Using the Following Image, solve for x

Answer:

$239.88

Step-by-step explanation:

:D

Answer:

2nd and 5th options

\((4x^2-9y^2)(4x^2+9y^2)\)
\((4x^2+9y^2)(2x+3y)(2x-3y)\)

Step-by-step explanation:

Notice you can factorize the first term using \(a^2-b^2=(a+b)(a-b)\)
so the factors are \(a=4x^2 \\\)  and \(b=9y^2\)  since 4^2=16 and 9^2=81
so the first factor form is
\((4x^2-9y^2)(4x^2+9y^2)\)
Then you can factor again the first polynomial (the second one cant be factor using real coefficient since terms are strictly positive)
again factors are \(a=2x\\\) and \(b=3y\\\)  so the second factor form is:

\((4x^2+9y^2)(2x+3y)(2x-3y)\)

We can see here that the solutions to the triangles are:

1. 62.2°.

2. 35.9°

3. 61.9°

4. 53.1°

We can see here that using trigonometric ratio formula, we find the values of x.

We see the following:

1. Cos x = 7/15 = 0.4666

x = \(cos^{-1}\) 0.4666 = 62.2°.

2. Sin x = 27/46 = 0.5869

x° = \(sin^{-1}\)  0.5869  = 35.9°

3. Sin x = 30/34 = 0.8823

x° = \(sin^{-1}\) 0.8823 = 61.9°

4. Tan x = 8/6 = 1.3333

x° = 1.3333 = 53.1°

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Answer:

simplify

Step-by-step explanation:

just simpify then theres an answer waiting for you to jearney on

a) The break-even points for the given cost and revenue functions are approximately x = 16.526 and x = 6.474.

b) The break-even points for the given cost and revenue functions are approximately x = 12.225 and x = 62.775.

c) The maximum profit for the given cost and revenue functions is approximately $843.75.

a) To find the break-even points, we need to determine the values of x where the total costs (C(x)) equal the total revenues (R(x)). We set C(x) = R(x) and solve for x:

C(x) = R(x)

1760 + 8x + 0.6x² = 100x - 0.4x²

Combining like terms and rearranging the equation, we get:

1x² - 92x + 1760 = 0

Solving this quadratic equation, we find two solutions for x:

x ≈ 16.526

x ≈ 6.474

b) Similarly, we set C(x) = R(x) and solve for x:

900 + 25x = 100x - x²

Rearranging the equation, we get:

x² - 75x + 900 = 0

Solving this quadratic equation, we find two solutions for x:

x ≈ 12.225

x ≈ 62.775

c) To find the maximum revenue, we need to determine the vertex of the revenue function R(x) = 100x - x². The x-coordinate of the vertex is given by x = -b / (2a), where a and b are the coefficients of the quadratic equation.

In this case, a = -1 and b = 100. Plugging in the values, we get:

x = -100 / (2 * -1) = 50

Substituting this value back into the revenue function, we find:

R(50) = 100(50) - (50)² = 5000 - 2500 = 2500

Therefore, the maximum revenue for the given cost and revenue functions is $2500.

To find the maximum profit, we need to subtract the total costs from the total revenues. Given that the cost function is C(x) = 900 + 25x, the profit function is P(x) = R(x) - C(x). Substituting the revenue and cost functions, we have:

P(x) = (100x - x²) - (900 + 25x)

P(x) = -x² + 75x - 900

To find the maximum profit, we need to determine the vertex of the profit function. Using the same formula as before, we find:

x = -75 / (2 * -1) = 37.5

Substituting this value back into the profit function, we find:

P(37.5) = -(37.5)² + 75(37.5) - 900 ≈ 843.75

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The chart showing the results of data collection for frequency of fast food consumption by each of three head of household age groups is an example of a frequency distribution chart.

A frequency distribution or frequency table is a way of organizing and presenting data by categorizing it into different groups or intervals and indicating the number of occurrences or frequency within each group. In this case, the data collected pertains to the frequency of fast food consumption for three different age groups of household heads.

The chart would typically have three columns representing the age groups (e.g., 18-30, 31-45, 46-60), and another column indicating the frequency or number of households within each age group that reported a specific frequency of fast food consumption (e.g., daily, weekly, monthly). The frequencies can be represented in numbers or percentages.

