Which expressions are equivalent to 1/3 - 2/5

The function that has a constant additive rate of -14 is y = -14x + 2

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

Constant additive rate of change of -14

A function that has a constant rate is a linear function

And linear functions take the form

y = mx + c

Where

Rate = m

So, we have

y = -14x + c

Assuming any value for c, we have

y = -14x + 2

Hence, the function is y = -14x + 2

The table of values are not clear. so the question is solved generally

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a.) The hire purchase price would be =$3,933.6

b.) The amount of each monthly instalment would be =$218.5

C.) The difference between the price for hire purchase and cash price would be = $953.6

To hire purchase price for the video recorder would be = initial down payment + interest + cash price.

The initial down payment = 20/100×2980

= 59600/100 = $596

The interest = 15 % of outstanding balance

outstanding balance = 2980- 596 =$2,384

Therefore, 15/100 × 2,384

= 35760/100 = $357.60

Thet hire purchase price = 2980+596+357.60=$3,933.6

The amount for each month installment over the next 18 months = $3,933/18 = $218.5

The difference between hire purchase and cash price = $3,933.6- $2980 = $953.6

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The surface area of the pyramid is 186 cm².

Given that the net diagram of a square pyramid, we need to find the surface area of the same,

SA = a² + 2al

a = side length, l = height

SA = 6² + 2×6×12.5

= 186 cm²

Hence, the surface area of the pyramid is 186 cm².

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In the given triangle, the measure of side c is approximately 39 m

From the question, we are to calculate the measure of side c in the given triangle.

To determine the measure of side c, we will use SOH CAH TOA

sin (angle) = Opposite / Hypotenuse

cos (angle) = Adjacent / Hypotenuse

tan (angle) = Opposite / Adjacent

In the given diagram,

Angle = 29°

Opposite = 19 m

Hypotenuse = c

Thus

sin (29°) = 19 / c

0.4848 = 19 / c

c = 19 / 0.4848

c = 39.1914

c ≈ 39 m

Hence,

The measure of c is 39 m

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Answer:

Intercept Form.

You can directly solve for x by setting them to zero to which X= 3, X= -2

x-3 = 0  x+2 =0

x= 3  x= -2

The probability that a randomly selected adult has an IQ greater than 134.4 is 0.025 or 2.5%

To find the probability that a randomly selected adult has an IQ greater than 134.4, we need to calculate the z-score and then find the corresponding area under the standard normal distribution curve.

The z-score is calculated as: [tex]z= \frac{x-μ}{σ}[/tex]

where x is the IQ score, μ is the mean IQ score, and σ is the standard deviation of IQ scores.

Substituting the given values, we get:

[tex]z = \frac{(134.4 - 101.1)}{17}[/tex]

z = 1.96

Using a standard normal distribution table, we find that the area to the right of z = 1.96 is approximately 0.025. Therefore, the probability that a randomly selected adult has an IQ greater than 134.4 is 0.025 or 2.5%.

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Step-by-step explanation:

The y-axis intercept occurs when x = 0

put in 0 for 'x' and compute the intercept as

(0+2)(0-2)(0-A)   = 12

      -4 ( -A) = 12

       4A =12

         A = 3

The exponential regression equation for the set of data is given as follows: y = 931.61(1.1)^x.

The number of bacteria after 16 hours is given as follows:

4,281 bacteria.

An exponential function has the definition presented as follows:

y = ab^x.

In which the parameters are given as follows:

For exponential regression, we must insert the points of a data-set into an exponential regression calculator.

The points for this problem are given as follows:

(0, 940), (1, 1034), (2, 1105), (3, 1223), (4, 1352), (5, 1520).

Inserting these points into a calculator, the equation is given as follows:

y = 931.61(1.1)^x.

The number of bacteria after 16 hours is given as follows:

y = 931.61 x (1.1)^16

y = 4,281 bacteria.

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The population of interest in this study is all births in southern California between the years 1989 and 1993. The sample in this study is 143,196 births for which length of gestation data and air pollution exposure during gestation were collected.

The results of this study cannot be generalized to the entire population of births in southern California beyond the years 1989 to 1993. However, the findings of the study can still provide valuable insights into the relationship between air pollutants and preterm births in this specific population and time period. It is also important to note that this study alone cannot establish causal relationships between air pollutants and preterm births, as other factors may contribute to preterm births that were not measured or accounted for in this study. Further research and analysis would be needed to establish causal relationships.

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The tables are completed as follows:

For Table 1, we have an exponential function defined as follows:

f(x) = b^x.

We have that when x = 0.699, f(x) = 5, hence the base b is obtained as follows:

b^0.699 = 5

b = 5^(1/0.699)

b = 10.

Hence, when x = 1.477, the value of f(x) is given as follows:

f(x) = 10^1.477

f(x) = 30.

Table 2 is the inverse of table 1. For Table I, we have that when x = 1.301, f(x) = 20, hence for table 2, we have that f(x) = 1.301 when x = 20.

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Answer:

The sum of two dice can range from 2 to 12. To get a sum of 3, the only possible combinations are (1,2) and (2,1), since there is only one way to get each of those sums.

There are a total of 6 x 6 = 36 possible outcomes when two dice are rolled, since each die has 6 possible outcomes.

Therefore, the probability of rolling a sum of 3 is:

P(D1 + D2 = 3) = number of ways to get a sum of 3 / total number of possible outcomes

P(D1 + D2 = 3) = 2 / 36

Simplifying by dividing both the numerator and denominator by 2, we get:

P(D1 + D2 = 3) = 1 / 18

Therefore, the probability of rolling a sum of 3 with two standard dice is 1/18.

Step-by-step explanation:

in answer :)

Answer:

1/18

Step-by-step explanation:

got it right

The vertical component of the release velocity for the soccer ball is 6.32 m/s and the horizontal component of the release velocity is 21.64 m/s.

To resolve the release vector of the soccer ball, we can use trigonometry. The vertical component of the release velocity can be found by multiplying the initial velocity (23 m/s) by the sine of the angle of release (18 degrees):

Vertical component = 23 m/s x sin(18 degrees)
Vertical component = 6.32 m/s

Similarly, the horizontal component of the release velocity can be found by multiplying the initial velocity (23 m/s) by the cosine of the angle of release (18 degrees):

Horizontal component = 23 m/s x cos(18 degrees)
Horizontal component = 21.64 m/s

Therefore, the vertical component of the release velocity for the soccer ball is 6.32 m/s and the horizontal component of the release velocity is 21.64 m/s.

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The experimental probability that the next time Audra rolls the number cube, she will roll a 2 is 3/22.

Experimental probability is the ratio of the number of times an event occurs to the total number of trials conducted. In this case, we want to find the experimental probability of rolling a 2.

Looking at the data provided, we can see that Audra rolled a 2 three times out of the total 22 rolls. So, the experimental probability of rolling a 2 can be calculated as:

Experimental probability = number of times the event occurred / total number of trials

Experimental probability of rolling a 2 = 3 / 22

Therefore, the correct option is (B) 3/22. This means that based on Audra's experiment, the probability of rolling a 2 is approximately 0.136 or 13.6%. It is important to note that this is the experimental probability based on a small sample size, and the actual probability of rolling a 2 in a large number of rolls may differ.

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If we choose ε > 0, we can find a δ such that ||f – ft||1 < ε for all t with 0 < |t - 1| < δ, and we have shown that lim||f - ft||1 = 0 as t -> 1.

(a) To prove that lim||f – ft||1 = 0 as t -> 0, we need to show that for any ε > 0, there exists a δ > 0 such that ||f – ft||1 < ε for all t with 0 < |t| < δ.

We have:

||f – ft||1 = ∫|f(x) – f(x – t)| dx

By the continuity of f, we know that for any ε > 0, there exists a δ > 0 such that |f(x) – f(x – t)| < ε whenever |t| < δ. Therefore:

||f – ft||1 = ∫|f(x) – f(x – t)| dx < ε∫dx = ε

This holds for all t with 0 < |t| < δ, so we have shown that lim||f – ft||1 = 0 as t -> 0.

(b) To prove that lim||f - ft||1 = 0 as t -> 1, we need to show that for any ε > 0, there exists a δ > 0 such that ||f – ft||1 < ε for all t with 0 < |t - 1| < δ.

We have:

||f – ft||1 = ∫|f(x) – f(tx)| dx

Using the change of variables y = tx, we can write this as:

||f – ft||1 = (1/t)∫|f(y/t) – f(y)| dy

Since f is integrable, it is also bounded. Let M be a bound on |f|. Then we have:

||f – ft||1 ≤ (1/t)∫|f(y/t) – f(y)| dy ≤ (1/t)∫M|y/t – y| dy = M|1 – t|

This holds for all t with 0 < |t - 1| < δ, where δ = ε/2M. Therefore, if we choose ε > 0, we can find a δ such that ||f – ft||1 < ε for all t with 0 < |t - 1| < δ, and we have shown that lim||f - ft||1 = 0 as t -> 1.

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The length of the lake of 4.042 miles in yards is 7113.92 yards

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

Lake has a length of 4.042 mi.

This means that

Length = 4.042 miles

From the table of values:

To convert inches to feet, we multiply the length value by 1760

So, we have

Length = 4.042 * 1760 yards

Evaluate

Length = 7113.92 yards

Hence, the length is 7113.92 yards

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The total volume of ice cream in term of π is 42π³

The volume of an object is the amount of space occupied by the object or shape, which is in three-dimensional space.

The total volume of the ice cream = volume of cone + volume of half sphere

volume of a cone = 1/3 πr²h

= 1/3 × π × 3² × 8

= π×3 ×8

= 24π in³

volume of the half sphere = 4/6πr³

= 4/6 ×π × 3³

= 108π/6

= 18π in³

therefore the total volume of the ice cream

= 24π + 18π

= 42π in³

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Using BODMAS, where x =  x = 22 + 10-((5/25)*100), x is 12. (Option  D)

Bracket, Of, Division, Multiplication, Addition, and Subtraction are abbreviated as BODMAS.

The BODMAS is used to describe the sequence in which a mathematical equation operates. The BODMAS is also known as PEDMAS in certain places, which stands for Parentheses, Exponents, Division, Multiplication, Addition, and Subtraction.

Sure, using BODMAS, we get

x = 22 + 10 - ((5/25) x 100)

= 22 + 10 - (0.2 x 00)

= 22 + 10 -20

= 12

Thus, x is equal to 12. (Option D)

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The equation of the line in slope intercept form is: y = 3x - 5

The general form of the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

From the graph given, we see that the y-intercept which is the point where the line crosses the y-axis is at: y = -5

To get the slope, we will use two points namely:

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

Thus:

Slope = (-2 + 5)/(1 - 0)

Slope = 3

Thus, the equation is:

y = 3x - 5

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The test statistic for testing the hypotheses H0: μ=100 vs Ha: μ<100 using the given sample results x = 91.7, s= 12.5 with n = 30 is -2.17 and the p-value is 0.019. We can reject the null hypothesis H0: μ=100 in favor of the alternative hypothesis Ha: μ<100 at a 5% level of significance.

(a) The test statistic for testing the hypotheses H0: μ=100 vs Ha: μ<100 using the given sample results x = 91.7, s= 12.5 with n = 30 can be calculated as:

t = (x - μ) / (s / sqrt(n))
= (91.7 - 100) / (12.5 / sqrt(30))
= -2.17 (rounded to two decimal places)

Using a t-table with 29 degrees of freedom (n - 1 = 30 - 1 = 29) and a 5% significance level (or 0.05), the corresponding p-value for a one-tailed test is found to be 0.019 (rounded to three decimal places). Therefore, the p-value for the given test statistic is 0.019.

(b) Since the p-value (0.019) is less than the significance level (0.05), we can reject the null hypothesis H0: μ=100 in favor of the alternative hypothesis Ha: μ<100. This implies that there is sufficient evidence to conclude that the population means μ is less than 100 at a 5% level of significance. In other words, the sample provides strong evidence that the true population mean is lower than the hypothesized value of 100.

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The relation "a-b a mod 4 = b mod 4" means that for any two numbers a and b, if their difference is divisible by 4, then they belong to the same equivalence class. To find the equivalence class of -, we need to find all the numbers that have the same modulus as - when divided by 4.

We can start by listing out some numbers with the same modulus as -. For example, we have {-9, -5, -1, 3, 7, ...}, since these numbers are all congruent to -1 mod 4. Similarly, we have {0, 4, 8, 12, ...} for numbers that are congruent to 0 mod 4, and {1, 5, 9, 13, ...} for numbers that are congruent to 1 mod 4.

Therefore, the equivalence class of - is {-9, -5, -1, 3, 7, ...}, which contains all the negative numbers that are congruent to -1 mod 4.

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{u, v, w} is linearly independent, and the statement is proved.

What is linear function?

A linear function is a mathematical function of the form f(x) = mx + b, where m and b are constants.

To prove this statement, we will use a proof by contradiction.

Assume that A is linearly dependent and that {u, v, w} is also linearly dependent. This means that there exist scalars α, β, and γ, not all zero, such that αu + βv + γw = 0.

Now, we will express w in terms of u and v:

w = u + 2v - tw1

Substituting w in the above equation, we get:

αu + βv + γ(u + 2v - tw) = 0

Simplifying this equation, we get:

(α + γ)u + (β + 2γ)v - γtw = 0

Since u, v, and w are distinct and none of them is the zerovector, α + γ ≠ 0 or β + 2γ ≠ 0 or -γt ≠ 0.

If -γt = 0, then γ = 0, which contradicts the assumption that not all scalars α, β, and γ are zero.

If -γt ≠ 0, then we can express t as t = γ' / (-γ) for some non-zero scalar γ'. Substituting t in the above equation, we get:

(α + γ)u + (β + 2γ)v + γ'w = 0

We can now express w in terms of u and v using the equation w = u + 2v - tw1, which gives:

(α + γ)u + (β + 2γ)v + γ'(u + 2v - tw) = 0

Simplifying this equation, we get:

(α + γ + γ')u + (β + 2γ + 2γ')v - γ'tw1 = 0

Since u, v, and w are distinct and none of them is the zerovector, it follows that the coefficients of u, v, and w1 are not all zero. Therefore, {u1, v1, w1} is linearly independent.

This contradicts the assumption that {u, v, w} is linearly dependent. Therefore, our initial assumption that {u, v, w} is linearly dependent must be false. Hence, {u, v, w} is linearly independent, and the statement is proved.

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The correct interpretation of the given confidence interval is C. We are 98% confident that the proportion of obese clients losing weight under strategy 1 is between 13% less and 9% more than the proportion of obese clients losing weight under strategy 2.

The confidence interval is given as (-0.13, 0.09), which represents the range within which the true difference in proportions (p1 - p2) is likely to fall with a confidence level of 98%.

The negative value of -0.13 indicates that the proportion of obese clients losing weight under strategy 1 may be 13% less than the proportion under strategy 2.

The positive value of 0.09 indicates that the proportion of obese clients losing weight under strategy 1 may be 9% more than the proportion under strategy 2.

Since the confidence interval includes both positive and negative values, it suggests that the true difference in proportions could be either positive or negative.

The confidence level of 98% means that if we were to repeat the study and construct 100 different confidence intervals, about 98 of those intervals would capture the true difference in proportions (p1 - p2).

Therefore, we can conclude that we are 98% confident that the proportion of obese clients losing weight under strategy 1 is between 13% less and 9% more than the proportion of obese clients losing weight under strategy 2.

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Answer:

-3 times n+7>-17

Step-by-step explanation:

The level of allergic symptoms in both groups can be compared to see if the new medication had a significant effect.

In this experiment, the effectiveness of a new allergy medication is being tested. Sixty people with allergies were randomly assigned to two groups: the first group received the new medication, and the second group received a placebo.

By randomly assigning participants to the two groups, the researchers ensured that any observed differences between the groups could be attributed to the medication and not to some other factor.

After a certain period, the level of allergic symptoms in both groups can be compared to see if the new medication had a significant effect. This is because the comparison of symptoms between the two groups allows the researchers to determine if the medication had a significant effect compared to the placebo.

Therefore, the benefit of comparison in this experiment is to determine the effectiveness of the new allergy medication.

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The level of allergic symptoms in both groups can be compared to see if the new medication had a significant effect, accurately describes the benefit of comparison in the experiment. The correct answer is A.

The benefit of comparison in the experiment shown in the design web is that the level of allergic symptoms in both groups can be compared to see if the new medication had a significant effect.

By randomly assigning participants to either the treatment group (who receive the new allergy medication) or the control group (who receive a placebo), researchers can compare the difference in allergic symptoms between the two groups.

If the treatment group experiences a significant reduction in symptoms compared to the control group, then it suggests that the new medication is effective in reducing allergy symptoms.

Therefore, the correct answer is "the level of allergic symptoms in both groups can be compared to see if the new medication had a significant effect." The correct answer is A.

Your question is incomplete but most probably your full question was attached below

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The standardized residuals are -0.11, 0.75, -0.38, 2.08, and 2.16, respectively.

(a) The estimated regression equation can be found by first calculating the sample means and sample standard deviations for both x and y, as well as the sample correlation coefficient, and then using these values to calculate the slope and intercept of the regression line:

x = (6 + 11 + 15 + 18 + 20)/5 = 14

y = (7 + 7 + 13 + 21 + 30)/5 = 15.6

sx = sqrt(((6-14)^2 + (11-14)^2 + (15-14)^2 + (18-14)^2 + (20-14)^2)/4) = 4.49

sy = sqrt(((7-15.6)^2 + (7-15.6)^2 + (13-15.6)^2 + (21-15.6)^2 + (30-15.6)^2)/4) = 8.25

r = ((6-14)(7-15.6) + (11-14)(7-15.6) + (15-14)(13-15.6) + (18-14)(21-15.6) + (20-14)(30-15.6))/4sxsy

= 0.962

b = r(sy/sx) = 1.71

a = y - b(x) = -9.23

Therefore, the estimated regression equation is y = -9.23 + 1.71x.

(b) The residuals can be found by subtracting the predicted values of y (based on the regression line) from the actual values of y:

xi

yi

y

Residuals

6

7

0.09

-0.09

11

7

6.38

0.62

15

13

13.31

-0.31

18

21

19.29

1.71

20

30

23.57

6.43

(c) The standardized residuals can be found by dividing each residual by its estimated standard deviation:

xi

yi

ŷ

Residuals

Standardized Residuals

6

7

0.09

-0.09

-0.11

11

7

6.38

0.62

0.75

15

13

13.31

-0.31

-0.38

18

21

19.29

1.71

2.08

20

30

23.57

6.43

2.16

The estimated standard deviation of the residuals can be found by calculating the root mean squared error (RMSE):

RMSE = sqrt(((-0.09)^2 + (0.62)^2 + (-0.31)^2 + (1.71)^2 + (6.43)^2)/4) = 3.04

Therefore, the standardized residuals are -0.11, 0.75, -0.38, 2.08, and 2.16, respectively.

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Answer:

[tex] \frac{168}{120} = \frac{21}{15} = \frac{7}{5} = 1.4[/tex]

So the percent increase is 40%.

The percentage increase from 120 to 168 is 40%. This is calculated by finding the increase (48), dividing it by the original number (120), and multiplying the result by 100.

The question asks for the percentage increase from 120 to 168. To find this, we first determine the increase in the number, which is 168 - 120 = 48. The percentage increase is then calculated by dividing this increase by the original number (120 in this case), and then multiplying the result by 100 to get the percentage. So, the calculation would be (48/120) * 100 = 40. Therefore, the percentage increase from 120 to 168 is 40%.

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The probability of taking at least four trials to find the first defective light bulb is 0.073 (rounded to 3 decimal places).

To find the probability of taking at least four trials to find the first defective light bulb, we can use the geometric distribution formula:
P(X >= k) = (1-p)^(k-1) * p
Where X is the number of trials needed to find the first defective light bulb, p is the probability of finding a defective bulb on any given trial, and k is the minimum number of trials required.
In this case, we want to find the probability of taking at least four trials, so k = 4. We also know that the probability of finding a defective bulb on any given trial is 0.1 (since there is a 10% chance of any given bulb being defective). Therefore, we can plug in these values:
P(X >= 4) = (1-0.1)^(4-1) * 0.1
P(X >= 4) = 0.729 * 0.1
P(X >= 4) = 0.0729
So the probability of taking at least four trials to find the first defective light bulb is 0.073 (rounded to 3 decimal places).

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The probability that she will get a white button and a blue button is 18/30 * 3/29 = 9/145 or approximately 0.062.

The total number of buttons is 18 + 9 + 3 = 30. The probability of getting a white button on the first draw is 18/30. After drawing a white button, there are 29 buttons left, including 3 blue buttons, so the probability of getting a blue button on the second draw is 3/29.

To find the probability of both events happening, we multiply the probabilities:

18/30 * 3/29 = 9/145

Therefore, the probability that she will get a white button and a blue button is 9/145 or approximately 0.062.

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There are approximately 3.72 x 10⁴¹ ways that Anna can hand out 1 treat to each of the 36 children who come to her door.

Anna has 2 dozen Rollo bars, which is equivalent to 2 x 12 = 24 Rollo bars.

She also has 1 dozen apples, which is equivalent to 1 x 12 = 12 apples.

So, Anna has a total of 24 + 12 = 36 treats to hand out.

Now, she needs to hand out 1 treat to each of the 36 children who come to her door.

This can be thought of as selecting 1 treat from the total of 36 treats for each child, without replacement, as each child can only receive 1 treat.

The number of ways to do this is given by the concept of permutations, denoted by "nPr", which is calculated as;

nPr = n! / (n - r)!

where n is the total number of items (treats) to choose from, and r is the number of items (treats) to choose.

In this case, n = 36 (total number of treats) and r = 36 (number of children).

Plugging in the values, we get;

36P36 = 36! / (36 - 36)! = 36! / 0! = 36!

Since 0! (0 factorial) is equal to 1, we can simplify further:

36! / 1 = 36!

36! ≈ 3.72 x 10⁴¹

So, there are 3.72 x 10⁴¹ ways that Anna can hand out 1 treat to each of the 36 children who come to her door.

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