Write the following equation symbolically.

The sum of h and 5 is equal to 8 less than 6 times y.

Answer:

A = (1/4)√(4 + 11 + 14)√(-4 + 11 + 14)√(4 - 11 + 14)√(4 + 11 - 14)

A = (1/4)√29√21√7

= about 16.32 mm²

Answer:

  16.27 mm²  (see comment)

Step-by-step explanation:

You want the area of a triangle with side lengths 11 mm and 14 mm, and the angle between them 12.2°.

The area is given by the formula ...

  A = 1/2ab·sin(C)

  A = 1/2(11 mm)(14 mm)·sin(12.2°) ≈ 16.27 mm²

The area of the triangle is about 16.27 square millimeters.

__

Additional comment

If you use Heron's formula for the area from the three side lengths, you find it is about 16.32 mm². That's the trouble with over-specified geometrical figures. The result you get depends on which of the given values you use. (To get the area accurate to 4 sf, the angle needs to be specified to 4 sf: 12.24°.)

  s = (4 +11 +14)/2 = 14.5

  A = √(s(s -a)(s -b)(s -c))

  A = √(14.5(14.5 -4)(14.5 -11)(14.5 -14)) = √(14.5·10.5·3.5·0.5) = √266.4375

  A ≈ 16.32

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Answer:

Both of the points are in the same x-axis (which is 4). However, they are different because one of them is shifted 9 units up and the other one is shifted 9 units down (their y-axis are different). Their quadrants are also different since (4,9) is at the first quadrant, while (4,-9) is at the fourth quadrant.

1) If the 10 kg sugar is Rs. 880 . Find the cost of 15 kg sugar.....

Solution,

let the required cost be Rs x

Here , the quantities of sugar and their cost are direct proportion

So, 10 : 15 = 8: x

\( \: \frac{10}{15} = \frac{880}{x} \\ x = \frac{880 \times 15}{10} \\ x = Rs1320\)

Hence , the cost of sugar is Rs.1320

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2) 50 students in a hostel have provisions for 21 days . How long would it last for 75 students?

Solution,

Let the required number of a day = x

Here , the number of student and the number of days are in inverse proportion.

•°• 50 : 75. = x : 21

\( \frac{50}{75} = \frac{x}{21} \\ x = \frac{50 \times 21}{75} \\ x = 14 \: days \\ \)

Hence, the provisions last for 14 days for75 students

~nightmare 5474~

1) The cost of 15 kg sugar is; Rs. 1320

2) The number of days that it would take the provisions to last for 75 students is; 14 days

1) Cost of 10 kg = Rs. 880

Thus, by proportion the cost of 15 kg sugar will be;

(15 × 880)/10

>> 13200/10

>> Rs. 1320

2) We are told that;

50 students = provisions for 21 days

Thus for 75 students the number of days the provisions would last them is gotten by proportion;

(50 × 21)/75

>> 1050/75

>> 14 days

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Answer: -4/3 or - 1 1/3

Step-by-step explanation: 2 times -2 = -4 and 3 times 1 is 3.

Answer:

Step-by-step explanation:

To show that the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\), we can simplify both sides of the equation using the properties of logarithms. Here are the steps:

Step 1: Simplify the expression on the left side:

\(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\)

Step 2: Apply the logarithmic property \(\ln(a) - \ln(b) = \ln\left(\frac{a}{b}\right)\) to combine the logarithms:

\(\ln\left(\frac{\sqrt{2} + 1}{\frac{1}{\sqrt{2}}}\right)\)

Step 3: Simplify the expression within the logarithm:

\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)}\right)\)

Step 4: Simplify the denominator by multiplying by the reciprocal:

\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)} \cdot \sqrt{2}\right)\)

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{\left(\frac{1}{\sqrt{2}}\right) \cdot \sqrt{2}}\right)\)

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)

Step 5: Simplify the numerator:

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)

\(\ln\left(\sqrt{2}(\sqrt{2} + 1)\right)\)

\(\ln\left(2 + \sqrt{2}\right)\)