This type of chart helps visualize the distribution of fast food consumption habits across different age groups, allowing for comparisons and analysis of patterns or trends. It provides a concise summary of the collected data and facilitates easy interpretation and understanding of the frequency distribution within each age group.

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Answer: (4,9)

Step-by-step explanation:

The equation that represent the relationship of the coffees is 3x + 5y = 68.

At a coffee shop, two sizes of coffee are sold. A medium coffee costs $3, and a large coffee costs $5.

The equation that represent the relationship between the number of medium coffees sold, x, and the number of large coffees sold, y, in an hour where sales totalled $68 is as follows:

where

Therefore, the equation is as follows:

3x + 5y = 68

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The critical value of t with df as 7 is 2.36, and the critical value of t with df as 102 is 2.62

In a hypothesis test, the critical value is a value that is used to decide whether to accept the null hypothesis or not. It is based on the level of significance that was selected, which is the highest likelihood that a Type I error could occur.

a)

On referring to the t-distribution table, which is statistical software, or a calculator to find the critical value of t for a 95% confidence interval with degrees of freedom (df) = 7. The two-tailed confidence level of 0.95 is the essential value. We discover that the crucial value of t for a 95% confidence interval with df = 7 is roughly 2.365 using a t-distribution table or program.

b)

The t-distribution table, statistical software, or a calculator are used in a similar manner to estimate the critical value of t for a 99% confidence interval with df = 102. The crucial value is equal to the 0.99 two-tailed confidence level. The crucial value of t for a 99% confidence interval with df = 102 is roughly 2.62, according to a t-distribution table or computer programme.

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Answer:

No.

Step-by-step explanation:

It does not pass the vertical line test, so the relation is not a function. This is because there are x-values that have several y-values. To be a function, a relation must have x-values that only have one y-value each.

Hope this helps!

Answer:

No

Step-by-step explanation:

Because for any given point along the x-axis it has 2 values along y-axis.

For a relation to be a function it must have only one value at y-axis along any given point along the x-axis

Answer:

37.68

Step-by-step explanation:

40 -2.32

= 37.68

Answer: is C. 22

Step-by-step explanation:

Answer:

16,242. 7 cm^3.

Step-by-step explanation:

We need to cut off a square piece at the 4 corners of the cardboard.

Let the length of their edges be x cm.

The volume of the box will be:

V = height * width * length

V = x(100-2x)(40-2x)

V = x(4000 - 200x - 80x + 4x^2)

V = x(4x^2 - 280x + 4000)

V =  4x^3 + - 280x^2 + 4000x

Finding the derivative:

dV / dx =  12x^2 - 560x + 4000  = 0  ( when  V is a maxm or minm.)

4(3x^2 - 140x + 1000) = 0

x =  37.86, 8.80.

Looks like x = 8.80 is the right value but we can check this out be looking at the sign of the second derivative:

V" =  24x - 560, when x = 8.8   V" is negative so this is a Maximum for V.

So the maximum volume of the box is when x = 8.8 so we have

V =  8.8(100-2(8.8)(40 - 2(8.8)

=  16,242. 7 cm^3.

The solution to the equation is x = 105/14 and y = -27/2

Simultaneous equations are two or more algebraic equations with the same unknown variables and the same value of the variables satisfies all such equations. This implies that the simultaneous equations have a common solution.

We use different methods to solve simultaneous equations. Some of the common methods are:

By substitution method

-7x + -5y = 15 ----- 1

7x + 3y = 12 ----- 2

from equation 1

7x = -15 -5y ----- 3

substitute 7x in equation 2

-15 - 5y + 3y = 12

-2y = 12 + 15

-2y = 27

y = -27/2

To find x, substitute y in equation 3

7x = -15 - 5(-27/2)

7x = -15 + 135/2

Multiplying both sides by 2

14x = -30 + 135

14x = 105

x = 105/14

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K=basketball, S= baseball

10K

5S

3 K & S

26 total

P(K) = 10/26, P(S) = 5/26 P(K^S) = 3/26

P(K v S) = P(K) + P(S) - P(K^S) = 10/26 + 5/26 - 3/26 = 12/26 = 6/13

Probability of randomly getting a student who plays either basketball or baseball = 6/13

The probability distribution of the sample mean is approximately normal, with mean of 24.4 points and standard deviation of 1.175 points.

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation given by the equation presented as follows: \(s = \frac{\sigma}{\sqrt{n}}\).

The mean is the same as the population mean, of 24.4 points, while the shape is approximately normal.

The standard error is given as follows:

\(s = \frac{4.7}{\sqrt{16}} = 1.175\)

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To determine if a function has a vertical asymptote, you need to consider its behavior as the input approaches certain values.

A vertical asymptote occurs when the function approaches positive or negative infinity as the input approaches a specific value. Here's how you can determine if a function has a vertical asymptote:

Check for restrictions in the domain: Look for values of the input variable where the function is undefined or has a division by zero. These can indicate potential vertical asymptotes.

Evaluate the limit as the input approaches the suspected values: Calculate the limit of the function as the input approaches the suspected values from both sides (approaching from the left and right). If the limit approaches positive or negative infinity, a vertical asymptote exists at that value.

For example, if a rational function has a denominator that becomes zero at a certain value, such as x = 2, evaluate the limits of the function as x approaches 2 from the left and right. If the limits are positive or negative infinity, then there is a vertical asymptote at x = 2.

In summary, to determine if a function has a vertical asymptote, check for restrictions in the domain and evaluate the limits as the input approaches suspected values. If the limits approach positive or negative infinity, there is a vertical asymptote at that value.

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Answer:

2.43 (units)

Step-by-step explanation:

Circumference of a circle is defined by C=2pi*r

Solving that equation for r --> 5.5 = 2* 3.14 * r

r=0.88 unit

Area of a circle = A= pi * r^2

Solve this equation by plugging in the r we just found. A = 3.14 * (0.88^2)

Answer: 2.43 units

In Pascal's Triangle, the first prime row is Row 5, where all entries except the 1s are non-prime numbers. The second prime row is Row 11, which also follows the same pattern with non-prime entries except for the 1s.

a) To find a row whose row number is prime, we can start from the second row (row index 1) and iterate through the rows of Pascal's Triangle, checking if each row number is prime. Let's find the first prime row:

Row 1: 1

Row 2: 1 1

Row 3: 1 2 1

Row 4: 1 3 3 1

Row 5: 1 4 6 4 1

Row 6: 1 5 10 10 5 1

Row 7: 1 6 15 20 15 6 1

Row 8: 1 7 21 35 35 21 7 1

Row 9: 1 8 28 56 70 56 28 8 1

Row 10: 1 9 36 84 126 126 84 36 9 1

Row 11: 1 10 45 120 210 252 210 120 45 10 1

Row 12: 1 11 55 165 330 462 462 330 165 55 11 1

Row 13: 1 12 66 220 495 792 924 792 495 220 66 12 1

Row 14: 1 13 78 286 715 1287 1716 1716 1287 715 286 78 13 1

Row 15: 1 14 91 364 1001 2002 3003 3432 3003 2002 1001 364 91 14 1

The first prime row is Row 5, and except for the 1s in that row, all the other entries are non-prime numbers.

b) Let's find another prime row:

Row 1: 1

Row 2: 1 1

Row 3: 1 2 1

Row 4: 1 3 3 1

Row 5: 1 4 6 4 1

Row 6: 1 5 10 10 5 1

Row 7: 1 6 15 20 15 6 1

Row 8: 1 7 21 35 35 21 7 1

Row 9: 1 8 28 56 70 56 28 8 1

Row 10: 1 9 36 84 126 126 84 36 9 1

Row 11: 1 10 45 120 210 252 210 120 45 10 1

Row 12: 1 11 55 165 330 462 462 330 165 55 11 1

Row 13: 1 12 66 220 495 792 924 792 495 220 66 12 1

Row 14: 1 13 78 286 715 1287 1716 1716 1287 715 286 78 13 1

Row 15: 1 14 91 364 1001 2002 3003 3432 3003 2002 1001 364 91 14 1

The second prime row is Row 11, and similar to the previous case, except for the 1s in that row.

