How do the values compare? Order the values from least to greatest. 1/2 , 2 , 2 1/2 , -1/2 , 1 1/2 , 2 1/2​

Answer: No

Step-by-step explanation:

to be proportional, both numbers have to increase by the same number

because if u multiply 6 by 2 you get 12, but when you multiply 10 by 2 you get 20, not 60 it would be proportional if you said 6 and 10 in to 12 and 20 in

Answer:

C and E

Step-by-step explanation:

ANP = BNP = 90 WILL PROVE THAT CD IS PERPENDICULAR TO AB.

Answer:

31.5 years.

Step-by-step explanation:

Half life is given by  \(= -\frac{ln(2)}{k}\). Where we use the natural logarithm. Plugging in a value of \(k = -0.022\) we get: 31.5 years for the half life.

The equation 2 log₅ x = log₅ 4 + log₅ 9 has two solutions: x = 6.

To solve the equation 2 log₅ x = log₅ 4 + log₅ 9, we can use logarithmic properties to simplify and find the value of x.

Using the properties of logarithms, we can rewrite the equation as follows:

2 log₅ x = log₅ (4 * 9)

Next, we simplify the right side:

2 log₅ x = log₅ (36)

Now, we can use the property of logarithms that states logₐ b = c is equivalent to aᶜ = b. Applying this property, we have:

x² = 36

Taking the square root of both sides, we get:

x =  √36

Since the square root of 36 can be either positive or negative, we have two possible solutions:

x = 6

It's important to note that when working with logarithmic equations, we must always check if the obtained solutions satisfy the domain restrictions of the original equation. In this case, since the logarithm has a base of 5, the solution x = 6.

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Answer

(2, 7) is not a solution to this system of equations.

The ordered pair doesn't fit into the second equation

Explanation

To check if the given ordered pair is a solution to this, we will insert the values into the two equations and if they fit into rach equation, then, the ordered pair is a solution for this.

y = x + 5

y = 4x + 1

(2, 7) means x = 2, y = 7

y = x + 5

7 = 2 + 5

7 = 7

y = 4x + 1

7 = 4(2) + 1

7 = 8 + 1

7 ≠ 9

The ordered pair doesn't fit into the second equation, hence, (2, 7) is not a solution to this system of equations.

Hope this Helps!!!

height of movable brigde 37cm

width of movable brigde 85 cm

Step-by-step explanation:

To calculate the correlation coefficient (r) given SSxx, SSxy, and other information, we need to use the following formula:

r = √(SSxy / SSxx)

Given SSxx = 950 and SSxy = 205.2, we can substitute these values into the formula:

r = √(205.2 / 950)

Calculating the value:

r = √(0.216)

r ≈ 0.465

The correlation coefficient (r) is approximately 0.465.

Interpretation: The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, the value of r = 0.465 indicates a positive linear relationship between the variables, but it's not a strong relationship. The closer the value of r is to 1 or -1, the stronger the relationship. Since r = 0.465 is relatively close to zero, it suggests a weak positive linear association between the variables being an analyzed.

hope it help you

The Pearson's correlation coefficient (r) based on given data is approximately 0.44, implying a moderate positive correlation.

The formula for calculating Pearson's correlation coefficient (r) in this case is given as: r = SSxy / sqrt(SSxx * SSyy). However, we don't have the value for SSyy directly, but we can calculate it. We know that SSyy = Σy² -(Σy)² / n. Given that Σy² is 2028 and Σy is 120 and number of samples n is 12, we can calculate SSyy as: SSyy = 2028 - (120)² / 12 = 52. Now, substitute SSxx = 950, SSxy = 205.2 and SSyy = 52 in the formula to find r: r = 205.2 / sqrt(950 * 52), giving us an r-value of approximately 0.44. This value of r suggests a moderate positive correlation between the variables in the dataset.

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The area of the smaller rectangle (KLMN) is 16.

Since rectangles ABCD and KLMN are similar, their corresponding sides are proportional.

Let's assume the length of side AB in rectangle ABCD is x, and the length of side KL in rectangle KLMN is y.

We can set up the proportion:

(x/y) = (20/16)

To find the area of the smaller rectangle, we need to determine the ratio of their areas.

Since the area of a rectangle is given by the product of its length and width, the ratio of the areas will be equal to the square of the ratio of their sides:

(Area of ABCD)/(Area of KLMN) = (x²)/(y²)

We are given that the area of ABCD is 25, so we have:

25/(Area of KLMN) = (x²)/(y²)

To find the area of KLMN, we need to substitute the values of x and y from the proportion:

25/(Area of KLMN) = (20/16)²

Simplifying the right side:

25/(Area of KLMN) = (5/4)²

25/(Area of KLMN) = 25/16

Cross-multiplying:

25 × 16 = 25 × (Area of KLMN)

400 = 25 × (Area of KLMN)

Dividing both sides by 25:

16 = Area of KLMN

Therefore, the area of the smaller rectangle (KLMN) is 16.

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Answer:

72 1/3

Step-by-step explanation:

Answer:

Elder brother: 25

Younger brother: 5

Step-by-step explanation:

38 - (4+4)= 30

Now trial all square numbers

e.g 2 + 4 = 6 (does not work)

5 + (5x5)= 30

The function g(x) in the form a(x-h)^2 + k is: \(g(x) = (x + 2)^2 - 4\)

Starting with\(f(x) = x^2\), the translation 2 units left and 4 units down would result in the following transformation:

g(x) = f(x + 2) - 4

Substituting\(f(x) = x^2:\)

\(g(x) = (x + 2)^2 - 4\)

Expanding the square:

\(g(x) = x^2 + 4x + 4 - 4\)

Simplifying:

\(g(x) = x^2 + 4x\)

Now we need to rewrite this expression in the form \(a(x-h)^2 + k.\) To do this, we will complete the square:

\(g(x) = x^2 + 4x\\g(x) = (x^2 + 4x + 4) - 4\\g(x) = (x + 2)^2 - 4\)

Therefore, the function g(x) in the form a(x-h)^2 + k is:

\(g(x) = (x + 2)^2 - 4\)

Where a = 1, h = -2, and k = -4.

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Answer:

simple interest=$97.50.

compound interest= $100.668

Step-by-step explanation:

Given:

Principal (P) = $750

Rate (R) = 6.5% (in decimal form, 0.065)

Time (T) = 2 years

Simple Interest = Principal*Rate*Time

Using the formula, the simple interest is calculated as follows:

Simple Interest = $750*0.065*2 = $97.50

Therefore, the simple interest for $750 with a 6.5% interest rate over 2 years is $97.50.

Again:

Compound Interest = Principal*(1 + Rate)^(Time)-Principal

Using the same values as above, the compound interest can be calculated as follows:

Compound Interest = $750*(1+0.065)^(2)-$750

= $750*1.065^2 -$750

= $750 × 1.134225 - $750

= $850.66875-$750

= $100.668

Therefore, the compound interest for $750 with a 6.5% interest rate over 2 years is $100.668

Below, you'll find a list of all the answers to the questions which are solved by using proportional relationship.

The general equation for a straight line is y=mx + c, where m represents the line's slope and expresses the rate of change of y per unit time with respect to x.

The point where the graph crosses the y-axis is called the y-intercept, or c.

Direct proportionality is also represented by y = mx. We can express m as follows: m = y/x

OR

y₁/x₁ = y₂/x₂

In our cafeteria, lemonade is made using a powdered drink mix. The quantity of water required to manufacture a certain amount of powdered drink mix is proportional to the number of scoops required. For every 2 scoops of mix, 1/2 gallon of water is required, and for every 5 scoops,

1 1/4 gallons of water are required.

The proportional formula is written as y = k x.

Using the information provided, we can now write: 2 scoops require 0.5 gallon of water.

1.25 gallon of water is required for 6 scoops.

This means that k = 2/0.5

k = 2/(1/2)

k = 2 x 2

k= 4

Equations describing the relationship can be expressed as y = 4x + c.

0.5 gallon of water is now required for 2 scoops.

2=4(1/2)+c

2=2+c

c=0

Therefore, the formula will be y = 4x.

The end includes a graph for y = 4x.

12 scoops of water:

12=4x

x=3 gallons of water is needed.

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Answer:

x = -3/2

Step-by-step explanation:

note: 1/125 can be written as 5 exponent -3 thus, 5^-3

Expressing it in this form, we can rewrite the above equation as

5^2x = 5^-3

As part of the laws of indices and logarithms, when the bases are the same and they are equating, You equate only the exponents

therefore, we have;

2x = -3

divide through by 2

x = -3/2

Answer:

\(d \approx 8.2\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra II

Step-by-step explanation:

Step 1: Define

Point F (2, 7)

Point G (4, -1)

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

Answer:

A) \(\int\frac{2x^2}{3}dx=\frac{2x^3}{9}+C\)

B) \(\int(5-x)^{23}dx=-\frac{(5-x)^{24}}{24}+C\)

Step-by-step explanation:

A)

So we have the integral:

\(\int\frac{2x^2}{3}dx\)

First, remove the constant multiple:

\(=\frac{2}{3}\int x^2\dx\)

Use the power rule, where:

\(\int x^ndx=\frac{x^{n+1}}{x+1}\)

Therefore:

\(\frac{2}{3}\int x^2\dx\\=\frac{2}{3}(\frac{x^{2+1}}{2+1})\)

Simplify:

\(=\frac{2}{3}(\frac{x^{3}}{3})\)

And multiply:

\(=\frac{2x^3}{9}\)

And, finally, plus C:

\(=\frac{2x^3}{9}+C\)

B)

We have the integral:

\(\int(5-x)^{23}dx\)

To solve, we can use u-substitute.

Let u equal 5-x. Then:

\(u=5-x\\du=-1dx\)

So:

\(\int(5-x)^{23}dx\\=\int-u^{23}du\)

Move the negative outside:

\(=-\int u^{23}du\)

Power rule:

\(=-(\frac{u^{23+1}}{23+1})\)

Add:

\(=-(\frac{u^{24}}{24})\)

Substitute back 5-x:

\(=-(\frac{(5-x)^{24}}{24})\)

Constant of integration:

\(=-\frac{(5-x)^{24}}{24}+C\)

And we're done!

The type of bias in this survey is question-wording bias because the question is influencing the response (option D).

Question-wording bias occurs when the words selected in the question influence a specific response. Here is one example:

In this question, the use of the word cruel qualifies bullfighting as negative, and therefore in most cases, people will answer that bullfighting should be forbidden.

This effect occurs in the question for this survey because the section given that an increase in drilling could result in increased tax revenue and additional jobs to the region indirectly states drilling is positive and therefore influences the response of those surveyed.

Note: This question is incomplete because some of the options are missing; here are the complete options:

What type of bias could be most likely affecting the survey results?

A. This is undercoverage bias because some segments of the population will be excluded from the sample.

B. This is response bias because those selected for the survey may not provide truthful opinions about oil drilling.

C. This is voluntary response bias because those most passionate about drilling will be more likely to register an opinion.

D. This is question-wording bias because the information given at the start of the question may lead those surveyed towards a desired response.

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Complete question :

A textile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. The company wishes to test the hypothesis H0 : μ = 12 against H1 : μ < 12 using a random sample of n = 4 specimens. Calculate the P-value if the observed statistic is xbar = 11.5. Suppose that the distribution of the sample mean is approximately normal.

Answer:

0.02275

Step-by-step explanation:

Given :

Population mean μ = 12

Standard deviation, σ = 0.5

Sample size, n = 4

Observed statistic, xbar = 11.5

H0 : μ = 12

H1 : μ < 12

The test statistic = (xbar - μ) ÷ σ/sqrt(n)

Test statistic =. (11.5 - 12) ÷ 0.5/sqrt(4)

Test statistic = - 0.5 ÷ 0.5/2

Teat statistic = - 0.5 / 0.25 = - 2

Since, it is stated that, distribution is approximately normal ; then we can use the Z distribution and obtain our Pvalue.

We could obtain P value using the Pvalue Z distribution calculator at α = 0.05, 1 - tail

Pvalue = 0.02275

Or

P(x < - 2) = 0.02275 (Z distribution table)

Answer:

the cost per or per liter,one kilogram,one pound e.t c is called pricing in mathematics

Answer:

Definition: Price is the value that is put to a product or service and is the result of a complex set of calculations, research and understanding and risk taking ability. A pricing strategy takes into account segments, ability to pay, market conditions, competitor actions, trade margins and input costs, amongst others.

Firstly we need to find the equation of the line drawn

The slope intercept form of the line equation is;

where;

m = slope

b = intercept (y axis)

From the graph, we can see that the y intercept is

No. The reported return rate appears lower than expected.

To determine whether the reported rate of return is reasonable or not, we can calculate the expected rate of return based on the investment amount and the ending value of the account.

First, we need to calculate the total number of quarters that have elapsed between the initial investment and the current quarter. Let's assume that the investment has been held for n quarters.

Then, we can use the following formula to calculate the expected rate of return:

Expected rate of return = (Ending value / Initial investment) ^ (1/n) - 1

Plugging in the given values, we get:

n = 1 (since we are only given information for a single quarter)

Initial investment = 26,245

Ending value = 26,292

Expected rate of return = (26,292 / 26,245) ^ (1/1) - 1 = 0.18%

Comparing the expected rate of return of 0.18% with the reported rate of return of -0.02%, we can see that they are quite different. However, it's important to note that a single quarter's rate of return may not be indicative of the overall performance of the investment.

Therefore, while the reported rate of return seems lower than expected, we would need to consider the performance over a longer period of time to make a more informed assessment of the investment's performance.

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Parallel lines have the same slope.

m = (y2-y1)/(x2-x1)

m = (-3-3)/(4-0)

m = -6/4 = -3/2

Substitute the values in y = mx + c,

-5 = (-3/2)(6) + c

-5 = -9 + c

c = 4

y = (-3/2)x + 4

Thus, Option D is the correct answer

Answer: $19

Step-by-step explanation:

Since we want 30 copies, let x=30.

\(C(30)=0.15(30)+14.50=19\)

Answer:

1039.23 square inches

Step-by-step explanation:

                      a = 20 inches

    \(\sf \boxed{\text{\bf Area of regular hexagon = $\dfrac{3\sqrt{3}}{2}a^2$}}\)

                                                   \(= \dfrac{3\sqrt{3}}{2}*20*20\\\\= 3\sqrt{3}*200\\\\= 1039.23 \ inches^2\)

Answer:

Step-by-step explanation:

2 3/4 ÷ 4 1/8

23/4×8/41

23×8/4×41

46/41

=1.122

So the answer is 1.122

The solution after divide 2 3/4 by 4 1/8 in fraction form is,

⇒ 2/3

We have to given that,

To divide 2 3/4 by 4 1/8.

Simplify it as,

2 3/4 ÷ 4 1/8

11/4 ÷ 33/8

11/4 x 8/33

(11 x 8) / (4x33)

2/3

Therefore, The solution after divide 2 3/4 by 4 1/8 in fraction form is,

⇒ 2/3

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The cost of gas is proportional to the volume of gas because a constant rate of $3.15 to 1 gallon of gas.

From the given table;

The volume of the first gas Layla bought = 3 gallons.

The cost of the 3 gallons = 9.45

Therefore the cost of 1 gallon = ?

That is:

3 gallons = $9.45

1 gallon = X

Make X the subject of formula:

X = 9.45/3 = $3.15

Therefore, the cost of 11 gallons of gas would be = 11×3.15 = $34.65. This is because the cost of 1 gallon would be = $3.15.

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Answer:

They made 3 8/11

Step-by-step explanation:

1) Always be polite and professional.

2) Specifically address the points that you disagree with.

3) Provide Evidence.

4) Close with a brief summary of your rebuttal.

Answer:

Although I believe ______, some may think that _______. However (evidence against their claim) shows that (explanation of evidence in 2-3 sentences)

The percentage population increase from 2001 to 2011 is 50%.

To calculate the percentage population increase from 2001 to 2011, you need the population figures for both years. Let's assume the population in 2001 was 100,000 and in 2011 it was 150,000.

The formula to calculate the percentage increase is:

Percentage Increase = ((New Value - Old Value) / Old Value) * 100

Plugging in the values:

Percentage Increase = ((150,000 - 100,000) / 100,000) * 100 = (50,000 / 100,000) * 100 = 0.5 * 100 = 50%

Therefore, the percentage population increase from 2001 to 2011 is 50%.

Please note that the actual population figures for the respective years need to be used in the calculation to obtain an accurate result. The example above is for illustrative purposes.

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