Which quadratic equation fits the data in the table?
x. y
-5 33
-2 9
-1 5
0 3
3 9
4 15
6 33

After 11 years, approximately 21 grams of Element X would remain.

Radioactivity is the process by which unstable atomic nuclei emit particles or energy in the form of electromagnetic radiation. This emission can be harmful to living organisms and can cause damage to cells and DNA. Radioactivity occurs naturally in the environment, but can also be artificially produced through nuclear reactions.

Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons in their nuclei. Isotopes can be either stable or unstable, with unstable isotopes undergoing radioactive decay over time. Isotopes are important in many fields, including nuclear energy, medicine, and environmental science.

We can use the formula N = N0 * (1/2)^(t/T), where N is the remaining mass after time t, N0 is the initial mass, T is the half-life, and t is the time elapsed.

In this case, T = 28 years and t = 11 years,

N = 50  (1/2)\(^{11/8}\)

N ≈ 21

Therefore, after 11 years, approximately 21 grams of Element X would remain.

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The decrease in diameter of the bar due to the applied load is -0.005434905d and the final diameter of the bar is 1.005434905d.

A compressive load of 80,000 lb is applied to a bar with a circular section of 0.75 in diameter and a length of 10 in.

if the modulus of elasticity of the bar material is 10,000 ksi and the Poisson's ratio is 0.3.

We have to determine the decrease in diameter of the bar due to the applied load.

Let d be the initial diameter of the bar and ∆d be the decrease in diameter of the bar due to the applied load, then the final diameter of the bar is d - ∆d.

Length of the bar, L = 10 in

Cross-sectional area of the bar, A = πd²/4 = π(0.75)²/4 = 0.4418 in²

Stress produced by the applied load,σ = P/A

= 80,000/0.4418

= 181163.5 psi

Young's modulus of elasticity, E = 10,000 ksi

Poisson's ratio, ν = 0.3

The longitudinal strain produced in the bar, ɛ = σ/E

= 181163.5/10,000,000

= 0.01811635

The lateral strain produced in the bar, υ = νɛ

= 0.3 × 0.01811635

= 0.005434905'

The decrease in diameter of the bar due to the applied load, ∆d/d = -υ

= -0.005434905∆d

= -0.005434905d

The final diameter of the bar,

d - ∆d = d + 0.005434905d

= 1.005434905d

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Answer:

x= -1/5

Let me know if you need an explanation :)

Answer:

C. An arithmetic sequence with a common difference of 6.

Step-by-step explanation:

A is incorrect because the common difference is not -9 (not constant).

B is incorrect because the common difference is not 3 (not constant).

C is the correct answer because the common difference is 6 (constant).

D is incorrect because this is an arithmetic sequence.

-------------------------------------------------------------------------------------------------------

-9 + 6 = -3

-3 + 6 = 3

3 + 6 = 9

9 + 6 = 15

The common difference is +6 (positive 6).

Hope that helps!

Please give me Brainliest!?!?

The progression −9, −3, 3, 9, 15 is an arithmetic sequence with a common difference of 6. The correct option is C.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression.

Given series is −9, −3, 3, 9, 15.

The common difference is calculated as,

-9 + 6 = -3

-3 + 6 = 3

3 + 6 = 9

9 + 6 = 15

As above it is observed that with the common difference of 6 we found the series,  −9, −3, 3, 9, 15.

Therefore, the progression −9, −3, 3, 9, 15 is an arithmetic sequence with a common difference of 6. The correct option is C.

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Using a system of equations, it is found that:

--------------------------

In a triangle, the sum of the interior angles is of 180º, thus:

\(x + y + z = 180\)

The second angle of the triangle  has a measure equal to the sum of two times the other two angles, then:

\(y = 2(x + z)\)

\(x + z = 0.5y\)

Replacing into the first equation, we find the second angle:

\(x + y + z = 180\)

\(0.5y + y = 180\)

\(1.5y = 180\)

\(y = \frac{180}{1.5}\)

\(y = 120\)

The measure of the second angle is of 120º.

