Twice Jill's Age Added To Three Times Tony's Age Is 44. Jill's Age Equals Tony's Age Plus 2 Years. Find Jill's And Tony's Age

The largest possible value of f(8) is 34.

The problem asks us to find the largest possible value of f(8), where f is a function that is continuous on the closed interval [4,8] and differentiable on the open interval (4,8), and satisfies the conditions f(4) = -6 and f'(x) ≤ 10 for all x in (4,8).

To find the largest possible value of f(8), we need to use the Mean Value Theorem (MVT), which is a theorem in calculus that relates the values of a differentiable function at the endpoints of an interval to the values of its derivative at some point in the interior of the interval.

The MVT states that if f is a function that is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists at least one c in the open interval (a,b) such that:

f'(c) = (f(b) - f(a)) / (b - a)

In other words, the derivative of the function at some point in the interval is equal to the average rate of change of the function over the interval.

In this problem, we apply the MVT to the interval [4,8] and use the given information to obtain an upper bound on f(8). We have:

f'(c) = (f(8) - f(4)) / (8 - 4)

Simplifying, we get:

f(8) - f(4) = 4f'(c)

Since f'(x) ≤ 10 for all x in (4,8), we have:

4f'(c) ≤ 4(10) = 40

Substituting this into the previous equation, we get:

f(8) - (-6) ≤ 40

f(8) + 6 ≤ 40

f(8) ≤ 34

Therefore, the largest possible value of f(8) is 34, which is the upper bound obtained using the Mean Value Theorem and the given conditions on f(x) and f'(x).

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The price of the tablet computer after discount and marked up is $663.3.

What is discount?

Discount is the state of having a bond's price lower than its face value. The difference between the purchase price and the item's par value is the discount.

Discounts are different types of price reductions or deductions from a product's cost. It is frequently employed in consumer transactions when consumers receive discounts on a range of goods. The % discount rate is provided.

Here the original price of tablet computer = $670

During a sale , store offered 10% discount then

=> Price of tablet computer = 670× ( 100%-10%) = 670 × 90%

Now after the sale the price of the tablet computer marked up 10%. Then,

=> Price of tablet computer = 670 × 90% × (100%+10%)

=> Price of tablet computer = 670 × 90% × 110%

=> Price of tablet computer = 670 × [tex]\frac{90}{100} \times \frac{110}{100}[/tex]

=> Price of tablet computer = 670 × 0.9 × 1.1 = $663.3

Hence the price of the tablet computer after discount and marked up is $663.3.

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[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\hspace{10em} \stackrel{slope}{m} ~=~ 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{ 4}(x-\stackrel{x_1}{(-3)}) \implies y -2= 4 (x +3)[/tex]

[tex]y-2=4x+12\implies y=4x+\underset{ \stackrel{\uparrow }{b} }{14}\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

The expression into non zero and non negative exponents are:

1) 1/7   (2) 1    (3)1/0.0000001    (4)5     (5) 0    (6) 4x³        (7) 4/5x⁶   (8)10a⁷b⁶/c⁷       (9) 1/y⁵z²      (10) 100    (11) 9/ab         (12) 9x²       (13) 14a⁴/b    (14) a⁵ⁿ       (15) 32

1) 7⁻¹ = 1/7

       = 0.143

2) (14abc)⁰ = 1

3) 10⁻⁹ = 1/10⁹ = 1/0.0000001

4) 5(xy)⁰ = 5(1) = 5

5) 0¹⁵= 0

All numbers beginning with 0 are 0.

6)   [tex]\frac{24x^{8} y^{4} }{6x^{5} y^{5} }[/tex] = 4x³

7) [tex]\frac{1}{5y^-1}[/tex]

8) [tex]\frac{10a^7b^{10} }{c^7}[/tex]

9) [tex]y^-5z^-2[/tex]

10) {(5xy)⁸/10}⁻² = (1/10)⁻² = 100

11) {(ab)/9)⁻¹ = 9/ab

12) 9/x⁻² = 9x²

13) 12b⁻¹/a⁻⁴ =12a⁴/b

14) 1/5⁻⁵ᵃ = a⁵n

15) (1/2)⁻⁵ = 32

Positive exponents indicate that the base should be multiplied by that amount.

For example, if the number is 10³, 10 must be multiplied by 10 10 10, which is 1000. If the variable is x⁹, then x must be multiplied by itself nine times:

Positive effect: If f(x) = ax for a positive real number a, then f(x) > 0 for each x. In other words, f(x) is always positive regardless of the value of x.

Understand that an exponent is the number of times a number is multiplied by itself. For example, 3² is equal to 3.3. In the case of a positive exponent, the number (the base) is multiplied by itself, while in the case of a negative exponent, the reciprocal of the number is multiplied by itself.

For example, 3⁻² = 1/3 1/3.

A positive exponent indicates the number of times to multiply the base number, and a negative exponent indicates the number of times to divide the base number. Negative exponents can be rewritten as 1/xⁿ. Example: 2⁻⁴ = 1 / (2⁴), or 1/16. The zero exponent rule states that any base with an exponent of zero equals one.

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Suppose a certain medical test has a false positive rate of 6 out of 3,500, then during the period in which 27 false positives were obtained, the number of people tested was 15,750.

Step 1: Determine the probability of a false positive. The probability of a false positive is given as 6 out of 3500, so it can be expressed as a fraction: 6/3500

Step 2: Determine the number of false positives in the given period. The problem states that 27 false positives returned during the period, therefore: False positive rate x number of people tested = number of false positives 6/3500 x number of people tested = 27

Step 3: Solve for the number of people tested. 6/3500 x number of people tested = 27 Number of people tested = 27 / (6/3500) Number of people tested = 15,750 Therefore, during the period in which 27 false positives were obtained, the number of people analyzed was 15,750.

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Answer:

10.8 miles

Step-by-step explanation:

Use Pythagorean Theorem

[tex]a^{2} +b^{2} = c^{2}[/tex]

[tex]9^{2} +6^{2} = c^{2}[/tex]

[tex]c^{2} = 117[/tex]

[tex]c=\sqrt{117}[/tex]

Rounded to 10.8

The probability of waiting longer than one hour for a taxi is approximately 0.5488

Let X be the time between arrivals of taxis at the intersection. Then, X follows an exponential distribution with a mean of 10 minutes, i.e., E(X) = 10.

We want to find the probability of waiting longer than one hour (i.e., 60 minutes) for a taxi. Let Y be the waiting time for a taxi. Then, Y = kX, where k is a constant.

We can find k as follows

E(Y) = E(kX) = kE(X) = 10k

Since the mean waiting time is one hour (i.e., 60 minutes), we have

E(Y) = 60 minutes = 1 hour

Therefore, we get

10k = 1

k = 1/10

Now we can find the probability of waiting longer than one hour for a taxi as follows

P(Y > 60) = P(kX > 60) = P(X > 6) [since k = 1/10]

where the last step follows from the fact that X follows an exponential distribution with mean 10, so P(X > x) = e^(-x/10) for any x > 0.

Therefore, we get

P(Y > 60) = P(X > 6) = e^(-6/10) = e^(-0.6) ≈ 0.5488

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The given question is incomplete, the complete question is:

The time between arrivals of taxis at a busy intersection is exponentially distributed with a mean of 10 minutes. (a) What is the probability that you wait longer than one hour for a taxi?

Answer:

School A: 240 students

School B: 380 students

Step-by-step explanation:

We get these answers by dividing the number of students in each school by 2.

I hope this helps!

Please mark me brainliest...

After answering the provided question, we can state that So the equation difference in the measures of the two angles is 63 degrees.

In mathematics, an equation is a proclamation stating the justice or two phrases. An equation is made up of two sides that are separated by an algebraic equation (=). Equations can be used to solve problems and find solutions to mathematical questions. They can involve different mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots.

Since ∠A is a right angle, its measure is 90 degrees.

Therefore, we have:

m∠B - m∠A = [(9x-24) - (11x+13)]°

m∠B - m∠A = (9x - 24 - 11x - 13)°

m∠B - m∠A = (-2x - 37)°

|m∠B - m∠A| = |-2x - 37|°

And since ∠A is a right angle, its measure is 90 degrees, so we have:

|m∠B - m∠A| = |-2x - 37|° = |90 - (11x + 13)|°

11x + 13 = 90

11x = 77

x = 7

m∠A = 90°

m∠B = (9x - 24)° = (9(7) - 24)° = 27°

|m∠B - m∠A| = |27 - 90|° = 63°

So the difference in the measures of the two angles is 63 degrees.

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The distance from point A to point B is 568.07ft.

What is the distance?

Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. The distance can refer to a physical length in physics or to an estimate based on other factors in common usage.

Here, we have

Given: A boat is heading toward a lighthouse, whose beacon light is 130 feet above the water. From point. A, the boat’s crew measures the angle of elevation to the beacon, 6°, before they draw closer. They measure the angle of elevation a second time from point  B at some later time to be 11°.

Assuming a flat earth

initial measurement

tan6 = 130 / d₁

d₁ = 130/tan6 = 1236.86... ft

d₂ = 130/tan11 = 668.79...ft

distance from A to B

1236.86 - 668.79 = 568.07ft

Hence, the distance from point A to point B is 568.07ft.

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Answer:

568

Step-by-step explanation:

i got this as a question and that was the correct answer

In the triangle , the value of x is 57.

What is triangle?

A triangle is a form of polygon with three sides; the intersection of the two longest sides is known as the triangle's vertex. There is an angle created between two sides. One of the crucial elements of geometry is this.

Certain fundamental ideas, including the Pythagorean theorem and trigonometry, rely on the characteristics of triangles. The angles and sides of a triangle determine its kind.

Here in the given triangle , SD=99 , SF=44 , RF = 76 and FE = 76+3x

RE = FE - RF

=> RE = 76+3x-76 = 3x

Now using triangle proportionality theorem then,

=> [tex]\frac{SF}{SD}=\frac{RF}{RE}[/tex]

=> [tex]\frac{44}{99}=\frac{76}{3x}[/tex]

=> 3x = [tex]\frac{76\times99}{44}[/tex] = 171

=> x = 171/3 = 57

Hence the value of x is 57.

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The measure of ∠BAC is 140° which is the interior angle of the circle.

It is given that the lines BD and CD are tangent to the circle.

It is required to find the measure of ∠BAC if ∠BDC = 40°

What is a circle?

It is described as a group of points, each of which is equally spaced from a fixed point (called the centre of a circle).

We have BD and CD are tangent to circle ∠BDC = 40°

Here we can see in the figure that ∠BAC is the interior angle.

∠ACD = 90° and ∠ABD=90° (because AC is the perpendicular to DC)

So the measure of the ∠BAC is:

= 360 - ∠ACD - ∠ABD - ∠BDC

= 360 - 90 - 90 - 40

= 140°

Thus, the measure of ∠BAC is 140° which is the interior angle of the circle.

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Answer:

x = 43 degrees

Step-by-step explanation:

47+90 degrees = 137

that little box means that is a 90-degree angle.

(because straight angles are measured 180 degrees) :

180 - 137 = 43

that missing part between 90 degrees (the box) and 47 degrees equals 43.

because 43 is positioned from x where it is, x is also equivalent to 43 degrees.

and just for bonus that's a 90 degree angle to the right of "x" and that's a 47 degree angle to the left of "x" because these angles are all OPPOSITE.

therefore they are congruent.

Answer:

it's going to be 7.4

Step-by-step explanation:

5 x 4 = 20

4 / 2 since you want to get radius

2 x 2 = 4 x pi for both half circles.

4 x pi = 12.5 --> 13

20 - 12.5663706 = 7.43 ---> 7.4

Answer for 9/10 + 5/8 = 61/40

A statement that shows the two mathematical expressions which are equal to each other is known as an equation. It may have one or more variables, and the objective is frequently to determine the values of the variables that hold the equation true.

According to the question; add two fractions, we need to find a common denominator.

The common denominator for 10 and 8 is 40.

therefore, to convert both fractions to have a denominator of 40:

9/10 = (9/10) × (4/4) = 36/40

5/8 = (5/8) × (5/5) = 25/40

Here the fractions have the same denominator (40), we can add them:

36/40 + 25/40 = 61/40

Therefore, 9/10 + 5/8 = 61/40.

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The round trip took Abdul 4/15 hours or approximately 16 minutes.

Let's start by finding the speed of the train. We know that the train goes 10 mph faster than the boat, and the boat goes 20 mph, so the speed of the train is:

20 + 10 = 30 mph

Now we can use the formula:

time = distance / speed

The distance traveled by Abdul in the round trip is 4 miles to the front entrance and 4 miles back to the parking lot, so a total of 8 miles.

Let's first find the time it takes Abdul to get to the park by train:

time_train = distance_train / speed_train

time_train = 4 / 30

time_train = 2/15 hours

So the total time for the round trip is:

total_time = time_train + time_boat

total_time = 2/15 + 1/5

total_time = 4/15 hours

Therefore, the round trip took Abdul 4/15 hours or approximately 16 minutes.

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Answer:

1.34453781513

Step-by-step explanation:

[tex]\frac{8}{5.95} =1.34453781513[/tex],

Answer: 60.84mm

Step-by-step explanation:

The area of Triangle is:

A = 1/2 * base * height

7.8mm * 3mm = 23.4mm

23.4mm * 1/2
= 11.7mm

Now, find the area of the rectangle:

A = Base * Height

9.3mm * 7.8mm = 72.54mm

Now subtract the area of the triangle from the area of the rectangle

72.54mm - 11.7mm = 60.84mm

The value of a in the revenue function of the local company is -780, which is obtained by using the given information about the revenue at a selling price of $25.

We are given that the revenue function of the local company is:

R(x) = (a - 20)x + 80,000

We also know that when the selling price is $25, the revenue is $60,000. We can use this information to solve for the value of a:

R(25) = (a - 20)(25) + 80,000 = 60,000

Simplifying this equation, we get:

25a - 500 + 80,000 = 60,000

25a + 79,500 = 60,000

25a = 60,000 - 79,500

25a = -19,500

a = -780

Therefore, the value of a is -780.

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Lily took a certain number, multiplied it by 3, and then subtracted 8 from the product, which resulted in 7. The initial number was 5.

The equation that describes this situation is: 3k - 8 = 7.

To solve for k, we can isolate the variable by adding 8 to both the sides of the equation:

3k - 8 + 8 = 7 + 8

3k = 15

Finally, we can solve for k by dividing both sides of the equation by 3:

k = 5

Therefore, Lily started with the number 5, tripled it to get 15, and then subtracted 8 to get an answer of 7.

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The correct answer is A. I., II., V.   I. The graph contains the point (0, 1), II.The graph falls from left to right., V. The domain is (-∞o, co), and the range is (0,00).

What is a graph?

In computer science and mathematics, a graph is a collection of vertices (also known as nodes or points) connected by edges (also known as links or lines).

The given function g(x) = (1/3)x is a linear function, not an exponential function. Therefore, none of the observations related to exponential functions apply to this function.

However, we can make some observations about the graph of this linear function:

1. The graph contains the point (0,1): This is true, as g(0) = (1/3)0 = 0, and the y-intercept of the graph is at (0,1).

2. The graph falls from left to right: This is true, as the slope of the line is positive (1/3), and as x increases, y increases at a slower rate.

3. The graph rises from left to right: This is false, as the slope of the line is positive and y increases as x increases.

4. The graph touches the x-axis: This is false, as the y-intercept of the graph is at (0,1), which is above the x-axis.

5. The domain is (-∞, ∞), and the range is (-∞, ∞): This is true, as the function is defined for all real numbers and can take on any real value.

6. The domain is (-∞, 0), and the range is (-∞, 0): This is false, as the function is defined for all real numbers and can take on positive values as well.

Therefore, the correct answer is A. I., II., V.

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Answer:

see below

Step-by-step explanation:

All you need to do is plot the coordinates on the plot.

ex (1,2); (2,2); (3,3) etc.

See attached screenshot

Answer:

42944[tex]cm^{2}[/tex]

Step-by-step explanation:

(240*180)-(16*16)

43200-256

42944

Step-by-step explanation:

Given that:

Part of the graph of the function f(x) = (x – 1)(x + 7) is shown below. Which statements about the function are true? Select three options. The vertex of the function is at (–4,–15). The vertex of the function is at (–3,–16). The graph is increasing on the interval x > –3. The graph is positive only on the intervals where x < –7 and where x > 1. The graph is negative on the interval x < –4.

Solution:

1) The vertex of the function is at (–4,–15).

Ans.This is false.

2) The vertex of the function is at (–3,–16).

Ans. This is true. from the graph it is clearly shown A is vertex of graph.Which is (-3,-16)

3)The graph is increasing on the interval x > –3.

Ans. This region is located in graph with red colour,here it is easily shown that in this region graph continuously increasing.

