I need help solving for x

a_2

a_3

a_4

a_5

Answer:

1, 5, 17, 53, 161

Step-by-step explanation:

Given:

First five terms of the sequence:

\(a_1=1\)

\(a_2=3a_1+2=3(1)+2=5\)

\(a_3=3a_2+2=3(5)+2=17\)

\(a_4=3a_3+2=3(17)+2=53\)

\(a_5=3a_4+2=3(53)+2=161\)

Rounding to the nearest whole number, the approximate volume of the mountain is 36 cubic kilometers.

Volume is a measure of the amount of space that a three-dimensional object occupies or contains. It is typically measured in cubic units, such as cubic meters, cubic centimeters, or cubic feet.

In the given question,

The volume of a cone can be calculated using the formula V = (1/3)πr²h, where r is the radius of the base, h is the height, and π is approximately 3.14.

Substituting the given values, we get:

V = (1/3) × 3.14 × 3² × 3.8

V ≈ 35.63

Rounding to the nearest whole number, the approximate volume of the mountain is 36 cubic kilometers.

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The most appropriate choice for heat  will be given by-

Amount of heat absorbed by the lead = 1455.12 J

What is heat?

Heat is the form of energy which caused in us the sensation of hotness or coldness.

SI Unit of heat is Joule                              

Here,

Mass (m) of block of lead = 300 gram

Specific heat capacity (c) of block of lead = 0.129 J/g°C.

Increase in temperature (\(\Delta\)t)  of block of lead= 59.9 - 22.3

                                                                           = 37.6° C

Amount of heat absorbed by the lead = \(300 \times 0.129 \times 37.6\)

                                                                = 1455.12 J

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The categories of the expressions are: 187.26 - (394 2/3) = negative, -3/7(1/3 - 11) = positive, (2/7 - 9/13) + (9/13 - 2/7) = zero and -18/13(0 - 13/18) = positive

From the question, we have the following parameters that can be used in our computation:

187.26 - (394 2/3)

When evaluated, we have

187.26 - (394 2/3) = -207.41

This means that

187.26 - (394 2/3) = negative

Next, we have

-3/7(1/3 - 11)

When evaluated, we have

-3/7(1/3 - 11) = 4.57

This means that

-3/7(1/3 - 11) = positive

Next, we have

(2/7 - 9/13) + (9/13 - 2/7)

When evaluated, we have

(2/7 - 9/13) + (9/13 - 2/7) = 0

This means that

(2/7 - 9/13) + (9/13 - 2/7) = zero

Lastly, we have

-18/13(0 - 13/18)

When evaluated, we have

-18/13(0 - 13/18) = 1

This means that

-18/13(0 - 13/18) = positive

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Answer:

u kind of forgot the attachment bestie

Since none of the 13 classmates had been given math homework between the original survey and Kelly's second survey, the sum of the values in the second data set is the same as the sum of the values in the original data set. Therefore, the change in the means can be determined without calculating the mean of either data set by considering the number of data points in each set.

Since both data sets have the same number of data points, the change in the means will be zero. This is because the mean is calculated by dividing the sum of the values by the number of data points, and since the sum of the values is the same in both data sets, the means will also be the same.

In other words, if the mean of the first data set is x, then the sum of the values in the first data set is 13x (since there are 13 classmates), and the sum of the values in the second data set is also 13x (since none of the values have changed). Therefore, the mean of the second data set will also be x, and the change in the means will be zero.

The correct option is B. because information about the population is not known and using the SD might create a biased result. The standard deviation (SD) can be used to measure the variation within a sample.

It provides information on how tightly clustered or dispersed a set of data is around the mean. However, when using the t-test to compare means, the standard error of the mean (SEM) is used instead of the SD. This is because the t-test compares the means of two samples to determine whether the differences between them are statistically significant.

The SEM is a measure of the precision of the sample mean estimate. It is the SD of the sample means and is used to estimate the precision of the population mean. It takes into account the sample size and provides a more accurate estimate of the population mean. Since information about the population is not known and using the SD might create a biased result, SEM is preferred over the standard deviation in calculating the standard error of the mean.

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2.5 hours the Kelly  spent driving.51 minutes John spent  for driving.1.20 hours Ebise spent driving.Since average speed = distance/time +> distance = speed*time,

x =the number of hours the Kelly  spent driving.

y = the number of hours John spent driving.

Z= the number of hours Ebise spent driving.

Since average speed = distance/time +> distance = speed*time,

y = x + 1.

By resolving the system of equations

y = x + 1

x*28 + y*82 + Z* 58,

average speed  = 70

we discover that

x = 2.5 hours

y = 51 minutes, respectively.

Z = 1. hr 20 minutes

2.5 hours the Kelly  spent driving.

51  minutes John spent  for driving.

1.20 hours Ebise spent driving.

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Answer:

Decagon

Step-by-step explanation:

A decagon has 10 vertices. which is greater than the number of vertices a pentagon, hexagon, and octagon has

Answer:

2/14, 1/7, 3/21, and 18/126

Step-by-step explanation:

Answer:

D. 14.7 m

Step-by-step explanation:

7 times 2 equals 14

7 times .1 equals .7

7 times 2.1 equals 14.7

Adjust the parameters as needed, such as the step size (h) and the final x-value (xn), and run the code to obtain the solution for y(x).

The resulting plot will show the solution curve.

To solve the given set of differential equations using the Runge-Kutta method in MATLAB, we need to convert the second-order differential equations into a system of first-order differential equations.

Let's define new variables:

y = y(x)

z = dz/dx

Now, we have the following system of first-order differential equations:

dy/dx = z (1)

dz/dx = -k/(2y) (2)

To apply the Runge-Kutta method, we need to discretize the domain of x. Let's assume a step size h for the discretization. We'll start at x = 0 and proceed until x = infinite.

The general formula for the fourth-order Runge-Kutta method is as follows:

k₁ = h f(xn, yn, zn)

k₂ = h f(xn + h/2, yn + k₁/2, zn + l₁/2)

k₃ = h f(xn + h/2, yn + k₂/2, zn + l₂/2)

k₄ = h f(xn + h, yn + k₃, zn + l₃)

yn+1 = yn + (k₁ + 2k₂ + 2k₃ + k₄)/6

zn+1 = zn + (l₁ + 2l₂ + 2l₃ + l₄)/6

where f(x, y, z) represents the right-hand side of equations (1) and (2).

We can now write the MATLAB code to solve the differential equations using the Runge-Kutta method:

function [x, y, z] = rungeKuttaMethod()

   % Parameters

   k = 1;              % Constant k

   h = 0.01;           % Step size

   x0 = 0;             % Initial x

   xn = 10;            % Final x (adjust as needed)

   n = (xn - x0) / h;  % Number of steps

   % Initialize arrays

   x = zeros(1, n+1);

   y = zeros(1, n+1);

   z = zeros(1, n+1);

   % Initial conditions

   x(1) = x0;

   y(1) = 0;

   z(1) = 0;

   % Runge-Kutta method

   for i = 1:n

       k1 = h * f(x(i), y(i), z(i));

       l1 = h * g(x(i), y(i));

       k2 = h * f(x(i) + h/2, y(i) + k1/2, z(i) + l1/2);

       l2 = h * g(x(i) + h/2, y(i) + k1/2);

       k3 = h * f(x(i) + h/2, y(i) + k2/2, z(i) + l2/2);

       l3 = h * g(x(i) + h/2, y(i) + k2/2);

       k4 = h * f(x(i) + h, y(i) + k3, z(i) + l3);

       l4 = h * g(x(i) + h, y(i) + k3);

       y(i+1) = y(i) + (k1 + 2*k2 + 2*k3 + k4) / 6;

       z(i+1) = z(i) + (l1 + 2*l2 + 2*l3 + l4) / 6;

       x(i+1) = x(i) + h;

   end

   % Plotting

   plot(x, y);

   xlabel('x');

   ylabel('y');

   title('Solution y(x)');

end

function dydx = f(x, y, z)

   dydx = z;

end

function dzdx = g(x, y)

   dzdx = -k / (2*y);

end

% Call the function to solve the differential equations

[x, y, z] = rungeKuttaMethod();

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The two column proof to justify the complementary angles are;

Statement 1. ∠1 and ∠2 are complementary

∠2 and ∠3 are complementary

Reason 1: Given

Statement 2: m∠1 + m∠2 = 90°

Reason 2: Definition of Complementary Angles

Statement 3. m∠2 + m∠3 = 90°

Reason 3: Definition of Complementary Angles

Statement 4: m∠1 + m∠2 = m∠2 + m∠3

Reason 4: Transitive property of equality

Statement 5: m∠1 = m∠3

Reason 5: Substitution Property of Equality

Complementary angles are defined as angles that sum up to 90 degrees.

