now, we can calculate the straight-line distance using the Pythagorean theorem:

Distance = √(Horizontal displacement² + Vertical displacement²)

= √((-2.9 km)² + (-3 km)²)

= √(8.41 km² + 9 km²)

= √(17.41 km²)

≈ 4.17 km

Therefore, the bird would fly approximately 4.17 km in a straight line from the starting point to the final point.

(b) Angle:

To determine the angle counterclockwise from the east, we can use trigonometry. The angle can be found using the inverse tangent function:

Angle = arctan(Vertical displacement / Horizontal displacement)

= arctan((-3 km) / (-2.9 km))

= arctan(1.034)

≈ 47.46 degrees

Therefore, the bird would fly at an angle of approximately 47.46 degrees counterclockwise from the east.

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Answer:

B

Step-by-step explanation:

the supplement is the angle that will add to the other angle to get 180 degrees. 180-129=51 which is B.

The z-scores that bound the middle 82% of the area under the standard normal curve are -1.34 and 1.34, entered in ascending order.

Given :The middle 82% of the area under the standard normal curve. Ascending order. Round the answers to two decimal places. So, we can solve this by using Excel. We know that the middle 82% of the area is the region between the z-scores whose cumulative probabilities are 9%2 = 91% on either side. Using the formula =NORM.INV(probability) for the inverse cumulative distribution function of the standard normal distribution, we can find the corresponding z-scores. The z-score at the 9th percentile is =NORM.INV(0.09) = -1.34 (rounded to two decimal places)The z-score at the 91st percentile is =NORM.INV(0.91) = 1.34 (rounded to two decimal places)

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An ordinal scale provides more information than a nominal scale since values linked with an ordinal variable will be in natural order, whereas values connected with the nominal variable won't.

Ordinal variables as well as nominal variables are the two categories of variables listed here. This sort of variable cannot be submitted to the same forms of statistical tests as interval and ratio variables, hence it is crucial to be able to recognize them accurately. Both of these variables fall within the qualitative category. This contrasts with interval as well as rate variables, both of which are categorized as quantitative.

An illustration of an ordinal variable is a Likert scale with words for mood (such as joyful, neutral, or sad). An illustration of a nominal variable is the names of cities in the Canadian province of Alberta.

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Answer:

1st side= 4m

2nd side= 8m

3rd side= 12m

Step-by-step explanation:

Let the first, second and third side of the triangle be a, b and c meters respectively.

a= b -4 -----(1)

c= 3a -----(2)

Perimeter of triangle

= a +b +c

= 24

a +b +c= 24 -----(3)

From (1): b= a +4 -----(4)

Subst. (2) and (4) into (3):

a +(a +4) +3a= 24

3a +a +a +4= 24

5a +4= 24

5a= 24 -4

5a= 20

Divide both sides by 5:

a= 20 ÷5

a= 4

Substitute a= 4 into (4):

b= 4 +4

b= 8

Substitute a= 4 into (2):

c= 3(4)

c= 12

Thus, the lengths of the first, second, and third side of the triangle are 4m, 8m and 12m respectively.

The concept of statistical significance is mathematically defined and widely accepted by those who use it to assess the usefulness of scientific claims.

However, there is no single definition for practical significance. It is subjective in nature, experiential, and each person decides what it is based on their own experiences.

Thus, it is clear that while Practical significance lacks a common definition, statistical significance has a mathematical definition and is widely accepted by those who use it to assess the usefulness of scientific claims. It is a subjective concept that each person decides for themselves based on their personal experiences.

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The graph of the inequality expression where the inequality expression is given as y ≤ 3/4x − 4 is (d)

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

The inequality expression is given as

y ≤ 3/4x − 4

The inequality symbol in the above inequality expression is

≤

This implies that the inequality expression is a less than or equal to

When an inequality expression has a sign of equal to, then the line of the inequality graph will be a solid line

Also, the inequality symbol implies that the bottom part is shaded

Hence, the graph of the inequality expression where the inequality expression is given as y ≤ 3/4x − 4 is (d)

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Answer:

a) i The company should buy 40 gallons from dairy I and 60 gallons from dairy

ii) What is the maximum amount of​ butterfat? The total amount of butterfat from Diary I and Diary II = 3.12% + 1.93%

=5.05%

b.The excess capacity of dairy I is 10 ​gallons, and for dairy II it is 30 gallons.

Step-by-step explanation:

a. How much milk from each supplier should the company buy to get at most 100 gallons of milk with the maximum amount of​ butterfat?

From the question, we are told that:

Milk from dairy I costs ​$2.40 per​ gallon, Milk from dairy II costs ​$0.80 per gallon.

Let's represent:

Number of gallons of Milk from dairy I = x

Number of gallons of Milk from dairy II = y

At most ​$144 is available for purchasing milk.

$2.40 × x + $0.80 × y = 144

2.40x + 0.80y = 144........ Equation 1

x + y = 100....... Equation 2

x = 100 - y

2.40(100 - y) + 0.80y = 144

240 - 2.4y + 0.80y = 144

-1.60y = 144 - 240

-1.6y = -96

y = -96/-1.6

y = 60

From Equation 2

x + y = 100....... Equation 2

x + 60 = 100

x = 100 - 60

x = 40

Therefore, since number of gallons of Milk from dairy I = x and number of gallons of Milk from dairy II = y

The company should buy 40 gallons from dairy I and 60 gallons from dairy

II. What is the maximum amount of​ butterfat?

From the question

Dairy I can supply at most 50 gallons averaging 3.9​% ​butterfat,

50 gallons = 3.9% butterfat

40 gallons =

Cross Multiply

= 40 × 3.9/50

= 3.12%

Dairy II can supply at most 90 gallons averaging 2.9​% butterfat.

90 gallons of milk = 2.9% butter fat

60 gallons of milk =

Cross Multiply

= 60 × 2.9%/90

=1.9333333333%

≈ 1.93%

The total amount of butterfat from Diary I and Diary II = 3.12% + 1.93%

=5.05%

b. The solution from part a leaves both dairy I and dairy II with excess capacity. Calculate the amount of additional milk each dairy could produce.

Excess capacity of Diary I =

50 gallons - 40 gallons = 10 gallons

Excess capacity of Diary II =

90 gallons - 60 gallons = 30 gallons

Therefore, the excess capacity of dairy I is 10 ​gallons, and for dairy II it is 30 gallons.