The position of a particle moving along the x axis is given by x(t) = 5.42 m-2.31 m/s t. at what time in s does the particle cross the origin?

Answer:

132

Step-by-step explanation:

C=5

3c - 2 = 13

2c = 10

4c + 1 = 21

4c + 2 = 22

length = (3c- 2) + (4c + 1)

length = 13 + 21

length = 34

width = (4c + 2) + (2c)

width = 22 + 10

width = 32

Perimeter

p = 2l + 2w

p = 2*34 + 2*32

p = 68 + 64

p = 132

Answer: Point P is a midpoint

Step-by-step explanation:

The required solution (a)  (5x - 2)(x - 3), (b)  (x + 5)² -25y² and (c)  (x - 6y)(x - 7y).

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

a, 5x(x-3)-2x+6
Simplifying,
= 5x(x - 3)-2(x - 3)
= (5x - 2)(x - 3)

b, x² - 25y² + 10x + 25
Simplifying,
= (x + 5)² -25y²

c, x² - xy - 42y²
Simplifying,
=  x² - xy - 42y²
= x² - 7xy + 6xy - 42y²
= x(x - 7y) + 6y(x - 7y)
= (x - 6y)(x - 7y)

Thus, the required solution (a)  (5x - 2)(x - 3), (b)  (x + 5)² -25y² and (c)  (x - 6y)(x - 7y).

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Mr. William's class has a higher rate of students with afterschool jobs because 9 over 30 is less than 8 over 25. Therefore, the second statement is correct.

Comparing the ratios of students with afterschool jobs in Ms. Talley's and Mr. William's classes.

Ms. Talley's class

Students have afterschool jobs = 9 out of 30

Ratio = \(\frac{9}{30}\)

Mr. William's class

Students have afterschool jobs = 8 out of 25

Ratio = \(\frac{8}{25}\)

Let us now compare the ratios:

9/30 = 0.3

8/25 = 0.32

Comparing the ratios, we can see that 0.32 is greater than 0.3.

As a result, compared to Ms. Talley's class, Mr. William's class has a higher percentage of students who have afterschool jobs.

Therefore, the correct statement is: Mr. William's class has a higher rate of students with afterschool jobs because 9 over 30 is less than 8 over 25.

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Answer:

an = 1.2 + (n - 1) 1.5

Step-by-step explanation: opt A on edg

The balance in the fund at the end of 23 years, with monthly deposits of $1,150 and a 3.25% annual interest rate, is approximately $449,069.51. The amount of interest earned over the period is approximately $420,630.49.

a. The balance in the fund at the end of the 23-year period, considering a monthly deposit of $1,150 and an annual interest rate of 3.25% compounded annually, is approximately $449,069.51.

To calculate the balance, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where A is the accumulated balance, P is the monthly deposit, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

In this case, we have monthly deposits, so we need to convert the annual interest rate to a monthly rate:

Monthly interest rate = (1 + 0.0325)^(1/12) - 1 = 0.002683

Using this monthly interest rate, we can calculate the accumulated balance over the 23-year period:

A = 1150 * [(1 + 0.002683)^(12*23) - 1] / 0.002683 = $449,069.51

Therefore, the balance in the fund at the end of the 23-year period is approximately $449,069.51.

b. The amount of interest earned over the 23-year period can be calculated by subtracting the total deposits from the accumulated balance:

Interest earned = (Monthly deposit * Number of months * Number of years) - Accumulated balance

Interest earned = (1150 * 12 * 23) - 449069.51 = $420,630.49

Therefore, the amount of interest earned over the 23-year period is approximately $420,630.49.

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Some of the sub-questions have been answered. I will provide explanation to the already answered questions and then answer the unanswered parts

1. The graph type

The three graph displayed are stem-and-leaf plots. The single numbers at the left-hand side are referred to as the stem, while the numbers at the right are called leaves.

2. The type of data

The three graphs display numerical data (i.e. numbers). Hence, the data are quantitative

3. The correct graph

To know the correct graph; the leaves on each line must be in ascending order and the delimiter to use is a blank space.

Only graph A obey the above illustration

4. Skewness

In graph A, the length of the leaves increases as we move from one stem to the other. This means that the graph is negatively skewed.

For a negative skewed stem plot, the mean is less than the median

5. The population size

This means that we count the number of leaves in the stem plot

The leaves are:

\(Leaves = \{0,8,4,8,0,4,6,2,2,2,6,6,6,0,0,0,0,2,4\}\)

So, the population size is: 19

6. The data set

To do this, we include the stem to the corresponding leaves.

So, we have:

\(Dataset= \{50,58,64,68,70,74,76,82,82,82,86,86,86,90,90,90,90,92,94\}\)

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Based on the evaluation of the conditions, the output "x < 0 and z > 0" will be printed. Therefore, the correct answer is B. x < 0 and z > 0.

The correct indentation of the statement would be as follows:

if (x > 0)

if (y > 0)

System.out.println("x > 0 and y > 0");

else if (z > 0)

System.out.println("x < 0 and z > 0");

Given that x = 1, y = -1, and z = 1, let's evaluate the conditions:

The first if statement checks if x > 0, which is true since x = 1.

Since the condition in the first if statement is true, we move to the inner if statement, which checks if y > 0. However, y = -1, so this condition is false.

The inner if statement is followed by an else if statement that checks if z > 0. Since z = 1, this condition is true.

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Answer:

(8/3, ∝)

Step-by-step explanation:

Definition

The Mean Value Theorem states that for a continuous and differentiable function \(f(x)\) on the closed interval [a,b], there exists a number c from the open interval (a,b) such that \(\bold{f'(c)=\frac{f(b)-f(a)}{b-a}}\)

Note:

A closed interval interval includes the end points. Thus if a number x is in the closed interval [a, b] then it is equivalent to stating a ≤ x ≤ b.

An open interval does not include the end points so if x is in the open interval (a, b) then a < x < b

This distinction is important

The function is \(y = f(x)=\ln\left(3x-8\right)\)

Let's calculate the first derivative of this function using substitution and the chain rule

Let

\(u(x) = 3x-8\\\\\frac{du}{dx} = \frac{d}{dx}(3x-8) = \frac{d}{dx}(3x) - \frac{d}{dx}8 = 3 - 0 =3\\\\\)

Substituting in the original function f(x), we get

\(y = ln(u)\\\\dy/du = \frac{1}{u}\)

Using the chain rule

\(\frac{dy}{dx}=\frac{dy}{du}.\frac{du}{dx}\)

We get

\(\frac{dy}{dx}=\frac{1}{u}3=\frac{1}{3x-8}3=\frac{3}{3x-8}\)

This has a real value for all values of x except for x = 8/3 because at x = 8/3, 3x - 8 = 0 and division by zero is undefined

Now \(ln(x)\) is defined only for values of x > 0. That means 3x-8 > 0 ==> 3x > 8 or x > 8/3

There is no upper limit on the value of x for ln(x) since ln(x) as x approaches ∝ ln(x) approaches  ∝ and  as x approaches ∝ 3/(3x-8) approaches 0

So the interval over which the mean theorem applies is the open interval (8/3, ∝)

At x = 8/3 the first derivative does not exist

Graphing these functions can give you a better visual representation

Answer:

128

Step-by-step explanation:

the criteria used when deciding upon the inclusion of a variable are A - Theory, B - t-statistic, C - Bias, and D - Adjusted R^2.

When deciding upon the inclusion of a variable, the following criteria are commonly used:

A - Theory: Theoretical justification is often considered to include a variable in a model. It involves assessing whether the variable is relevant and aligns with the underlying theory or conceptual framework.