Now, let's simplify the right side of the equation:

Step 1: Simplify the expression on the right side:

\(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\)

Step 2: Simplify the expression within the logarithm:

\(-\ln\left(\frac{\sqrt{2} - 1}{\sqrt{2}}\right)\)

Step 3: Apply the logarithmic property \(\ln\left(\frac{a}{b}\right) = -\ln\left(\frac{b}{a}\right)\) to switch the numerator and denominator:

\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)

Step 4: Simplify the expression:

\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)

\(-\ln\left(\frac{\sqrt{2}(\sqrt{2} + 1)}{1}\right)\)

\(-\ln\left(2 + \sqrt{2}\right)\)

As we can see, the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) simplifies to \(\ln(2 + \sqrt{2})\), which is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\).

The value of x in the lines is 126 degree

We are given that;

Three parallel line and one intersecting line

Angles= (x-6) and 60

Now,

By supplementary angles property

Angle 1 + Angle 2 = 180 degree

Substituting the values of angles

x-6 + 60 = 180

x + 54 = 180

x = 180-54

x = 126

Therefore by supplementary angles answer will be 126 degree.

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Answer:

Equidistant

Step-by-step explanation:

When we have a point lying on the angle bisector, it stands at an equal distance from the two sides of the angle

The purpose of the angle bisector is to divide the angle into two different equal parts

So, for a point to lie on this, it means it of the same distance from the two points of the angle

Answer:

5.84$

Step-by-step explanation:

dividing 17.52$ by 3 will get you 5.84 inverted 5.84$+5.84$+5.84$=17.52$

The test Statistic and the corresponding p- value,  the p- value to our significance  position to make a decision,the p- value is  lower than 0.05, we fail to reject the null  thesis.    

 The  mean sodium content for a single serving of a certain cereal is lesser than the  mortal  demand for  swab, which is 220 milligrams per day. A salutary study has shown that high sodium input may be related to ulcers, stomach cancer, and migraine headaches, making it important to cover sodium input.   Using a  arbitrary sample of 20  analogous servings of the cereal, with a mean sodium content of 244 milligrams and a standard  divagation of24.5 milligrams, we can conduct a  thesis test to determine if the average sodium content is significantly lesser than 220 milligrams.   Assuming the distribution of sodium contents to be normal, we can use a one- sample t- test with a significance  position of0.05. Our null  thesis is that the mean sodium content is equal to 220 milligrams, while our indispensable  thesis is that it's lesser than 220 milligrams.   We reject the null  thesis and conclude that the average sodium content for a single serving of  similar cereal is significantly lesser than 220 milligrams.

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Answer: RTGVTFGVTTGSGT

Step-by-step explanation:

With the help of the quotient, we know that the time the water balloon dropped from the rooftop is 1.3sec.

So, h(t) = 24:

Then, calculate as follows:

Therefore, with the help of the quotient, we know that the time the water balloon dropped from the rooftop is 1.3sec.

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Answer:

this is the answer.

Step-by-step explanation:

Find the Equation of a Line Given That You Know Its Slope and Y-Intercept. The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept.

the value of x is  16.97

Given that:

The right angled triangle has hypotenuse of 18 units

Its one other side measures 6 units.

The length of unknown side is denoted by length x units.

To find:

Value of x

The Pythagoras theorem states that:

"In a right angled triangle, the square of length of its hypotenuse is equal to sum of square of other two sides' lengths"

Using Pythagoras theorem for given right triangle we have:

Thus, for given right triangle, the value of x is given as:

18²=\(x^{2} +\)6²

324=\(x^{2}\)+36

\(x^{2}\)=324-36

\(x^{2}\)=288

\(x\)=√288

\(x\)=16.97

the value of x is  16.97

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41 clients can be checked out in an hour on a lane with a checker and a bagger. Only 25 people can be checked out per hour at a checker-only line.

a. The Good'n'Fresh Grocery Store's total production and average labor productivity are 92 customers per hour and 23.5 customers per hour per worker, respectively.

