i need to make this 20 characters so this is the question in the photo please help

Answers

Answer 1

The combined fraction in the context of this problem is given as follows:

(4x² + 12x - 9)/(x² + 8x + 15).

How to obtain the combined fraction?

The fractional expression in the context of this problem is given as follows:

(x + 6)/(x² + 8x + 15) + 3x/(x + 5) - (x - 3)/(x + 3).

(x + 5)(x + 3) = x² + 8x + 15, hence the denominator of the simplified expression is given as follows:

x² + 8x + 15.

Applying the least common factor, the numerator of the simplified expression is given as follows:

x + 6 + 3x(x + 3) + (x - 3)(x + 5) = x + 6 + 3x² + 9x + x² - 3x + 5x - 15

x + 6 + 3x(x + 3) + (x - 3)(x + 5) = 4x² + 12x - 9

Hence the combined expression is given as follows:

(4x² + 12x - 9)/(x² + 8x + 15).

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Related Questions

In the accompanying diagram, m<A=32° and AC = 10. Which equation could be used to find x in ∆ABC?

1. x=10 sin [32°]
2. x=10 cos [32°]
3. x = 10 tan [32°]
4. x=10/cos32​

Answers

The equation x = 10 tan (32°) could be used to find x in ∆ABC.

RIGHT TRIANGLE

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  The greatest side of a right triangle is called the hypotenuse. And, the other two sides are called legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.

The Pythagorean Theorem says: (hypotenuse)²= (leg1)²+(leg2)² . And the main trigonometric ratios are: sin (x) , cos  (x) and tan  (x) , where:

[tex]sin(x)=\frac{opposite\ side}{hypotenuse} \\ \\ cos(x)=\frac{adjacent\ side}{hypotenuse}\\ \\ tan(x)=\frac{sin(x)}{cos(x)} =\frac{opposite\ side}{adjacent\ side}[/tex]

The question gives the value of the two sides and the value of an angle. From the trigonometric ratios presented before, you can write:

[tex]tan(32)=\frac{opposite\ side}{adjacent\ side}=\frac{x}{10} \\ \\ x=10\ tan (32\°)[/tex]

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a quadrilateral that is not a rectangle is inscribed in a circle. what is the least number of arc measures needed to determine the measures of each antgle in the quadrialteral

Answers

The least number of arc measures needed to determine the measures of each angle in the inscribed quadrilateral is 2.

To determine the measures of each angle in the quadrilateral, we need to find the central angles of the arcs that intersect the quadrilateral's vertices. Since the quadrilateral is not a rectangle, it is not a cyclic quadrilateral, which means that its opposite angles do not add up to 180 degrees.

Therefore, we need to use the fact that the sum of the measures of the opposite angles in an inscribed quadrilateral is 360 degrees. Let the angles of the quadrilateral be A, B, C, and D, with opposite angles A and C, and B and D. We can find the measure of arc AC by drawing a chord connecting the endpoints of AC and finding the central angle that intercepts it. Similarly, we can find the measure of arc BD.

Now, we can use the fact that the sum of the central angles that intercept arcs AC and BD is equal to 360 degrees. Let these angles be x and y, respectively. Then, we have:

x + y = 360

We can solve for one of the variables, say y, in terms of the other:

y = 360 - x

Substituting this into the equation for arc BD, we have:

2x + 2(360 - x) = arc BD

Simplifying this equation, we get:

arc BD = 720 - 2x

Now, we can use the fact that the sum of the measures of angles A and C is equal to the measure of arc AC, and the sum of the measures of angles B and D is equal to the measure of arc BD. Therefore, we have:

A + C = arc AC
B + D = arc BD = 720 - 2x

We need to find the least number of arc measures needed to determine the measures of A, B, C, and D. Since we have two equations and two variables (x and A), we can solve for both variables. Then, we can use the equations for B and D to find their measures.

Solving for A in terms of x, we have:

A = arc AC - C
A = 360 - x - C

Substituting this into the equation for B + D, we have:

(360 - x - C) + B + D = 720 - 2x

Simplifying this equation, we get:

B + D = 360 + x - C

Now, we have three equations and three variables (x, A, and C). We can solve for each variable in terms of x, and then use the equation for B + D to find their measures.

Therefore, the least number of arc measures needed to determine the measures of each angle in the quadrilateral is two: arc AC and arc BD.

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Interpret the probability. In 100 trials of this experiment, it is expected about (Round to the nearest whole number as needed.) to result in exactly 15 flights being on time

Answers

Hence, it is expected that 14 flights will arrive on time out of the 100 trials of this experiment.

