find two different parametric equations for the rectangular equation giveny=x^5+5

Y=-x+3 is the slope-intercept form equation for the line.

The slope or gradient of a line is a numerical representation of a line's steepness and direction in mathematics. The reason for this usage is unknown, although it first appears in English in O'Brien (1844), who wrote "y = mx + b," and in Todhunter (1888), who wrote "y = mx + c." The letter m is widely used to signify slope.

The slope can be calculated by comparing the "vertical change" to "horizontal change" between any two distinct points on a line. In cases when the ratio is expressed as a quotient ("rise over run").

From the above graph,

The line is passing through the points (-1, 4) and (3, 0)

Let the slope intercept form be

y= mx +c

Slope m=(0-4/3+1)

=-4/4

= -1

y= -x+c

The equation is passing through the point (3, 0)

-3+c=0

c=3

y= -x+3

Therefore, y=-x+3 is the slope-intercept form equation for the line.

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Answer:

(783.806 ; 805.994)

Step-by-step explanation:

Given the sample :

X : 799.2,784.3,803.8,806.8,780.5,794.8

Sample size, n = 6

Sample mean, xbar = Σx / n = 794.9

Sample standard deviation, s = 10.574 ( calculator)

Tcritical at 95%, df = 6 - 1 = 5 equals 2.57

Confidence interval :

Xbar ± standard error

Standard Error = Tcritical * s/√n

Standard error = 2.57 * 10.574/√6 = 11.094

Lower boundary = (794.9 - 11.094) = 783.806

Upper boundary = (794.9 + 11.094) = 805.994

(783.806 ; 805.994)

a. The missing values of the logarithm expression is log₃(40).

b. The missing values of the logarithm expression is log₅(8).

c. The missing values of the logarithm expression is  log₂(1/25).

The missing values of the logarithm expression is calculated as follows;

(a). log₃5 + log₃8, the expression is simplified as follows;

log₃5 + log₃8 = log₃(5 x 8) = log₃(40)

(b). The log expression is simplified as;

log₅3 - log₅X = log₅3/8

log₅X = log₅8

X = 8

(c).  The log expression is simplified as;

-2log₂5 = log₂Y

log₂5⁻² = log₂Y

5⁻² = Y

1/25 = Y

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Answer:

450

Step-by-step explanation: 90x 5 = 450  hoped i helped

\(\text{if }x>7\text{, then }|x|>7\) is a valid argument

\(|y|>7\text{, so }y=7\) is not a valid argument

For the first argument: \(\text{if }x>7\text{, then }|x|>7\)

From the definition of absolute value function

\(|x|=x\)   if \(x\ge0\)

That is every positive number is its own absolute value. Since

\(x>7\implies x\ge0\),

we can argue that

\(x>7\implies |x|>7\)

so the first argument is valid

For the second argument: \(|y|>7\text{, so }y=7\)

From the definition of absolute value function

\(|y|:=\left \{ {y\text{ if }y\ge0}\atop{-y\text{ if }y<0} }\right\)

This means that

\(|y|>7:=\left \{ {y>7\text{ if }y\ge0}\atop{-y>7\text{ if }y<0} }\right\)

or

\(|y|>7:=\left \{ {y>7\text{ if }y\ge0}\atop{y<-7\text{ if }y<0} }\right\)

no part of the definition allow for the option \(y=7\). So the second argument is not valid.

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Answer:

Step-by-step explanation:

Hello!

So in the refrigerator factory there are three shifts. Each shift records their quality based on the quantity of defective and working parts assembled.

Using a Chi-Square test of independence you have to test the claim that quality and shifts are independent.

The hypotheses are:

H₀: The variables are independent.

H₁: The variables are not independent.

α: 0.05

\(X^2= sum\frac{(O_{ij}-E_{ij})^2}{E_{ij}} ~X_{(r-1)(c-1)}\)

r= total number of rows

c= total number of columns

i= 1, 2 (categories in rows)

j=1, 2, 3 (categories in columns)

To calculate the statistic you have to calculate the expected frequencies for each category:

\(E_{ij}= \frac{O_{i.}*O_{.j}}{n}\)

\(O_{i.}\) Represents the marginal value of the i-row

\(O_{.j}\) Represents the marginal value of the j-column

\(E_{11}= \frac{O_{1.}*O_{.1}}{n}= \frac{21*40}{120}= 7\)

\(E_{12}= \frac{O_{1.}*O_{.2}}{n}= \frac{21*40}{120}= 7\)

\(E_{13}= \frac{O_{1.}*O_{.3}}{n}= \frac{21*40}{120}= 7\)

\(E_{21}= \frac{O_{2.}*O_{.1}}{n}= \frac{99*40}{120}= 33\)

\(E_{22}= \frac{O_{2.}*O_{.2}}{n}= \frac{99*40}{120}= 33\)

\(E_{23}= \frac{O_{2.}*O_{.3}}{n}= \frac{99*40}{120}= 33\)

\(X^2_{H_0}= \frac{(7-7)^2}{7} + \frac{(5-7)^2}{7} + \frac{(9-7)^2}{7} + \frac{(33-33)^2}{33} + \frac{(35-33)^2}{33} + \frac{(31-33)^2}{33} = 1.385= 1.34\)

Using the critical value approach, the rejection region for this test is one-tailed to the right, the critical value is:

\(X^2_{(c-1)(r-1);1-\alpha }= X^2_{2; 0.95}= 5.991\)

Decision rule:

If \(X^2_{H_0}\) ≥ 5.991, reject the null hypothesis.

If \(X^2_{H_0}\) < 5.991, do not reject the null hypothesis.

The value of the statistic is less than the critical value, the decision is to not reject the null hypothesis.

At 5% significance level, you can conclude that the shift the pieces were assembled and the quality of said pieces are independent.

I hope this helps!

Answer:

Assuming a Poisson distribution for the weekly sales, the probability that the store will sell exactly seven card tables in a given week is 0.060

Step-by-step explanation:

In order to calculate the probability that the store will sell exactly seven card tables in a given week we would have to calculate the following formula:

probability that the store will sell exactly seven card tables in a given week= e∧-λ*λ∧x/x!

According to the given data furniture store sells four card tables in a week, hence λ=4

Therefore, probability that the store will sell exactly seven card tables in a given week=e∧-4*4∧7/7!

probability that the store will sell exactly seven card tables in a given week=0.060

Assuming a Poisson distribution for the weekly sales, the probability that the store will sell exactly seven card tables in a given week is 0.060

Answer:

Brandon wants $490 in 16 years by investing "x" dollars in an account that pays  5% compounded quarterly.   How much is "x"?

Principal = Total / [ (1 + (r/n) )^ n * years]

n = 4 (for compounded quarterly)

Principal = 490 / [ (1. + (.05/4)) ^ 4 * 16]

Principal = 490 / [ (1.0125)^ 64]

Principal = 490 / 2.2145324106

Principal = 221.2656710971

So, if we invested 221.27 for 16 years at 5% compounded quarterly interest,  we would have a total of $490.00

Step-by-step explanation:

Answer:

221

Step-by-step explanation:

I just know

Answer:

yes it is

Step-by-step explanation:

Answer:

Because the triangle with the legs 2 and 2 would need to have a third leg less than 4 and greater than 0 and a triangle with side lengths 2 and 4 would need a third side of less than 6 and greater than 2

Step-by-step explanation:

Answer:

12% or 13% rounded

Step-by-step explanation:

.25 of 2.00 is .125 or 12% or 13% rounded

Answer:

We can correctly rewrite the equation: 4(5+3) = 2(22-6) by distributing each side.

4(5+3) = 2(22-6)

4(8) = 2(16)

32 = 32

Once you finish distributing each side, you can check to see if it is equal on both sides.

Step-by-step explanation:

Step-by-step explanation:

4(5 + 3) = 2(22 - 6)

4(8) = 2(16)

32 = 32

Answer:

D

Step-by-step explanation:

Which expression has a lesser value than -10?

a. 8+ (-12)= -4

b. – 14 – 2 + 8= -16+8= -8

c. 4-(-12)= 16

d. - 2 +(- 12) + 2 = -12

Answer:

Step-by-step explanation:

a.

8 +(-12) = 8-12 = -4

-4 > -10

b.

14-2+8 = 12+8 = 20

20 > -10

c.

4-(-12) = 4+12 = 16

16 > -10

d.

-2+(-12)+2 = -2-12+2 = -14+2 = -12

-12 < -10

Answer:

0.0013 = 0.13% probability that a randomly chosen bag will weigh more than 15.6 ounces.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 15.0 ounces and a standard deviation of 0.2 ounces.

This means that \(\mu = 15, \sigma = 0.2\)

What is the probability that a randomly chosen bag will weigh more than 15.6 ounces?

This is 1 subtracted by the p-value of Z when X = 15.6. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{15.6 - 15}{0.2}\)

\(Z = 3\)

\(Z = 3\) has a p-value of 0.9987.

