what must be true and what letter is the answer?

Answer:

x=4

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

-6 + x/4 = -5

-6+6 + x/4 = -5+6

x/4 = 1

x/4 *4 = 1*4

x = 4

hope this helped :)

The total number of seats in this theater is \(1776\) due to the biggest theater having 33 rows.

A series is referred to in broad terms in a particular way. The succeeding terms are calculated by increasing or decreasing the preceding term's value. Occasionally an expression comes after each phrase in the series.

For instance, there are 7 options for the first seat, 6 for the second (since one has already been taken), five for the third, four for the fourth, and so on. Therefore there are 5040 different ways to set up a row of seven seats with seven persons in it.

First row, \(a = 16\)

Common difference, \(d=2\) additional seats

Number of rows, \(n = 33\)

\(sn=\frac{n}{2}*(2a+(n-1)*d)\)

So, we have

\(S33 = \frac{33}{2} * (2 * 16 + (33 - 1) * 2)\)

\(S33 = \frac{33}{2} * (2 * 16 + 32*2)\)

\(S33=\frac{33}{2}*(32+64)\)

\(S33=16.5*(32+64)\)

\(S33 = 18.5 * 96\)

\(S33 = 1776\)

Hence, the total seats in this​ theater are \(1776\)

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To calculate the volume of a cylindrical storage vessel, we need to use the formula: Volume = π * r^2 * h. where π is approximately 3.14159, r is the radius, and h is the height (or depth) of the cylinder.

Given that the diameter of the cylinder is 4m, the radius (r) is half of the diameter, which is 4m / 2 = 2m. The depth (h) is given as 3.5m.

Now, let's calculate the volume: Volume = 3.14159 * (2m)^2 * 3.5m

Volume ≈ 3.14159 * 4m^2 * 3.5m

Volume ≈ 3.14159 * 16m^2 * 3.5m

Volume ≈ 3.14159 * 56m^3

Volume ≈ 175.9292m^3

Since we want to convert the volume to kilometers, we need to divide by 1,000,000 (1,000 meters in a kilometer). Volume ≈ 175.9292m^3 / 1,000,000.  Volume ≈ 0.0001759292km^3.  Therefore, the cylindrical storage vessel will hold approximately 0.0001759292 cubic kilometers.

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The only statement that must be based on the quadrilateral properties is; Option B: Base angles of quadrilateral Z are congruent

Some of the properties of a quadrilateral are;

1) They have four vertices.

2) They have four sides.

3) The sum of all interior angles is 360°.

4) They have two diagonals.

5) A quadrilateral can be regular or irregular.

Now, from the description of Quadrilaterals T and Z, we can say that;

- The base angles of quadrilateral T are not congruent since at least one pair of parallel side is congruent.

- Base angles of quadrilateral z are congruent since opposite sides are congruent.

- Consecutive angles of quadrilateral Z are not congruent

- Opposite angles of quadrilateral T are not supplementary.

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Answer:

13.2 g

Step-by-step explanation:

let x = grams sugar in a 200 ml glass

16.5 g sugar / 250 ml = x g sugar / 200 ml

x(250) = (16.5)(200)

x =  (16.5)(200) / (250) = 3300 / 250 = 13.2

Answer:  there are 13.2 g sugar in a 200 ml glass of juice

The least three numbers that when added together give a number multiple of 7 are:

2, 3 and 7

Prime numbers are numbers that have only two divisors, but these two divisors are always the same number and the number 1.

If we want to know a number that comes from the sum of three prime numbers and that in turn is divisible by 7, then let's identify the prime numbers from 0 to 20:

2, 3, 5, 7, 11, 13, 17, 19

Let's start with the lowest ones:

The three numbers are: 2, 3 and 7.