b. Two lanes with a checker and a bagger, and one lane with a checker only, are the ideal configurations for reassigning the workers to duties.

a. The total output of the Good’n’Fresh Grocery Store is:

Total output = 2 lanes x 46 customers/lane/hour + 2 lanes x 25 customers/lane/hour

             = 92 customers/hour

The average labor productivity is:

Average productivity = Total output / Total number of workers

                    = 92 customers/hour / 4 workers

                    = 23 customers/hour/worker

                    ≈ 23.0 customers/hour/worker                    

Therefore, the total output is 92 customers per hour, and the average labor productivity is 23.0 customers per hour, per worker.

b. With three lanes, the best way to reallocate the workers to tasks is to have:

Two lanes with a checker and a bagger, and one lane with a checker only.

This way, each lane will have one checker and one bagger, which is the most efficient way to operate a lane. The total output will be:

Total output = 3 lanes x 46 customers/lane/hour

            = 138 customers/hour

The average labour productivity is:

Average productivity = Total output / Total number of workers

                    = 138 customers/hour / 4 workers

                    = 34.5 customers/hour/worker

                    ≈ 34.5 customers/hour/worker                    

Therefore, the total output is 138 customers per hour, and the average labour productivity is 34.5 customers per hour, per worker.

c. With four lanes, the best way to reallocate the workers to tasks is to have:

Two lanes with a checker and a bagger, and two lanes with a checker only.

This way, each lane will have either one checker and one bagger or one checker only, which is the most efficient way to operate a lane. The total output will be:

Total output = 4 lanes x 46 customers/lane/hour

            = 184 customers/hour

The average labour productivity is:

Average productivity = Total output / Total number of workers

                    = 184 customers/hour / 4 workers

                    = 46 customers/hour/worker

                    ≈ 46.0 customers/hour/worker                    

Therefore, the total output is 184 customers per hour, and the average labour productivity is 46.0 customers per hour, per worker.

d. With five lanes, the best way to reallocate the workers to tasks is to have:

Two lanes with a checker and a bagger, and three lanes with a checker only.

This way, each lane will have either one checker and one bagger or one checker only, which is the most efficient way to operate a lane. The total output will be:

Total output = 5 lanes x 46 customers/lane/hour

            = 230 customers/hour

The average labour productivity is:

Average productivity = Total output / Total number of workers

                    = 230 customers/hour / 4 workers

                    = 57.5 customers/hour/worker

                    ≈ 57.5 customers/hour/worker                    

Therefore, the total output is 230 customers per hour, and the average labour productivity is 57.5 customers per hour, per worker.

e. Yes, we observe diminishing returns to capital in this example because adding more lanes does not increase output proportionally. Adding a third lane increases output by 46 customers/hour, adding a fourth lane increases output by 46 customers/hour, and adding a fifth lane increases output by 46 customers/hour. Therefore, the marginal output of adding each additional lane is decreasing. The correct multiple-choice answer is:

Certainly, adding a fifth lane won't boost productivity.

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The length of the light strand is 28.72 feet.

Simply put, trigonometric functions—also called circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.

Given A holiday tree is formed by extending single strands of lights,

height of pole = 22 feet

angle made by strands of light = 5π/18

it forms a right angle with the ground,

with  the sine function, we can calculate the length of the strand,

here height of the pole is perpendicular and strands form a hypotenuse,

sinФ = perpendicular/hypotenuse

Ф = 5π/18

sin(5π/18) = 0.766

sin(5π/18) = 22/hypotenuse

hypotenuse = 22/0.766

hypotenuse = 28.72 feet

Hence the length is 28.72 feet.

