how would i solve this problem as an ordered pair ? -x + 3y = 1; x - 2y = 2 (

The variable that you would have to plot on the y axis (height) is the dependent variable while the variable that is on the x axis (arm span) is the independent or the explanatory variable.

The slope was gotten through the use of the points  (37,39) and (19,25)

This gave the slope of 7/9. This tells us that  height of the person got to be raised by 7/9 inches when arm span increases by 1 inch.

From the given model, a person that has the arm span of 66 would have the height of

12 + 7/9 * 66

= 63.3 inches

A person who is  74 inches height the arm span of = 62*9/7

= 79. 71 inches.

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For a taxable income of $1,80,900, the effective tax rate is 21.11%.

Marginal tax is the tax rate applied to an individual’s last dollar of income. It is the additional tax that must be paid on any additional income earned. In other words, it is the tax rate that applies to an individual’s income after all deductions. For example, if an individual’s income is $50,000 and the marginal tax rate is 25%, then the individual must pay an additional $12,500 in taxes on top of the $25,000 in taxes already paid on their $50,000 income.

Marginal tax rates are progressive, meaning that as an individual’s income increases, the marginal tax rate will increase as well. The marginal tax rate is important to understand because it helps individuals determine how much additional income they will need to earn in order to make up for the taxes they will have to pay on that income. It is also important to understand how marginal tax rates can affect tax planning strategies.

To determine the effective tax rate for a taxable income of $180,900, calculate the sum of the marginal tax rates for each tax bracket that the $180,900 falls into. The taxable income of $180,900 is greater than $89,075 and less than $170,050. The marginal tax rates for these two tax brackets are 22% and 24%, respectively. The sum of the marginal tax rates is 46%. Divide the sum by the taxable income of $180,900 to get the effective tax rate of 21.11%. Round the final answer to the nearest hundredth to get 21.11%.

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The forced spring-mass system is described by the differential equation d²y/dt² + 5y = 8sin(at), where a is a parameter.

To determine the value of a for which the system exhibits resonance, we need to find the frequency at which the driving force matches the natural frequency of the system. The natural frequency is given by ω₀ = √(k/m), where k is the spring constant and m is the mass.

In this case, the natural frequency is √(5), since the coefficient of y in the differential equation is 5. Resonance occurs when the frequency of the driving force matches the natural frequency, so we set ω₀ = a and solve for a. Hence, a = √(5).

For the value of a found in part (a), which is a = √(5), the general solution of the forced spring-mass system can be obtained by using the method of undetermined coefficients. The complementary solution is y_c(t) = c₁cos(√(5)t) + c₂sin(√(5)t), where c₁ and c₂ are arbitrary constants.

To find the particular solution, we assume y_p(t) = Asin(√(5)t) + Bcos(√(5)t), where A and B are coefficients to be determined. Substituting this into the differential equation and solving for A and B, we can find the general solution for the given value of a.

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There is sufficient evidence to conclude that the population standard deviation is different from 0.1.

What is test statistic?

A test statistic is a figure obtained from a statistical analysis. It explains how far your observed data is from the null hypothesis, which states that there is no correlation between the variables or distinction between the sample groups.

Given,

            \(H_0:\sigma =0.1\\H_a:\sigma \neq 0.1\)

Test statistic:

Chi square=(20-1)*0.25^2/0.1^2=118.75

df=20-1=19

p-value=CHIDIST(118.75,19)=0.0000

Reject the null hypothesis.

Hence, there is sufficient evidence to conclude that the population standard deviation is different from 0.1.

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Answer: RM 5200

Step-by-step explanation:

Principal = RM5000

Rate = 4%

Time = 1 year

Simple Interest = PRT

= 5000 × 4% × 1

= 5000 × 0.04 × 1

= 200

Now, the total savings will be the addition of the principal and the interest which will be:

= RM 5000 + RM 200

= RM 5200

Answer:

same here hyarhaha what to do

The variance of a sample is 4,096. And for interquartile, the difference between the largest and smallest values. The correct answer is option D

To calculate the variance we have a small formula:

v=s^2-----(1)

v=variance

s=Standard deviation

so, given that s=64

substitute in equation(1)

v=64*64

v=4096.

variance: The variance is a measure of variability. It is calculated by taking the average of squared deviations from the mean.

Variance is denoted by a symbol: σ2.

Interquartile range (IQR) is a measure of statistical dispersion, which is used to spread the data. The IQR is also called midspread.

To calculate the IQR, the data set is divided into quartiles. These quartiles are denoted by Q1 (another name is the lower quartile), Q2 (the median), and Q3 (also called the upper quartile). The lower quartile corresponds with the 25th percentile and the upper quartile corresponds with the 75th percentile, so IQR = Q3 −  Q1

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Answer:

Step-by-step explanation:

\(6z - 16 = 2z \\ - 16 = - 6z + 2z \\ - 16 = 4z \\ - \frac{16}{4} = - 4 = z\)

Answer:

48 different ways

Step-by-step explanation:

To solve this question, we use the Fundamental Counting Principle technique.

Fundamental Counting Principle can be defined as the way by which we determine the possibility or the number of possible outcomes for an event.

If we have event X and event Y and event Z, then the number of possible outcomes = X × Y × Z

For the above question, we have 3 events

Event 1 : 4 students ( Stephanie, Charles, Tim, and Rachel)

Event 2: 3 subjects ( Math, Reading, And Science)

Event 3 : 4 tutors.

Therefore,the many different ways can the students, tutors, and subjects can be be uniquely combined is:

= 4 × 3 × 4

= 48 different ways

Answer:

Geometric mean = 15

Step-by-step explanation:

Geometric mean is square root of both numbers product.

9×25=225

√225=15

Answer:

221

Step-by-step explanation:

5 is the first term, then:

5 + 16 = 21

22 is the last term

5 + 21 = 26

6 + 20 = 26

7 + 19 = 26

.....

.....

12 + 14 = 26

and

13

There are 8 sum of 26 each and 13

Then:

8*26 + 13 = 221

Answer:

Step-by-step explanation: T20 = (-1)^20 3520(c)^15(d)^20

= 35c20c^15 d^20

Answer: 1 meter squared

Step-by-step explanation: 1 meter by one meter is one meter squared

Answer:

\( \sf \: \frac{75}{12} \: (or) \: 6.25\)

Step-by-step explanation:

Given problem,

\( \sf \rightarrow \: 15 \times \frac{5}{12} \)

Let's solve the problem,

\( \sf \rightarrow \: 15 \times \frac{5}{12} \)

\( \sf \rightarrow \: \frac{(15 \times 5)}{12} \)

\( \sf \rightarrow \: \frac{75}{12} = 6.25\)

Hence, the product is 6.25.

Answer:

8

Step-by-step explanation:

They only won 25%

25%=1/4

32/4=8

They won 8 games

Answer:

They won 8 out of 32 games... i think, ill edit it if there is a problem

Step-by-step explanation:

32 x 25% = 8

or

32 x 0.25 = 8

Either one works.

Answer:

yes you are correct :)

Step-by-step explanation:

The group you wish to generalize your results to is called the population (option b).

In statistical terms, the population refers to the entire set of individuals, items, or elements that possess certain characteristics of interest and from which a sample is drawn.

When conducting research or experiments, it is often not feasible or practical to collect data from the entire population due to factors such as time, cost, and accessibility.

Instead, a smaller subset known as a sample is selected to represent the larger population.

The purpose of sampling is to obtain information about the population by studying a more manageable and representative subset.

The goal is to make inferences and draw conclusions about the population based on the characteristics observed in the sample.

Generalizing the results from a sample to the population involves assuming that the sample is representative and accurately reflects the larger population.

Statistical techniques and methods are used to estimate population parameters, such as means, proportions, or relationships between variables, based on the data collected from the sample.

It is important to recognize that the accuracy of generalizations depends on the quality of the sample and the sampling methods employed. Additionally, sampling error (option c) refers to the variability or discrepancy between sample statistics and population parameters, which is inherent in the process of sampling.

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Answer:

x=-2

y=5

Step-by-step explanation:

x+2y=8   equation-1  

-x+3y=17 equation-2

5y=25

Both side divided 5,

y=5

Equation-1, y=5

x+2(5)=8

x+10=8

Both side -10

x+10-10=8-10

x=-2

Equation-2, y=5

-x+3(5)=17

-x+15=17

Both side -15

-x+15-15=17-15

-x=2

x=-2

The p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis that the news is read equally for both age groups.

