EQUATIONS AND INEC
Worked examples
a) Solve these simultaneous equation by eliminating by subtraction.
5a + 2b = 16 equation 1
3a + 2b = 12 equation 2​

Answer:

n-4=-15

Step-by-step explanation:

Answer:

29%

Step-by-step explanation:

\(\frac{145}{500} = \frac{x}{100} \\\\\)

500/5 = 100

145/5 = 29

Answer: Extrapolation ,from the above can be defined as using a linear regression equation and any x- value to predict any y-value.

Step-by-step explanation:

Extrapolation regression makes use of estimated regression equation to predict a new value y for specific X values not in the range of the sampled data used to estimate our regression equation

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Answer:

7A: 84

7B: 15

7C i: HCF = 3

7C ii: LCM = 420

Step-by-step explanation:

See attached

There can be 90% confident that the population mean salary of college graduates who took a statistics course is between $60,947.78 and $66,652.22.

To construct a 90% confidence interval for estimating the population means μ of salaries for college graduates who took a statistics course, we can use the formula:

Confidence interval = sample mean ± (critical value) x (standard error)

First, we need to find the critical value from the t-distribution table with a degree of freedom of n-1. Since we have 49 college graduates, our degrees of freedom are 48. Looking at the table, the critical value for a 90% confidence level is 1.677.

Next, we need to find the standard error, which is calculated by dividing the standard deviation by the square root of the sample size. In this case, the standard error is $11,936/sqrt(49) = $1703.05.

Substituting these values into the formula, we get:

Confidence interval = $63,800 ± 1.677 x $1703.05
Confidence interval = $63,800 ± $2852.22

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Answer:

12.5%

Step-by-step explanation:

1/8 is .125

as a percent, you would multiply .125 by 100 to get the percentage

.125(100) = 12.5

12.5%

Answer:

12.5%

Step-by-step explanation:

The information given in the question is not enough to determine the number of individuals who participated in the study. The t(12) value reported by the researcher indicates that the study had 12 degrees of freedom, which means that there were 12 participants in the study. However, the p-value provided in the question, p > .05, does not give us enough information to determine whether the results of the study are statistically significant or not.

To determine the significance of the study, we would need to know the significance level that was used to test the null hypothesis. If the significance level was .05 or less, then the results would be considered statistically significant, and we would reject the null hypothesis. If the significance level was greater than .05, then the results would not be statistically significant, and we would fail to reject the null hypothesis. Without this information, we cannot determine the significance of the study or the number of individuals who participated in it.

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Answer:

1. Diego has to move 2 places back to be 25th .

2.a. Jade is right. She'll get 2 prizes .

2.b.The blueberry muffin and the carrot cake

Step-by-step explanation:

[Every fifth customer will get a free bagel.]`-------

This means that anyone on the line who is a multiple of 5 will get a free bagel. Example-  5th customer,10th customer, or the 15th customer and so on..

[Every ninth customer will get a free blueberry muffin]--------

This means that anyone on line who is a multiple of 9 will get a free blueberry muffin. Example- the 9th customer, 18th customer etc...

[Every 12th customer will get a free slice of carrot cake. ]----------

This means that anyone on line who is a multiple of 12 will get a free carrot cake. Example- the 12th customer, 24th customer, 36th customer etc...

THEREFORE, (ANSWERS TO THE QUESTION)

1. Yes, he is right  in order to get the prize. To get at least one prize, he should go two places behind and become the 25th customer {since he s a multiple of 5}.He will get a free bagel.

2.a. Yes, Jade will get a prize. She can get a free blueberry muffin and a free slice of carrot cake .

2.b. Yes, it is possible for Jade to win more than one prize because she is the 36th customer and 36 is a multiple of both 9 and 12

\(\\\)

Answer:

The direction of relationship changes at least once.

