find domain and range, what it’s max or min if it has any!

Answer:

x<12

Step-by-step explanation:

Let's solve your inequality step-by-step.

x−3<9

Step 1: Add 3 to both sides.

x−3+3<9+3

x<12

Answer:

x<12

Answer:

6.3333333

Step-by-step explanation:

6 = 4

9.5=X

cross multiply

6x=38

Divide both sides by 6

x=6.3333333

Answer: 14.25 inches in 9.5 hours.

Step-by-step explanation:

The rate of inches per hour is 1.5. In 9.5 hours, this would add up to 14.25 inches.

The five-number summary is:

Minimum: 9

First Quartile: 16.5

Median: 25.5

Third Quartile: 39

Maximum: 51

3. Range = 42

4. Interquartile range = 22.5

Given the data for the lengths as, 36, 15, 9, 22, 36, 14, 42, 45, 51, 29, 18, 20, to find the five-number summary of the data set, we would follow the steps below:

1. The numbers in ordered from the smallest to the largest would be:

9, 14, 15, 18, 20, 22, 29, 36, 36, 42, 45, 51

2. The five-number summary for the lengths in minutes would be:

3. Range of the data = max - min = 51 - 9 = 42

4. The interquartile range for the data set = Q3 - Q1 = 39 - 16.5

Interquartile range for the data set = 22.5

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Answer:

add more info

Step-by-step explanation:

The required rate of return (or minimum acceptable rate of return) is 20 percent. If the net cash flows are $15,000 per year for ten years, the total cash flow is $150,000. The project's cost is $47,500. We can now apply the net present value formula to determine whether or not the project is feasible.

Net Present Value (NPV) = Cash flow / (1 + r)^n - Cost Where, r is the discount rate, n is the number of years, and Cost is the initial outlay.

Net Present Value = 150000 / (1 + 0.20)^10 - 47500

Net Present Value = $67,482.22

Since the NPV is positive, the project is feasible. When calculating net present value, it's important to remember that a positive NPV implies that the project is expected to generate a return that exceeds the cost of capital, whereas a negative NPV indicates that the project is expected to generate a return that is less than the cost of capital, and as a result, it should be avoided.

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Since the strain of bacteria doubles every 5 minutes, we can use the exponential growth formula to calculate the number of bacteria present at any given time. The formula is given by:

N = N0 * 2^(t/d)

where:

N = final number of bacteria

N0 = initial number of bacteria (1 in this case)

t = time elapsed (96 minutes)

d = doubling time (5 minutes)

Plugging in the values into the formula:

N = 1 * 2^(96/5)

Using a calculator or simplifying the exponent:

N ≈ 1 * 2^19.2

Since we're dealing with whole numbers, we can round the exponent to the nearest whole number:

N ≈ 1 * 524,288

Therefore, at the end of 96 minutes, there could be approximately 524,288 bacteria present.

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The exponential equation that represents the function is 3x².

The finite difference between two consecutive values of f(x) is given by:

Δf(x) = f(x+1) - f(x)

Δf(-6) = f(-5) - f(-6) = 75 - 108 = -33

Δf(-5) = f(-4) - f(-5) = 48 - 75 = -27

Δf(-4) = f(-3) - f(-4) = 27 - 48 = -21

Δf(-3) = f(-2) - f(-3) = 12 - 27 = -15

The second finite differences are:

Δ²f(-6) = Δf(-5) - Δf(-6) = 6

Δ²f(-5) = Δf(-4) - Δf(-5) = 6

Δ²f(-4) = Δf(-3) - Δf(-4) = 6

Since the second finite differences are constant, the function is a quadratic polynomial of the form;

f(x) = ax² + bx + c

f(-6) = 108 = 36a - 6b + c

f(-5) = 75 = 25a - 5b + c

f(-4) = 48 = 16a - 4b + c

The final equation becomes;

36a - 6b + c = 108 ---- (1)

25a - 5b + c = 75 ------ (2)

16a - 4b + c = 48 -------- (3)

solve the equation, using crammers rule,

a = 3, b = 0, c = 0

f(x) = 3x²

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Answer:  the fraction form is 331/500

Step-by-step explanation:

To calculate the final grade in the course, we need to take into account the weighted grade scale and the fact that the lowest exam score will be dropped.

Let's break down the calculation step by step:

Calculate the average exam score after dropping the lowest score:

Exam 1: 90%

Exam 2: 86%

Exam 3: 92%

Exam 4: 84%

We drop the lowest score, which is Exam 2 (86%), and calculate the average of the remaining three exam scores:

Average exam score = (90% + 92% + 84%) / 3

= 88.67%

Calculate the weighted score for each category:

Homework (HW): 15% of the final grade

Exams (average of three exams): 60% of the final grade

Final Exam: 25% of the final grade

Weighted HW score = 100% * 15%

= 15%

Weighted Exam score = 88.67% * 60%

= 53.20%

Weighted Final Exam score = 78% * 25%

= 19.50%

Calculate the final grade:

Final Grade = Weighted HW score + Weighted Exam score + Weighted Final Exam score

Final Grade = 15% + 53.20% + 19.50%

                    = 87.70%

The final grade in the course, taking into account the weighted grade scale and dropping the lowest exam score, is 87.70%

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Answer:

Step-by-step explanation:

y=10

Since segment AD bisects angle BAC, the value of x is equal to 14.6.

In Mathematics, an angle bisector can be defined as a type of line, ray, or segment, that bisects or divides a line segment exactly into two (2) equal angles.

By applying the angle bisector theorem to this triangle (ΔABC), we have:

AB/BD = AC/DC

19/x = 17/(20 - x)

17x = 19(20 - x)

17x = 380 - 19x

19x + 17x = 380

26x = 380

x = 380/26

x = 14.6.

In conclusion, we can reasonably infer and logically deduce that the value of x in triangle ABC is 14.6.

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Given the data set:

2, 5, 7, 2, 11, 13, 5, 7, 1, 10, 10, 2, 3, 5, 1, 11

Let's find the box plot that correctly displays the data set shown.

The maximum value achieved by f(x) on the interval [0,6] is 21, which occurs at x=3. The minimum value is -12, which occurs at x=0 and x=6.

To find these values, we take the derivative of f(x), set it equal to zero, and solve for x. We then plug in the values of x and evaluate f(x) to find the corresponding maximum and minimum values.

Since the derivative is positive to the left of x=3 and negative to the right, we know that we have a maximum value at x=3.

Similarly, since the derivative is negative to the left of x=0 and positive to the right of x=6, we know that we have minimum values at x=0 and x=6. The graph of f(x) also confirms these results.

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The solution of the given linear inequality will be  -10/3 <= t <= -2.

What are linear inequalities?

Inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in Maths. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠). The different types of inequalities in Maths are polynomial inequality, rational inequality, absolute value inequality.

The symbols ‘<‘ and ‘>’ express the strict inequalities and the symbols ‘≤’ and ‘≥’ denote slack inequalities. A linear inequality seems exactly like a linear equation but there is a change in the symbol that relates two expressions.

e.g. y>x+2

Now,

Given inequality is -2 I-3t-8I <=-4

So there are two inequalities 1. -2+3t+8<=-4 2. -2-3t-8<=-4

1. 3t+6<=-4   2.-3t-10<=-4

1. t>=-10/3    2. t<=-2

Hence,

          The solution of the given linear inequality will be  -10/3 <= t <= -2.

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the inequality that is true when p = 3.4 is J. 8.5 ≥ 2.5p.

To determine which inequality is true when p = 3.4, we can substitute the value of p into each inequality and see which one holds true.

Given:

p = 3.4

F. 3p < 10.2

Substituting p = 3.4:

3 * 3.4 < 10.2

10.2 < 10.2

This inequality is not true.

G. 13.6 ≤ 3.9p

Substituting p = 3.4:

13.6 ≤ 3.9 * 3.4

13.6 ≤ 13.26

This inequality is not true.

H. 5p > 17.1

Substituting p = 3.4:

5 * 3.4 > 17.1

17 > 17.1

This inequality is not true.

J. 8.5 ≥ 2.5p

Substituting p = 3.4:

8.5 ≥ 2.5 * 3.4

8.5 ≥ 8.5

This inequality is true.

Therefore, the inequality that is true when p = 3.4 is J. 8.5 ≥ 2.5p.

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Cassius Corporation needs to sell to make a profit of $31,500 to sell the number of units that needs to be sold is 9,400 units.  It can be found this out by using a formula that takes into account the company's sales revenue, variable expenses, fixed expenses, and contribution margin.Therefore Option D is correct.

The contribution margin is the amount of money left over from sales revenue after deducting variable expenses. In this case, we know that Cassius Corporation's contribution margin is $73,500.

To find out how many units the company needs to sell, we can use the following formula:

(Number of units * Contribution margin per unit) - Fixed expenses = Target profit

We know that the fixed expenses are $67,200 and the target profit is $31,500.

The contribution margin per unit by dividing the contribution margin by the number of units sold, which in this case is 7,000 units. This gives us a contribution margin per unit of $10.50.

Substituting these values into the formula, we get:

(Number of units * $10.50) - $67,200 = $31,500

Simplifying this expression:

(Number of units * $10.50) = $98,700

Number of units = $98,700 / $10.50

Number of units = 9,400 (rounded to the nearest whole unit)

The number of units that must be sold to achieve a target profit of $31,500 is closest to 9,400 units. Option (D) is correct.

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The rate of the current in the stream was 6 mph.

Distance is defined as the product of speed and time.

Let's assume the speed of the current "c" and the time it takes the boat to travel upstream "t". We can then set up the following two equations:

Upstream: 4/(10-c) = t

Downstream: 4/(10+c) = t - 10

We can then solve for c by substituting the value of t from the first equation into the second equation and solving for c. This gives us:

4/(10-c) = t

4/(10+c) = t - 10

4/(10+c) = (10-c)/(10-c)

4 = 10 - c

c = 6

Thus, the rate of the current in the stream on that day was 6 miles per hour.

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Answer:

the one with the answer -10

Step-by-step explanation:

Answer:

So you do -8 + -2 which equals -10. it is the 3rd answer

Step-by-step explanation:

Answer:

A, all real numbers

Step-by-step explanation:

The domain is the x value and the x value is the domain.

So when you take a look at the x values, it keeps going on and on

So when x values or y values keep going on forever we call that all real numbers

Hope this helps! Plz mark brainliest!

Answer:

both cost $12

Step-by-step explanation:

Let's say the price of a senior citizen ticket is s dollars and the price of a child ticket is c dollars.

For, say, 7 senior citizen tickets, the cost would be s 7 times, or s * 7. Similarly, 6 child tickets would cost 6c. The total amount of (senior citizen ticket cost) + (child ticket cost) would equal the total sales.

Therefore,

first day:

7s + 6c = 156

second day:

7s + 3c = 120

7s + 6c = 156

7s + 3c = 120

we can solve this by solving for c in terms of s in one equation and plugging that into the other equation

7s + 6c = 156

subtract 7s from both sides to isolate the c and its coefficient

156 - 7s = 6c

divide both sides by 6 to isolate c

(156-7s)/6 = c

26-(7/6)s = c

plug that into the other equation

7s+3c = 120

7s + 3 (26-(7/6)s) = 120

7s + 78 - (21/6)s = 120

7s + 78 - (7/2)s = 120

(7/2)s + 78 = 120

subtract 78 from both sides to isolate s and its coefficient

(7/2)s = 42

multiply both sides by 2/7 to isolate s

12 = s

26 - (7/6)s = c

26 - 14 = c = 12

To evaluate the integral \[\int_{-5}^{5} \sqrt{25 - x^2 }dx\] in terms of areas, we need to interpret it as the area of a certain region. First, we note that the integrand $\sqrt{25 - x^2}$ represents the radius of a semicircle centered at the origin with radius 5. Thus, the integral represents the area of the region bounded by the $x$-axis and the upper half of the semicircle.

To find this area, we can split it up into infinitesimally small rectangles of width $dx$, each with height $\sqrt{25 - x^2}$. The area of each rectangle is given by $dA = \sqrt{25 - x^2} dx$. Summing up these infinitesimal areas from $x = -5$ to $x = 5$, we get the total area of the region as: \[\int_{-5}^{5} \sqrt{25 - x^2 }dx = \int_{-5}^{5} dA = A.\]

To compute this integral, we can use the substitution $x = 5\sin(\theta)$, which gives $dx = 5\cos(\theta) d\theta$. Also note that when $x = -5$, we have $\theta = -\frac{\pi}{2}$ and when $x = 5$, we have $\theta = \frac{\pi}{2}$. Thus, we can rewrite the integral as: \[\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} (25\cos^2(\theta)) d\theta.\]

Using the trig identity $\cos^2(\theta) = \frac{1+\cos(2\theta)}{2}$, we can simplify the integral as: \[\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} (25\cos^2(\theta)) d\theta = \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{25}{2} (1+\cos(2\theta)) d\theta.\]

Evaluating the integral gives: \[\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{25}{2} (1+\cos(2\theta)) d\theta = \left[\frac{25}{2}\left(\theta + \frac{1}{2}\sin(2\theta)\right)\right]_{-\frac{\pi}{2}}^{\frac{\pi}{2}} = \frac{25}{2}(\pi - (-\pi)) = \boxed{\frac{25}{2}\pi}.\] Thus, the integral evaluates to $\frac{25}{2}\pi$, which represents the area of the region bounded by the $x$-axis and the upper half of the semicircle centered at the origin with radius 5.
To evaluate the integral ∫[-5, 5] √(25 - x²) dx by interpreting it in terms of areas, follow these steps:

1. Identify the function: The given function is f(x) = √(25 - x²).

2. Visualize the graph: The graph of this function represents the top half of a circle with radius 5, centered at the origin (0,0).

3. Determine the region of interest: Since the integral is over the interval [-5, 5], the region of interest is the entire top half of the circle.

4. Calculate the area: As this region is a semicircle (half of a circle), we can use the area formula for a circle (A = πr²) to find the area of the semicircle.

Area of the semicircle = (1/2) * π * r² = (1/2) * π * 5² = (1/2) * π * 25 = (25/2)π

So, the integral ∫[-5, 5] √(25 - x²) dx, when interpreted in terms of areas, represents the area of the top half of a circle with radius 5. The area of this region is (25/2)π square units.

The given integral represents the area of a semicircle with radius 5. Thus, the value of the integral is equal to half the area of a circle with radius 5, which is 12.5π or approximately 39.27.

The integral\(\int_{-5}^{5} \sqrt{25 - x^2 }dx\) represents the area between the x-axis and the curve\(y = \sqrt{25 - x^2}\)for x ranging from -5 to 5. This curve is the top half of a circle with radius 5 centered at the origin. To find the area of this semicircle, we can divide it into infinitely many narrow strips of width dx and height\(\sqrt{25 - x^2}\). The area of each strip is approximately \(\sqrt{25 - x^2} dx\), and the total area of the semicircle is obtained by summing up the areas of all such strips, which gives:

Area of semicircle = \(\int_{-5}^{5} \sqrt{25 - x^2} dx\)

This integral can be evaluated using a trigonometric substitution or by using the formula for the area of a circle, which is\(A = \pi r^2\). Since the given semicircle has radius 5, its area is half the area of the corresponding circle, which is 25π. Therefore, the value of the integral is:

\(\int_{-5}^{5} \sqrt{25 - x^2} dx = \frac{1}{2} (25\pi) = 12.5\pi\) approx 39.27.

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The total spending figures indicate that Joe's demand for pizza is elastic as his total spending decreases when the price decreases, suggesting he is responsive to price changes.

a. The demand curve for Joe's pizza can be plotted by using the equation Q = 30 - 2P, where Q represents the quantity of pizza consumed and P represents the price per slice.

On the graph, the vertical axis represents the price (P), and the horizontal axis represents the quantity (Q). The vertical intercept occurs when Q is 0, which corresponds to P = 15. The horizontal intercept occurs when P is 0, which corresponds to Q = 30.

b. The total spending on pizza at P = 5 is $100, and the total spending at P = 4 is $88. This information indicates that Joe's total spending decreases as the price of pizza decreases.

Based on this, we can infer that Joe's elasticity of demand for pizza between P = 5 and P = 4 is elastic. When the price decreases from $5 to $4, the total spending decreases, indicating that the demand is responsive to price changes.

c. When P = 9, we can substitute this value into the demand function to calculate the corresponding quantity: Q = 30 - 2(9) = 30 - 18 = 12. To calculate Joe's consumer surplus, we need to find the area of the triangle formed by the demand curve and the price line.

The consumer surplus is given by (1/2) ˣ  (9 - P) ˣ  Q = (1/2) ˣ (9 - 9) ˣ  12 = 0.d. If the price of pizza rises to $15 per slice, we can again substitute this value into the demand function to find the corresponding quantity: Q = 30 - 2(15) = 30 - 30 = 0.

Joe's consumer surplus at this new price would be zero since he is not consuming any pizza at that price, resulting in no surplus.

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Answer:

X = 20

Step-by-step explanation:

This is an example of a supplementary angle.

A supplementary angle adds up to 180 degrees.

Therefore, in order to find x in this situation you will have to put both angles (added) equal to 180, like this:

5x + 80 = 180

Now, it is simple algebra from here. Solve for x:

5x = 100

x = 20

In conclusion, x is equal to 20.

I hope this helps!!

If you have any questions let me know!

- Kay :)

Answer:

X=20

Step-by-step explanation:

6x + 24 = 6x + 8

Cancel equal terms

24=8

the statement is false(Ø)

Answer:

a. 10^- 3

b. 10^- 7

c. 10^- 8

d. 10^- 9

e. 1 / 10^6

a.

1 / 10. 1 / 10. 1 / 10

= 1 / ( 10 x 10 x 10 )

= 1 / 1000

= 1 / 10^3

= 10^- 3

b.

1 / 10. 1 / 10. 1 / 10. 1 / 10. 1 / 10. 1 / 10. 1 / 10

= 1 / ( 10 x 10 x 10 x 10 x 10 x 10 x 10 )

= 1 / 10000000

= 1 / 10^7

= 10^- 7

c.

( 1 / 10. 1 / 10. 1 / 10. 1 / 10. )^2

= ( 1 / 1000 )^2

= ( 1 / 10^3 )^2

= ( 10^- 3 )^2

= 10^( - 3 x 2 )

= 10^- 6

d.

( 1 / 10. 1 / 10. 1 / 10 )^3

= ( 1 / 1000 )^3

= ( 1 / 10^3 )^3

= ( 10^- 3 )^3

= 10^( - 3 x 3 )

= 10^- 9

e.

( 10. 10. 10. )^- 2

= ( 10^3 )^- 2

= ( 1 / 10^3 )^2

= 1 / 10^( 3 x 2 )

= 1 / 10^6

Answer:

90 km/h

Step-by-step explanation:

To solve this problem you first need to convert minutes to hours since the unit is km/h. Doing this we get half an hour (1 hour=60 mins so you divide 30 by 60) after converting you simply divide 45 by 1/2 or .5 to get the answer.

The point would be the solution (25,40).

Let

The number of tacos sold is represented by x.

x denotes the quantity of burritos sold.

We are aware of this,

⇒ x + y 62

⇒ 3.75x + 6y = 330

The triangle shaded region is the answer

(25,40)

The point is one possible solution (25,40).

Remember that if an ordered pair is a solution to a system of inequalities, then the ordered pair must reside on the solution's region.

That indicates there were 30 tacos sold and 30 burritos sold.

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Answer:

11 ?

Step-by-step explanation:

your question is a little bit strange and it's hard to understand, but the midpoint you need to find like this: AB/2 22/2=11

Answer: 700

Step-by-step explanation:

Answer:

700

Step-by-step explanation:

copy and paste