Question 5 (1 point)
Find the value of y. Round to the nearest hundredth (2 decimals).
16
24°
y =
Blank 1:

a)  The x-intercepts of the graph of f(x) are x = 2.5 and x = -1.

b) The coordinates of the vertex are (0.75, -5.125).

c) By using the x-intercepts and vertex obtained in Parts A and B, we can accurately depict the shape and positioning of the parabolic graph of f(x).

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x.

Setting f(x) = 0:

\(2x^2 - 3x - 5 = 0\)

To solve this quadratic equation, we can either factor it or use the quadratic formula. In this case, factoring is not straightforward, so let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 2, b = -3, and c = -5. Substituting these values into the quadratic formula:

x = (-(-3) ± √((-3)^2 - 4(2)(-5))) / (2(2))

x = (3 ± √(9 + 40)) / 4

x = (3 ± √49) / 4

x = (3 ± 7) / 4

This gives us two possible solutions:

x1 = (3 + 7) / 4 = 10/4 = 2.5

x2 = (3 - 7) / 4 = -4/4 = -1

Therefore, the x-intercepts of the graph of f(x) are x = 2.5 and x = -1.

Part B: To determine whether the vertex of the graph of f(x) is a maximum or minimum, we need to consider the coefficient of the x^2 term in the function f(x). In this case, the coefficient is positive (2), which means the parabola opens upward and the vertex represents a minimum point.

To find the coordinates of the vertex, we can use the formula x = -b / (2a). In our equation, a = 2 and b = -3:

x = -(-3) / (2(2))

x = 3 / 4

x = 0.75

To find the corresponding y-coordinate, we substitute x = 0.75 into the function f(x):

f(0.75) = 2(0.75)^2 - 3(0.75) - 5

f(0.75) = 2(0.5625) - 2.25 - 5

f(0.75) = 1.125 - 2.25 - 5

f(0.75) = -5.125

Therefore, the coordinates of the vertex are (0.75, -5.125).

Part C: To graph the function f(x), we can follow these steps:

Plot the x-intercepts obtained in Part A: (2.5, 0) and (-1, 0).

Plot the vertex obtained in Part B: (0.75, -5.125).

Determine if the parabola opens upward (as determined in Part B) and draw a smooth curve passing through the points.

Extend the curve to the left and right of the vertex, ensuring symmetry.

Label the axes and any other relevant points or features.

By using the x-intercepts and vertex obtained in Parts A and B, we can accurately depict the shape and positioning of the parabolic graph of f(x).

The x-intercepts help determine where the graph intersects the x-axis, and the vertex helps establish the lowest point (minimum) of the parabola. The resulting graph should show a U-shaped curve opening upward with the vertex at (0.75, -5.125) and the x-intercepts at (2.5, 0) and (-1, 0).

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Adding 10 people to the classroom does not change the number of air molecules present. The volume of the classroom remains the same, and the air molecules can still be calculated using the same method.

The number of air molecules in a classroom can be determined using the ideal gas law equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature. Assuming standard temperature and pressure (STP) of 1 atmosphere and 0 degrees Celsius, one mole of any gas occupies 22.4 liters or 0.0224 m^3.

Given that the classroom dimensions are 9 meters x 8 meters x 2.7 meters, we can calculate the volume:

V = 9 x 8 x 2.7 = 194.4 m^3

Converting the volume to liters, we have:

V = 194.4 x 1000 = 194,400 liters

To determine the number of moles in the classroom, we divide the volume by the molar volume:

n = V / 22.4 = 194,400 / 22.4 = 8,678.57 moles

Since one mole of gas contains 6.022 x 10^23 molecules (Avogadro's number), the number of air molecules in the classroom is approximately:

1.5 x 10^25 molecules

Adding 10 people to the classroom does not change the number of air molecules present. The volume of the classroom remains the same, and the air molecules can still be calculated using the same method.

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The statements which are correct about the relationship in discuss are as follows;

It follows from the task content that the company converts the number of water gallons used to units in a bid to bill customers.

It therefore follows from the statement above and by virtue of the linear relationship as represented by the equation; u = 748g that the independent variable is; g while the dependent variable is; u.

remarks:

g is the dependent variable.

u is the dependent variable.

g is the independent variable.

u is the independent variable.

The variables cannot be labeled without a table of values.

The variables cannot be labeled since any value can be selected for either.

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(i) The meaning of the differential equation dP/dt = kP is that it represents the rate of change of the population (P) with respect to time (t) being proportional to the population size. The constant parameter k determines the growth rate of the population.

(ii) To solve the initial value problem, we can separate variables and integrate:

∫ (1/P) dP = ∫ k dt

ln|P| = kt + C

P = e^(kt+C) = e^C * e^(kt)

Considering the initial condition P(0) = P0, we can determine the value of the constant C:

P0 = e^C * e^(k*0) = e^C

C = ln(P0)

Therefore, the solution to the initial value problem is:

P = P0 * e^(kt)

In the long run, as t approaches infinity, the exponential term e^(kt) becomes very large, leading to unbounded growth of the population. This means that the population will continue to increase without limit.

(iii) The unconstrained growth model is appropriate under the assumption that there are no limiting factors or constraints on population growth, such as limited resources or competition. In reality, most populations are subject to constraints, and their growth cannot continue indefinitely. This model does not align with the situation Thanos is describing because he believes that unchecked growth will lead to the extinction of populations, whereas the unconstrained growth model implies unlimited growth.

(iv) If the population size is suddenly cut in half, we can represent it by changing the initial condition. Let's denote the new initial population size as P1. The model becomes:

P = P1 * e^(kt)

In this case, the parameter P1 would change to represent the new population size, while the growth rate parameter k remains the same. This new model would reflect a population that starts with a reduced size but continues to grow according to the same growth rate as before.

It's important to note that these population models provide a simplified representation of population dynamics and do not account for all the complexities and factors involved in real-world populations.

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Answer:

1.  x=-4

Step-by-step explanation:

The range of value of x in the inequality x/7 ≥ -6 is x≥ -42

Inequality, is a statement of an order relationship. Some terms used in inequality are ,greater than, greater than or equal to, less than, or less than or equal to. They are used between two numbers or algebraic expressions.

greater than has the sign >

greater than or equal to has the sign ≥

less than has the sign < and

less than or equal to has ≤

solving the range of value of x in the inequality x/7 ≥- 6

multiply both sides by 7

x ≥ -42

Therefore the range of value of x is x ≥ -42

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Answer:

Leonard’s balance is −$8.00.

Step-by-step explanation:

Answer:

179.37

Step-by-step explanation:

35874 ÷ 200 = 179.37

Answer:

\(x = 2\)

Step-by-step explanation:

Given

Conjecture: \(x + 3 < x^2\) --- (Missing)

Required

Which value of x prove the conjecture otherwise

To do this , we simply substitute the values of x in the options

\(1.\ x = -\frac{1}{3}\)

This is negative;

So, there is no need to check

\(2.\ x = -3\)

This is also negative;

So, there is no need to check

\(3.\ x = 2\)

\(x + 3 < x^2\)

\(2 + 3 < 2^2\)

\(5 < 4\)

This value of x is false because 5 is not less than 4

\(4.\ x = 3\)

\(x + 3 < x^2\)

\(3 + 3 < 3^2\)

\(6 < 9\)

Step-by-step explanation:

3/7x - 2/14 = 3

6x-2/14=3

6x-2=42

6x=44

x=22/3

Answer:

Hello your handwriting is bad I don't understand

Based on the alternate exterior angles theorem, the value of x is: 5.

According to the alternate exterior angles theorem, when two parallel lines are cut by a transversal, the alternate exterior angles are congruent. Therefore, if m∠H = (2x+7)° and m∠K = (5x−8)°, we can set up the equation:

(2x + 7)° = (5x − 8)°

Solving for x we get:

2x + 7 = 5x - 8

Subtracting 2x from both sides:

2x + 7 - 2x = 5x - 8 - 2x

7 = 3x - 8

Adding 8 to both sides:

15 = 3x

Dividing both sides by 3:

x = 5

So the value of x is 5.

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The three computations covered by the reliability factor table are sample size, index of reliability, and index of precision. Sample size deals with the size of the sample being used in order to achieve a desirable level of reliability.

Index of reliability is used to measure the consistency of results achieved over multiple trials. It does this by calculating the total number of items that contribute significantly to the final result. Finally, the index of precision measures the effect size of the sample, which is determined by comparing the results from the sample with the expected results.

The sample size computation gives the researcher an idea of the number of items that should be included in a sample in order to get the most reliable results. This is done by taking into account a number of factors including the variability of the population, the type of measurements used, and the desired level of accuracy.

The index of reliability is commonly calculated by finding the ratio of the number of items contributing significantly to the total result to the total number of items in the sample. This ratio is then multiplied by 100 in order to get a final score.

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Using trigonometric relations we can see that θ  = 34.68°

We want to find the angle theta and we want to use the "sec" function to do so.

Remember that:

sec(θ) = 1/cos(θ)

Also notice that we have a right triangle, then the value of the hypotenuse is:

h = √(9² + 13²) = 15.81

We know the trigonometric relation

cos(θ) = (adjacent cathetus)/hypotenuse

Then:

sec(θ) = hypotenuse/(adjacent cathetus)

sec(θ) = 15.81/13

sec(θ) = 1.216

Now we can write that as:

cos(θ) = 1/1.216 (and return to the original trigonometric relation)

And use the inverse cosine function:

θ = Acos(1.216) = 34.68°

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No longer narrowly pre-occupied with their own national pasts, historians are increasingly cosmopolitan (Option D) in that they often take a trans-national perspective.

Sentence completions test the skill to use the information observed in complex and incomplete sentences in order to correctly complete them.

It tests a candidate's vocabulary power and skill to follow the logic of sentences.

Now, given:

Hence, No longer narrowly pre-occupied with their own national pasts, historians are increasingly cosmopolitan (Option D) in that they often take a trans-national perspective.

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Answer:

B = an event that in the second turn it will land on Lose a Turn. Based from the given wheel, there are 24 equal parts with three $500 and one Lose a Turn. Thus, the probability of landing on $500 then lose a turn is 1921 .

this is possible IF thewheele consists of 24 parts

The chance of landing on $500 and then Lose A Turn will be 1/192. Then the correct option is C.

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

The diagram is given below.

The total number of the events will be

Total events = 24

Then the chance of landing on $500 will be

The number of favorable events will be

Favorable events = 3

⇒ 3/24

⇒ 1/8

Then the chance of the Lose A Turn will be

Favorable event = 1

⇒ 1/24

The chance of landing on $500 and then Lose A Turn will be

P = (1/24)(1/8)

P = 1/192

The chance of landing on $500 and then Lose A Turn will be 1/192.

Then the correct option is C.

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Answer:

\( - \sin( \beta ) \times - \sin( \beta ) \\ = ( { \sin}^{2} \beta ) \\ = \sqrt{1 - { \cos }^{2} \beta } \)

A dog is on a leash that is tied to a tree. The leash is 6 feet long. If the center of the tree could be considered the origin (0,0), the equation of the circle will be \((x)^2 + (y)^2 = 6^2\)

If a circle O has a radius of r units length and it has got its center positioned at (h, k) point of the coordinate plane, then, its equation is given as:

\((x-h)^2 + (y-k)^2 = r^2\)

A dog is on a leash that is tied to a tree. The leash is 6 feet long. If the center of the tree could be considered the origin (0,0),

we have r = 6

the equation of the circle will be

\((x-h)^2 + (y-k)^2 = r^2\)

\((x-0)^2 + (y-0)^2 = r^2\\\\(x)^2 + (y)^2 = 6^2\)



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The missing part of the equation is \(-7.0\times10^4 s^2kg⋅m^2 / 1000000.\)

To fill in the missing part of the equation, let's analyze the given information and the desired conversion. The equation is:

\((-7.0\times 10^4 s^2g⋅m^2)\cdot \pi = ? s^2kg\cdot m^2\)

In this equation, we have a quantity expressed in\(s^2g\cdot m^2\) units on the left-hand side. To convert it to \(s^2kg\cdot m^2\) units, we need to multiply it by a conversion factor.

To perform the conversion, we can use the fact that 1 kg is equal to 1000 g. Therefore, the conversion factor we need is:

1 kg / 1000 g

To ensure that the units cancel out correctly, we need to square this conversion factor because we have \(s^2g\cdot m^2\) on the left-hand side. So the missing part of the equation is:

\((-7.0\times 10^4 s^2g\cdot m^2)\cdot \pi = (-7.0\times 10^4 s^2g\cdot m^2)\cdot (1 kg / 1000 g)^2\)

Simplifying this expression, we get:

\((-7.0\times10^4 s^2g\cdot m^2)\cdot \pi = -7.0 \times10^4 s^2kg\cdot m^2 / 1000000\)

Therefore, the missing part of the equation is \(-7.0 \times 10^4 s^2kg\cdot m^2 / 1000000.\)

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Answer: k 2 + 3 g − 6

hope this helps

Given that $OF = 9$ and $OF' = 12,$ where $F$ and $F'$ are the foci of the ellipse, we can determine the lengths of the major and minor axes.

In an ellipse, the sum of the distances from any point on the ellipse to the two foci is constant. This property is expressed by the equation:

$$PF + PF' = 2a,$$

where $P$ is any point on the ellipse and $a$ is the semi-major axis. In our case, $P = O,$ and since $OF = 9$ and $OF' = 12,$ we have:

$$9 + 12 = 2a,$$

$$21 = 2a.$$

Therefore, the semi-major axis $a$ is equal to $\frac{21}{2} = 10.5.$

The distance between the center of the ellipse and each focus is given by $c,$ where $c$ is related to $a$ and the semi-minor axis $b$ by the equation:

$$c = \sqrt{a^2 - b^2}.$$

We can solve for $b$ using the distance to one focus:

$$c = \sqrt{a^2 - b^2},$$

$$c^2 = a^2 - b^2,$$

$$b^2 = a^2 - c^2,$$

$$b = \sqrt{a^2 - c^2}.$$

Substituting the known values:

$$b = \sqrt{10.5^2 - 9^2},$$

$$b = \sqrt{110.25 - 81},$$

$$b = \sqrt{29.25},$$

$$b \approx 5.408.$$

Therefore, the semi-minor axis $b$ is approximately $5.408.$

Finally, we can determine the lengths of the major and minor axes:

The major axis $\overline{AB}$ is twice the semi-major axis, so $\overline{AB} = 2a = 2(10.5) = 21.$

The minor axis $\overline{CD}$ is twice the semi-minor axis, so $\overline{CD} = 2b = 2(5.408) \approx 10.816.$

Therefore, the major axis $\overline{AB}$ is $21$ units long, and the minor axis $\overline{CD}$ is approximately $10.816$ units long.

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Answer:

n = 10

Step-by-step explanation:

Using the rule of exponents

• \(a^{m}\) × \(a^{n}\) = \(a^{(m+n)}\)

• \((a^m)^{n}\) = \(a^{mn}\)

Then

2² × \(2^{n}\) = \((2^4)^{3}\)

\(2^{2+n}\) = \(2^{12}\)

Since the bases on both sides are equal, both 2 then equate exponents

2 + n = 12 ( subtract 2 from both sides )

n = 10

Answer:

5.48

Step-by-step explanation:

Convert

√30 to a decimal.

5.47722557

Find the number in the hundredth place 7 and look one place to the right for the rounding digit 7. Round up if this number is greater than or equal to 5 and round down if it is less than 5.

Answer:

\(31 {x}^{2} - 2\)

Step-by-step explanation:

\(10 {x}^{2} - 5 + 21{x}^{2} + 3 \\ 31 {x}^{2} -2\)

Answer:

its d

Step-by-step explanation:

The first car has a higher miles per gallon rating with 27.03

The miles per gallon (mpg) rating for a car, we can use the formula

mpg = 100 / (gallons per 100 miles)

For the first car with a rating of 3.7 gallons per 100 miles

mpg = 100 / 3.7 ≈ 27.03 mpg

For the second car with a rating of 4.3 gallons per 100 miles

mpg = 100 / 4.3 ≈ 23.26 mpg

Comparing the two mpg ratings, we find that the first car has a greater mpg rating of 27.03 mpg compared to the second car with a rating of 23.26 mpg. Therefore, the first car has a higher mpg rating.

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A collegiate basketball player hits 80% of his free throw attempts. Assuming free throw attempts are independent, he will try 100 free throws this season the answers are as follows:

a) The mean of X is 80.

b) The standard deviation of X is 4.

c) The probability that the basketball player makes at least 90 of these attempts is approximately is 0.0062.

d) If the basketball player instead attempts only 10 free throws, the probability that he makes at most 4 of these is 0.0064.

As per the question given,  

a) The mean of X is given by the formula: mean = n * p, where n is the number of trials and p is the probability of success on each trial. In this case, the player attempts 100 free throws with a probability of success of 0.8, so the mean is:

mean = 100 * 0.8 = 80

Therefore, the correct answer is 80.

b) The standard deviation of X is given by the formula: standard deviation = sqrt(n * p * (1 - p)). Substituting the values, we get:

standard deviation = sqrt(100 * 0.8 * 0.2) = 4

Therefore, the correct answer is 4.

c) To find the probability that the player makes at least 90 free throws, we can use the normal approximation to the binomial distribution. The mean is 80 and the standard deviation is 4, so we can standardize the value of X as follows:

z = (90 - 80) / 4 = 2.5

Using a standard normal distribution table, we can find the probability that Z is greater than 2.5, which is approximately 0.0062.

Therefore, the correct answer is 0.0062.

d) If the player attempts only 10 free throws, the number of successful attempts X follows a binomial distribution with n=10 and p=0.8. The probability that he makes at most 4 of these attempts is:

P(X <= 4) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4)

Using the binomial distribution formula, we can calculate each of these probabilities and sum them up. Alternatively, we can use a binomial probability table or a calculator to find the cumulative probability.

Using a binomial probability calculator, we get:

P(X <= 4) = 0.0064 (rounded to four decimal places)

Therefore, the correct answer is 0.0064.

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