Step-by-step explanation:

Curvilinear relationship is a relationship between two variables where if one variable increases the other variable also increases but up to certain point after which one variable increases and other decreases. This type of relationship is referred as non monotonic function.

Answer:

Probability helps us to know the chances of an event occurring. The probability that the first card is an even number and the card is greater than 7 is 0.15.

Step-by-step explanation:

Probability helps us to know the chances of an event occurring.

The probability that a first card is an even number and the card is greater than 7 is

Probability = (5/10)×(3/10) = 15/100 = 0.15

Hence, the probability that the first card is an even number and the card is greater than 7 is 0.15.

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To find 2A, where A is the matrix [3 -1 2 0], we multiply each element of A by 2. Thus, 2A is [6 -2 4 0].

To calculate 2A, we multiply each element of the matrix A by 2.

Given that A is [3 -1 2 0], multiplying each element by 2 yields:

2A = [23 2(-1) 22 20] = [6 -2 4 0].Therefore, 2A is [6 -2 4 0]. Each element in A has been multiplied by 2 to obtain the corresponding element in 2A.

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According to the question we have (5, 2) isn't a response of the linear equation system because one of equations is erroneous.

Salt water, rub whiskey, and sucrose dissolved in water are a few examples of solutions. When you watch hard after combining salt and water, you can no longer see the sodium chloride, indicating that the combination is uniform.

In chemistry, a solution containing of two or more compounds in their relative proportions. The composition of the solution can be continually changed up to the solubility limit. Although solution of gas and solids are possible, the term "solution" is most frequently used to refer to the liquid condition of matter.

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Answer:

50%.

Step-by-step explanation:

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To predict the cost of driving 1800 miles per month, substitute 1800 in the given function C(d) = 0.2d + 280C(1800) = 0.2 (1800) + 280= $640 per month. Therefore, the cost of driving 1800 miles per month is $640.

(b) Graph is shown below:(c)The slope of the graph represents the rate of change of the cost of driving a car per mile. The slope is given by 0.2, which means that for every mile Lynn drives, the cost increases by $0.2.The y-intercept of the graph represents the fixed cost (amount she pays even if she does not drive).

The y-intercept is given by 280, which means that even if Lynn does not drive the car, she has to pay $280 per month.The linear function gives a suitable model in this situation because the monthly cost increases as the number of miles driven increases.

This is shown by the positive slope of the graph. The fixed cost is also included in the function, which is represented by the y-intercept. Therefore, a linear function is a suitable model in this situation.

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With a p-value of 0.000, the test statistic is 2.834.

A statistical test's calculation of a number is known as a test statistic. It explains the distance between your observed data and the null hypothesis, which states that there is no correlation between the variables or difference between the sample groups,

given

                sample size            sample mean            sample sd

 City 1           12                                 66000                   1100

 City 2          12                                 68000                  2200

mean is 71121 point ,41 standard deviation is sample size, the test hypothesis greater than 69110 point.

find dust statistics which are there , equation t, which equals x, bar minus mu, and sigma by rho type, is used to determine the test statistic.

The square root of 41 points equals minus 69110. Is it accurate that our test numbers come out to 1.719? Next, we need to determine the p value. P value is derived from x. Since our alpha in this instance is.05, our significance is more relevant than the p value.

Accordingly, there is little to no pay disparity between registered nurses in the two locations.

With a p-value of 0.000, the test statistic is 2.834.

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Given: A man is standing at a distance of 15 m from a tree whose height is 22m.Now he sees a bird on th tree. The eye is 1.5 m above ground level, we have the find the angle of this elevation.

Let us draw the figure,

Now, we have to find the angle of elevation that is angle BCA.

Using trigonometric ratios ,we can easily find this angle,

Here, we have taken the perpendicular as 22-1.5=20.5m

So,

This is the required angle of elevation,that is, 53.8 degrees.

It is true that the population mean can be used to refer to the expected value of a random variable X.

The anticipated value of a random variable in probability theory is the long-run average of all iterations of the experiment.

The expected value in rolling a six-sided die is 3.5, since the average of all the numbers that come up will approach 3.5 as the number of rolls approaches infinity. An expected value is a key aspect of many decision-making situations, including gambling, insurance, and stock evaluation. The expected value can also be referred to as the population mean.

The statement "The expected value of a random variable X can be referred to as the population mean" is therefore accurate.

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Answer:

The answer is 1

The rate of return on this investment is -0.2191.

To calculate the approximate real rate of return on your investment, we need to account for inflation and adjust the nominal rate of return.

Nominal Rate of Return = (Sale Price + Dividends - Purchase Price) / Purchase Price

Inflation Rate = 2.5% (as stated in the question)

Adjusted Nominal Rate of Return = (1 + Nominal Rate of Return) / (1 + Inflation Rate) - 1

Now let's calculate the values:

Nominal Rate of Return = ($56.90 + $2.00 - $78.00) / $78.00 = -$19.10 / $78.00 ≈ -0.2451

Adjusted Nominal Rate of Return = (1 - 0.2451) / (1 + 0.025) - 1 ≈ -0.2191

The approximate real rate of return on this investment is approximately -0.2191, indicating a negative return. This means that the investment has experienced a loss after accounting for inflation.

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Answer:

y+3=2x+4

Step-by-step explanation:

The three possibilities for a linear system, in terms of free variables, rank and nullity, are

Three possibilities for a linear system.

No solution    Signal equation 0 = 1

Infinitely many solutions One or more free variables nullity ≥ 1

Unique solution Zero free variables nullity = 0

No Solution. There is no solution to a system of equations exactly when a signal

equation 0 = 1 occurs during the application of swap, multiply and combination

rules. We report the system inconsistent and announce no solution. Infinitely Many Solutions. The situation of infinitely many solutions occurs when

there is at least one free variable to which an invented symbol, say t1, is assigned.

Since this symbol takes the values −∞ < t1 < ∞, there are an infinity of solutions.

The condition rank less than n can replace a reference to the number of free variables.

Unique Solution. There is a unique solution to a system of equations exactly when

zero free variables are present. This is identical to requiring that the number n of

variables equal the number of lead variables, or rank = n.

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The 95% confidence interval for the standard deviation of the height of students at UH is given by; CI = (1.81, 4.03)

How to find the confidence interval for standard deviation?

The formula for the confidence interval for the standard deviation is given by the formula;

CI = √[(n - 1)s²/(χ²ₙ ₋ ₁, α/2)], √[(n - 1)s²/(χ²ₙ ₋ ₁, (1 - α)/2)]

We are given;

Sample size; n = 19

D F = n - 1 = 19 - 1 = 18

Standard Deviation; s = 3.2

Confidence Level; CL = 95% = 0.95

Significance level; α = 1 - 0.95 = 0.05

Thus, using Chi-square distribution table online we have;

χ²₁₃, ₀.₀₂₅  = 24.736

(χ²₁₃, ₀.₉₇₅) = 5.01

Now, the 95% confidence interval for the standard deviation of the height of students at UH is given by :-

CI = √[(18 * 3.2²/(24.736)], √[(18 * 3.2²/(5.01)]

CI = (1.81, 4.03)

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Answer: An 18-month loan with a 4.75% annual simple interest rate.

Step-by-step explanation: “I am so proud of you”

The original price of the bracelet, before tax $0.68

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

Amount = $0.72

Sales tax = 6%

Using the above as a guide, we have the following:

Amount = Original amount * (1 + Sales tax)

Substitute the known values in the above equation, so, we have the following representation

0.72 = Original amount * (1.06)

So, we have

Original amount = 0.68

Hence, the original amount = 0.68

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PSA stands for Prostate-specific antigen. A normal PSA level is considered to be 4.0 ng/mL. In this case study, the PSA level is 7.2 ng/mL which means it is elevated or high.

What bones are close to the prostate?

In males, the prostate gland is located in front of the rectum and under the bladder. The prostate gland is situated in a way that allows it to be in contact with different bones including the pubic bone, coccyx, and the bones in the pelvic area.

Risk factors associated with getting prostate cancer are:

Age (older than 50 years)

Race (African American)

Family history

Genetic predisposition

Lifestyle

Factors that may lead to prostate cancer are lack of exercise, poor diet, and smoking.

If a patient has frequent prostatitis, they may not have a higher risk of getting prostate cancer. However, prostatitis can make the PSA level rise, causing a need for further testing and diagnosis.

Treatment plan:

Chemo/XRT or cancer itself may cause a patient to become anemic. However, it depends on the patient's current health condition. If a patient's anemia is related to their cancer treatment, their doctor may adjust their treatment plan accordingly.

Anemia can be caused by chemotherapy because it can damage the bone marrow, where new blood cells are made.

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A confusion interval of 99 percent between  -0.020 and 0.120 for the difference in the true percentage of the population that say "Yes".

What does confidence interval mean?

If you repeat your experiment or resample the population in the same manner, the confidence interval is the range of values you expect your estimate to fall within a specific proportion of the time.

In point a:

The confidence interval will not provide convincing proof that only the two population prolongations differentiate because a 99 percent confidence interval for both the difference throughout the true promotion around -0.020 and 0.120 is included 0.

In point b:

This confidence interval gives strong evidence also that two population proportions were identical because there is a confusion interval of 99 percent between  -0.020 and 0.120 for the difference in the true percentage of the population that say "Yes".

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The complete question is -

A CBS News poll asked 606 randomly selected women and 442 randomly selected men, "Do you think putting a special tax on junk food would encourage more people to lose weight?" 170 of the women and 102 of the men said "Yes." A 99% confidence interval for the difference (Women – Men) in the true proportion of people in each population who would say "Yes" is –0.020 to 0.120.

a. Does the confidence interval provide convincing evidence that the two population proportions are different? Explain your answer.

b. Does the confidence interval provide convincing evidence that the two population proportions are equal? Explain your answer.

Answer:

8.06

Step-by-step explanation:

find the slope by

\(d=\sqrt{(5-1)^{2} + (3 - (-4))^{2} } \\\\ d= \sqrt{65} \\d= 8.062258\)

22 ml of rboh is titrated with 35 ml of 0.9 m hf. The concentration of the base is 1.43M.

Titration is a method of chemical analysis in which the amount of a sample's ingredient is determined by adding an exact known amount of a different substance to the measured sample in which the desired constituent interacts in a specific, known proportion. Titrating reagent, or titrant, is often added to a standard solution (i.e., a solution of known concentration) using a burette, which is essentially a long, graduated measurement tube with a stopcock and a delivery tube at its bottom end. When the equivalence point is achieved, the addition is terminated.

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Answer:

1  4(3-r)  or  12-4r

2.  7( 8-m) or 56-7m

3.   -2

Step-by-step explanation:

1) |4r−12| , if r<3

|4r-12|

Factor out a 4

4|r-3|

|r-3| will be less than 0 since r is less than 3

So we can rewrite it as 3-r to remove the absolute value signs and make it positive

4 (3-r)

12 -4r

2.   |7m–56| , if m<8

Factor out a 7

7| m-8|  

|m-8| will be less than 0 since m is less than 8

So we can rewrite it as  8-m to remove the absolute value signs and make it positive

7( 8-m)

56-8m

3) |z−7|−|z−9| , if z<7

|z-7| will be less than 0 since z is less than 7  and |z-9| will be less than 0 since z is less than 7

So we can rewrite it as  7-z  and 9-z to remove the absolute value signs and make it positive

7-z - (9-z)

Distribute the minus sign

7-z-9+z

-2