B - t-statistic: The t-statistic is used to determine the statistical significance of a variable. A variable with a significant t-statistic suggests that it has a meaningful relationship with the dependent variable and may be included in the model.

C - Bias: Bias refers to the presence of systematic errors in the estimation of model parameters. It is important to consider the potential bias introduced by including or excluding a variable and assess whether it aligns with the research objectives.

D - Adjusted R^2: Adjusted R^2 is a measure of the goodness of fit of a regression model. It considers the trade-off between the number of variables included and the overall fit of the model. Adjusted R^2 helps in assessing whether the inclusion of a variable improves the model's explanatory power.

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Answer:

It will take 47 hours

Step-by-step explanation:

We can have the exponential function as follows;

P = I( 1 + r)^n

if the initial value was x , the final will be 2x

The change rate is 1.5% , which is r, this is same as;

1.5/100 = 0.015

So what we want to calculate is the n attached

This will be;

2x = x ( 1 + 0.015)^n

2 = 1.015^n

ln 2 = n ln 1.015

n = ln 2/ln 1.015

n = 46.55

This is approximately 47 hours

Answer:

24 and 1 (1 x 24 = 24)

12 and 2 (2 x 12 = 24)

6 and 4 (4 x 6 = 24)

8 and 3 (3 x 8 = 24)

Answer:

Step-by-step explanation:

I hope this helps!

Answer:

\( {ax}^{3} + 4ax \\ \)

factorise out a and x :

\( { \boxed{answer{= ax( {x}^{2} + 4) }}}\\ but \: farther \: more : \\ = ax( {x}^{2} + {2}^{2} )\)

but from general factorization:

\({ \boxed{( {a}^{2} + {b}^{2}) = {(a + b)}^{2} - 2ab }}\)

a » x

b » 2

therefore:

\( = ax \{ {(x + 2)}^{2} - 2(x)(2) \} \\ \\ = { \boxed{ \boxed{ax( {x + 2)}^{2} - 4x }}}\)

The most general antiderivative of h(t)=-3sin(t)/cos^2(t) is F(t)=3sec(t)+C, where C is a constant of integration.

To find the antiderivative of h(t), we first recognize that -3sin(t)/cos^2(t) can be rewritten as -3cos^(-2)(t) * sin(t). We can then use the substitution u = cos(t), du = -sin(t) dt to obtain ∫ -3cos^(-2)(t) * sin(t) dt = ∫ -3/u^2 du. Integrating with respect to u, we get 3/u + C = 3sec(t) + C, where C is a constant of integration. Therefore, the most general antiderivative of h(t) is F(t) = 3sec(t) + C, where C is a constant of integration.

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Based on this evaluation, the correct answer is:

d. "false : 14 is 104"

The value of 's' after the given statement can be determined by evaluating each part of the expression step by step:

1. Evaluate (!true): Since 'true' is negated using the '!' operator, this expression becomes 'false'.

2. Concatenate " : " to "false": The resulting string also becomes "false : ".

3. Calculate (10 + 4): This arithmetic expression is equals to  14.

4. Concatenate "14" to "false : ": The resulting string becomes equal to "false : 14".

5. Finally, concatenate " is 104" to "false : 14": The final value of 's' becomes "false : 14 is 104".

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According to the given information, 46% of people believe that there is life on other planets. A scientist, who disagrees with this finding, conducted a survey of 120 randomly selected individuals and found that 48 of them believed in life on other planets. To determine if there is sufficient evidence to conclude that the percentage differs from 48 at a significance level (α) of 0.10, a hypothesis test is needed.

The null hypothesis (H0) states that the percentage is equal to 48%, while the alternative hypothesis (H1) states that the percentage differs from 48%. In this case, the sample proportion (p) is 48/120 = 0.4, and the hypothesized proportion (p0) is 0.48.

To perform the hypothesis test, we need to calculate the test statistic (z) and compare it to the critical values. The test statistic can be calculated using the formula z = (p - p0) / √(p0 * (1 - p0) / n), where n is the sample size. After calculating the test statistic, we compare it to the critical values corresponding to α = 0.10.