Now, from the question, we are given that;

∠1 and ∠2 are complementary, and ∠2 and ∠3 are complementary.

From the image attached, we can get a two column proof based on the given questions as;

Statement 1. ∠1 and ∠2 are complementary

∠2 and ∠3 are complementary

Reason 1: Given

Statement 2: m∠1 + m∠2 = 90°

Reason 2: Definition of Complementary Angles

Statement 3. m∠2 + m∠3 = 90°

Reason 3: Definition of Complementary Angles

Statement 4: m∠1 + m∠2 = m∠2 + m∠3

Reason 4: Transitive property of equality

Statement 5: m∠1 = m∠3

Reason 5: Substitution Property of Equality

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Complete Question is;

Identify the correct justification for each step, given that ∠1 and ∠2 are complementary, and ∠2 and ∠3 are complementary.

1. ∠1 and ∠2 are complementary

∠2 and ∠3 are complementary

2. m∠1 + m∠2 = 90°

3. m∠2 + m∠3 = 90°

4. m∠1 + m∠2 = m∠2 + m∠3

5. m∠1 = m∠3

Answer: x = -7

Step-by-step explanation:

4(1 - x) + 2x = -3(x + 1)

First, use distributive property

4 - 4x + 2x = -3x + -3

Combine like terms

4 - 2x = -3x - 3

Add 3x to each side

4 + x = -3

Subtract 4 from each side

x = -7

Answer:

-2

1. Equation at the end of step 1  ((4•(1-x))+3x)-(0-2•(x-1))  = 0

2. Equation at the end of step 2 (4 • (1 - x) +  3x) -  -2 • (x - 1)  = 0

3. Equation at the end of step 3  x + 2  = 0

4. End of equation Solve  :    x+2 = 0

Your equation is wrong. See below for correct equation.

The ball will hit the ground when h(t) is 0.

Here is the set up:

0 = -16t^2 + 5t + 5

Solve for t to find your answer.

Answer:

4d-16/1, 8d-32/2, 12d-48/3, etc.

Step-by-step explanation:

Just throw a denomiator under the expression and adjust the expression accordingly.

Answer:

C, 27 degrees

Step-by-step explanation:

complementary is 2 angles that their measures add to 90 degrees;

90-63=27

27 degrees

uwu

To determine if the packaging process is capable or if an adjustment is needed, we can calculate the process capability index (Cpk) using the given information.

The process capability index (Cpk) is calculated as the minimum of two ratios: Cp and Cpk.

Cp (Process Capability):

Cp = (Upper Specification Limit - Lower Specification Limit) / (6 * Standard Deviation)

In this case:

Upper Specification Limit = 264 + 13 grams = 277 grams

Lower Specification Limit = 264 - 13 grams = 251 grams

Standard Deviation = 1.03 grams

Cp = (277 - 251) / (6 * 1.03) ≈ 4.04

Cpk (Process Capability Index):

Cpk = min[(Upper Specification Limit - Process Mean) / (3 * Standard Deviation), (Process Mean - Lower Specification Limit) / (3 * Standard Deviation)]

Process Mean = 43.5 grams

Upper Specification Limit = 277 grams

Lower Specification Limit = 251 grams

Standard Deviation = 1.03 grams

Cpk = min[(277 - 43.5) / (3 * 1.03), (43.5 - 251) / (3 * 1.03)]

= min[233.5 / 3.09, -207.5 / 3.09]

= min[75.58, -67.22]

= -67.22 (since the negative value is smaller)

The process capability index (Cpk) is -67.22, which indicates that the process is not capable of meeting the specifications. An adjustment is needed to bring the process back within the desired range.

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Answer:

I guess the answer could be C

Answer:

The correct option is (b).

Step-by-step explanation:

Given that,

The length of the string = 39 m

The kite is level with the top of a building that is 24 meters high.

We need to find the angle of elevation of the kite.

A right-angled triangle will form such that its hypotenuse is 39 m and height is 24 m. Using trigonometry to solve this.

\(\sin\theta=\dfrac{P}{H}\\\\\sin\theta=\dfrac{24}{39}\\\\\theta=\sin^{-1}\left(0.61538\right)\\\\\theta=37.98^{\circ}\)

So, the angle of elevation of the kite is 37.97°. The correct option is (b).