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Answer:

Step-by-step explanation:

ΔABC transformed by 5/2 to A'B'C':

A' = -10, 15

B' = -15, 10

C' = 5, -5

Answer:

attached below

Step-by-step explanation:

minus 2 from each side in order to isolate T with the coefficient. To get rid of the coefficient multiply to get 1 which is 5 in this case. Then the answer will be 75

Answer:

12 girls

Step-by-step explanation:

30*(2/5)=12

Answer:

x ≥ 3

Step-by-step explanation:

- 3(2x - 1) ≤ x - 18 ← distribute parenthesis on left side

- 6x + 3 ≤ x - 18 ( subtract x from both sides )

- 7x + 3 ≤ - 18 ( subtract 3 from both sides )

- 7x ≤ - 21

divide both sides by - 7, reversing the symbol as a result of dividing by a negative quantity.

x ≥ 3

Answer:

F(-x) = 0

Step-by-step explanation:

What is F(-x)?

F(-x) = F(-1)

F(x) = x³ + 1                              F(-1)

F(-1) = -1³ + 1

F(-1) = -1 + 1

F(-1) = 0

So, F(-x) = 0

Answer:

f(-1) = 0

Step-by-step explanation:

Evaluating a function for f(-x) is the same as evaluating it for f(-1).

So we plug in -1 instead.

f(-1) = x³ + 1  

      = (-1)³ + 1 (here we cube -1)

      = -1 + 1     (here we subtract)

      = 0           (and, this is the answer)

\(\therefore\) The answer is f(-1) = 0

\(\\ \bull\sf\dashrightarrow Radius=\dfrac{Diameter}{2}\)

Now

\(\\ \bull\sf\dashrightarrow Radius_1=\dfrac{7.8}{2}=3.9\)

\(\\ \bull\sf\dashrightarrow Radius_2=\dfrac{8.4}{2}=4.2\)

The length of each side of the square is 16 cm, the perimeter is 64 cm, and the area is 256 cm^2.

Let's solve the problem step by step. We have a square ABCD, and we need to find the length of its sides when the diagonal is 16√2 cm long.

In a square, the diagonal forms a right triangle with the sides. The sides of a square are equal in length, so let's assume the length of one side of the square is 'x' cm.

Using the Pythagorean theorem, we can find the relationship between the side length and the diagonal:

x^2 + x^2 = (16√2)^2

2x^2 = 512

Dividing both sides by 2, we have:

x^2 = 256

Taking the square root of both sides:

x = √256

x = 16 cm

So, the length of each side of the square is 16 cm.

To find the perimeter of the square, we simply multiply the length of one side by 4 since all sides are equal:

Perimeter = 4 * 16 cm = 64 cm

To find the area of the square, we square the length of one side:

Area = (16 cm)^2 = 256 cm^2

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Note the complete question is:

Find the length of side of square ABCD when diagonal is 16√2 cm long. Also find the perimeter and area of the square?

If 750 people go to this store each day, 75 people would be sampled and 60 people would be expected to use a coupon

Probability is the likelihood of occurrance of an event. It is given by:

Probability = number of occurrence / total number of possible occurence

A cashier samples the transaction of every 10th person who goes though the line at a craft store out of 40 people, 32 used a coupon.

Probability of using coupon = 32/40 = 0.8

Hence if 750 people go to this store each day, number of people sampled = 75.

Number of people expected to use the coupon = 75 * 0.8 = 60

If 750 people go to this store each day, 75 people would be sampled and 60 people would be expected to use a coupon

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Answer:

Domain: The set of 0

Range: The set of 16

Step-by-step explanation:

A real-world example of a relation that is a function is

Domain: The set of voters.

Range: The set of candidates.

during an election.

A function is a relationship from a set of inputs called domain to a set of outputs called range, such that not more than one value is assigned to an input.

For the given example we understand that each state has two senators hence the relation is not a function.

A real-world example of a relation that is a function is

Domain: The set of voters.

Range: The set of candidates.

during an election.

This is a function because one voter can vote for only one candidate.

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Answer:

Step-by-step explanation:it cant be A or B because its not negative so it has to be C or D and its not D because its not in the 3s its in the ones still it did not evean have a 3.

so the best answer i whould have to say C

plz give brainlynis

Answer:

This is the correction of the other person who answered the answer is D

Step-by-step explanation:

Answer: d

Step-by-step explanation: