standard position intersects the unit circle at (√30/7,-√19/7). What is cot(θ)?

The production schedule for maximum profit is; X = 3 and Y = 6 with a maximum profit of $960

We are told that  two products X and Y, has a total production capacity of 9 tones per day, X and Y requiring the same production capacity

The firm has a permanent contract to supply at least 2 tones of X and at least 3 tones of Y per day to another company.

Let product A be x and product B be y. Therefore we have the following inequalities and constraints as;

x + y ≤ 9

x ≥ 2

y ≥ 3

Now, we are told that each tonne of A requires 20 machine hours of production time and each tonne of B requires 50 machine hours of production time. The daily maximum possible number of machine hours is 360. Thus, we have;

20x + 50y ≤ 360

Wea re told that all the firm's output can be sold and the profit made is $80 per tonne of A and $120 per tonne of B. Thus, we have the inequality as;

Z = 80x + 120y  maximize

The solution from the graph attached is;

x = 3, y = 6

Thus, the maximum profit is;

Z = 80(3) + 120(6)

Z = 960

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Answer:

I think it is 5/12 but might be wrong

Step-by-step explanation:

Subtracted 1/3 from 3/4

Approximately 0.0228 or 2.28% of your yard has more than 5 inches of snow.

Approximately 0.9759 or 97.59% of your yard has between 4 and 5.25 inches of snow.

A Z-score is defined as the fractional representation of data point to the mean using standard deviations.

z-score = (X-ц )/σ

Standardize the value of 5 using the given mean and standard deviation:

Z = (5 - 4.5) / 0.25 = 2

Using a standard normal distribution table or a calculator, we can find the area to the right of Z = 2.

The area to the left of Z = 2 is 0.9772. Therefore, the area to the right of Z = 2 is:

1 - 0.9772 = 0.0228

This means that approximately 0.0228 or 2.28% of your yard has more than 5 inches of snow.

Standardized the values of 4 and 5.25 using the given mean and standard deviation:

Z_4 = (4 - 4.5) / 0.25 = -2

Z_5.25 = (5.25 - 4.5) / 0.25 = 3

Using a standard normal distribution table, we can find that the area to the left of Z = -2 is 0.0228 and the area to the left of Z = 3 is 0.9987. Therefore, the area between Z = -2 and Z = 3 is:

0.9987 - 0.0228 = 0.9759

This means that approximately 0.9759 or 97.59% of your yard has between 4 and 5.25 inches of snow.

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A) The type of triangles are congruent triangles

B) By the use of SAS Congruency Postulate

C) The distance across for the sink hole is: 52.2 ft

D) The perimeter of triangle ABC is: 172.2 feet.

A) Congruent triangles are defined as the triangles created because of the phrasing "you recreate the same triangle" mentioned in the instructions. Congruent triangles are basically identical carbon copies of each other.

B) If we knew the measure of angle ACB, and then mad use of it to form angle ECD, then we would have enough information to know that triangle ACB was congruent to triangle ECD. Therefore, it would be useful to do the SAS (side angle side) congruence rule.

C) We know that:

AB = ED = 52.2

AB is the distance across the sink hole. Thus, it is 52.2 feet

D) AB = 52.2

BC = 70

AC = 50

Thus:

Perimeter of triangle ABC = AB + BC + AC

Perimeter of triangle ABC = 52.2 + 70 + 50

Perimeter of triangle ABC = 122.2 + 50

Perimeter of triangle ABC = 172.2

The perimeter of triangle ABC is 172.2 feet.

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Answer:

Step-by-step expA) The type of triangles are congruent triangles

B) By the use of SAS Congruency Postulate

C) The distance across for the sink hole is: 52.2 ft

D) The perimeter of triangle ABC is: 172.2 feet.

How to solve congruent triangles?

A) Congruent triangles are defined as the triangles created because of the phrasing "you recreate the same triangle" mentioned in the instructions. Congruent triangles are basically identical carbon copies of each other.

B) If we knew the measure of angle ACB, and then mad use of it to form angle ECD, then we would have enough information to know that triangle ACB was congruent to triangle ECD. Therefore, it would be useful to do the SAS (side angle side) congruence rule.

C) We know that:

AB = ED = 52.2

AB is the distance across the sink hole. Thus, it is 52.2 feet

D) AB = 52.2

BC = 70

AC = 50

Thus:

Perimeter of triangle ABC = AB + BC + AC

Perimeter of triangle ABC = 52.2 + 70 + 50

Perimeter of triangle ABC = 122.2 + 50

Perimeter of triangle ABC = 172.2

The perimeter of triangle ABC is 172.2 feet.

lanation:

Twenty standard cartons of octal boxes weigh a total of 1,100 pounds. The weight per carton is 55 pounds.

Given that twenty standard cartons of octal boxes weigh a total of 1,100 pounds. We need to find the weight per carton.

How to find the weight per carton? To find the weight per carton, we need to divide the total weight of twenty standard cartons of octal boxes by 20.Let's assume the weight of each carton be x.

Therefore, the equation can be formed asx * 20 = 1,100 Solving the above equation for x, x = 1,100/20 Therefore, the weight per carton is 55 pounds. So, twenty standard cartons of octal boxes weigh a total of 1,100 pounds.

The weight per carton is 55 pounds.

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Answer:

The least three-digit number which leaves a remainder of 1 when divided by 5 or 6 is 101.

Step-by-step explanation:

This is because 101 is the smallest three-digit number which is not a multiple of either 5 or 6. To see that 101 is the smallest such number, you can check that 100 and 99 are both multiples of both 5 and 6, and 98 is a multiple of 6.

Answer:

7 and 16

Step-by-step explanation:

let the 2 numbers be x and y , then

y = x + 9 → (1)

2(x + y) = 46 ( divide both sides by 2 )

x + y = 23 → (2)

substitute y = x + 9 into (2)

x + x + 9 = 23

2x + 9 = 23 ( subtract 9 from both sides )

2x = 14 ( divide both sides by 2 )

x = 7

and y = x + 9 = 7 + 9 = 16

The 2 numbers are 7 and 16

A common denominator is a shared multiple of the denominators of the fractions involved when adding or subtracting fractions. It enables fraction comparison and addition/subtraction.

Simplification is the process of reducing a fraction to its simplest form by dividing the numerator and denominator by their greatest common divisor. This is done to represent fractions in the simplest terms viable.

Conversion: The process of transferring a fraction from one form to another while retaining its equal value is known as conversion. Finding a common denominator or expressing a fraction in terms of a specified unit or fraction may be required.

Fraction Addition/Subtraction: When adding or subtracting fractions, a common denominator is required. This entails determining a common multiple of

To rewrite the expression 3 + 1/5 + 2/3 using fifteenths as the common denominator, we need to find a common denominator for 5 and 3, which is 15 (since 5 and 3 are both factors of 15).

First, let's convert the fractions 1/5 and 2/3 to fifteenths:

\((\frac{1}{5})(\frac{3}{3}) = \frac{3}{15}\)

\((\frac{2}{3})(\frac{5}{5}) = \frac{10}{15}\)

Now we can rewrite the expression using the common denominator:

\(3 + \frac{3}{15}+\frac{10}{15}\)

The calculated output value for an input value of 5 is (c) 10

From the question, we have the following parameters that can be used in our computation:

Kerrin is making an input-output table for the rule "add 5."

This means that

Output = input + 5

In this case, we have

input = 5

substitute the known values in the above equation, so, we have the following representation

Output = 5 + 5

Evaluate

Output =10

Hence, the output is 10

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Answer: C) Closed circle at -5; shading to the left

The given inequality \(3x \le -15\) solves to \(x \le -5\) when we divide both sides by 3. The inequality sign does not change because we didn't divide both sides by a negative number.

The graph has a closed circle at -5 to include this value as part of the solution set. Shading is to the left to indicate values smaller than -5. Overall, the graph says "x can be -5 or smaller". If you wanted to exclude -5, you would say \(x < -5\) and use an open circle; but that's not the case here.

Answer:

C) Closed circle at -5; shading to the left

Step-by-step explanation:

Answer:

5259544316

Step-by-step explanation:

Given that:

Length of string = 7

Either begins with 2 consonants or ends with 2 vowels :

Either or :

A U B = A + B - (AnB)

Number of vowels in alphabet = 5

Number of consonants = 21

2 consonants at beginning :

First 2 consonants, then the rest could be any:

21 * 21 * 26 * 26 * 26 * 26 * 26 = 5239686816

3 vowels at the end :

First 4 letters could be any alphabet ; last 3 should be vowels.:

26 * 26 * 26 * 26 * 5 * 5 * 5 = 57122000

2 consonants at beginning and 3 vowels at the end :

21 * 21 * 26 *26 *5* 5 * 5 = 37264500

Hence,

2 consonants at beginning + 3 vowels at end 2 consonants at beginning - 2 consonants at beginning and 3 vowels At end

(5239686816 + 57122000) - 37264500

= 5259544316

Hence, number of 7 alphabet strings that begins with 2 consonants and end with 3 vowels = 5259544316

Answer:

-77.625

Step-by-step explanation:

Convert 6 3/4 into a mixed number with decimal fraction:  6.75.

Then multiply this 6.75 by (-11.5).  Using a calculator, we get:

-77.625

The relationship of congruency that describes that the given triangles are congruent is SAS.

We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.

Given, are two triangles with an included angle of 76° and the corresponding sides are congruent to each other.

∴ The relationship that shows that the triangles below are congruent are

side angle side or SAS.

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Reasons

Answer:

3.7142

Step-by-step explanation:

Answer:

3 remainder 15

Step-by-step explanation:

your welcome

Answer:

7.008, 7.090, 7.180

Step-by-step explanation:

Out of the 400 surveyed students, 327 were either seniors or commuters.

To find the number of students who were either seniors or commuters out of the 400 surveyed students, we need to add the number of seniors and the number of commuters while avoiding double-counting those who fall into both categories.

According to the information given:

There were 262 seniors.

There were 215 commuters.

150 of the seniors were also commuters.

To avoid double-counting, we need to subtract the number of seniors who were also commuters from the total count of seniors and commuters.

Seniors or commuters = Total seniors + Total commuters - Seniors who are also commuters

= 262 + 215 - 150

= 327

Therefore, out of the 400 surveyed students, 327 were either seniors or commuters.

It's important to note that in this calculation, we accounted for the overlap between seniors and commuters (150 students who were both seniors and commuters) to avoid counting them twice.

This ensures an accurate count of the students who fall into either category.

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Applying the sine rule the value of side w is calculated to be 6.2

The size of w is calculated using the sine rule which states that the ratio of a side and the opposite angles are equal

the formula is

Sin A / a = Sin B / b = Sin C / c

applying the formula for the problem

Sine W / w = Sine X / x

plugging in the values

Sine 38 / w = Sine 84 / 10

cross multiplying

w = 10 x Sin 38 / Sine 84

x = 6.185

x =  6.2 to the nearest tenth

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Answer:

9/8 or 1 1/8

Step-by-step explanation:

Answer:

9/8 or  1  1/8

Step-by-step explanation:

find common denominator, its 8 for this problem so put \(\frac{1}{2} = \frac{4}{8}\)

\(\frac{5}{8} +\frac{4}{8} = \frac{9}{8}\)

The surface area of the triangular prism would be =324,000cm²

To calculate the surface area of the triangular prism the formula that should be given would be as follows:

Surface area of triangular prism;

Surface area of triangular prism;= bh+(b1+b2+b3)l

where:

base length = 20cm

height = 15cm

length = 18cm

SA = 20×15(20+15+25)×18

= 300×60×18

= 324,000cm²

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The best describes reason the proof is not correct is c. The proof violates the parity property.

The reason the attempted proof of the statement "The difference between any odd integer and any even integer is odd" is not correct is "The proof violates the parity property."

The student incorrectly subtracted an even integer from an odd integer and concluded that the result is odd. However, the difference between an odd integer and an even integer is always odd, which can be proven directly as follows:

Let n be any odd integer and m be any even integer. Then, by definition, n = 2k + 1 and m = 2j for some integers k and j. The difference between n and m is:

n - m = (2k + 1) - 2j

= 2k - 2j + 1

= 2(k - j) + 1

Since k and j are integers, k - j is also an integer. Therefore, the difference between any odd integer and any even integer is of the form 2x + 1, where x is an integer, which is an odd integer.

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Answer:

(A) $8,439.91

Step-by-step explanation:

Just took test

Answer:

3/8

Step-by-step explanation:

Two triangles = one square

Since there are 4 squares, then there are 8 triangles

We see one triangle is shaded.

We also see one square is shaded, which means 2 triangles are shaded.

2 + 1 = 3 triangles shaded. Since there are a total of 8 triangles, then the fraction would be 3/8

Answer:

the length of the pole is 9.90 feet.

Step-by-step explanation:

Answer:

x = 16

Step-by-step explanation:

Opposite sides are equal in a parallelogram

AD = BC

5x - 12 = 3x + 20

5x - 3x = 20 + 12

2x = 32

x = 32/2

x = 16

The lowest common denominator of the fraction is 6

The lowest common denominator (LCD) is the smallest common multiple of the denominators of a set of fractions. It is used to add or subtract fractions with different denominators.

The LCD of a set of fractions is the smallest number that is divisible by all the denominators in the set. When all the denominators are divided into the LCD, each fraction has an equivalent fraction with the same value and a denominator equal to the LCD.

In the fraction given;

x / 3 + x / 2 = 20

The lowest common denominator is 6

Using 6, we can divide through each of the fraction.

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Answer:

7.11\(\leq\)-7.1

Step-by-step explanation:

Answer:

Question 1- C. 7.11 > -7.1

Question 2- True

Question 3- -3 < -1 and -3 ≤ -1

Question 4- I don't know

Question 5- {3,4}

Step-by-step explanation:

I ran it through the calculator only on question 4 I didn't know the answer

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