Now, working to find the measures of the first and of the third angles:

\(x + z = 0.5y \rightarrow x + z = 60 \rightarrow x = 60 - z\)

The third  angle has a measure equal to ten less than the first angle, then:

\(z = x - 10\)

Since \(x = 60 - z\)

\(z = 60 - z - 10\)

\(2z = 50\)

\(z = \frac{50}{2}\)

\(z = 25\)

And

\(x = 60 - z = 60 - 25 = 35\)

The measure of the first angle is of 35º.

The measure of the third angle is of 25º.

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The purchase price in dollars of the television that has been marked up 25% of the retail price of $4,500 would be $5,625.

To find the purchase price of the television in dollars, follow these steps:

1. Determine the markup amount: 25% of the retail price ($4,500).
2. Subtract the markup amount from the retail price to find the purchase price.

Step 1: Calculate the markup amount:
25% of $4,500 = 0.25 × 4,500 = $1,125

Step 2: Subtract the markup amount from the retail price:
$4,500 (retail price) - $1,125 (markup) = $3,375

The purchase price of the television in dollars is $3,375.

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Answer:

it's so easy solve by own

you are my child I am your dad hah haha

Answer:

a = 35

Step-by-step explanation:

\(a^2+b^2=c^2\\a^2+12^2=37^2\\a^2+144=1369\\a^2=1225\\a=35\)

Answer:

-------------------------

Each coordinate of the midpoint is the average of endpoints:

Therefore M is (13, 14).

Answer:

7 and 1

Step-by-step explanation:

3.25% is the percentage of two-year-old sardines that are less than 19 cm in length.

At two years of age, sardines inhabiting Japanese waters have a length distribution that is approximately normal with mean 20.2 cm and standard deviation 0.65 cm.

In order to draw a bell curve for the given problem, we need to calculate the z-scores for different values of length and use a standard normal distribution table.

Z-score = (x - μ) / σ

Where x is the value of length, μ is the mean, and σ is the standard deviation.

Now, let's draw the bell curve for the following questions.

a) Here, x = 19 cm, μ = 20.2 cm, σ = 0.65 cm

Z-score = (x - μ) / σ

= (19 - 20.2) / 0.65

= -1.846

Let's look into the standard normal distribution table to find the area under the curve for the z-score of -1.846, which is equal to 0.0325.

So, the percentage of two-year-old sardines that are less than 19 cm in length is 0.0325 or 3.25%.

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The correct option among the given choices is c. is often performed automatically, without awareness

A healthy habit is a behavior or action that people consistently engage in, usually without giving it any conscious thought.

These routines get established with these habits, which are frequently carried out automatically and unknowingly. frequently brushing your teeth, washing your hands before eating, using the stairs instead of the elevator, and exercising frequently are a few examples of healthy habits.

Therefore, option C is the most accurate description of a healthy habit.

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The null hypothesis significance testing is a popular method for testing hypotheses in statistics, but there are two issues with this process that can be problematic.

Firstly, the process is overly reliant on p-values, meaning that any type of false positive or false negative is possible.

Secondly, it does not account for the variability of the data, which can lead to misinterpretations and inaccurate results. Both of these issues can lead to incorrect conclusions, making null hypothesis significance testing a flawed process.

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Answer: $39.50

Step-by-step explanation:)

\(1+(0.2)^2=1+0.04=\boxed{1.04}\)

Answer:

1.44

Step-by-step explanation:

1 2/10 squared = 1.44

Since the two angles are equal, hence the angles B and angle 2 are congruent.

Congruent triangles are triangles that are similar to each other

Since the sum of the interior angles of a triangle is 180°, then

m∠B + 50° + 65° = 180°

Determine the value of <B

m∠B = 180° - (50° + 65°)

m∠B  = 180° - 115°

m∠B= 65°.

Similarly, the sum of angle on a straight line is 180 degrees

m∠2 + 50° + 65° = 180°

m∠2 = 180° - (50° + 65°)

m∠2 = 180° - 115°

m∠2= 65°

As we can see that the two angles are equal, hence the angles B and angle 2 are congruent.

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Answer:

Protractor

Step-by-step explanation:

You use a ruler to draw a straight line.

You use a protractor to draw an angle.

A straight line is to a ruler and an angle is to protractor.

"A protractor is a simple measuring instrument that is used to measure angles. A common protractor is in the shape of a semicircle with an inner scale and an outer scale and with markings from 0 degrees and 180 degrees on it."

"A math ruler is used to measure the length in both metric and customary units. The rulers are marked with standard distance in centimeters in the top and inches in the bottom and the intervals in the ruler are called hash marks."

A straight line is to a ruler and an angle is to protractor.

A protractor is a simple measuring instrument that is used to measure angles. A common protractor is in the shape of a semicircle with an inner scale and an outer scale and with markings from 0 degrees and 180 degrees on it.

Cosine is a trigonometric function that for an acute angle is the ratio between the leg adjacent to the angle when it is considered part of a right triangle and the hypotenuse.

A math ruler is used to measure the length in both metric and customary units. The rulers are marked with standard distance in centimeters in the top and inches in the bottom and the intervals in the ruler are called hash marks.

A calculator is a device that performs arithmetic operations on numbers. The simplest calculators can do only addition, subtraction, multiplication, and division.

Hence, A straight line is to a ruler and an angle is to protractor.

Option (C) is correct.

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In this scenario, we are given the following information: sample size (n) is 49, sample mean (P) is 50, sample standard deviation (s) is 7, null hypothesis (H₀) states that the population mean (μ) is greater than or equal to 52, and the alternative hypothesis (Hₐ) states that the population mean is less than 52.

The test statistic for this situation is the t-statistic, which measures the difference between the sample mean and the hypothesized population mean, taking into account the sample size and the sample standard deviation. It is used to assess the evidence against the null hypothesis. In this case, since the alternative hypothesis states that the population mean is less than 52, we have a left-tailed test. To calculate the t-statistic, we use the formula:

t = (P - μ) / (s / √n)

Plugging in the given values:

t = (50 - 52) / (7 / √49) = -2 / (7 / 7) = -2

Therefore, the test statistic for the provided information is -2. This value represents the standardized difference between the sample mean and the hypothesized population mean, accounting for the sample size and standard deviation. It indicates that the sample mean is 2 standard deviations below the hypothesized population mean of 52.

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The general solution of `y" - 16y = 0` is `y = c1 cos(4x) + c2 sin(4x) + c3 cosh(4x) + c4 sinh(4x)`

The general solution of the fourth-order differential equation

`y" - 16y = 0` is `y = c1 cos(4x) + c2 sin(4x) + c3 cosh(4x) + c4 sinh(4x)`.

Where `c1, c2, c3,` and `c4` are arbitrary constants.

The steps to finding the general solution of the fourth-order differential equation `y" - 16y = 0` are as follows:

Step 1: Find the characteristic equationThe characteristic equation is `r^4 - 16 = 0`.

Step 2: Solve the characteristic equation

Solving `r^4 - 16 = 0` by factoring gives`(r^2 - 4)(r^2 + 4) = 0`.

This yields `r = ±2` and `r = ±2i`.

Thus, the characteristic roots are `2, -2, 2i,` and `-2i`.

Step 3: Write the general solution

The general solution of `y" - 16y = 0` is `y = c1 cos(4x) + c2 sin(4x) + c3 cosh(4x) + c4 sinh(4x)`, where `c1, c2, c3,` and `c4` are arbitrary constants.

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Answer:

10

Step-by-step explanation:

9x10=90 then add the shipping and get 100

The x-coordinate of the point which divide the line segment is 3.

Given the coordinates in the figure are J(1,-10) and K(9,2) and the 1:3 is the ratio in which the line segment is divided.

When the ratio of the length of a point from both line segments is m:n, the Sectional Formula can be used to get the coordinate of a point that is outside the line.

To find the x-coordinate we will use the formula x=(m/(m+n))(x₂-x₁)+x₁.

Here, m:n=1:3 and x₁=1 from the point J(1,-10) and x₂=9 from the point K(9,2).

Now, we will substitute these values in the formula, we get

x=(1/(1+3))(9-1)+1

x=(1/4)(8)+(1)

x=8/4+1

x=3

Hence, the x-coordinate of the point that divides the directed line segment from k to j into a ratio of 1:3 is 3 units.

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Answer:

b. 3

Step-by-step explanation:

got it correct

Answer:

Hi, there your answer is

Question5: B.(x+3)(x-10)

Queston 6: D.(2x-2)(x+3)

Step-by-step explanation:

Answer: Lakesha gave away eighth tenths (8/10) of her cookies

Step-by-step explanation:

portion/Fraction of cookies given to Bailey =three tenths =3/10

portion/Fraction  of cookies given to Helen =Five  tenths =5/10

fraction of cookies  given away by  Lakesha= 3/10 +5/10=8/10 =eighth tenths

The feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

To determine whether the feasible set for each system of constraints is convex, we need to analyze the constraints individually and examine their intersection.

a) (x1)² + (x2)² > 9

This constraint represents points outside the circle with a radius of √9 = 3. The feasible set includes all points outside this circle.

b) x1 + x2 ≤ 10

This constraint represents points that lie on or below the line x1 + x2 = 10. The feasible set includes all points on or below this line.

c) x1, x2 > 0

This constraint represents points in the positive quadrant, where both x1 and x2 are greater than zero.

Now, let's analyze the intersection of these constraints:

Considering the first two constraints (a and b), we can see that the feasible set consists of all points outside the circle (constraint a) and below or on the line x1 + x2 = 10 (constraint b).

To determine whether the feasible set is convex, we need to check if any two points within the set create a line segment that lies entirely within the set.

If we consider the points (5, 5) and (3, 7), both points satisfy the individual constraints (a) and (b). However, the line segment connecting these two points, which is the line segment between (5, 5) and (3, 7), exits the feasible set since it passes through the circle (constraint a) and above the line x1 + x2 = 10 (constraint b).

Therefore, the feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

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The Intermediate Value Theorem guarantees that there exists a root of f(x) within the interval [2, 3].

a. f(x) = ln(x-1) + 0.5sin(2x) has a root,

Let's consider the interval [2, 3]:

f(2) = ln(2-1) + 0.5sin(2 x 2) = ln(1) + sin(4) ≈ 0.5 - 0.757 ≈ -0.257

f(3) = ln(3-1) + 0.5sin(2 x 3) = ln(2) + sin(6) ≈ 0.693 - 0.279 ≈ 0.414

Since f(2) is negative and f(3) is positive, the Intermediate Value Theorem guarantees that there exists a root of f(x) within the interval [2, 3].

b. Now, let's use the bisection method to approximate the root of f(x) accurate to 2 decimals.

First, we find the midpoint of the interval [2, 3]:

c = (2 + 3) / 2 = 2.5

Evaluate f(c):

f(2.5) = ln(2.5-1) + 0.5sin(2*2.5) ≈ 0.916 - 0.649 ≈ 0.267

Since f(2.5) is positive, we can conclude that the root lies within the interval [2, 2.5].

New interval: [2, 2.5]

Next, we find the midpoint of the new interval:

c = (2 + 2.5) / 2 = 2.25

Evaluate f(c):

f(2.25) = ln(2.25-1) + 0.5sin(2*2.25) ≈ 0.810 - 0.567 ≈ 0.243

Since f(2.25) is positive, we update the interval to [2, 2.25].

New interval: [2, 2.25]

c = (2 + 2.25) / 2 = 2.125

f(2.125) = ln(2.125-1) + 0.5sin(2*2.125) ≈ 0.730 - 0.481 ≈ 0.249

Since f(2.125) is positive, we update the interval to [2, 2.125].

New interval: [2, 2.125]

c = (2 + 2.125) / 2 = 2.0625

f(2.0625) = ln(2.0625-1) + 0.5sin(2*2.0625) ≈ 0.685 - 0.402 ≈ 0.283

Since f(2.0625) is positive, we update the interval to [2, 2.0625].

New interval: [2, 2.0625]

c = (2 + 2.0625) / 2 ≈ 2.03125

f(2.03125) = ln(2.03125-1) + 0.5sin(2*2.03125) ≈ 0.662 - 0.368 ≈ 0.294

Since f(2.03125) is positive, we update the interval to [2, 2.03125].

We continue this process until the desired accuracy is reached. As the interval becomes smaller, we approach the root of the function.

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The Intermediate Value Theorem guarantees that there exists a root of f(x) within the interval [2, 3].

Let's consider the interval [2, 3]:

The Root lies between 2 and 3.

Here f(2)=-0.3784012 < 0 and f(3)=0.5534394 > 0

∴ The root lies between 2 and 3

x0=(2+3)/2

x0=2.5

f(x0)=f(2.5)=ln(1.5)+0.5sin(5)=-0.073997<0

Here f(2.5)=-0.073997<0 and f(3)=0.5534394>0

The root lies between 2.5 and 3

x1=(2.5+3)/2

x1=2.75

f(x1)=f(2.75)=ln(1.75)+0.5sin(5.5)=0.2068456>0

Here f(2.5)=-0.073997<0 and f(2.75)=0.2068456>0

The root lies between 2.5 and 2.75

x2=(2.5+2.75)/2

x2 =2.625

f(x2)=f(2.625)=ln(1.625)+0.5sin(5.25)=0.0560406>0

We continue this process until the desired accuracy is reached. As the interval becomes smaller, we approach the root of the function.

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Answer:

D

Step-by-step explanation:

You can just use the vertical line test and make sure there aren’t two pints that cross like the circle doesn’t pass the vertical line test because it hit the circle at two points at the same time.

Answer:

d

Step-by-step explanation:

no need

When the cosine of an angle (0) is 3/5 and the angle lies in quadrant 4, the exact value of the sine of that angle is -4/5.

To find the exact value of sin(0), we can utilize the Pythagorean identity, which states that \(sin^2(x) + cos^2(x) = 1,\) where x is an angle in a right triangle. Since the terminal side of the angle (0) is in quadrant 4, we know that the cosine value will be positive, and the sine value will be negative.

Given that cos(0) = 3/5, we can determine the value of sin(0) using the Pythagorean identity as follows:

\(sin^2(0) + cos^2(0) = 1\\sin^2(0) + (3/5)^2 = 1\\sin^2(0) + 9/25 = 1\\sin^2(0) = 1 - 9/25\\sin^2(0) = 25/25 - 9/25\\sin^2(0) = 16/25\)

Taking the square root of both sides to find sin(0), we have:

sin(0) = ±√(16/25)

Since the terminal side of (0) is in quadrant 4, the y-coordinate, which represents sin(0), will be negative. Therefore, we can conclude:

sin(0) = -√(16/25)

Simplifying further, we get:

sin(0) = -4/5

Hence, the exact value of sin(0) when cos(0) = 3/5 and the terminal side of (0) is in quadrant 4 is -4/5.

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Note the correct and the complete question is

Q- Find the exact value of sin(0) when cos(0) =3/5 and the terminal side of (0) is in quadrant 4​ ?

Step-by-step explanation:

(1/3a^2-4b)^6 for such an expansion the general term is

\(tr + 1 = \binom{6}{r} \times ( \frac{1}{3} {a}^{2} ) ^{6 - r} \times (4b)^{r} \)

we want b^2 so r=2

so the formula transform to:

C6,2*(1/3)^4*a^8*4^2*b^2 so the coefficient of a^8b^2 is

(6*5/2*1)*(1/3^4)*4^2=

6*5*4*4/2*3*3*3*3=16*5/27=80/27