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Answer:

A=18 because 6+18 (was 6+a) is 24 - 11 = 13

Step-by-step explanation:

A=18

Answer:

a = 4

Step-by-step explanation:

add 11 on the = side 11+13 = 24

now you're left with: 6a=24

divide 6÷24

a= 4

Therefore, the number of ways a student can work 7 out of 10 questions on the exam is 120, which corresponds to option (D).

The number of ways a student can work 7 out of 10 questions on an exam can be calculated using the concept of combinations.

The formula for combinations is given by:

C(n, k) = n! / (k!(n - k)!)

Where n is the total number of items and k is the number of items chosen.

In this case, the student is choosing 7 questions out of a total of 10, so we have:

C(10, 7) = 10! / (7!(10 - 7)!) = 10! / (7!3!)

Simplifying:

10! = 10 * 9 * 8 * 7!

3! = 3 * 2 * 1

C(10, 7) = (10 * 9 * 8 * 7!) / (7! * 3 * 2 * 1)

The 7! terms cancel out:

C(10, 7) = (10 * 9 * 8) / (3 * 2 * 1)

C(10, 7) = 120

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Answer: 18.27

Step-by-step explanation:

Area  of Shaded = Area of pie -  Area of triangle

Area of pie = (angle)/360 * \(\pi \\\) r²

Area of pie = 90/360 * \(\pi\) * 8²

Area of pie = 50.27

Area of triangle = 1/2 bh

Area of triangle = 1/2 8(8)

Area of triangle = 32

Area of shaded =  50.27 - 32

Area of shaded = 18.27

Answer:

-10

Step-by-step explanation:

Answer:

67%

Step-by-step explanation:

Given : A department store buys 300 shirts at a cost of $1800 .

Then By unitary method , the cost of one shirt = Cost of 300 shirts divided by 300

= $1800 ÷ 300 = $6

i.e. cost of one shirt = $6

Also, Selling price of one shirt = $10

Price mark up = Selling price - Cost price

= $10-$6 = $4

The  percent mark up=

(rounded to the nearest percent)

Hence, the percent markup = 67%

Answer:

-9x²+x-10

Step-by-step explanation:

To write a polynomial in standard form, you write starting with the term with the highest degree, or exponent (in this case, the #x^2# term), and then in decreasing order. Since the #x^2# term is the term with the highest degree: To classify a polynomial by degree, you look at the highest exponent, or degree

Hii :))

Given polynomial is of the form ⇨ \(\:\underline{\tt\:-10-9^{2}+x}\)

﹋﹋﹋﹋﹋

A standard polynomial comes in the form of ax² + bx + c.

﹋﹋﹋﹋﹋

So, by rearranging \(\downarrow\)

\( \tt - 10 - 9 {x}^{2} + x \\ \rightarrow \: \boxed{\tt \: - 9 {x}^{2} + x - 10}\)

﹋﹋﹋﹋﹋

We rearranged it like this :-

﹋﹋﹋﹋﹋

\(\overbrace{ \underbrace{ \sf \: \infty \: Carry \: on \: Learning \: \infty }}\)

ᴛʜᴇᴇxᴛʀᴀᴛᴇʀᴇꜱᴛʀɪᴀʟ

Step-by-step explanation:

it's simple:

Answer:

Trechelle's reasoning is incorrect.

Step-by-step explanation:

the cost is $88.2. hope it helps bye.

Answer:The length of the other diagonal is: C. 15 feet.

Step-by-step explanation:

If the class collected $660 from ticket sales, the drama class sold a total of 90 student tickets. Let's assume that the number of adult tickets sold is x.

Since the drama class sold 25 more student tickets than adult tickets, the number of student tickets sold can be expressed as (x + 25).

The total revenue from ticket sales is given as $660. Adult tickets cost $6 each and student tickets cost $3 each. Therefore, the total revenue can be expressed as 6x + 3(x + 25).

Setting up the equation: 6x + 3(x + 25) = 660.

Simplifying the equation: 6x + 3x + 75 = 660.

Combining like terms: 9x + 75 = 660.

Subtracting 75 from both sides: 9x = 585.

Dividing both sides by 9: x = 65.

Therefore, the drama class sold 65 adult tickets.

To find the number of student tickets sold, we substitute the value of x into the expression (x + 25): (65 + 25) = 90.

Thus, the drama class sold 90 student tickets.

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