21/5gal

Take 21 and divide by 5

4.2 per gal

62.05/15gal

Take 62.05 and divide by 15

4.1366666 per gal

The better deal is 4.136666 per gallon

Answer: 21/5 is the better deal

Step-by-step explanation:

The equations represents each graph shown on the coordinate system are:

a) y = 3x + 2

b) y = 2

c) y = 2x - 2

What is the system of linear equations?

A system of linear equations is a group of one or more linear equations that can be solved by using a simultaneous equation or elimination method. Therefore, by using the substitution method and writing the solution of the system in terms of coordinate point (x, y) = (-1, 1).

We have,

The points where a line passes through them in each given graph:

a) (-1, -1) and (0, 2)

b) (-1, 0) and (2, 0)

c) (0, -2) and (1, 0)

To write the equation of a line in slope-intercept form (y = mx + b), we need to find the slope of the line (m) and the y-intercept (b).

To find the slope of the line, we can use the slope formula:

m = (y₂ - y₁) ÷ (x₂ - x₁)

a)

(-1, -1) and (0, 2)

m = (y₂ - y₁) ÷ (x₂ - x₁)

m = (2 - (-1)) ÷ (0 - (-1))

m = 3 ÷ 1

m = 3

The y-intercept is the point where the line intersects the y-axis. This point is (0, b), where b is the y-intercept.

Since the given line passes through points (0, 2),

y = 3x + b

2 = 3(0) + b

b = 2.

The equation:

y = 3x + 2

b)

(-1, 0) and (2, 0)

m = (y₂ - y₁) ÷ (x₂ - x₁)

m = (0 - 0)  ÷  (2 - (-1))

m = 0

the y-intercept of the line passes through points (0, 2),

y = (0)x + b

2 =  b

b = 2.

The equation:

y = 2

c)

(0, -2) and (1, 0)

m = (0 - (-2)) ÷ (1 - (0))

m = 2 ÷ 1

m = 2

the y-intercept of the line passes through points (0, -2),

y = 2x + b

2 =  2(-2) + b

b = -2.

The equation:

y = 2x - 2

Hence, the equations represents each graph shown on the coordinate system are:

a) y = 3x + 2

b) y = 2

c) y = 2x - 2

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The significance level of a test is the probability of rejecting the null hypothesis when it is true.

Significance level (alpha, α) is a value that is used to define the borderline between the null hypothesis being rejected or not. It is selected before the beginning of the experiment or study. The most common significance level used is α = 0.05. This means there is a 5% chance of rejecting the null hypothesis even if it is true.

If the p-value is smaller than alpha, the null hypothesis is rejected, and the alternative hypothesis is accepted. The significance level is also known as a Type I error. A Type I error occurs when the null hypothesis is rejected, and the alternative hypothesis is accepted when the null hypothesis is true. This means that the researcher concludes that there is a difference when, in fact, there is none.

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Answer:

x=0 or x=6

Step-by-step explanation:

Step 1: Divide both sides by -4.

−4(|−2x+6|)

−4

=

−24

−4

|−2x+6|=6

Step 2: Solve Absolute Value.

|−2x+6|=6

We know either−2x+6=6or−2x+6=−6

−2x+6=6(Possibility 1)

−2x+6−6=6−6(Subtract 6 from both sides)

−2x=0

−2x

−2

=

0

−2

(Divide both sides by -2)

x=0.

The probability of workers who earn between rs. 35,000 and rs. 52,000 is 99.62 %.

A data set with a normal distribution has the majority of its values clustered in the middle of the distribution and the remaining values tapering off symmetrical toward either end.

For the given question;

z = (x - μ)/σ

In which,

x = sample mean

μ = mean  (48,000)

σ = standard deviation (1500)

x = 35,000 and x = 52,000

For x = 35,000.

z = (35,000 - 48,000)/1500

z = -8.66

Check the p value from table

p(z = -8.66) = 0

For x = 52,000

z = (52,000 - 48,000)/1500

z = 2.66

p(z = 2.66) = 0.99617

P(35,000 < x < 52,000) = 0.99617 - 0

P(35,000 < x < 52,000) = 0.99617

Thus, the probability of workers who earn between rs. 35,000 and rs. 52,000 is 99.62 %.

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Answer:

$18.48

Step-by-step explanation:

Find perimiter of room

4+4+7+7 =22

22•0.84 = 18.48

$18.48

Answer:

they are neither. if they were parallel they would be the same. if they were perpendicular they would be opposite reciprocal. So it is neither