If the test statistic falls within the critical region, we reject the null hypothesis and conclude that there is sufficient evidence to claim that the percentage differs from 48%. If it falls outside the critical region, we fail to reject the null hypothesis and cannot conclude that the percentage differs from 48% based on this sample.

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The ratio of corresponding sides for the given similar triangles is 2/5.

In the given options, the ratio of corresponding sides is provided for each set of similar triangles. Let's analyze each option to determine the correct ratio:

a. 10

This option only provides a single number and does not specify the ratio of corresponding sides. Therefore, it is not the correct answer.

b. 4/5

This option provides the ratio 4/5 for the corresponding sides of the similar triangles. However, the ratio can be simplified further.

To simplify the ratio, we divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 5 is 1.

Dividing 4 and 5 by 1, we get:

4 ÷ 1 = 4

5 ÷ 1 = 5

Therefore, the simplified ratio is 4/5.

c. 10/85

This option provides the ratio 10/85 for the corresponding sides of the similar triangles. However, this ratio cannot be simplified further, as 10 and 85 do not have a common factor other than 1.

Therefore, the correct ratio of corresponding sides for the given similar triangles is 2/5, as determined in option b.

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Answer:

P=7

Step-by-step explanation:

7-3=4

4/2=2

therefore,

p=7

Answer:

$160

Step-by-step explanation:

Step one:

given data

Principal = $2000

rate= 8%

time t= 1 year

Required

The Simple interest paid after 1 year

Step two:

Simple interest = PRT/100

Simple interest = 2000*8*1/100

Simple interest = 16000/100

Simple interest =$160

The simple interest paid after 1 year is $160

Answer:

Step-by-step explanation:

What does Moon Shadow communicate by contrasting his father's kites with a bunch of paper and sticks"?

A) Function is increasing on (-∞, -1) and (7/2, ∞), and decreasing on (-1, 7/2).

b)  The local minimum value of f is; 5608/2197 at x = -42/13, and the local maximum value of f is 139/8 at x = 7/2.

(a) To determine the intervals on which f is increasing or decreasing, we need to determine the critical points and then check the sign of the derivative on the intervals between them.

f(x)=8x³-42x-48x + 4

f'(x) = 24x² - 90

Setting f'(x) = 0, we get

24x² - 90 = 0

24x² = 90

x =±  √3.75

So, the critical points are;

x = -1 and x = 7/2.

We can test the sign of f'(x) on the intervals as; (-∞, -1), (-1, 7/2), and (7/2, ∞).

f'(-2) = 72 > 0, so f is increasing on (-∞, -1).

f'(-1/2) = -25 < 0, so f is decreasing on (-1, 7/2).

f'(4) = 72 > 0, so f is increasing on (7/2, ∞).

Therefore, f is increasing on (-∞, -1) and (7/2, ∞), and decreasing on (-1, 7/2).

(b) To determine the local maximum and minimum values of f, we need to look at the critical points and the endpoints of the interval (-1, 7/2).

f(-1) = -49

f(7/2) = 139/8

f(-42/13) = 5608/2197

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Answer:

x = -18

Step-by-step explanation:

4+ x / -9 = 6

x / -9 = 6 - 4

x / -9 = 2

x = 2*-9

x = -18

found this deimos Google hope this helps -

x in (-oo:+oo)

x/4-9 = 6 // - 6

x/4-9-6 = 0

1/4*x-15 = 0 // + 15

1/4*x = 15 // : 1/4

x = 15/1/4

x = 60

Answer:

f(x)= -(x-3)^2+1

Step-by-step explanation:

vertex form is a(x-h)^2+k where (h,k)

first find the vertex of the quadratic function which is (3,1)

second substitute h with 3, k with 1, and a with -1 as it was a in the quadratic function