What is the probability?

The probability of an occurrence is a number used in mathematics to describe how likely it is that the event will take place. In terms of percentage notation, between 0% and 100% it is expressed as a number between 0 and 1, or . The higher the likelihood, the more likely it is that the event will take place.

What is the trials?

 when we refer to an experiment or trial, we mean a random experiment. When difference  between a trial and an experiment, think of the experiment as a larger entity created by the fusion of several trials.

Unless otherwise stated,A trial is any specific outcome of a random experiment. In other words, a trial of the experiment is what we call when we conduct an experiment.

according to question, the number of on-time flights in 100 trials as a binomial random variable with parameters n = 100 (the number of trials) and p (the chance of success, i.e., a flight being on time), presuming that the probability of a flight being on time is the same in all trials.

The expected number of on-time flights in 100 trials is E(X) = np if the same of a flight being on time is p. Given that E(X) = 15, we determine p ,

E(X) = n p = 15 n = 100

p = [tex]\frac{E(X)}{n} = \frac{15}{100}[/tex] = 0.15

Therefore, it is probability that 0.15 %of flights will arrive on time.

To determine the expected  number of trials from a total of 100

Using the probability mass function of the binomial distribution, we can get the expected probability of trials out of 100 that result in precisely 15 flights departing on time:

[tex]P(X = 15)=(100 choose 15) * 0.15^{15} * 0.85^{85}[/tex]

We can calculate this 0.144 get  using a calculator.

therefore it is expected that 14 flights will arrive on time out of the 100 trials of this experiment. It should be noted that while this is an expected value, random fluctuation may cause the actual number of on-time flights in each trial to deviate somewhat from this figure.

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What is an equation of the line that passes
through the points (-1, -6) and (6, 1)?

Answers

Answer:

y = x - 5

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

Slope = rise/run or (y2 - y1) / (x2 - x1)

Points (-1, -6) and (6, 1)

We see the y increase by 7, and the x increase by 7, so the slope is

m = 7/7 = 1

Y-intercept is located at (0, -5)

So, the equation is y = x - 5

[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1}-\stackrel{y1}{(-6)}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{(-1)}}} \implies \cfrac{1 +6}{6 +1} \implies \cfrac{ 7 }{ 7 } \implies 1[/tex]

[tex]\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}{(-6)}=\stackrel{m}{ 1}(x-\stackrel{x_1}{(-1)}) \implies y +6 = 1 ( x +1) \\\\\\ y+6=x+1\implies {\Large \begin{array}{llll} y=x-5 \end{array}}[/tex]

Help please? I just need an answer. A clear explanation earns brainliest.

Answers

the simplified  form  of expression is: -(x² + 2x - 2)/((x+2)*(x+4))

what is expression  ?

In mathematics, an expression is a combination of numbers, variables, operators, and/or functions that represents a mathematical quantity or relationship. Expressions can be simple or complex

In the given question,

To evaluate the expression 1/(x+2) - (x+1)/(x+4), we need to find a common denominator for the two terms. The least common multiple of (x+2) and (x+4) is (x+2)(x+4).

So, we can rewrite the expression as:

(1*(x+4) - (x+1)(x+2))/((x+2)(x+4))

Expanding the brackets, we get:

(x+4 - x² - 3x - 2)/((x+2)*(x+4))

Simplifying the numerator, we get:

(-x² - 2x + 2)/((x+2)*(x+4))

Therefore, the simplified expression is:

-(x² + 2x - 2)/((x+2)*(x+4))

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40000 is divided by the smallest number so that the result is a perfect cube. find the cube root of the resulting number.

Answers

The Cube root of the resulting number is 8.

The smallest number that 40000 can be divided by so that the result is a perfect cube, we need to factorize 40000 into its prime factors:

[tex]40000 = 2^6 \times 5^4[/tex]

To make this a perfect cube, we need to ensure that the powers of each prime factor are multiples of 3.

The smallest number we can divide 40000 by so that the result is a perfect cube is:

[tex]40000 = 2^6 \times 5^4[/tex]

Now we can find the cube root of the resulting number:

[tex]3\sqrt (40000 \div 100) = 3\sqrt400 = 8.[/tex]

Factories 40000 into its prime components in order to determine.

The least number that the result may be divided by while still producing a perfect cube.

The powers of each prime factor must be multiples of three in order for this to be a perfect cube.

The least number that 40000 may be divided by to produce a perfect cube is:

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PLEASE HELP AND EXPLAIN AND SHOW WORK ON HOW YOU GOT THE ANSWER I WILL MARK YOU BRAINLIEST. PLEASE EXPLAIN HOW YOU GOT THE ANSWER!!!

Answers

The terms arranged in order from smallest to biggest are: (-2)³, -√25, √11, 10, and 4² after comparing the values of the final numbers.

How to arrange the terms of numbers in ascending order

We shall first simplify the numbers to get their final values and then compare to which is smaller as follows:

4² = 4 × 4 = 16

-√25 = -5

10 = 10

√11 = 3.3166

(-2)³ = -2 × -2 × -2 = -8

In conclusion, we have by comparing the final values of the numbers the terms arranged from smallest to the biggest as: (-2)³, -√25, √11, 10, and 4².

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In a Harris Poll survey of smokers, 848 of a sample of 1010 smokers agreed that smoking would probably shorten their lives. Harris announces a margin of error of ±
3 percentage points for all samples of about this size. Opinion polls announce the margin of error for 95% confidence.
Part 1: What is the actual margin of error (in percent) for the large-sample confidence interval from this sample?
a) 3%
b) 1.15%
c) 2.26%
d) 6%
Part 2: The margin of error is largest when ^p
= 0.5. What would the margin of error (in percent) be if the sample had resulted in ^p
= 0.5? Give your answer to 2 decimal places.
Part 3: Why do you think that Harris announces a ±
3% margin of error for all samples of about this size?
a) Because the margin of error for samples of about this size is no less than the announced margin of error.
b) Because the confidence level from the announced margin of error is closer to the actual confidence level than the one computed from a single sample.
c) Because the margin of error for samples of about this size is no more than the announced margin of error.
d) Because the large-sample margin of error from a single sample is not accurate.

Answers

Part 1- The actual margin of error (in percent) for the large-sample confidence interval from this sample is c) 2.26%.

Part 2- The margin of error (in percent) would be 3.1% if the sample had resulted in p-hat = 0.5.

Part 3- The reason why Harris announces a ±3% margin of error for all samples of about this size is c) because the

margin of error for samples of about this size is no more than the announced margin of error.

Part 1: The actual margin of error for the large-sample confidence interval from this sample can be calculated using the

formula: Margin of error = (z-score)*(standard error),

where the z-score for 95% confidence level is 1.96 and the standard error is [tex]\sqrt{[(p-hat \times(1-p-hat))/n]}[/tex]

Here, p-hat (proportion of smokers who agreed that smoking would probably shorten their lives) = 848/1010 = 0.84 and

n (sample size) = 1010.

Plugging these values into the formula, we get

Margin of error =[tex]1.96\times(sqrt[(0.84\times(1-0.84))/1010])[/tex] = 0.026 = 2.6%.

Part 2: The margin of error is largest when p-hat = 0.5, which means that the sample is equally split between two

options.

In this case, the standard error becomes [tex]\sqrt{[(0.5\times(1-0.5))/1010] } = 0.0158.[/tex]

Using the same formula as in Part 1, we get

Margin of error = [tex]1.96\times0.0158 = 0.031 = 3.1%.[/tex]

Part 3: The reason why Harris announces a ±3% margin of error for all samples of about this size is c) because the

margin of error for samples of about this size is no more than the announced margin of error.

This means that Harris is being conservative in their estimate of the margin of error and is ensuring that they do not

overstate the precision of their results. Additionally, they may want to account for other sources of error such as non-

response bias or sampling bias, which can also contribute to the overall margin of error.

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ehat are the roots of the polynominal equation? use a grapghing calculator and make 0=y,and find the x intercepts. x2 + x - 72=0 enter you answers in the boxes.

Answers

Therefore, the roots of the polynomial equation x² + x - 72 = 0 are -9 and 8.

What is quadratic equation?

A quadratic equation is a type of polynomial equation of the second degree, which means it has one or more terms in which the variable is raised to the power of two, but no higher powers.Quadratic equations can have zero, one, or two real solutions, depending on the values of a, b, and c. These solutions are also called the roots or zeros of the equation.

Here,

To find the roots of the polynomial equation x² + x - 72 = 0, we can set y = 0 and solve for x. This is equivalent to finding the x-intercepts of the graph of the function f(x) = x² + x - 72.

We can use the quadratic formula to solve for x:

x = (-b ± √(b² - 4ac)) / (2a)

where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.

In this case, a = 1, b = 1, and c = -72, so we have:

x = (-1 ± √(1² - 4(1)(-72))) / (2(1))

x = (-1 ± √(1 + 288)) / 2

x = (-1 ± √(289)) / 2

x = (-1 ± 17) / 2

Therefore, the roots of the polynomial equation x² + x - 72 = 0 are:

x = -9 or x = 8

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The table of values forms a quadratic function f(x). X f(x)
−2 48
−1 50
0 48
1 42
2 32
3 18
4 0

What is the equation that represents f(x)?
f(x) = –2x2 – 4x + 48
f(x) = 2x2 + 4x – 48
f(x) = x2 + 2x – 24
f(x) = –x2 – 2x + 24

Answers

To form a suitable quadratic equation using the values from the table given in the question also  considering the event of forming a equation that represents f(x) is Option A.
In order to find the equation that is  represented by f(x), we have to implement the standard form of a quadratic function
f(x) = ax² + bx + c
here a, b and c = constants.
We can utilize the given table of values to evaluate these constants.

Now, we have to  place each x value into f(x) to get the concerning y value. Then we can utilize these points to create three equations with three undetermined (a, b and c).
Evaluating these equations will give us the values of a, b and c.

Now, the table of values given in the question is

f(-2) = 48 = 4a - 4b + c
f(-1) = 50 = a - b + c
f(0) = 48 = c
f(1) = 42 = a + b + c
f(2) = 32 = 4a + 4b + c
f(3) = 18 = 9a + 3b + c
f(4) = 0 = 16a + 4b + c


Calculating these equations

a = -2
b = -4
c = 48

Hence, the equation that represents f(x) is f(x) = -2x² - 4x + 48.

The correct option for the given question after considering the given conditions is Option A.

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The complete question is
The table of values forms a quadratic function f(x). X f(x)−2 48
f(−1) = 50
f(0) = 48
f(1) = 42
f(2) = 32
f(3) = 18
f(4) = 0

What is the equation that represents f(x)?
a) f(x) = –2x² – 4x + 48
b) f(x) = 2x² + 4x – 48
c) f(x) = x² + 2x – 24
d) f(x) = –x² – 2x + 24


I need help please I will give brainliest to the best answer...

Answers

The value of x in the intersecting chords that extend outside circle is 5

Calculating the value of x

From the question, we have the following parameters that can be used in our computation:

intersecting chords that extend outside circle

Using the theorem of intersecting chords, we have

4 * (x + 6 + 4) = 6 * (x - 1 + 6)

Evaluate the like terms

So, we have

4 * (x + 10) = 6 * (x + 5)

Using a graphing tool, we have

x = 5

Hence. the value of x is 5

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what is 72% written in a deciamal

Answers

the answer is 0.72….

In Exercises 19-22, two triangles can be formed using the given meas- urements. Solve both triangles. 14. 19. A = 64°, a = 16,. 20. B 38°,. 21. C 68°,.

Answers

Two triangles can be formed using the given measurements,

19. Triangle 1: A = 64°, B ≈ 53.07°, C ≈ 62.93°, a = 16, b ≈ 14.83, c ≈ 16.64

Triangle 2: A = 64°, B ≈ 126.93°, C ≈ 9.07°, a = 16, b ≈ 80.17, c ≈ 8.98

20. Triangle 1: A ≈ 52°, B = 38°, C ≈ 94°, a ≈ 22.57, b = b, c ≈ 34.60

Triangle 2: A ≈ 128°, B = 38°, C ≈ 14°, a ≈ 22.57, b = b, c ≈ 16.66

19. We are given angle A and the side opposite to it, a. We can use the law of sines to find the other sides and angles of the triangle:

a/sin(A) = b/sin(B) = c/sin(C)

b/sin(B) = a/sin(A)

b = a × sin(B)/sin(A)

b = 16 × sin(64°)/sin(180°-64°-90°)

b ≈ 14.83

c/sin(C) = a/sin(A)

c = a × sin(C)/sin(A)

c = 16 × sin(68°)/sin(64°)

c ≈ 16.64

Therefore, the two triangles are:

Triangle 1: A = 64°, B ≈ 53.07°, C ≈ 62.93°, a = 16, b ≈ 14.83, c ≈ 16.64

Triangle 2: A = 64°, B ≈ 126.93°, C ≈ 9.07°, a = 16, b ≈ 80.17, c ≈ 8.98

20. We are given angle B. Let the length of the side opposite to B be b. We can use the fact that the angles in a triangle add up to 180° to find angle A, and then use the law of sines to find the remaining sides and angles:

A = 180° - 90° - 38°

A = 52°

a/sin(A) = b/sin(B) = c/sin(C)

a/sin(52°) = b/sin(38°)

c/sin(C) = b/sin(38°)

c = b*sin(C)/sin(38°)

The angles in a triangle add up to 180°, so we have:

C = 180° - A - B

C ≈ 94°

Substituting the values of A, B, and C in the above equations, we get:

a ≈ 22.57

b = b

c ≈ 34.60

Therefore, the two triangles are:

Triangle 1: A ≈ 52°, B = 38°, C ≈ 94°, a ≈ 22.57, b = b, c ≈ 34.60

Triangle 2: A ≈ 128°, B = 38°, C ≈ 14°, a ≈ 22.57, b = b, c ≈ 16.66

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The question is -

In Exercises 19-22, two triangles can be formed using the given measurements.

Solve both triangles.

19. A = 64°, a = 16,

20. B 38°

Slope-intercept (0, -2) , (9,1)

Answers

Answer:
Do you have a graph or anything?

please solve correctly my grade depends on it

Answers

Just use the pythagorean theorem to solve the hypotenuse!

(3^2)+(2^2)=x^2

9+4=13^2

[tex]\sqrt{13}[/tex] = [tex]\sqrt{x}[/tex]

[tex]13^{2}[/tex] km

Hope this helps <3

Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 12 people took the trip. She was able to purchase coach tickets for ​$190 and first class tickets for ​$980. She used her total budget for airfare for the​ trip, which was ​$4650. How many first class tickets did she​ buy? How many coach tickets did she​ buy?

Answers

Sarah then purchased 9 coach seats as by increasing the first equation by 190 and deducting it from the second equation.

what is equation ?

An equation is a logical statement that utilises the equal sign to demonstrate the equality of two expressions. Factors, constants, and mathematical like addition, reduction, multiply, division, and exponentiation can all be found in it. Equations are utilised to find solutions for problems in both mathematics and the real world.

given

Let's use the letters "c" for the quantity of coach tickets and "f" for the quantity of first-class tickets. We are aware that there were 12 travellers in all, so

c + f + 1 = 12

We also know that the entire cost of the airfare was $4650, with coach tickets costing $190 and first-class tickets costing $980. With this knowledge, we can construct the equation shown below:

[tex]190c + 980f = 4650 - 980[/tex]

When we simplify this equation, we obtain:

[tex]190c + 980f = 3670[/tex]

Elimination can now be used to find either "c" or "f." By increasing the first equation by 190 and deducting it from the second equation, let's get rid of "c":

[tex]190c + 190f + 190 = 2280[/tex]

-190c - 980f = -3670

-790f = -1390

f = 1.76

We can round "f" up to 2 because we cannot have a fractional number of persons.

c + 2 + 1 = 12

c = 9

Sarah then purchased 9 coach seats as by increasing the first equation by 190 and deducting it from the second equation.

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Kiran swims z laps in the pool. Clare swims 18 laps, which is 9/5
times as many laps as Kiran. How many laps did Kiran swim?
Equation:
Solution: z=

Answers

we use linear equation in one variable to solve the problem. Kiran swam 10 laps in the pool.

Let's represent the number of laps Kiran swam as "z".

We know that Clare swam 18 laps, which is 9/5 times as many laps as Kiran. We can represent this relationship with the following equation:

18 = (9/5)z

To solve for z, we can isolate it by multiplying both sides of the equation by the reciprocal of 9/5, which is 5/9:

18 * (5/9) = (9/5)z * (5/9)

10 = z

Therefore, Kiran swam 10 laps in the pool.

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Find unknown sides and angle of the triangle

Answers

The sides and the angle of the right triangle are a = 10√2, b = 10√2 and B = π / 4.

How to find the missing information of a right triangle

In this problem we need to determine the values of two sides and an angle of the right triangle. This can be done by means of the following properties:

A + B + C = π

sin A = a / c

cos A = b / c

tan A = a / b

Where:

A, B, C - Angles of the right triangle, in radians.a, b, c - Sides of the right triangle.

If we know that A = π / 4, C = π / 2 and c = 20, then the missing angle and missing sides are, respectively:

B = π - π / 4 - π / 2

B = π / 4

cos (π / 4) = b / 20

b = 20 · cos (π / 4)

b = 10√2

sin (π / 4) = a / 20

a = 20 · sin (π / 4)

a = 10√2

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A ball is thrown into the air with an initial upward velocity of 48 ft/s. Its height (h) in feet after t seconds is given by the function h=-16t^2+48t+64. After how many seconds will the ball hit the ground?

Answers

Answer: Let the experienced one help you out! Therefore, the ball hits the ground after 4 seconds. Read the explanation down below:

Brainliest?

Step-by-step explanation:

To find when the ball hits the ground, we need to find the value of t when h=0, since at that point the height of the ball is zero, indicating that it has reached the ground.

We have the equation:

h = -16t^2 + 48t + 64

Setting h to zero, we get:

0 = -16t^2 + 48t + 64

Dividing both sides by -16, we get:

0 = t^2 - 3t - 4

Now we can use the quadratic formula to solve for t:

t = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = -3, and c = -4.

Plugging in these values, we get:

t = (-(-3) ± sqrt((-3)^2 - 4(1)(-4))) / 2(1)

t = (3 ± sqrt(9 + 16)) / 2

t = (3 ± 5) / 2

So we have two solutions:

t = (3 + 5) / 2 = 4

t = (3 - 5) / 2 = -1

The negative solution doesn't make sense in this context, so we discard it. Therefore, the ball hits the ground after 4 seconds.

A concert ticket costs $65. If 25,300 tickets are available, how much money will be made in concert tickets if every
ticket is sold. Create an equation to represent this situation. Write the equation in function notation. State the
ordered pair for 25,300 tickets and explain your solution.

Answers

Answer:

$ 1644500

Step-by-step explanation:

Find the points on the surface z2 = xy +16 closest to the origin. The points on the surface closest to the origin are (Type an ordered triple. Use a comma to separate answers as needed. )

Answers

The points on the surface z² = xy + 16 closest to the origin are: (-4,4,0) and (4, -4, 0)

We know that the distance between an arbitrary point on the surface and the origin is d(x, y, z) = √(x² + y² + z²)

Using Lagrange multipliers,

L(x, y, z, λ) = x² + y² + z² + λ(z² - xy - 16)

We have partial derivatives.

[tex]L_x[/tex] = 2x - λy

[tex]L_y[/tex] = 2y - λx

[tex]L_z[/tex] = 2z + 2zλ

[tex]L_\lambda[/tex] = z² - xy - 16

Now we set each partial derivative to zero to find critical points.

[tex]L_x[/tex] = 0

2x - λy = 0

[tex]L_y[/tex] = 0

2y - λx = 0

After solving above equations simultaneously we get (x + y)(x - y) = 0

i.e., x = -y   OR   x = y

[tex]L_z[/tex] = 0

2z + 2zλ = 0

z = 0  OR  λ = 0

Consider [tex]L_\lambda[/tex] = 0

z² - xy - 16 = 0

-xy = 16                  ............(as z = 0)

when x = y then -y² = 16 which is not true.

So, consider x = -y

-(-y)y = 16

y² = 16

y = ±4

when y = 4 then we get x = -4

and when y = -4 then we get x = 4

Therefore, the closest points are:(-4,4,0) and (4, -4, 0)

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a p-value a. can be positive or negative. b. is a probability. c. can be smaller than 0 but no larger than 1. d. can be larger than 1 but no smaller than 0. e. can only range in value from -1 to 1.

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A p-value is a probability.

A p-value is the probability of obtaining a test statistic as extreme or more extreme.

The observed value, assuming the null hypothesis is true.

It ranges in value from 0 to 1 and represents the strength of evidence against the null hypothesis.

A p-value cannot be negative, as it is a probability and probabilities are always between 0 and 1.

A p-value also cannot be larger than 1, as it represents a probability.

A probability cannot exceed 1.

Finally, a p-value cannot be smaller than 0, as it represents a probability.

A probability cannot be negative.

the correct option is b. is a probability.

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What happens to the value of the function as the number of iterations increases? Be specific with the value.

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Without knowing which specific function you're referring to, the answer to this question may depend on the type of function and the nature of the iterative process applied to it. In some cases, the function value may converge towards a limiting value as the number of iterations increases, while in other cases it may oscillate or diverge.

For example, in the case of the fixed-point iteration method used to find the root of a function, the value of the function typically converges towards the root as the number of iterations increases. More specifically, if we have a function f(x) and a starting guess x0 for its root, we can use the iterative formula x(+1)=g(x()), where g(x) is some function that we set based on f(x), to generate a sequence of increasingly accurate approximations to the root. As the number of iterations increases, this sequence of approximations typically converges towards the root of the function, unless some conditions are not met (e.g., the method is not well-suited for some functions, or the iteration formula is not properly set.)

In the case of other types of iterative methods or other functions, however, the behavior of the function value as the number of iterations increases may differ. For instance, in some cases, the function value may oscillate between two or more values or diverge to infinity as the number of iterations increases.

Therefore, the specific behavior of the function value as the number of iterations increases may depend on the specific function being evaluated and the iterative method used.

you roll a 6-sided dice. what is the probability that you rolled a 5, given that the number rolled was greater than 3?

Answers

The probability that you rolled a 5, given that the number rolled was greater than 3, is 1/3 or approximately 0.333.

We need to find the probability that you rolled a 5, given that the number rolled was greater than 3. Let's break this down step by step:

1. Identify the total number of outcomes: Since it is a 6-sided dice, there are 6 possible outcomes (1, 2, 3, 4, 5, and 6).

2. Determine the number of outcomes greater than 3: The outcomes greater than 3 are 4, 5, and 6. There are 3 possible outcomes that satisfy this condition.

3. Identify the number of outcomes that result in rolling a 5: There is only 1 outcome that results in rolling a 5.

4. Calculate the probability: To find the probability, divide the number of outcomes that result in rolling a 5 (1) by the total number of outcomes greater than 3 (3).

Probability = (Number of outcomes with a 5) / (Number of outcomes greater than 3) = 1/3

So, the probability that you rolled a 5, given that the number rolled was greater than 3, is 1/3 or approximately 0.333.

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The probability that the number rolled was a 5, given that it was greater than 3, is [tex]$\frac{1}{3}$[/tex].

The number rolled was greater than 3, it must be either a 4, 5, or 6.

The probability that the number rolled was a 5, given that it was greater than 3.

Let [tex]$A$[/tex] be the event that the number rolled is a 5 and let [tex]$B$[/tex] be the event that the number rolled is greater than 3.

Then, we want to find. [tex]$P(A|B)$[/tex], the probability of [tex]$A$[/tex] given [tex]$B$[/tex].

By Bayes' theorem, we have:

Bayes' theorem (alternatively Bayes' law or Bayes' rule), named after Thomas Bayes, describes the probability of an event, based on prior knowledge of conditions that might be related to the event.

The risk of developing health problems is known to increase with age, Bayes' theorem allows the risk to an individual of a known age to be assessed more accurately by conditioning it relative to their age, rather than simply assuming that the individual is typical of the population as a whole.

One of the many applications of Bayes' theorem is Bayesian inference, a particular approach to statistical inference.

The probabilities involved in the theorem may have different probability interpretations.

Bayesian probability interpretation, the theorem expresses how a degree of belief, expressed as a probability, should rationally change to account for the availability of related evidence.

Bayesian inference is fundamental to Bayesian statistics, being considered by one authority as; "to the theory of probability what Pythagoras's theorem is to geometry."

[tex]$P(A|B) = \frac{P(B|A)P(A)}{P(B)}$[/tex]

[tex]$P(A) = \frac{1}{6}$[/tex], since there is only one way to roll a 5 on a 6-sided die.

[tex]$P(B) = \frac{3}{6} = \frac{1}{2}$[/tex], since there are three outcomes (4, 5, or 6) that satisfy. [tex]$B$[/tex], out of a total of six possible outcomes.

[tex]$P(B|A)$[/tex], the probability of rolling a number greater than 3, given that the number rolled is a 5, note that. [tex]$B$[/tex] is true only if the number rolled is a 4, 5, or 6.

Since there is only one way to roll a 5, and only one of these three outcomes satisfies. [tex]$A$[/tex], we have:

[tex]$P(B|A) = \frac{1}{1} = 1$[/tex]

Substituting these values into Bayes' theorem, we get:

[tex]$P(A|B) = \frac{P(B|A)P(A)}{P(B)} = \frac{1 \cdot \frac{1}{6}}{\frac{1}{2}} = \frac{1}{3}$[/tex]

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Verify that the segments are parallel.

10. CD || AB

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Answer: Prove that the triangles are similar, and therefore the lines have the same slope and are parallel.

Eddie Clauer sells a wide variety of outdoor equipment and clothing. The company sells both through mail order and via the internet. Random samples of sales receipts were studied for mail-order sales and internet sales, with the total purchase being recorded for each sale. A random sample of 17 sales receipts for mail-order sales results in a mean sale amount of $84. 80 with a standard deviation of $19. 25. A random sample of 12 sales receipts for internet sales results in a mean sale amount of $77. 10 with a standard deviation of $26. 25. Using this data, find the 90% confidence interval for the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases. Assume that the population variances are not equal and that the two populations are normally distributed.

Step 1 of 3 :

Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Step 2 of 3

Find the Staandard error of the sampling distrbution to be used in constructing the confidence interval

Step 3 of 3

you were to ask to construct the 90% confidence interval, given the following information

Answers

The 90% confidence interval for the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases is approximately [-6.62, 22.02].

The critical value that should be used in constructing the confidence interval.

Since we are looking for a 90% confidence interval, we need to find the critical value associated with a 5% level of significance in a two-tailed test.

Using a t-distribution with (n1-1) + (n2-1) degrees of freedom and a significance level of 0.05, we find the critical value to be:

t-critical = 1.717 (using a t-distribution table or a calculator)

Step 2 of 3:

Next, we need to find the standard error of the sampling distribution to be used in constructing the confidence interval.

Since the population variances are not equal, we need to use the Welch-Satterthwaite equation to calculate the standard error:

SE = sqrt[([tex]s1^2[/tex]/n1) + ([tex]s2^2[/tex]/n2)]

where s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Substituting the given values, we get:

SE = sqrt[([tex]19.25^2[/tex]/17) + ([tex]26.25^2[/tex]/12)]

SE ≈ 8.35

Step 3 of 3:

To construct the 90% confidence interval, we can use the formula:

(mean1 - mean2) ± t-critical * SE

where mean1 and mean2 are the sample means, and t-critical and SE are the values calculated in steps 1 and 2.

Substituting the given values, we get:

= (84.80 - 77.10) ± 1.717 x 8.35

= 7.70 ± 14.32

Therefore,

The 90% confidence interval for the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases is (approx) [-6.62, 22.02].

We can be 90% confident that the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases falls within this interval.

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Write your answer as an integer or decimal.
please help

Answers

The value of angle GFH is 18°

What is circle geometry?

A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.

A theorem in circle geometry starts that angle in the same segment are equal. In triangle EFG, angle F and G are on the same segment, this means that angle F and G are equal.

Represent angle F as x

therefore 144+2x = 180° ( sum of angle in a triangle)

2x = 180-144

2x = 36

x = 36/2 = 18°

Therefore the measure of angle GFH is 18°

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dora drove east at a constant rate of 75 kph. one hour later, tim started driving on the same road at a constant rate of 90 kph. for how long was tim driving, before he caught up to dora? a. 5 hours b. 4 hours c. 3 hours d. 2 hours

Answers

Tim was driving for 5 hours before he caught up to Dora.

The answer is (a) 5 hours.

To solve this problem, we can use the formula:
distance = rate × time
Let's denote the time Tim drove as t hours.

Since Dora started driving one hour earlier, her driving time would be (t + 1) hours.
Dora's distance: 75 kph × (t + 1)
Tim's distance: 90 kph × t
Since Tim catches up to Dora, their distances will be equal:
75(t + 1) = 90t
Now we can solve for t:
75t + 75 = 90t
75 = 15t
t = 5.

The answer is (a) 5 hours.

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Write the functions in standard form:
h(x)=2(x-3)²-9
h(x)=
p(x) = -5(x + 2)² + 15
p(x)=

Answers

Answer:

[tex]h(x)=2x^2-12x+9[/tex],  [tex]p(x)=-5x^2-20x-5[/tex]

Step-by-step explanation:

To get to the standard form of a quadratic equation, we need to expand and simplify. Recall that standard form is written like so:

[tex]ax^2+bx+c[/tex]

Where a, b, and c are constants.

Let's expand and simplify h(x).

[tex]2(x-3)^2-9=\\2(x^2+9-6x)-9=\\2x^2+18-12x-9=\\2x^2+9-12x=\\2x^2-12x+9[/tex]

Thus, [tex]h(x)=2x^2-12x+9[/tex]

Let's do the same for p(x).

[tex]-5(x+2)^2+15=\\-5(x^2+4+4x)+15=\\-5x^2-20-20x+15=\\-5x^2-5-20x=\\-5x^2-20x-5[/tex]

Thus, [tex]p(x)=-5x^2-20x-5[/tex]

Round the number. Write the result as the product of a single digit and a power of 10.
4,241,933,200

Answers

Rounding 4,241,933,200 to a single digit times a power of 10 would result in:

4.2 × 10^9

To round to this value, we drop all the digits after the tens digit (which is 2), and then round the tens digit up to 3 because the digit to its right (which is 9) is greater than or equal to 5. Finally, we append nine zeros to the end of the number to represent the power of 10.
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