1 - 0.9987 = 0.0013

0.0013 = 0.13% probability that a randomly chosen bag will weigh more than 15.6 ounces.

Answer:

\(\textsf{B)} \quad f(x) = 5 \sin (16x) + 7}\)

Step-by-step explanation:

The sine function is periodic, meaning it repeats forever.

\(\boxed{f(x) = A \sin (B(x + C)) + D}\)

where:

Given values:

Calculate the value of B:

\(\dfrac{2\pi}{B}=\dfrac{\pi}{8}\implies 16\pi=B\pi\implies B=16\)

Substitute the values of A, B C and D into the standard formula:

\(f(x) = 5 \sin (16(x + 0)) + 7\)

\(f(x) = 5 \sin (16x) + 7\)

Therefore, the sine function with an amplitude of 5, a period of π/8, and a midline at y = 7 is:

\(\Large\boxed{\boxed{f(x) = 5 \sin (16x) + 7}}\)

The Surface Area of cylinders are: 100 yd² , 264 m², 226  mm²

The Surface Area of Can is 219 cm².

We know the formula for Surface Area of Cylinder

= 2πrh

1. Radius = 2 yd

Height = 8 yd

So, Surface Area of Cylinder

= 2πrh

= 2 x 3.14 x 2 x 8

= 100 yd²

2. Radius = 7 m

Height = 6 m

So, Surface Area of Cylinder

= 2πrh

= 2 x 3.14 x 6 x 7

= 264 m²

3. Radius = 3 mm

Height = 12 mm

So,  Surface Area of Cylinder

= 2πrh

= 2 x 3.14 x 3 x 12

= 226  mm²

4. Radius = 3.5 cm

Height = 10 cm

So, Surface Area of Can

= 2πrh

= 2 x 3.14 x 3.5 x 10

= 219 cm²

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Answer:

The impulse on an object is equal to the change in momentum of the object. In this case, the ball's initial momentum is 10 kg * 15 m/s = 150 kg m/s. After the collision, the ball's final momentum is -10 kg * 23 m/s = -230 kg m/s.

The change in momentum of the ball is: -230 kg m/s - 150 kg m/s = -80 kg m/s.

So, the impulse on the ball is -80 kg m/s.

The point (4,6) means it took Ziah 4 minutes to run 6 blocks.

This is because any point is of the form (x,y) where in this case

x = number of minutes

y = number of blocks

The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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Answer:

  see attached

  H31 = -0.2

Step-by-step explanation:

The matrix sum H is the element-by-element sum of corresponding elements of F and G. For example, H31 = F31 +G31 = -4.7 +4.5 = -0.2.

__

For repetitive calculations using the same formula, it is convenient to do them using a spreadsheet.

Answer: 7

Step-by-step explanation:

The percentage of students who play a sport but do not like physical education = 16%

The correct answer is an option (B)

The complete two way frequency table for given situation would be,

                                                    Play a Sport  Do not Play a Sport    Total

Like Physical Education                    150                 72                          222

Do Not Like Physical Education        28                 164                         192

Total                                                    178                 236                        414

Now we find the percentage of students who play a sport, and  do not like physical education.

The total number of students who play sport.

n = 178

And the number of students who play a sport but do not like physical education are 28.

Using percentage formula, the required percentgae would be,

P = 28/178 × 100

P = 15.73%

P ≈ 16%

Therefore, the correct answer is an option (B)

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Find the complete question below.

It should be noted that the expression that can be used to identify the x-values for which f(x)>-2 will be -2 <= x <= 2. This is illustrated in the graph.

It should be noted that a graph is a diagram that is used to show the relationship that exists between the data presented or the information.

In this case, ut should be noted that the expression that can be used to identify the x-values for which f(x)>-2 will be -2 <= x <= 2. This is illustrated in the graph.

The graph is attached below.

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The equation of the line 'q' perpendicular to the line 'p' is y = - (7/9)x - 5.

We are aware that there are many types of equations for lines, with the general type being Ax + By + c = 0,

And the slope-intercept form equation is y = mx + b, m is the slope, and b is the y-intercept.

We know, Lines perpendicular to each other have slopes that are negative reciprocals of each other.

Therefore, The line q passing through (9, - 6) has a slope of - (7/9).

Now, - 6 = - (7/9)(9) + b.

- 6 = - 1 + b.

b = -5.

Hence, y = - (7/9)x - 5 is the equation of the line q.

Q. The equation for line p can be written as y= (9/7)x - 9.

Line q is perpendicular to line p and passes through (9, - 6), what is the equation of line q?

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The coefficient values will indicate the change in the dependent variable (hrswork) for a one-unit change in the independent variable (wage, educ, and nchild).

To examine this, we would use a regression analysis to look at the relationship between each of these variables and the hours worked per week. We would create a model with wage, educ, and nchild as the independent variables, and hrswork as the dependent variable. We can then analyze the coefficient of each of these variables to measure the effect they have on the hours worked per week. The coefficient values will indicate the change in the dependent variable (hrswork) for a one-unit change in the independent variable (wage, educ, and nchild).

1. Load the work hrs.rds dataset.

2. Examine the data to identify the independent and dependent variables. In this case, the independent variables are wage, educ, and nchild, and the dependent variable is hrswork.

3. Use a regression analysis to examine the relationship between the independent and dependent variables.

4. Create a model with wage, educ, and nchild as the independent variables, and hrswork as the dependent variable.

5. Analyze the coefficient of each of the independent variables to measure the effect they have on the dependent variable (hrswork).

6. Interpret the results to determine the effect of the independent variables on the dependent variable.

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Answer:

.29

Step-by-step explanation: Subtract first by last

Answer:

0.29m longer

Step-by-step explanation:

Longest jump = 4.27m

Shortest jump = 3.98m

4.27 - 3.98 = 0.29m

Answer:

The constant is that every bag costs $3.55

Step-by-step explanation:

When the bag of peanuts costs $3.55 then Constant of proportionality is 3.55

The constant of proportionality is the ratio between two directly proportional quantities

Here,

Every bag of  peanuts costs $3.55

Consider the number of bags =  x

Cost of the peanut bag = y

Therefore

y is directly proportional to x

y = kx

Where k is the constant of proportionality

k = \(\frac{y}{x}\)

if the cost of the one bag is $3.55

Then \(k=\frac{3.55}{1}\)

k=3.55

Hence, When every bag of peanuts cost constant of proportionality is 3.55

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The lenght of AB side is 4.

To be a parallelogram, the length of parallel sides must be the same. This is a propierty of parallelograms.

In a parallelogram:

Now all we have to do is solve the equation:

Now we know the value of Q and we can replace it in AB=4Q-8

The lenght of AB is 8.

To be sure we can check what happends when we replace Q in CD=Q+4

With this, AB=CD and we know we have the correct answer

Answer:

$20

Step-by-step explanation:

Gym city fees are:

Sign up = 30

6 monthly sub = 6 x 25 = 150

Total fees = 30 + 150

FitnessExpress fees are:

Sign up = 20

6 monthly sub = 6 x 30 = 180

Total fees = 20 + 180 = 200

Therefore, the difference between the two is $20

Answer:

10x

Step-by-step explanation:

Answer:

10 x

Step-by-step explanation:

I think it's the answer

A) There are 330 possible ways to form the committee if any EE and any CE can be included.

B) There are 210 possible ways to form the committee if one particular CE must be in the committee.

C) The total number of ways to form the committee with two particular CE excluded is 205

In this case, we are given a scenario where a committee is to be formed from a group of chemical and electrical engineers. Let's dive into the details of the problem and explore how probability can be used to solve it.

(a) If any EE and any CE can be included, we need to find the number of ways to form a committee of 7 members from a group of 6 CE and 5 EE. In this case, the order in which the committee members are selected does not matter, so we can use the formula for combinations.

The total number of ways to select 7 members from a group of 11 engineers is given by:

C(11,7) = 11! / (7! * 4!) = 330

(b) If one particular CE must be in the committee, we can first select that CE and then form the rest of the committee from the remaining engineers. The probability of selecting that particular CE is 1/6, since there are 6 CE in total.

Once we have selected that particular CE, we need to select 6 more members from a group of 5 EE and 5 CE (excluding the one we have already selected). The total number of ways to do this is given by:

C(10,6) = 10! / (6! * 4!) = 210

(c) If two particular CE cannot be in the same committee, we can use the principle of inclusion-exclusion to find the total number of ways to form the committee.

First, we find the total number of ways to form the committee without any restrictions. This is given by:

C(11,7) = 330

Next, we find the number of ways to form the committee with both particular CE included. This is given by:

C(9,5) = 126

We subtract this from the total number of ways to form the committee to get the number of ways with at least one of the particular CE excluded:

330 - 126 = 204

However, we have counted the case where both particular CE are excluded twice, so we need to add this back in:

C(7,7) = 1

Therefore, the total number of ways to form the committee with two particular CE excluded is:

204 + 1 = 205

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