This is true.

4)The graph is positive only on the intervals where x < –7 and where x > 1.

Ans: Yes,it is true.

Because when x<-7 graph is decreasing but have positive values and when x>1,graph is increasing and have positive values.

5)The graph is negative on the interval x < –4.

Ans:Yes,yellow part is shown the region of x<-4

here value of graph continuously decreasing.

Hope this helps!

The statements B, D and E can be used to justify that the function is linear.

A function is the central idea of calculus in mathematics. Certain types of functions are the relations. A function in mathematics is a rule that generates a different output for each input x. A mapping or transformation in mathematics serves as the representation of a function. Several people use letters like f, g, and h to denote these operations.

Here in the question,

Given equation is y = 2x - 5

Now we know that the general form of a equation is y = mx + c

So, y = 2x - 5 is a linear equation as it is in the slope equation form.

Now, from the equation,

Slope, m = 2.

Graph of the function is a straight line.

Therefore, we can say that the equation is a linear equation as it has a slope, m=2. The graph is a straight line, and the equation is in the form of y = mx+c.

Hence, the statements B, D and E can be used to justify that the function is linear.

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The complete question is:

Consider the function defined by

y x = − 2 5.

Which statements can be used to justify that the function is linear?

Select all that apply.

A The coefficient of x is greater than 1.

B The function has a constant slope of 2.

C The function has a negative y –intercept.

D The graph of the function is a straight line.

E The equation is written in the form y mx b = +.

PLS HELP ASAP!

Therefore , the solution of the given problem of fraction comes out to be  a = 2/9.

Any arrangement of parts or pieces that are the same dimension can represent the whole. Quantity is referred to in standard English as "a portion" in a given measure. 8, 3/4. Fractions are included in wholes. In mathematics, integers are represented by the ratio which is the divisor to the ratio. These are all examples of basic fractions that are divided by whole integers. The residue is a difficult fraction even though the fraction itself includes a fraction.

Here,

We can begin by separating out the variable component (a + 6) on one side of the equation and simplifying to find a:

=> 9/10 = 8/(a + 6)

Adding (a + 6) to both edges results in:

=> 9/10 * (a + 6) = 8

As the left edge is widened:

=> 9a/10 + 54/10 = 8

54/10 from both groups subtracted:

=> 9a/10 = 2/10

By 9/10ths dividing both sides:

=> a = (2/10)/(9/10)

=> a = 2/9

The answer is therefore a = 2/9.

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The calculated value of the lateral area of the rectangular prism is 272 cm².

We know that the surface area of the rectangular prism is 392 cm², and the area of the base is 60 cm².

The base area is the same as the top area

Therefore, the sum of the areas of the four sides of the rectangular prism is:

392 cm² - 2 * 60 cm² = 272 cm²

The lateral area of a rectangular prism is the sum of the areas of the four sides, excluding the top and bottom faces.

Therefore, the value of the lateral area of the rectangular prism is 272 cm².

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Answer:

x -intercept  ---> (-6,0)

y-intercept ---> (0, 9)

Step-by-step explanation:

3x = -18

3x/3 = -18/3

x = (-6,0)

-2y = -18

-2y/-2 = -18/-2

y = (0, 9)

Answer:

(-11, -14)

Step-by-step explanation:

Point (-8, -9)

Translation left 3 units

(-8, -9) → (-11, -9)

Down 5 units

(-11, -9) → (-11, -14)

So, the final point will be at (-11, -14)

Answer: (i) The length of the wire is 2147.76 cm.

(ii) The volume of the wire is 43.16 cm^3.

Step-by-step explanation:

Given : Diameter of copper wire = 8mm = 0.08cm

length of the cylinder = 24 cm

diameter of the cylinder = 49 cm

(i) To calculate the length of the wire.

As we know, surface area of the cylinder = πrl = 3.14*28.5*24 = 2147.76cm.

Hence, the surface area of the cylinder will be the length of the wire, as the wire is evenly wrapped n the surface of the cylinder.

Therefore, the length of the wire is 2147.76 cm.

(ii) To calculate the volume of the wire.

As we know, the formula for the volume of the cylinder = πr^2h

now the volume of the wire is = 3.14*0.08*0.08*2147.76 = 43.16 cm^3.

Therefore, the volume of the wire is 43.16 cm^3.

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