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a. To find the present value at t=10, we need to calculate the value of f(t) at t=10. Using the given function f(t) = 500e^(0.04t), we substitute t=10 into the equation:

\(\displaystyle \text{Present value} = f(10) = 500e^{0.04(10)}\)

Simplifying the exponent:

\(\displaystyle \text{Present value} = 500e^{0.4}\)

Evaluating the exponent:

\(\displaystyle \text{Present value} = 500(2.71828^{0.4})\)

Calculating the value inside the parentheses:

\(\displaystyle \text{Present value} = 500(1.49182)\)

Calculating the product:

\(\displaystyle \text{Present value} \approx 745.91\)

Therefore, the present value at t=10 is approximately $745.91.

b. To find the accumulated money flow at t=10, we need to calculate the integral of f(t) from 0 to 10. Using the given function f(t) = 500e^(0.04t), we integrate the function with respect to t:

\(\displaystyle \text{Accumulated money flow} = \int_{0}^{10} 500e^{0.04t} dt\)

Integrating:

\(\displaystyle \text{Accumulated money flow} = 500 \int_{0}^{10} e^{0.04t} dt\)

Using the properties of exponential functions, we can evaluate the integral:

\(\displaystyle \text{Accumulated money flow} = 500 \left[ \frac{{e^{0.04t}}}{{0.04}} \right]_{0}^{10}\)

Simplifying:

\(\displaystyle \text{Accumulated money flow} = 500 \left( \frac{{e^{0.4}}}{{0.04}} - \frac{{e^{0}}}{{0.04}} \right)\)

Calculating the exponential terms:

\(\displaystyle \text{Accumulated money flow} = 500 \left( \frac{{e^{0.4}}}{{0.04}} - \frac{1}{{0.04}} \right)\)

Evaluating the exponential term:

\(\displaystyle \text{Accumulated money flow} = 500 \left( \frac{{1.49182}}{{0.04}} - \frac{1}{{0.04}} \right)\)

Calculating the subtraction:

\(\displaystyle \text{Accumulated money flow} = 500 \left( \frac{{1.49182 - 1}}{{0.04}} \right)\)

Calculating the division:

\(\displaystyle \text{Accumulated money flow} = 500 \times 12.2955\)

Calculating the product:

\(\displaystyle \text{Accumulated money flow} \approx 6147.75\)

Therefore, the accumulated money flow at t=10 is approximately $6147.75.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Part 1

Explanation:

The term "categorical" is the same as "nominal". Either refers to data labels or names, rather than numbers. The three categories are: Left, Right, No preference. We cannot apply math operations to names like this. It makes no sense to average Left vs Right vs No Preference.

==========================================================

Part 2

Explanation:

Recall that the value of mu is calculated like so: \(\mu = \sum xp(x)\)

In other words, we multiply each x value with its corresponding p(x) probability. Then we add up those results to get mu. There's one glaring problem though: we aren't given numeric values for x. So there's no way to compute any of the x*p(x) values. Therefore, we don't have a mu value either. It doesn't make sense to determine what the center is when given labels. We would need x to take on values from the set {0,1,2,3,...} if we wanted to compute a mu value.

==========================================================

Part 3

Explanation:

The value of sigma depends heavily on the value of mu.

One formula for sigma is \(\displaystyle \sigma = \sqrt{p(x_i)*\sum_{i=1}^{n}(x_i-\mu)^2\)

which is often abbreviated to \(\displaystyle \sigma = \sqrt{p(x)*\sum(x-\mu)^2\)

Because we can't find mu, we can't find sigma either.

Also, it makes no sense to determine how spread out categorical labels are. How can we determine the distance from "Left" to "Right"? The x values need to be numeric so we can calculate a numeric standard deviation from it.

Answer:

8x + 80

Step-by-step explanation:

positive side

Answer:

15x^6y^15

Other:

Brainliest? Thanks!

If you save $2,015.82 every year at an interest rate of 8%, you can retire in 30 years and live another 25 years while still having enough money to spend $80,000 per year.

To calculate the amount you need to save per year for the next 30 years, we can use the future value of an ordinary annuity formula.

The future value of an ordinary annuity formula is:

\(FV = P \cdot \left(\frac{(1 + r)^n - 1}{r}\right)\)

Where:

FV = Future value of the annuity

P = Payment amount per period

r = Interest rate per period

n = Number of periods

In this case:

P = Amount you need to save per year

r = 8% = 0.08 (annual interest rate)

n = 30 (number of years)

We want the future value (FV) to be equal to the amount needed to spend per year during retirement, which is $80,000.

Using the formula, we can calculate the amount you need to save per year:

\(\$80,000 = P \cdot \left[\left(1 + 0.08\right)^{30} - 1\right] / 0.08\$\)

Simplifying the equation:

\($80000 = P \cdot [1.08^{30} - 1] / 0.08$\)

$80,000 * 0.08 = P * [1.08³⁰ - 1]

$6,400 = P * [1.08³⁰ - 1]

Dividing both sides by [1.08³⁰ - 1]:

\($P = \dfrac{\$6400}{1.08^{30} - 1}$\)

Calculating [1.08³⁰ - 1]:

[1.08³⁰ - 1] ≈ 3.172024

Dividing $6,400 by 3.172024:

P ≈ \($\frac{6,400}{3.172024} \approx$ $2,015.82\) (rounded to the nearest cent)

Therefore, you need to save approximately $2,015.82 per year into your investment account at the end of each year for the next 30 years.

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Answer:

1.0

Step-by-step explanation:

We should assume that 4x = x+3 according to the task description.

4x = x+3

3x = 3

x = 1

Answer:

1. Cooking

2. Construction

3. On a computer

Step-by-step explanation:

Answer:

Step-by-step explanation:

g = c + x           |subtract c from both sides

g - c = c - c + x

g - c = x → x = g - c

Hello there!

Question:-

\(g = c + x\)

We need to find the value of x.

Solution:-

\(\sf \longmapsto \: g = c + x\)

Note that g , c and x equals to 1g,1c and 1x.

\(\sf \longmapsto \: 1g =1 c +1 x\)

Flip the equation:-

\(\sf \longmapsto \: 1c + 1x = g\)

Add -c to both sides:-

\(\sf \longmapsto \: 1c+1x+( - c)=1g+ (- c)\)

On Simplification:-

\(\sf \longmapsto \: 1c - 1c + 1x = 1g - c\)

\(\sf \longmapsto \: 0 + x = 1g - c\)

\(\sf \longmapsto \: x = 1g - c\)

______________________________________

Henceforth the value of x is :-

\(\boxed{\huge\tt x = g - c}\)

_________________________________

Please let me know if you have any questions.

~MisterBrian

Answer: 2 because of the constant proportionality

Step-by-step explanation: hope this helps!

Answer:
Josh's percentage profit would be 52.5%.

Step-by-step explanation:

Total cost:

Josh buys 120 books for £4 each, so the total cost is:

Total cost = 120 books * £4/book = £480

Total revenue:

Josh sells half of the books for £5 each, which means he sells (1/2) * 120 = 60 books at £5 each. So, the revenue from this sale is:

Revenue = 60 books * £5/book = £300

Josh also sells 40% of the books for £7 each, which means he sells 0.4 * 120 = 48 books at £7 each. So, the revenue from this sale is:

Revenue = 48 books * £7/book = £336

The remaining books that Josh sells at £8 each are (1 - 0.5 - 0.4) = 0.1 or 10% of the total books. Therefore, the revenue from this sale is:

Revenue = 10% * 120 books * £8/book = £96

Total revenue = £300 + £336 + £96 = £732

Profit:

Profit = Total revenue - Total cost = £732 - £480 = £252

Percentage profit:

Percentage profit = (Profit / Total cost) * 100%

Percentage profit = (£252 / £480) * 100% ≈ 52.5%

Therefore, Josh's percentage profit is approximately 52.5%.

The probability when the value of W = 1 is 0.1 , probability when the value of W = 10 is 0.2 and probability when the value of W = 25 is 0.7  .

In the question ,

the marked price slips are $1, $1, $1, $10 and $25 .

If the winner selects two slips of paper, then the possible outcomes would be ,

total number of slips is = 5 ,

Total number of cases possible = ⁵C₂ = 10

There would be only 1 case in which the winner will win $1

that means when both the slips selected has $1.

So, P(Winning $1) = 1/10 = 0.1

the number of cases to win $10 is {(1,10) , (10,1)}

So , P(Winning $10) is

= 2/10 = 0.2

So , P(Winning $25) is

= 1 - (0.1 \(+\) 0.2)

= 0.7

Therefore , the required probability P(Winning $1) = 0.1 , P(Winning $10) = 0.2 and P(Winning $25) = 0.7

The given question is incomplete , the complete question is

A box contains five slips of paper, marked $1, $1, $10, $25, and $25. The winner of a contest selects two slips of paper at random and then gets the larger of the dollar amounts on the two slips. Define a random variable w by w = amount awarded. Determine the probability distribution of w. (Hint: Think of the slips as numbered 1, 2, 3, 4, and 5, so that an outcome of the experiment consists of two of these numbers.)

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No, not all square numbers have an odd number of factors. In fact, square numbers can have either an odd or an even number of factors, depending on their prime factorization.

A square number is a number that can be expressed as the product of an integer multiplied by itself. For example, 4 is a square number because it can be written as 2 * 2.

When we analyze the factors of a square number, we find that each factor has a corresponding pair that multiplies to give the square number. For instance, the factors of 4 are 1, 2, and 4. We can see that the pairs are (1, 4) and (2, 2). Thus, 4 has an even number of factors.

However, there are square numbers that have an odd number of factors. Consider the square number 9, which is equal to 3 * 3. The factors of 9 are 1, 3, and 9. In this case, 9 has an odd number of factors.

In conclusion, while some square numbers have an odd number of factors (like 9), others have an even number of factors (like 4). The determining factor is the prime factorization of the square number.

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Answer:

98cm^2

Step-by-step explanation:

The triangle is equilateral and each side is 14cm

area of triangle: h*b/2

The amount of salt in the tank after 10 minutes is 4.5 lbs.

The initial amount of salt in the tank is 100 * 0.05 = 5 lbs.

The amount of salt that leaves the tank each minute is 2 * 0.05 = 0.1 lbs.

The amount of salt that enters the tank each minute is 0 lbs.

Therefore, the net amount of salt in the tank is decreasing by 0.1 lbs per minute.

If we let t be the number of minutes, then the amount of salt in the tank at time t is given by

salt = 5 - 0.1t

To find the amount of salt in the tank after 10 minutes, we can set t = 10 and evaluate the expression. This gives us

salt = 5 - 0.1 * 10 = 4.5 lbs

Therefore, the amount of salt in the tank after 10 minutes is 4.5 lbs.

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Answer:

c. 1/12= 0.0833= 8.33%

Step-by-step explanation:

Answer:

d. 20

Step-by-step explanation:

To answer the question given, we will follow the steps below:

we need to first find p(3)

p(x) = x+ 7/ x-1

we will replace all x by 3 in the equation above

p(3) = 3+7 / 3-1

p(3) = 10/2

p(3) = 5

Similarly to find q(2)

q (x) = x^2 + x - 2,

we will replace x by 2 in the equation above

q (2) = 2^2 + 2 - 2

q (2) = 4 + 0

q (2) = 4

The product of p(3) and q(2)   =   5 × 4   = 20

As a result, if a bicycle covers 50 miles in 25 minutes, their speed is 120 miles per hour.

Speed is defined in physics as the distance covered in a unit of time. What determines the velocity vector's magnitude is a scalar quantity. An item is said to be travelling faster or slower depending on its speed. It has zero speed if it isn't moving at all.

Therefore, a bicycle travelling 50 miles in 25 minutes is moving at a speed of 120 miles per hour.

Miles might mean two different things. As a noun, it refers to a linear measurement unit that is 1,760 yard. It also has the adverbial meanings of greatly or far.

When the distance is 50 miles, the relationship between speed, s, and time, t, can be written as follows:

s = d/t

where d is the distance traveled, and t is the time it takes.

The distance is 50 miles in this instance, and the travel time is 25 minutes, or 25/60 hours.

When we enter these values into the formula above, we obtain:

120 miles per hour is equal to s = 50/(25/60).

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Answer:

Set A) Here are the solutions to the problems:

Jill owes $4 + $4 + $4 = $12 altogether.

Joey owes $4 * 4 = $16 altogether.

The product of -7 and -6 is 42.

Each friend owes $49 / 7 = $7.

-81 divided by 9 is -9.

-100 divided by -10 is 10.

The total amount owed by all 18 customers is 18 * $15 = $270.

The product of -12 and -13 is 156.

-16 times 4 is -64.

The quotient when -45 is divided by -9 is 5.

Set B) Here are the equations and solutions to the problems:

What number is 12 less than 35?

Equation: n = 35-12

Solution: n = 23

What number added to 23 equals 41?

Equation: n + 23 = 41

Solution: n = 18

What number less 29 is 61?

Equation: n - 29 = 61

Solution: n = 90

What number added to 36 equals 53?

Equation: n + 36 = 53

Solution: n = 17

What number added to 19 equals 43?

Equation: n +19 =43

Solution: n =24

What number divided by 4 equals 12?

Equation: n/4 =12

Solution: n=48

What number times 12 equals 96?

Equation: n*12=96

Solution: n=8

What number divided by 8 equals 11?

Equation: n/8=11

Solution: n=88

What number times 19 equals 190?

Equation: n*19=190

Solution: n=10

What number divided into 42 equals 6?

Equation: n/6=42

Solution: n=252

Answer:

Set A):

1. Jill owes $12 altogether ($4 + $4 + $4 = $12).

2. Joey owes $16 altogether ($4 + $4 + $4 + $4 = $16).

3. The product of -7 and -6 is 42.

4. Each friend owes $7 ($49 ÷ 7 = $7).

5. -81 divided by 9 is -9.

6. -100 divided by -10 is 10.

7. The total amount owed by all 18 customers is $270 ($15 × 18 = $270).

8. The product of -12 and -13 is 156.

9. -16 times 4 is -64.

10. The quotient when -45 is divided by -9 is 5.

Set B):

1. Equation: n = 35 - 12

Solution: n = 23

2. Equation: n + 23 = 41

Solution: n = 18

3. Equation: n - 29 = 61

Solution: n = 90

4. Equation: n + 36 = 53

Solution: n = 17

5. Equation: n + 19 = 43

Solution: n = 24

6. Equation: n/4 = 12

Solution: n = 48

7. Equation: n * 12 = 96

Solution: n = 8

8. Equation: n/8 = 11

Solution: n = 88

9. Equation: n * 19 = 190

Solution: n = 10

10. Equation: n/42 = 6

Solution: n = 252

Step-by-step explanation:

We are given the following functions:

We are asked to determine:

This is equivalent to:

Substituting the functions:

Now, we use the following property:

Applying the property we get:

Solving the products:

Simplifying we get:

And thus we get the desired expression.

Now, we are asked to determine:

This is the product of the functions. Substituting we get:

Solving the products:

Since we can't simplify any further this is the final answer.

The maximum profit is achieved when approximately 312.5 units of lab equipment are sold.

The revenue function R(x) represents the amount of money the company earns from selling x units of lab equipment. It is given by the equation:

R(x) = -0.32x^2 + 270x

The costs function C(x) represents the expenses incurred by the company for producing and selling x units of lab equipment. It is given by the equation:

C(x) = 70x + 52

To determine the company's profit, we subtract the costs from the revenue:

Profit = Revenue - Costs

P(x) = R(x) - C(x)

Substituting the given revenue and costs functions:

P(x) = (\(-0.32x^2 + 270x)\) - (70x + 52)

Simplifying the equation:

P(x) = -0.32x^2 + 270x - 70x - 52

P(x) = -\(0.32x^2\)+ 200x - 52

The profit function P(x) represents the amount of money the company makes from selling x units of lab equipment after deducting the costs. It is a quadratic function with a negative coefficient for the x^2 term, indicating a downward-opening parabola. The vertex of the parabola represents the maximum profit the company can achieve.

To find the maximum profit and the corresponding number of units sold, we can use the vertex formula:

x = -b / (2a)

For the profit function P(x) = -\(0.32x^2 + 200x\)- 52, a = -0.32 and b = 200.

x = -200 / (2 * -0.32)

x = 312.5

Therefore, the maximum profit is achieved when approximately 312.5 units of lab equipment are sold.

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Answer:

12.5

Step-by-step explanation:

37.50÷15=2.5

2.5×5=12.5

Answer: $12.50

Step-by-step explanation:

You have to divide 37.5 by 15 which is 2.5 then multiply that by 5 which is 12.5.