To test whether the proportion of individuals who read newspapers to find out the news is the same for both age groups, we can use a hypothesis test for two proportions. Let p1 be the true proportion of individuals who read newspapers in the age group 36-50, and let p2 be the true proportion of individuals who read newspapers in the age group over 50.

The null hypothesis is that the proportions are equal, i.e., H0: p1 = p2. The alternative hypothesis is that the proportions are not equal, i.e., Ha: p1 ≠ p2.

We can use a significance level of 5%, which means that we will reject the null hypothesis if the p-value is less than 0.05.

To conduct the test, we can calculate the sample proportions of individuals who read newspapers in each age group:

p-hat1 = 25/50 = 0.5

p-hat2 = 30/50 = 0.6

We can also calculate the pooled proportion, which is the weighted average of the two sample proportions:

p-hatp = (25 + 30) / (50 + 50) = 0.55

Using the sample proportions and the pooled proportion, we can calculate the test statistic:

z = (p-hat1 - p-hat2) / √(p-hatp × (1 - p-hatp) × (1/50 + 1/50))

= (0.5 - 0.6) / √(0.55 × 0.45 × (1/50 + 1/50))

= -1.52

The p-value for this test is the probability of getting a test statistic as extreme or more extreme than the observed value of -1.52, assuming the null hypothesis is true. Since this is a two-tailed test, we need to calculate the probability of getting a z-score less than -1.52 or greater than 1.52.

Using a standard normal table or a calculator with a normal distribution function, we can find the p-value:

p-value = P(Z ≤ -1.52) + P(Z ≥ 1.52) ≈ 0.129

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Answer:

 distance divided by rate = time aka D/R=T

Step-by-step explanation:

this is what i learned at least hope it helps

The equation that represents the distance traveled by the car is equal to d = 50 x t.

To calculate the speed of an object, it is necessary to relate the distance traveled and the time required to travel that distance, so that:

                                                \(V = \frac{d}t}\)

Thus, as we are given the value of a velocity and if we are asked for the expression that represents the distance traveled depending on the time, we have:

                                        \(50 miles/hour = \frac{d}{t}\)

                                             \(d = 50 \times t\)

So, the equation that represents the distance traveled by the car is equal to d = 50 x t.

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The scalar field f such that g = ∇f for g(x) = ||x||x is f = ||x||. The gradient of f, denoted as ∇f, is a vector field that represents the rate of change of f at each point.

To find f, we need to integrate g with respect to x along a path from a reference point to the desired point. The path can be represented as a curve C.

The line integral of g along C is given by ∫g · dr, where dr is the differential displacement vector along C. Since g(x) = ||x||x, we can substitute g into the line integral equation.
∫g · dr = ∫(||x||x) · dr

In this case, we can choose the path C as a straight line from the origin to the point x. This makes the line integral path-independent.

Now, let's calculate the line integral:
∫(||x||x) · dr = ∫(||x||x1 + ||x||x2 + ||x||x3) · (dx1 + dx2 + dx3)

Using the properties of dot product and linearity, we can simplify the expression:
∫(||x||x) · dr = ∫(||x||dx1)x1 + ∫(||x||dx2)x2 + ∫(||x||dx3)x3

Since ||x|| is a constant along the path C, we can take it out of the integral:

∫(||x||dx1)x1 + ∫(||x||dx2)x2 + ∫(||x||dx3)x3 = ||x|| ∫dx1 x1 + ||x|| ∫dx2 x2 + ||x|| ∫dx3 x3

Integrating dx1, dx2, and dx3 gives:
||x||x1 + ||x||x2 + ||x||x3 = g(x)

Comparing this result with g(x) = ||x||x, we see that f = ||x|| satisfies g = ∇f.

Therefore, the scalar field f such that g = ∇f for g(x) = ||x||x is f = ||x||.

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Given the right triangle:

Where a is the short side. Then, using the definition of the sine function:

But we know that:

Finally:

An arithmetic sequence is a list of numbers with a definite pattern.

If we take any number and subtract the previous number, the result is the same constant.(common difference)

-4, -40, -400, -4000,

-40-(4)= -40+4 = -36

-400-(-40)= -400+40 = -360

Not arithmetic

-11,-8,-5,-2

-8-(-11) = -8+11 = 3

-5-(-8)= -5+8 = 3

-2-(-5)=-2+5 = 3

Arithmetic

Common difference: d= 3

23, 17, 11, 5,

17-23 = -6

11-17= -6

5-11 = -6

Arithmetic

Common difference: d =-6

The estimated value of τ is 36 ± 2.7 MPa, with an uncertainty of 7.5%.

The equation given for maximum shear stress τ in terms of crack width w and constant k is:

τ = τ₀(1 − kw)

Plugging in the given values for τ₀, w, and k, we get:

τ = 50 MPa(1 − 0.28 mm−1 × 1.0 mm) = 36 MPa

So the estimated value of τ is 36 MPa.

To find the uncertainty in the estimate, we use the formula for error propagation:

δτ = √((∂τ/∂τ₀)² δτ₀² + (∂τ/∂w)² δw² + (∂τ/∂k)² δk²)

where δτ₀, δw, and δk are the uncertainties in τ₀, w, and k, respectively.

Taking the partial derivatives of τ with respect to τ₀, w, and k, we get:

∂τ/∂τ₀ = 1 − kw

∂τ/∂w = −kτ₀

∂τ/∂k = −τ₀w

Plugging in the values for τ₀, w, and k, we get:

∂τ/∂τ₀ = 1 − 0.28 mm−1 × 1.0 mm = 0.72

∂τ/∂w = −0.28 mm−1 × 50 MPa = −14 MPa/mm

∂τ/∂k = −50 MPa × 1.0 mm = −50 MPa·mm

Assuming an uncertainty of δk = 0.04 mm−1 for k and negligible uncertainties for τ₀ and w, we get:

δτ = √((0.72)² × 0² + (−14 MPa/mm)² × (0.1 mm)² + (−50 MPa·mm)² × (0.04 mm−1)²)

δτ = 2.7 MPa

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Answer:

11. 10

12. -9v + 7

13. 1-10b

14. 5n+10

15. 12v

16. 0

17. 0

18. -4n+10

19. 9b - 9

20. 5v-8

Hope it help.

Answer: 13: 1-10b

14: 5n +10

15: 12v

16: nothing

17 0

18: 10 -4n

19: 11 + 5b

20: 5x + -8

Step-by-step explanation:

13: 6b + 4b = 10b

1-0=1

1-10b

14: n+4n = 5n

5n+10

15: 10v + 2v = 12v

16: 6v - 6v = 0

17: -2 +2 =0

18: 9 + 1 = 10

5n + n = 4n

10 - 4n

19: 10 + 1 = 11

7b-2b = 5b

11 + 5b

20: 1 -9 = -8

5x + -8

Population density of the wolves is 0.156 wolves per square mile.

The term "population density" refers to the measurement of population per unit land area.

To get population density of wolves in Yellowstone park, we divide the estimated number of wolves by the park's area which give us:

= 540 / 3,471

= 0.15557476231

= 0.1557 wolves per square mile.

By rounding to the thousandth, the population density of wolves in Yellowstone park is 0.156 wolves per square mile.

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Answer:

90 hours - 26 hours = kyoko has 64 hours left to complete her goal of reaching 90 hours.

Answer:

Below

Step-by-step explanation:

Vertex is at  (h,k) = (-3,3)

Vertex form of the parabola is then

  y = a ( x - -3)^2 + 3        <======need to find 'a'

the 'P' value is   the distance form the vertex to the focus   (which is the same as the distance from the vertex to the directrix )

 for this parabola    P = 1    

       you should know that   P = 1/(4a)   so   1 = 1 / (4a)  shows a = 1/4

then your parabola becomes   y = 1/4 (x+3)^2 + 3    BUT 'a'  needs to be modified to a negative because it is a upside down (dome-shaped) parabola so

                      y = -1/4 (x+3)^2 + 3  

or          y = -1/4 x^2  - 6/4x + 3/4