k(n)=3n+2; Find k(0)

Answer:

Step-by-step explanation:

Use similar triangles and proportions to solve:

\(\frac{4}{6}=\frac{10}{6+x}\) and cross multiply:

4(6 + x) = 60 and

24 + 4x = 60 and

4x = 36 so

x = 9

Answer:

100units^2

Step-by-step explanation:

Using pythagoras theorem, it states that 36+64= area of the unknown

a) The value of circumference of circle is,

C  = 219.8 Inches

b) The value of area of circle is,

A = 3,846.5 in²

Given that;

The diameter of circle is, 70 inches

a) Circumference of circle is,

C = π × diameter,

So, We get;

C = 3.14 × 70

C  = 219.8 Inches

b) The area of circle is,

A = πr²,

And, Radius is 1/2 of diameter,

Hence, Radius = 70/2 = 35 inches

Thus, We get;

A =  3.14 × 35²

A = 3.14 × 1225,

A = 3,846.5 in²

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Okay, here we have this:

Considering the provided expression, we are going to solve and simplify it, so we obtain the following:

Finally we obtain that the expression is equal to -22/5.

Given data:

The number of hour Stacy studied maths is 2/6 hour.

The number of hour Stacy studied science is 3/6 hour.

The total number of hours Stacy studied in 5 days is,

Thus, the total number of hours Stacy studied in 5 days is 25/6 hours, so option (D) is correct.

If P(B)=0.3, P(A|B)=0.5, P(B')=0.7and P(A|B')=0.8, then the value of the probability P(B|A)= 0.2113

To find the value of P(B|A), follow these steps:

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Answer:

multiply by 49.8 or add 10975 cm.

To plot the intercepts of the equation 5x - 4y = 20, we need to find the x-intercept and the y-intercept.

- The x-intercept is (4, 0).
- The y-intercept is (0, -5).
- The slope of a line parallel to this line is 3.
- The slope of a line perpendicular to this line is -4/5.

1. X-intercept:

x = 4

So, the x-intercept is (4, 0).

2. Y-intercept:

y = -5

So, the y-intercept is (0, -5).

To find the slope of the line parallel to the line passing through the points (-3, -9) and (0, 0), we can use the formula:

slope = (y2 - y1) / (x2 - x1)

(a) Parallel line slope:

slope = (0 - (-9)) / (0 - (-3))

     = 9 / 3

     = 3

Therefore, the slope of the line parallel to the line passing through the points (-3, -9) and (0, 0) is 3.

(b) Perpendicular line slope:

For a line perpendicular to another line, the slope is the negative reciprocal of the original slope. The original slope is 3, so the perpendicular slope is -1/3.

Therefore, the slope of the line perpendicular to the line passing through the points (-3, -9) and (0, 0) is -1/3.

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The sample size of the actors is the number of actors Darrien selected

The sample size is 15

From the question, we understand that:

Darrien has 60 actors

This represents the population of the experiment.

Then he selected 15 of the actors, and 8 of them have previous acting experience.

The 15 actors he selected represents the sample of the experiment

Hence, the sample size is 15

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Answer:

There is no pic u might want to repost it^^

Step-by-step explanation:

A correlation coefficient is a numerical index that reflects the relationship between two variables.

The correlation coefficient helps us to know how strong is the relation between two variables. Its value is always between +1 to -1, where, the numerical value shows how strong is the relation between them and, the '+' or '-' sign shows whether the relationship is positive or negative.

The given blank in the sentence can be filled with two variables.

Hence, A correlation coefficient is a numerical index that reflects the relationship between two variables.

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Answer:

1.) y=3x

2.) y= -2/3 x + 1

3.)y = -2/3 x - 4

4.) y = 4

5.) y = x + 5

6.) y = 2x

Answer: Angle 4 shows Angle EHD

Step-by-step explanation:

The two angles are vertically opposite angles so that’s why they are equal

Answer:

The account balance after 24 months will be $23,092.70

Step-by-step explanation:

Given data

P= $20,000

r= 7.77%= 0.077

t= 2 years

A= ?

n= 24

The compound interest formula is

\(A= P(1+t)^t\)

Inserting our values to solve for A we have

\(A= 20000(1+\frac{0.077}{24} )^2^*^2^4\\\\A= 20000(1+0.003 )^2^*^2^4\\\\A= 20000(1.003 )^2^*^2^4\\\A= 20000(1.003 )^4^8\\\A= 20000*1.15463517818\\\A= 23092.7035636\\\A= 23,092.70\)

The work done in lifting a bag of mulch was 504 Joules.

To find the amount of work done in this scenario, you can use the formula for work, which is work = force x distance x cos(theta), where force is measured in newtons (N), distance is measured in meters (m), and theta is the angle between the force and the displacement.

In this case, first, you lifted the bag of mulch 1.2 meters against gravity and the force applied is 45N and the displacement is 1.2m, the formula becomes:

work = force x distance x cos(theta) = 45 N x 1.2 m = 54 J

After, you carry the bag of mulch 10 meters, and the force applied is still 45N and the displacement is 10m, so the formula becomes:

work = force x distance x cos(theta) = 45 N x 10 m = 450 J

Therefore, the total amount of work done in lifting the bag of mulch 1.2 meters and carrying it at a distance of 10 meters is 54 J + 450 J = 504 J.

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Answer:

6k-5

Step-by-step explanation:

Answer:

k

Step-by-step explanation:

6-5=1

1*k=k

The equivalent fractions for 2/3 is (3×2)/(3×3) = 6/9 and for  5/12 is (4×5)/(4×12) = 20/48.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

The equivalent fraction for 2/3 is (3×2)/(3×3) = 6/9.

The equivalent fraction for 5/12 is (4×5)/(4×12) = 20/48.

We have to multiply the same number to both the numerator and denominator to get equivalent fractions.

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To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

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To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

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The blocks will be filled as follows -

y = 5(x) + b

33 = b

The general equation of a straight line is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given is the slope of the line passing through the point (4, 53).

Now, from the question, we can write -

y = 5x + b

For the point -

(4, 53)

We can write -

53 = 5 x 4 + b

b = 53 - 20

b = 33

Therefore, the blocks will be filled as follows -

y = 5(x) + b

33 = b

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Answer:

Eric forgot to add 2 to both sides.

Step-by-step explanation:

He forgot to add 2 to both sides so that he cancel out the -2 from the equation. Then the equation would become 2/5v=6 the you would divide those two and your answer would be  1/15.

A two digit positive number is any number between 0 and 99, inclusive, and can be written in numerical, expanded, word, or fraction form.

The two digit positive number is any number between 0 and 99, inclusive. This includes all the numbers from 00 to 99. All of these numbers are considered positive because they are not negative numbers. A two digit positive number can be composed of two single digits, such as 12, or one single digit followed by a zero, such as 30. They can also be composed of two successive numbers, such as 23, or two successive numbers with a zero in between, such as 40.Two digit positive numbers can also include decimal numbers, such as 12.3 or 0.45. These decimal numbers will always have two digits to the left of the decimal point.

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Answer:

other leg = 16 cm

Step-by-step explanation:

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

let x represent the other side , then

12² + x² = 20²

144 + x² = 400 ( subtract 144 from both sides )

x² = 256 ( take square root of both sides )

x = \(\sqrt{256}\) = 16

then the other leg is 16 cm

The length of the other leg will be 16cm if a right triangle has one leg with a length of 12 cm and hypotenuse with a length of 20 cm.

Using Pythagoras theorem:

h² = a² + b²

here,

h = length of hypotenuse side

a = length of one leg

b = length of another leg

Given that,

h = 20cm, a = 12cm

Therefore, (20cm)² = (12cm)² + b²

or b² = \(\sqrt{(20cm)^{2}-(12cm)^{2} }\)

or b = \(\sqrt{256cm^{2} }\)

or b = 16 cm

Therefore, The length of the other leg will be 16cm if a right triangle has one leg with a length of 12 cm and hypotenuse with a length of 20 cm.

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Answer:

188

Step-by-step explanation:

Answer:

x ≤ 4, look for the bold title for the numberline

Step-by-step explanation:

Subtract 7 to both sides

x + 7 ≤ 11

  -7    -7

x ≤ 4

That is the answer.

Can you provide a number line?

The parent function is f(x) = 7x + 5.

So let's find the equation for each transformation:

a) The function f reflected about the y-axis and translated 3 units left.

A reflection about the y-axis can be calculated just changing the sign of the variable x:

Now, in order to translate 3 units left, we just need to add 3 units to the x-value:

b) The function f stretched vertically by a factor of 3 and translated up by 2 units.

In order to stretch up the function, we multiply the whole function by the factor:

Then, to translated 2 units up, we add 2 units of the function:

c) The function f translated 2 units down and 3 units right.

To do a translation of 2 units down, we subtract 2 units of the function, and to translate 3 units right, we subtract 3 units from the value of x:

d) The function f stretched vertically by a factor of 2 and translated down by 3 units.

In order to stretch up the function, we multiply the whole function by the factor:

Then, to translated 3 units down, we subtract 3 units of the function:

Answer:

Step-by-step explanation:

Create the equation 8x-4=36. Adding 4 to both sides gets 8x=40. Dividing both sides by 8 gets us x=5.

Step-by-step explanation:

the process is show in the above picture.

The threshold hmax for which the Euler method, when applied to the linear ODEs obtained from the linearization of the given ODE system, will be stable for all h is hmax = 2.

To find the threshold hmax for which the Euler method, when applied to the linear ODEs, will be stable for all h, we need to consider the stability of the linear system.

The linearization of the ODE system around the equilibrium (-1,1) gives the following matrix:

A = [∂f/∂x ∂f/∂y]

[∂g/∂x ∂g/∂y]

where f = t' - x² + y² and g = y' - xy - y - x - 1.

Evaluating A at (-1,1) gives:

A = [2 -2]

[0 -1]

The characteristic equation of A is given by:

det(A - λI) = 0

=> |2-λ -2 | = (2-λ)(-1-λ) = 0

| 0 -1-λ |

Solving for λ, we get λ = 2 or λ = -1.

Since one of the eigenvalues is positive, the equilibrium point is unstable.

Now, the Euler method applied to the linear ODEs gives:

\(x_{n+1} = x_n + hf(x_n, y_n) = x_n + h(t_n - x_n + y_n)\)

\(y_{n+1} = y_n + hg(x_n, y_n) = y_n + h(-x_n - y_n - 1)\)

where f and g are the linear functions obtained from the linearization of the ODE system.

Substituting the values of f and g and simplifying, we get:

\(x_{n+1}\) = (1-h)\(x_n + hy_n + ht_n\)

\(y_{n+1}\) = -\(hx_n + (1-h)y_n - h\)

The stability of the Euler method depends on the eigenvalues of the coefficient matrix of the difference equations, which are given by:

B = [1-h h ]

[-h 1-h]

The characteristic equation of B is given by:

det(B - λI) = 0

=> |1-h-λ h | = [(1-h-λ)² - h²] = λ² - 2(1-h)λ + h² - 1 = 0

| -h 1-h-λ|

Solving for λ, we get:

λ = (1-h) ± √((1-h)² - h²)

For the method to be stable, the absolute value of λ should be less than or equal to 1. Therefore, we have:

|(1-h) ± √((1-h)² - h²)| ≤ 1

Solving for h, we get:

0 ≤ h ≤ 2

Therefore, the threshold hmax for which the Euler method will be stable for all h is hmax = 2.

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