Solve the quadratic equation by using either a numeric or a graphic approach

Answer:

x < 3

Step-by-step explanation:

The last step is to divide by -2. When you divide by a negative number you must reverse (flip) the inequality symbol.

-6 < -2x

-6/-2 > -2x/-2

3 > x

This is the same as

x < 3 (see the pointy side pointing at the x and the wide open side facing the 3)

The laptop will be worth $0.001286 after 15 years if its worth becomes 1/3 each year.

We can solve this problem by using the formula for geometric sequences,

an = a₁r^(n-1), here in this case, an is the worth of the laptop after n years, r is the rate at which the worth is changing that 1/3 in this case and a₁ is the value of the laptop currently. Substituting the given values, we get:

a₁₅ = 600(1/3)¹⁵⁻¹

a₁₅ = 600(1/3)¹⁴

a₁₅ = 600x0.0000021433

a₁₅ = 0.001286

Therefore, after 15 years, the laptop is worth approximately $0.001286.

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The points on the graph of f(x) = log9x are (20, 4.5), (11/9, 0.087183), (2439, 3.168910), (181, 2.55231), and (2, 1).

The points on the graph of f(x) = log9x can be calculated by substituting the given values of x in the equation. For example,

f(-1/81) = log9(-1/81) = log9(-1) - log9(81) = undefined

f(20) = log9(20) = log9(2*2*2*5) = log9(2) + log9(2) + log9(2) + log9(5) = 1 + 1 + 1 + 1.5 = 4.5

f(11/9) = log9(11/9) = log9(11) - log9(9) = 1.041393 - 0.954210 = 0.087183

f(-13) = log9(-13) = log9(-1) - log9(13) = undefined

f(2439) = log9(2439) = log9(3*13*37) = log9(3) + log9(13) + log9(37) = 0.477121 + 1.11394 + 1.579789 = 3.168910

f(181) = log9(181) = log9(3*3*7*7) = log9(3) + log9(3) + log9(7) + log9(7) = 0.477121 + 0.477121 + 0.84509 + 0.84509 = 2.55231

f(2) = log9(2) = log9(2) = 1

Hence, the points on the graph of f(x) = log9x are (20, 4.5), (11/9, 0.087183), (2439, 3.168910), (181, 2.55231), and (2, 1).

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-6.75  is a rational number.

Let us understand about natural, whole, integer, rational, and irrational numbers one by one.

Natural number:

Natural numbers are numbers that start from 1 and end at infinity. These are non-negative numbers.

Whole number:

Whole numbers are numbers that start from 0 and end at infinity.

We can also natural numbers including 0 is known as whole numbers.

These are non-negative numbers.

Integer:

An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.

Rational number:

A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p, and a non-zero denominator q.

Also, the decimal representation of the rational number is terminating and recurring.

Irrational number:

An irrational number is a number that can not be expressed as the quotient or fraction p/q of two integers, a numerator p, and a non-zero denominator q.

Also, the decimal representation of the irrational number is non-terminating and non-recurring.

The given number is -6.75.

The decimal form is terminating.

So, it is a rational number.

Thus, -6.75  is a rational number.

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Answer:-11

Step-by-step explanation:

Answer:

a=3

Step-by-step explanation:

Answer:

A: 13

Step-by-step explanation:

4a-3 = 9

add 3 to both sides

4a-3 = 9

  +3   +3

the -3 and +3 will cancel each other out

and from adding the 3 to the 9 will turn the 9 into 12!

Now your equation will look like this

4a = 12

Next divide both sides by 4. the 4 will cancel out the other 4.\

now you will have your answer

a = 3

so now substitute the A with 3 in

4a+1

so it will be

4(3)+1

4 times 3 is equal to 12

then 12+1 = 13

I hope this helps! :)

Thus, the gage pressure exerted on the reservoir of the inclined manometer is 17.5 Pa.

To determine the gage pressure exerted on the reservoir of an inclined manometer, we need to use the following formula:

ΔP = ρghsin(θ)

Where:
- ΔP is the pressure difference between the two arms of the manometer
- ρ is the density of the fluid
- g is the acceleration due to gravity
- h is the height difference between the two arms of the manometer
- θ is the angle of inclination

In this case, we are given that the fluid has a specific gravity of 0.7, which means that its density can be calculated as:

ρ = specific gravity x density of water
ρ = 0.7 x 1000 kg/m³
ρ = 700 kg/m³

We are also given that the manometer reads 10.2cm, which represents the height difference between the two arms of the manometer.

Finally, we are told that the manometer is inclined at an angle of 15 degrees.

Using these values, we can plug them into the formula and solve for ΔP:

ΔP = ρghsin(θ)
ΔP = 700 kg/m³ x 9.81 m/s² x 0.102 m x sin(15°)
ΔP = 17.5 Pa

Therefore, the gage pressure exerted on the reservoir of the inclined manometer is 17.5 Pa.

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Answer:

Step-by-step explanation: 4 5/6

Decimal: 4.83 repeating

Fraction: 0.83 repeating

Happy to help.

Answer:To find out how much change Lucinda received, we subtract the cost of the video game from the amount she paid:

Amount paid - Cost of the video game = Change

$100 - $63.48 = $36.52

Therefore, Lucinda received $36.52 in change.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: it’s A and C (45 ft and 37 ft) I think

This hypothesis test is testing the proportion of commuting students who walk to school.

Hence, you perform a one-sample proportion test.

The alternative hypothesis has a "less than" symbol in it and both of the hypotheses compare the parameter to the value 0.5.

The value of your test statistic is -1.885, which results in a p-value of 0.030.

You could also find the critical value, which is -1.645.

Using the p-value or the critical value, you determine that you reject the null hypothesis.

This means that there is significant evidence to say that the proportion of commuting students that walk is less than half at the 10% level of significance.

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Answer:

y = 4

or (0, 4)

Step-by-step explanation:

intersecting the y-axis is basically when x is equal to 0.

1.5(0) +4.5y = 18

y = 4

So your y-intersect is (0, 4) and thats when it intersects the y-axis.

Amanda's answer correct is not correct. The correct answer is 4 R2, because she might have incorrectly divide the first digit of 34, which is 3, by 8. She should have moved on to the next digit instead

Amanda's answer, 3 R10, is not correct.

When we divide 34 by 8, we want to know how many times 8 goes into 34, and what is left over. We start by dividing 8 into the first digit of 34, which is 3. 8 cannot go into 3, so we move on to the next digit, which is 34.

We can see that 8 goes into 34 four times, because 8 x 4 = 32. This means that the whole number part of the answer is 4.

But there is still a remainder left over. To find the remainder, we subtract 32 from 34, which gives us 2.

Therefore, the correct answer is 4 R2.

Amanda's mistake may have been to incorrectly divide the first digit of 34, which is 3, by 8. She should have moved on to the next digit instead.

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The value of x in this equation is -¼ so, the approximate solution to the equation "-1+3=12x+5" is (x = -¼).

As equation given is -1+3=12x+5

Thus, 2 = 12x+5

12x = -3

x = -3/12

x = -¼

Hence the value of x in this equation is -¼.

The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x+3=8 only has one variable. As a result, this equation has a single solution, x = 5/2. A linear equation with two variables, however, has two solutions.

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Answer:

Degrees = Radians x 180/π

or

Degrees = 57.2958  x radians

Step-by-step explanation:

1 radian = 180/π degrees

1 radian = 57.2958 degrees

Multiply radians by this factor of 57.2958  to get the equivalent measure in degrees

π radians = 180°

2π radians = 360° which is the number of degrees in a circle

For anything greater than 2π radians you will have to subtract 360°

For example, 7 radians using the formula is 7 x (57.2958  ) ≈ 401.07°

But this still falls in the first quadrant, so relative to the x-axis it is
401.07 - 360 = 41.07°

On solving the provided question, we can say that - the area of the provided circle is A = \(113.04 cm^2\)

Every point in the plane that is a certain distance away from a certain point forms a circle (center). It is, thus, a curve formed by points moving in the plane at a fixed distance from a point. At every angle, it is also rotationally symmetric about the center. A circle is a closed two-dimensional object where every pair of points in the plane are equally spaced out from the "center." A line that goes through the circle creates a specular symmetry line. At every angle, it is also rotationally symmetric about the center.

here,

radius, r = 6 cm

Area of circle = \(\pi X r^2 = 3.14 X 6 X 6 \\\)

A = \(113.04 cm^2\)

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To write a function that represents the profit after t years, we can use the exponential growth formula \(P(t) = P(0) \cdot (1 + r)^t\)

The function that represents the profit after t years is P(t) = 830 * (1.58)^t.

To write a function that represents the profit after t years, we can use the exponential growth formula:

\(P(t) = P(0) \cdot (1 + r)^t\)

Where:
- P(t) represents the profit after t years
- P(0) represents the initial profit
- r represents the growth rate per year
- t represents the number of years

In this case, the initial profit is $830 and the growth rate is 58% per year. Let's substitute these values into the formula:

P(t) = 830 * (1 + 0.58)^t

Simplifying the equation, we have:

P(t) = 830 * (1.58)^t

This function represents the profit after t years, given an initial profit of $830 and a growth rate of 58% per year.

For example, if we want to calculate the profit after 5 years, we can substitute t = 5 into the equation:

P(5) = 830 * (1.58)^5

P(5) = 830 * 4.619

P(5) ≈ 3833.38

So, after 5 years, the profit is approximately $3833.38.

This function can be used to calculate the profit after any number of years.

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the cost is lower when using the service every 10 days, the hotel should use the pickup-and-delivery service every 10 days to minimize costs.

To determine how often the hotel should use the pickup-and-delivery service, we need to compare the costs of storing the dirty towels and clean towels with the costs of the pickup-and-delivery service.

Let's calculate the costs of storing the towels:

Dirty towel storage cost per day: 600 towels x $0.02 = $12 per day

Clean towel storage cost per day: 600 towels x $0.01 = $6 per day

Next, let's calculate the costs of the pickup-and-delivery service:

Fixed charge per pickup and delivery service: $81

Variable cost per towel: 600 towels x $0.60 = $360

Now, let's compare the costs:

If the hotel uses the pickup-and-delivery service every 10 days, the total cost would be:

10 days  ($12 + $6) + $81 + $360 = $267

If the hotel uses the pickup-and-delivery service every 9 days, the total cost would be:

9 days  ($12 + $6) + $81 + $360 = $255

Since the cost is lower when using the service every 10 days, the hotel should use the pickup-and-delivery service every 10 days to minimize costs.

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A probability of 0.48 means that there is a 48% chance that a player will be dealt a particular hand in the card game.

If you play the card game 100 times, it may not be possible that you will be dealt this particular hand exactly 48 times because theoretical probability differs from experimental probability.

The concept of probability deals with the likelihood of an event occurring, but it does not guarantee the occurrence of that event in every individual trial.

While the expected value is that you will be dealt this hand around 48 times out of 100 games, the actual results can differ due to the random nature of the card shuffling process. You could be dealt the hand more or fewer times in any given set of 100 games.

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Complete question:

In a certain card​ game, the probability that a player is dealt a particular hand is 0.48. Explain what this probability means. If you play this card game 100​ times, will you be dealt this hand exactly 48 ​times? Why or why​ not?

In a certain card game, the probability of being dealt a particular hand represents the likelihood of receiving that specific hand out of all possible combinations.

The probability of being dealt a particular hand in a card game indicates the chance of receiving that specific hand out of all possible combinations. It is a measure of how likely it is for the player to get that specific combination of cards. The probability is typically expressed as a fraction, decimal, or percentage.

However, when playing the card game 100 times, it is highly unlikely that the player will be dealt the same hand exactly the same number of times. This is because the card shuffling and dealing process in the game is usually random. Each time the cards are shuffled, the order and distribution of the cards change, leading to different hands being dealt. The probability remains the same for each individual game, but the actual outcomes may vary.

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The measure of angle A in a right triangle with base 5 cm and hypotenuse 10 cm is approximately 38.21 degrees.

We can use the inverse cosine function (cos⁻¹) to find the measure of angle A, using the cosine rule for triangles.

According to the cosine rule, we have:

cos(A) = (b² + c² - a²) / (2bc)

where a, b, and c are the lengths of the sides of the triangle opposite to the angles A, B, and C, respectively. In this case, we have b = 5 cm and c = 10 cm (the hypotenuse), and we need to find A.

Applying the cosine rule, we get:

cos(A) = (5² + 10² - a²) / (2 * 5 * 10)

cos(A) = (25 + 100 - a²) / 100

cos(A) = (125 - a²) / 100

To solve for A, we need to take the inverse cosine of both sides:

A = cos⁻¹((125 - a²) / 100)

Since this is a right triangle, we know that A must be acute, meaning it is less than 90 degrees. Therefore, we can conclude that A is the smaller of the two acute angles opposite the shorter leg of the triangle.

Using the Pythagorean theorem, we can find the length of the missing side at

a² = c² - b² = 10² - 5² = 75

a = √75 = 5√3

Substituting this into the formula for A, we get:

A = cos⁻¹((125 - (5√3)²) / 100) ≈ 38.21 degrees

Therefore, the measure of angle A is approximately 38.21 degrees.

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Answer:

B

Step-by-step explanation:

A)  -4

B)  results in a non-terminating, non-repeating decimal, which is irrational

C)  2

D)  4

Therefore, the total number of ways the lights can be arranged on the string is: 14! / (2! * 4! * 5! * 2!).

To find the number of ways the lights can be arranged on a string, we need to calculate the total number of permutations.

The total number of lights is 2 red lights + 4 yellow lights + 5 blue lights + 1 green light + 2 pink lights = 14 lights.

Since all the lights are distinct, we can arrange them in 14! (factorial) ways. However, since there are repetitions of certain colors, we need to account for that.

The red lights are identical, so we divide by 2! (the number of permutations of the red lights among themselves).

The yellow lights are identical, so we divide by 4! (the number of permutations of the yellow lights among themselves).

The blue lights are identical, so we divide by 5! (the number of permutations of the blue lights among themselves).

The pink lights are identical, so we divide by 2! (the number of permutations of the pink lights among themselves).

Therefore, the total number of ways the lights can be arranged on the string is:

14! / (2! * 4! * 5! * 2!)

You can calculate this expression to find the specific number of arrangements.

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Answer:

Nope.

Step-by-step explanation:

Answer:

y=-3/5x-16/5

Step-by-step explanation:

(-2,-2). When x of the line is -2, y of the line must be -2.

(8,-8). When x of the line is 8, y of the line must be -8.

Given the probabilities P(A) = 0.7, P(Ac) = 0.3, P(B|A) = 0.4, and P(B|Ac) = 0.8, the joint probabilities can be calculated as follows: P(A and B) = 0.28, P(A and Bc) = 0.42, P(Ac and B) = 0.12, and P(Ac and Bc) = 0.18.

The joint probability P(A and B) represents the probability of events A and B occurring simultaneously. It can be calculated using the formula P(A and B) = P(A) * P(B|A). Given that P(A) = 0.7 and P(B|A) = 0.4, we can multiply these probabilities to obtain P(A and B) = 0.7 * 0.4 = 0.28.

It can be calculated as P(A and Bc) = P(A) * P(Bc|A). Since the complement of event B is denoted as Bc, and P(Bc|A) = 1 - P(B|A), we can calculate P(A and Bc) as P(A) * (1 - P(B|A)) = 0.7 * (1 - 0.4) = 0.42.

Finally, P(Ac and Bc) represents the probability of both event A and event B not occurring. It can be calculated as P(Ac and Bc) = P(Ac) * P(Bc|Ac). Using P(Ac) = 0.3 and P(Bc|Ac) = 1 - P(B|Ac), we can calculate P(Ac and Bc) as P(Ac) * (1 - P(B|Ac)) = 0.3 * (1 - 0.8) = 0.18.

Therefore, the joint probabilities are: P(A and B) = 0.28, P(A and Bc) = 0.42, P(Ac and B) = 0.24, and P(Ac and Bc) = 0.18.

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The correct formula that defines an arithmetic sequence is option d) tn = 5n + 14.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. In other words, each term can be obtained by adding a fixed value (the common difference) to the previous term.

In option a) tn = 5 + 14, the term does not depend on the value of n and does not exhibit a constant difference between terms. Therefore, it does not represent an arithmetic sequence.

Option b) tn = 5n² + 14 represents a quadratic sequence, where the difference between consecutive terms increases with each term. It does not represent an arithmetic sequence.

Option c) tn = 5n(n+14) represents a sequence with a varying difference, as it depends on the value of n. It does not represent an arithmetic sequence.

Option d) tn = 5n + 14 represents an arithmetic sequence, where each term is obtained by adding a constant value of 5 to the previous term. The common difference between consecutive terms is 5, making it the correct formula for an arithmetic sequence.

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When x = -2 , f(x) = 4 , when x = 0, f(x) = 8 ,and when x = 5, f(x) = 18.

Given function:

f(x) = 2x + 8

when x = -2

f(-2) = 2(-2) + 8

= -4 + 8

f(-2) = 4

when x = 0

f(0) = 2(0) + 8

= 8

f(0) = 8

when x = 5

f(5) = 2(5) + 8

= 10 + 8

f(5) = 18

Therefore when x = -2 , f(x) = 4 , when x = 0, f(x) = 8 ,and when x = 5, f(x) = 18.

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Answer:

Based on the given information, it is not possible to definitively determine whether the number generator is fair or not. However, we can make some observations and inferences:

We know that 70% of the socks in the drawer are black, which means that in a random selection of 10 socks, we would expect to see around 7 black socks on average.

The dot plot shows the number of black socks in 10 trials of the number generator. We can see that the number of black socks varies from 0 to 10, with some frequencies being higher than others.

Without knowing the exact frequencies or probabilities, we can see that the dot plot does not appear to be centered around 7 black socks, which is what we would expect from a fair number generator. However, it is difficult to determine whether the deviations from 7 are statistically significant or not, without more information.

Therefore, based on the given information, the most accurate statement is:

The number generator's fairness cannot be determined with certainty from the given data, but there are indications that it may not be perfectly fair.

Step-by-step explanation:

Answer:

answer would be B : (0, -8); x = 0

Step-by-step explanation: