If α and β are the zeroes of the polynomial ax^2 + bx + c, find the value of α^2 + β^2

Answer:

they will meet in 1 hour (9:00 AM)

Step-by-step explanation:

since mia goes 3 mph, and sanjana goes 5 mph, the total distance they travel is 8mph because 5+3=8. the distance is 8 miles, so 8/8=1 hour  so 8 am +1 hour=9:00 AM

a. There are 54 elements in the sample space.

b. P(A) = 0.2778

c. No, events A and B are not mutually exclusive.

d. No, events A and C are not mutually exclusive.

a. To find the total number of elements in the sample space, we need to multiply the number of cards by the number of possible outcomes from the coin toss. Therefore, the sample space has 54 elements (9+11+7) x 2.

b. The probability of event A is the probability of picking a green card first (9/27) multiplied by the probability of getting a head on the coin toss (1/2). Therefore, P(A) = (9/27) x (1/2) = 0.2778 (rounded to 4 decimal places).

c. Events A and B are not mutually exclusive because it is possible to pick a red or blue card and still have a head on the coin toss. Therefore, there are some elements in the sample space that belong to both events.

d. Events A and C are not mutually exclusive because it is possible to pick a green card and still have a head on the coin toss. Therefore, there are some elements in the sample space that belong to both events.

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The coordinate system with x-coordinates between -180 and 180 is likely to be the geographic coordinate system, specifically longitude values. This system represents positions on the Earth's surface using two angles: longitude (x-coordinates) and latitude (y-coordinates).

Longitude values range from -180 degrees (180 degrees West) to 180 degrees (180 degrees East) along the Earth's equator. Latitude values, on the other hand, range from -90 degrees (90 degrees South) to 90 degrees (90 degrees North). The origin (0, 0) of this coordinate system is the intersection of the Prime Meridian (Greenwich Meridian) and the Equator.

The units for these coordinates are typically expressed in decimal degrees (DD). These values can be converted into other units such as degrees-minutes-seconds (DMS) or radians, depending on the application or preference. When working with geographic coordinate systems, it is essential to consider the Earth's curvature and potential distortions when calculating distances or areas.

In summary, if a data set has x-coordinates between -180 and 180, the coordinate system is most likely the geographic coordinate system, representing longitude values. The coordinates are typically expressed in decimal degrees, and their positions relate to the Earth's surface.

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The difference in the dollar value of Assistantship (Stipend) between art and science fields with  standard errors is equal to 1.214.

Mean      24041.62203                 25952.36501

Sample mean difference between Assistantship (stipend) in arts and science is equal to

=  $25952.36501 - $24041.62203

= $1910.74298.

Hypothesized mean difference is 0 (there is no difference in stipend between the two fields).

Variance        621483.0801            615193.5853

Sample size    521                             479

Standard error of the difference is,

=√[(variance in arts / sample size in arts) + (variance in science / sample size in science)]

= √[(615193.5853 / 479) + (621483.0801 / 521)]

= $49.77

t-statistic

= (sample mean difference - hypothesized mean difference) / standard error of the difference

Substitute the values into the t-statistic formula,

⇒ t-statistic = ($1910.74298 - 0) / $49.77

⇒ t-statistic = 38.39

t-critical value for a two-tailed test with 992 degrees of freedom at a significance level of 0.05 is 1.9624.

t-statistic (38.39) > t-critical value (1.9624)

⇒Reject the null hypothesis that there is no difference in stipend between the two fields.

standard errors

= t-statistic / √(sample size)

= 38.39 / √(479 + 521)

= 38.39 /31.62

=1.214

Therefore,  the difference in the dollar value of Assistantship (Stipend) between these two fields is 1.214 standard errors away from the hypothesized difference.

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Answer:

a = 1, b = 3, c = 1, d = 2, e = 6, and f = 8

Step-by-step explanation:

The given exponential functions are;

2ˣ, 3·2ˣ, and  \(2^{3 \cdot x}\)

Let f(x) = 2ˣ, h(x) = 3·2ˣ, and g(x) = \(2^{3 \cdot x}\)

From the table for investigating the dilations of exponential function, we have;

a = f(0) = 2⁰ = 1

b = h(0) = 3·2⁰ = 3 × 1 = 3

c = g(0) = \(2^{3 \times 0}\) = 2⁰ = 1

d = f(1) = 2¹ = 2

e = h(1) = 3·2¹ = 3 × 2 = 6

f = g(1) = \(2^{3 \times 1}\) = 2³ = 8.

Answer:

x=0 and x=5/2

Step-by-step explanation:

Combine like terms.

-2x=0

x=0/-2

x=0

-4x=-10

x=-10/-4

x=5/2

The value of y for the function y = cos(-60°) is y = -1/2, option A is correct.

An equation with trigonometric functions that holds true for all of the variables in it is known as a trigonometric identity. A few normal geometrical characters incorporate the Pythagorean personality, the total and distinction characters, and the twofold point characters.

Using the unit circle and the trigonometric identity for cosine, we know that:

cos(-60°) = cos(360° - 60°)

               = cos(300°)

               = cos(180° + 120°)

               = -cos(120°)

               = -1/2

Therefore, the value of y for the function y = cos(-60°) is y = -1/2.

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The kinematic equation of the motion of the paintbrush dropped 35 feet height from the ground and the 1.85 seconds reaction time of the 6 feet person standing directly below, indicates that they will be hit  by the paintbrush before they can move out of the way.

The kinematic equation of motion describe the motion of a body that moves under constant acceleration, without consideration of the forces causing the body to move.

The height from which the paintbrush is dropped from the roof to the ground = 35 feet

Height of the person standing directly below where the brush falls = 6 feet

The reaction time of the person = 1.85 seconds

The kinematic equation of motion of free fall of an object is presented as follows;

s = u·t + 0.5·g·t²

Where; s = The height through which the paintbrush falls

u = The initial velocity of the paintbrush = 0

g = The acceleration due to gravity ≈ 32.1741 ft/s²

The height the paintbrush falls before meeting the 6 feet tall person, s = 35 feet - 6 feet = 29 feet

Therefore, we get;

29 = 0 × t + 0.5 × 32.1741 × t²

t² = 29 ÷ (0.5 × 32.1741) ≈ 1.803

The time it takes the paintbrush to fall 29 feet, t, is therefore;

t = √(29 ÷ (0.5 × 32.1741)) ≈ 1.343

It takes the paintbrush to reach the height of the person standing directly below in just about 1.3 seconds after it is dropped, before the person can react to move away in 1.85 seconds, therefore, they will be hit by the paintbrush before they can move out of the way.

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In the inverse we replace the place of x by y .

\(g(x) = \sqrt[3]{x} - 3 \\ \\ x = \sqrt[3]{y} - 3 \\ \sqrt[3]{y} = x + 3 \\ y = {(x + 3)}^{3} \\ y = {(x + 3)}^{2} (x + 3) \\ y = ({x}^{2} + 6x + 9)(x + 3) \\ \\ y = {x}^{3} + 6 {x}^{2} + 9x + 3 {x}^{2} + 18x + 27 \\ \\ y = {x}^{3} + 9 {x}^{2} + 27x + 27 \\ \\ \\ g(x)^{ - 1} = {x}^{3} + 9 {x}^{2} + 27x + 27 \)

I hope I helped you^_^

The values of the sides are 47 and 17

It is important to note that opposite sides of a parallelogram are equal or congruent.

From the diagram shown, we can see that;

Line BC and Line AD are opposite.

Then.

BC = AD

substitute the values

37 -2x = 8x - 33

collect the like terms

37 + 33 = 8x + 2x

add the values

10x = 70

Make 'x' the subject

x = 7

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Answer:

mr martin was a hero in my eyes he saved many lives and was one of the strongest people to ever live (who is mr martin?)

Step-by-step explanation:

Answer:35 dollars

Step-by-step explanation:

(7.)  The value of tan x is ±1/3. The option 3 is correct answer. (8.) The length of side a can be found to be -99 cm. The option 4 is correct answer. (9.) The value of cos A is 0.4904 and A is approximately 60.63°. The option 3 is correct answer.

7. sin x = 1/4,

we can use the identity

tan x = sin x / cos x  ......(i)

To determine the value of tan x.

Since sin x = 1/4,

we know that

cos x = √(1 - sin²x)

         = √(1 - (1/4)²)

         = √(1 - 1/16)

         = √(15/16)

         = √15/4.

Now put the value in  equation (i), so we get the tan x as

tan x = sin x/cos x

        = (1/4) / (√15/4)

        = ±1/√15

        = ±1/3.

8. In a right triangle ABC with side b = 18cm and side c = 15cm, we can use the Pythagorean theorem to find the length of side a.

Applying the theorem, we have

a² = c² - b²

    = 15² - 18²

    = 225 - 324

    = -99 cm

Since side lengths cannot be negative, there is no real solution for side a. Therefore, the answer is "None of the above."

9. In triangle ABC with sides

AB = 42cm,

BC = 37cm, and

AC = 26cm,

we can use the Law of Cosines to determine angle A.

Applying the Law of Cosines, we have

cos A = (b² + c² - a²) / (2bc)

         = (37² + 26² - 42²) / (2 * 37 * 26)

         = (1369 + 676 - 1764) / (2 * 37 * 26)

         = 281 / 1924

         ≈ 0.146.

Taking the inverse cosine of this value, we find

A ≈ cos⁻¹ (0.146)

  ≈ 60.63°.

Therefore, the answer is option 3 "cos A = 0.4904 and A = cos⁻¹ (0.4904) ≈ 60.63°."

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Complete Question:

7. Without finding angle & given: sin x = 1/4 find tan x

(1.) tan z = ±1/V15

(2.) tan x = ± √/15

(3.) tan x =±1/3

(4.) None of the above

8. A triangle ABC with right angle B has sides b = 18cm and c = 15cm. Find the length of a to two decimal places.

(1.) 9.20 cm

(2.) 19.20 cm

(3.) 10.95cm

(4.) None of the above

9. In triangle ABC, AB = 42cm, BC = 37cm and AC = 26cm. Solve this triangle.

(1.) cos A = 1/√2 and A = 60°

(2.) cos A = 0.1244 and A = cos¯¹ (0.1244) = 16.61⁰

(3.) cos A = 0.4904 and A = cos⁻¹(0.4904) = 60.63⁰

(4.) None of the above

The outcomes contained in one or the other of two random events, or possibly in both, make up the union of two events.

In probability theory, the union of two events refers to the set of outcomes that are present in either one or both of the events. It represents the combination of all possible outcomes from the individual events.

For example, let's consider two events A and B. The union of these events, denoted as A ∪ B, includes all the outcomes that belong to event A, event B, or both. It represents the combined set of outcomes from the two events.

Mathematically, the union of two events is defined as:

A ∪ B = {x | x ∈ A or x ∈ B}

So, when we talk about the outcomes contained in one or the other of two random events, or possibly in both, we are referring to the union of those events. The union captures all the possible outcomes that can occur in either event or in both events simultaneously.

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Answer:

B

Step-by-step explanation:

31.112 is actually greater than 30.678 because 31 is a greater number than 30. so the statement stated is false.

24.510 is greater than 24.5 because if you add 2 zeros to 24.5, it would be 24.500(adding zeros after decimal point doesnt change the value). 24.500 is less than 24.510. the numbers are not equal.

72.49 is greater than 72.469 because if you add a zero to 72.49, it will be 72.490. 72.490 is greater than 72.469.

Basically only B is true because 81 is greater than 80.

The relationship between the ages of drivers and the number of violations is a strong negative correlation. The correct option is E.

Correlation is the relationship between any set of data when taken as a whole because the term "co" signifies together. The correlation coefficient, which in statistics is a number between -1 and +1, measures the linear dependency of the collection of data.

A correlation coefficient is always a value between -1 and 1. The closest coefficient to -1, the correlation is a strong negative correlation. The closest coefficient to 1, the correlation is a strong positive correlation. The closest coefficient to 0, there is no correlation at all. The coefficient -0.61 shows a strong negative correlation.

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Answer:

5.625 which is 5 5/8.

Step-by-step explanation:

Answer:12x - 24 = 12 - 3

Step-by-step explanation:If you use the distrubutive property to solve this then 4 * 3x = 12x, 4 * 6 = 24, and then do the other side 3 * 4x = 12x, 3 * 3 = 9. There you have your answer. Unless it was suppose to be -12x = 3.

Answer:

No solution

Step-by-step explanation:

Use Distributive property.

4 · 3x = 12x

4 · (-6) = -24

Your equation should look like this now:

12x - 24 = 3(4x - 3)

Use Distributive property on the right side now.

3 · 4x = 12x

3 · (-3) = -9

Your equation now:

12x - 24 = 12x - 9

Add 24 to both sides.

Your equation:

12x = 12x + 15

Subtract 12x from both sides.

15 is left

So there is no solution.

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The range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

To measure the amount of money college students spend on rent per month, the most appropriate measure of spread would be the range. The range is the simplest measure of spread and is calculated by subtracting the lowest value from the highest value in a data set. In this case, the range would be $1,300 - $300 = $1,000.

The median would not be the best choice in this scenario because it only represents the middle value in a data set. It does not take into account extreme values like the $1,300 rent expense.

Standard deviation would not be the most appropriate measure of spread in this case because it calculates the average deviation of each data point from the mean. However, it may not accurately represent the spread when extreme values like the $1,300 rent expense are present.

The interquartile range (IQR) would not be the best choice either because it measures the spread of the middle 50% of the data set. It does not consider extreme values and would not accurately represent the range of rent expenses in this scenario.

In summary, the range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

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Answer:

2N÷4=7N-5/3

Hope this helps!

Answer:  25 ways.

Step-by-step explanation:

first we have  1,2,6. this can appear once.

4, can appear in twice.

\(= (3+2) * 5\\= 5*5\\= 25ways\)

by not including itself, an appearing on the left side. one number can be written 25ways

Answer:

a. 6x^2

b. 70x^2

c. -360s^2

d. -60x^2

Step-by-step explanation:

They need to wash approximately 41 cars in order to have enough money to pay for the trip.

Proving Theorems about Lines and Angles: Tutorial

To calculate the number of cars they need to wash in order to have enough money to pay for the trip, we need to consider the total cost of the trip and the amount of money they have available.

The total cost of the trip includes the registration fee, transportation and food expenses, and hotel costs.

The registration fee is $110, transportation and food costs are $375, and the hotel cost per person is $42.

Let's calculate the total cost of the trip:

Total cost = Registration fee + Transportation and food costs + Hotel costs

Total cost = $110 + $375 + ($42 x 4) [since there are four student government officers]

Total cost = $110 + $375 + $168

Total cost = $653.

Now, we subtract the available budget from the total cost to find the remaining amount they need to earn:

Remaining amount = Total cost - Budgeted amount

Remaining amount = $653 - $450

Remaining amount = $203

Since they can earn money by having a car wash and charge $5 per car, we can calculate the number of cars they need to wash:

Number of cars = Remaining amount / Amount earned per car

Number of cars = $203 / $5

Number of cars ≈ 40.6

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Answer:

1. area of new pen = 11 \(\frac{1}{4}\) \(ft^{2}\)

2. i. 5 feet by 2\(\frac{1}{4}\) feet

ii. 2 ½ feet by 4 ½ feet

Step-by-step explanation:

The size of the pen as planned = 5 ft long by 4 ½ ft wide

Area of the pen = length x width

                           = 5 x 4 ½

                           = 5 x \(\frac{9}{2}\)

Area of the pen = \(\frac{45}{2}\)

                           = 22 ½ \(ft^{2}\)

But, Krista has to make the pen ½ the size of planned. So that;

area of new pen = ½ x 22 ½

        = ½ x \(\frac{45}{2}\)

        = \(\frac{45}{4}\)

        = 11 \(\frac{1}{4}\)

area of new pen = 11 \(\frac{1}{4}\) \(ft^{2}\)

The area of the new pen would be 11 \(\frac{1}{4}\) \(ft^{2}\).

The possible values she could use are:

i. 5 feet by 2\(\frac{1}{4}\) feet

ii. 2 ½ feet by 4 ½ feet

Answer:

Volume = 1526.04 cubic units

Step-by-step explanation:

Formula for volume of a cone:

V = πr²h/3

If we use 3.14 for pi, we get 1526.04:

V = 3.14(9)^2(18)/3

V = 1526.04

70 cm or 0.7 m

3.5 x 100 = 350

350 / 5 = 70

The zobt value for a sample mean of 52.1 with a population mean of 47.2 and a population deviation of 6.4, and a sample size of 8 is approximately 3.19.

We can use the formula for calculating the z-score:

z = (x - μ) / (σ / √n)

where x is the sample mean, μ is the population mean, σ is the population deviation, and n is the sample size.

Plugging in the given values, we get:

z = (52.1 - 47.2) / (6.4 / √8) ≈ 3.19

Therefore, the zobt value for a sample mean of 52.1 with a population mean of 47.2 and a population deviation of 6.4, and a sample size of 8 is approximately 3.19.

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Answer:

x=10

Step-by-step explanation: