ABCD is a rectangle AD = 3x-12 AB=x+4
Perimeter of rectangle is 38 cm work out length AD

When two objects are massive and close to each other, the gravitational force between them is strong.

Gravity is a fundamental force of nature that exists between any two objects in the universe. The strength of the gravitational force depends on two factors: the masses of the two objects and the distance between them.

The larger the masses of the two objects, the greater the gravitational force between them. Likewise, the closer the objects are to each other, the stronger the gravitational force.

This relationship is described by Newton's Law of Gravitation, which states that the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

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The statement is False. At a significance level of alpha equal to .05, if your model has a p-value close to 0 for the overall f test, but none of the individual variables in the model have a p-value <0.05, then you do not have an issue with multi-collinearity. Therefore the given statement is false.

A p-value is a measure of the strength of evidence against the null hypothesis. The smaller the p-value, the stronger the evidence against the null hypothesis.

When the p-value is less than or equal to the significance level alpha, then we reject the null hypothesis. In general, when the overall F-test has a low p-value and none of the individual variables in the model have a p-value less than 0.05, it is an indication of multi-collinearity.

Multi-collinearity is a situation in which two or more independent variables in a multiple regression model are highly correlated with each other. It can lead to unstable estimates of the regression coefficients and make it difficult to interpret the results of the model.

In conclusion, at a significance level of alpha equal to .05, if your model has a p-value close to 0 for the overall f test, but none of the individual variables in the model have a p-value <0.05, then you do not have an issue with multi-collinearity. The statement is false.

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The average rate of increase is $69 per year (to the nearest dollar).

What is average rate of increase?

The  function is defined as the average rate at which one measurement is changing(here increasing) with respect to another change. So an average rate of change function is a system that calculates the amount of change in one data divided by the corresponding amount of change in another.

The fees in 1997( x₁ say) was $3042( y₁ say)

fees in 2000(x₂ say) was $3250 ( y₂ say)

The formula is for change in average rate is  [tex]\frac{ y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

average rate of increase= (3250-3042)/(2000-1997)

                                        = 208/3

                                         =69.33

so average rate of increase to the nearest dollar  is $69 per year.

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Answer:

6

Step-by-step explanation:

imagine that EF continues through F and ends on AB. this point, that is on segment AB, is what i will call G.

AFG is similar to CFE.

the length of segment GF is 18-4=14.

now we know 2 side lengths of triangle GAF: FA is 21 and FG is 14.

FE is similar to GF with a factor of 4/14 = 2/7.

FE is similar to FC with this same ratio: (2/7) * 21 = 6

therefore, the length of FC is 6.

When you take a strip of paper, put two half twists in it, and glue the ends together and then cut it lengthwise along the center core line, it results in two interlocked loops.What you get is two interlocked loops when you cut it lengthwise along the center core line. This occurs because the paper strip has been twisted twice. The twist that was made in the paper strip produces two loops that are intertwined after it is cut down the center line.Paper is quite a flexible substance. When it's twisted, it retains its new shape. Because of this, when you twist a strip of paper, it retains its new form. When the strip is bent and connected to form a loop, the twisted part becomes embedded in the paper's core. This produces two loops that are interconnected. When the loop is sliced down the middle, the two loops remain interconnected since the twists in the strip have become embedded in the core.

The interquartile range (IQR) of the given data set is 16.

To find the interquartile range (IQR), we first need to calculate the first and third quartiles of the data set:

Arrange the data set in order from smallest to largest:

22, 26, 28, 30, 32, 35, 35, 42, 45, 49, 50

Find the median (middle value) of the lower half of the data set (the first quartile, Q1):

22, 26, 28, 30, 32, 35

The median of this set is 29, which is halfway between 28 and 30.

Find the median (middle value) of the upper half of the data set (the third quartile, Q3):

35, 42, 45, 49, 50

The median of this set is 45.

Calculate the IQR by subtracting Q1 from Q3:

IQR = Q3 - Q1

   = 45 - 29

   = 16

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A grouped frequency table (grouped frequency conveyance) is an approach to coordinating an enormous arrangement of information into additional reasonable gatherings.

The grouped frequency table

________________________________________________________

 Width (in mm) C.F. Class Interval Frequency ________________________________________________________

 ≥ 20 50 20 - 30 50 - 44

= 6 ≥ 30 44 30 - 40 44 - 28

= 16

 ≥ 40 28 40 - 50 28 - 20

= 8

 ≥ 50 20 50 - 60 20 - 15

= 5

 ≥ 60 15 60 - 70 15 - 0

= 15

_____________________________________________________

                                                                                          ∑f = 50

The gatherings that we arrange the mathematical information into are called class intervals. They can have something similar or different class widths and should not cover.

The principal segment is for the gatherings where we compose the class intervals.

The center section is for the count marks.

The last segment is the frequency section where we can include the count marks.

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the complete question is:

The widths of 50 leaves of a plant were measured in mm and their cumulative frequency distribution is shown in the following table. Make frequency distribution table for this . CLASS FREQUENCY >20 50 >30 44 >40 28 >50 20 ​>60 15

Answer: 56

Step-by-step explanation:

I guess and checked all the numbers that add up to 11

The minimum value of the function g(x) = (x-3)² occurs at the vertex of the parabola, which is located at x = 3. At this point, the value of the function is g(3) = (3-3)² = 0.

To see why this is the case, we can use the fact that the vertex of a parabola in the form f(x) = a(x-h)² + k is located at (h,k). In the case of g(x) = (x-3)², we have a = 1, h = 3, and k = 0, so the vertex is located at (3,0).

Since the parabola opens upwards (the coefficient a is positive), the value of the function is minimized at the vertex.

Therefore, the minimum value of g(x) is 0, which occurs at x = 3.

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Answer: $2240.59

Step-by-step explanation:

To calculate the compound interest paid when an amount is borrowed at 5% p.a for 26 years and compounded monthly, you can use the formula:

A = P(1 + r/n)^(nt)

where:

A = the amount of money you will have after t years

P = the principal amount (the amount borrowed)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time (in years) for which the money is borrowed

In this case, we have:

P = the amount borrowed (not given in the question)

r = 5% p.a, or 0.05 as a decimal

n = 12 (since the interest is compounded monthly)

t = 26 years

We need to find the amount of compound interest paid, so we need to find the difference between the amount of money you will have after 26 years (A), and the amount you borrowed (P).

Let's assume the amount borrowed (P) is $1000. Then, we can substitute these values into the formula:

A = 1000(1 + 0.05/12)^(12*26)

A = 1000(1.004167)^312

A = 1000(3.240590)

A = $3240.59

So, after 26 years, the amount of money you will have is $3240.59. The compound interest paid is the difference between the amount borrowed and the final amount:

Compound interest paid = $3240.59 - $1000

Compound interest paid = $2240.59

Therefore, the compound interest paid if the amount is borrowed at 5% p.a for 26 years and compounded monthly is $2240.59.

A = $36,594.00

A = P + I

where

P (principal) = $10,000.00

I (interest) = $26,594.00

First, convert R as a percent to r as a decimal

r = R/100

r = 5/100

r = 0.05 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 10,000.00(1 + 0.05/12)(12)(26)

A = 10,000.00(1 + 0.0041666666666667)(312)

A = $36,594.00

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $10,000.00 at a rate of 5% per year compounded 12 times per year over 26 years is $36,594.00.

The probability that more than a fifth (i.e. 6 or more) of the 10 buyers would prefer green is 0.3981.

To conduct a study of the color preferences of new car buyers, a researcher wishes to conduct a research. Suppose that 30% of the population prefers green. If ten buyers are selected at random, what is the probability that more than a fifth of the buyers will prefer green?

The random variable X represents the number of buyers who prefer green. When n = 10 and p = 0.3, this is a binomial probability experiment. P(X > 2) is the probability that more than a fifth of the buyers would prefer green.P(X > 2) = 1 - P(X ≤ 2)P(X > 2) = 1 - [P(X = 0) + P(X = 1) + P(X = 2)]P(X > 2) = 1 - [C(10,0) (0.3)^0 (0.7)^10 + C(10,1) (0.3)^1 (0.7)^9 + C(10,2) (0.3)^2 (0.7)^8]P(X > 2) = 1 - [1(0.7)^10 + 10(0.3)(0.7)^9 + 45(0.3)^2 (0.7)^8]P(X > 2) = 0.2743

Therefore, the probability that more than a fifth of the buyers would prefer green is 0.2743, rounded to four decimal places.

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The friends error was in the terms factored out in the second step

It looks like your friend attempted to factor the polynomial using the distributive property of multiplication, but made an error in the second step.

first step 3x^3+x^2+3x+1

second step 3x^2(x+1)+3(x+1)

third step 3(x^2+1)(x+1)

the error is in the terms factored out in the second step: 3x^2 and 3

The correct factorization of the polynomial is:

3x^3 + x^2 + 3x + 1

= x^2(3x + 1) + 1(3x + 1)

= (3x^2 + 1)(x + 1)

The term factored out is: x^2 and 1

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Answer:

D) x=20

Step-by-step explanation:

On the spinner we have numbers from 0 to 9.

It is 10 numbers and we hit only 0,1, 2 and 3 (4 f them)

Lateya have propability [tex]\frac{4}{10}[/tex] to hit those numbers.

[tex]\frac{4}{10} *50=4*5=20[/tex]

a) Time taken to reach maximum height is 0.5 sec.

b) Highest point is 484 feet

c) Time to hit the water is 6 sec.

A statement proving the equality of two mathematical expressions is known as an equation.

a) h(t) = - 16t² +16t + 480

Differentiation with respect to t, we get,

h(t)' = - 32t + 16

Again differentiation with respect to t, we get,

h(t)" = -32 is less than 0

Then maximum value of height,

h(t)' = 0

- 32t + 16= 0

t = 1/2 = 0.5

Therefor, Time taken to reach maximum height is 0.5 sec.

b) for highest point; Put value of t in equation

h(0.5) = -16(0.5)²+16(0.5)+480 = 484

Highest point is equal to 484 feet

c) 0 =  -16t² + 16t + 480

0 =  -16 ( t² - t - 30 )

( t - 6 ) ( t + 5) = 0

t = 6, t = -5        (negative value is neglect)

Time to hit the water is 6 sec.

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The quadratic polynomial with the given zeros is:

y = x² - 7/3

If we have a quadratic equation whose zeros are a and b, then we can write it as:

y = (x - a)*(x - b)

in this case the zeros are √7/3 and -√7/3

Then the quadratic equation is:

y = (x - √7/3)*(x +  √7/3)

y = x² - 7/3

That is the quadratic polynomial.

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The given statement, "the margin-of-error refers to the number of percentage points by which survey results may vary" is true because the margin of error is an important factor to consider when interpreting the results of a poll.

In a poll, the margin of error refers to the amount of random sampling error that is expected to be present in the results of the survey. It is a measure of the statistical uncertainty associated with using a sample of a population to make inferences about the opinions or characteristics of the entire population.

The margin of error is typically reported as a plus or minus percentage, such as "plus or minus 3 percentage points," and it represents the range of values within which the true population parameter is likely to fall with a certain level of confidence. For example, if a poll has a margin of error of plus or minus 3 percentage points with a 95% level of confidence, this means that if the poll were conducted 100 times, the results would be expected to fall within plus or minus 3 percentage points of the true population parameter in 95 of those surveys.

Therefore, the margin of error is an important factor to consider when interpreting the results of a poll and helps to provide a measure of the precision and reliability of the survey findings.

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Answer:

[tex]y = 6x - 4[/tex]

Step-by-step explanation:

To find the equation of the line that passes through the given points (-1, -10) and (3, 14), first find the slope by inputting the points into the slope formula.

[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]

Let (x₁, y₁) = (-1, -10)

Let (x₂, y₂) = (3, 14)

Therefore, the slope of the equation is:

[tex]\implies m=\dfrac{14-(-10)}{3-(-1)}=\dfrac{14+10}{3+1}=\dfrac{24}{4}=6[/tex]

Now that we have determined the slope of the line, we can input the found slope and either of the two given points into the point-slope formula to create the equation of the line.

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]

Substituting m = 6 and (x₁, y₁) = (-1, -10) into the point-slope formula:

[tex]\implies y-(-10)=6(x-(-1))[/tex]

Simplifying:

[tex]\implies y+10=6(x+1)[/tex]

[tex]\implies y+10=6x+6[/tex]

[tex]\implies y=6x-4[/tex]

Therefore, the equation of the line that passes through (-1,-10) and (3,14) is:

[tex]\boxed{y = 6x - 4}[/tex]

Answer:

6x - y - 4 = 0

Step-by-step explanation:

To find:-

Solution:-

We are here given two lines and we are interested in finding out the equation of the line passing through the given points.

Firstly here we will find out the slope of the line as ,

[tex]:\implies \sf m =\dfrac{y_2-y_1}{x_2-x_1}\\[/tex]

Now on substituting the respective values, we have;

[tex]:\implies \sf m =\dfrac{-10-14}{-1-3} \\[/tex]

[tex]:\implies \sf m = \dfrac{-24}{-4}\\[/tex]

[tex]:\implies \sf\pink{ m = 6}\\[/tex]

Now we can use the point slope form of the line to find out the equation of the line . The point slope form of the line is ,

[tex]:\implies \sf \pink{ y - y_1 = m(x_2-x_1)}\\[/tex]

Take any one of the given points for (x₁,y₁) . Here i am taking (3,14) .

Now finally substitute the respective values,

[tex]:\implies \sf y - 14= 6(x -3 )\\[/tex]

[tex]:\implies \sf y- 14= 6x - 18 \\[/tex]

[tex]:\implies \sf 6x - y - 18 + 14 = 0\\[/tex]

[tex]:\implies \sf\pink{ 6x - y -4 = 0 }\\[/tex]

Hence the required equation of the line in standard form is 6x - y - 4 = 0 .

The volume of a cone is given by the formula:

V = (1/3) * pi * r^2 * h

where r is the radius of the base and h is the height of the cone.

Substituting the given values, we get:

V = (1/3) * pi * 9^2 * 23

V = (1/3) * pi * 729 * 23

V = 6,859 pi

Therefore, the volume of the cone is 6,859 pi cubic units.

Answer:

h(x) = (x^2 - 64)

Step-by-step explanation:

If the solutions to h of x = 0 are x = -8 and 8, then h(x) must be a quadratic function with roots at x = -8 and x = 8.

One way to write the quadratic function that satisfies these conditions is:

h(x) = (x+8)(x-8)

where a is some non-zero constant that determines the shape of the parabola.

Expanding the above equation, we get:

h(x) = (x^2 - 64)

Therefore, one possible quadratic function that could represent h is:

h(x) = (x^2 - 64)

where a is any non-zero constant.

Answer:

The radius of the hubcap is half of its diameter, which is:

r = d/2 = 26/2 = 13 cm

The area of the hubcap, in square centimeters, is given by the formula:

A = πr²

Substituting the value of r, we get:

A = 3.14 x 13²

A = 3.14 x 169

A = 530.66

Therefore, the area of the hubcap is approximately 530.66 square centimeters.

Step-by-step explanation:

I did this question and the correct answer is 169π.

Step-by-step explanation:

Answer:

D (D)

Step-by-step explanation:

We can know from the question that each face has two A, two B, and two C, two D, and two E. And these three faces are the sides of the triangular pyramid (Each face vertex is D).

∴ We can get the picture of the fourth face.

∴ There are two A, two B, two C, one D, and two E in the picture.

∴ The middle of the fourth face is D.

*See the attachment*

Answer:

D

Step-by-step explanation:

Answer: x^2-22x+121

I believe this is correct.

A chi-squared statistic provides strong evidence in favor of the alternative hypothesis if its value is A.  a large positive number.

Chi-squared statistics or chi-squared test is a statistical method used to find out if there is a significant difference between the expected and observed frequencies in one or more categories of a contingency table. This test is used to determine whether the null hypothesis can be rejected or not. Chi-squared statistics are a non-parametric test that helps to determine whether the data is close to what is expected or not. This test is used when the data is ordinal or nominal.

Chisquare test is often used for: Testing if the observed frequencies of a nominal variable are significantly different from the expected frequencies Assessing if two or more distributions are the same. The chi-squared statistic provides evidence for or against the null hypothesis. A large positive value of the chi-squared statistic indicates that the null hypothesis can be rejected.

Therefore, option A. a large positive number, is the correct answer.

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Answer:

Step-by-step explanation:

Answer:

55

Step-by-step explanation:

Answer:

(8÷2+9)×9−10²

hope this helped!

Red-green color blindness is controlled by an x-linked gene in humans. The allele that causes color blindness is rare and recessive to the allele for normal vision. A man and woman both with normal vision had color-blind fathers. If this man and woman have a child, Therefore, the probability of a child being color-blind is 25%.

Red-green color blindness is an X-linked recessive disorder. This means that the gene for the disorder is found on the X chromosome. Because males have only one X chromosome (inherited from their mother), they will develop color blindness if they inherit the allele from their mother. On the other hand, females need to inherit two copies of the allele, one from each parent, to develop the disorder.A man with normal vision will have the genotype XY, and the woman will have the genotype XX.

Each child of the couple will receive one X chromosome from the mother and one Y chromosome from the father. The probability of the child inheriting the allele for color blindness from its father is 0 because he has no alleles for color blindness.

The probability of the child inheriting the allele for color blindness from its mother is 1/2 because the mother's X chromosome has a 1/2 probability of carrying the allele. Because the mother is a carrier, the probability of the child receiving the allele is 1/2.

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Take note that Bus 18 is the most reliable in terms of trip times among the line plots shown above. With our understanding of the interquartile range, we can solve this. (IQR)

We must compare the metrics of data variability in order to identify the bus that consistently produces the best accurate results. Range and interquartile range are the metrics of variability that we can utilise in this situation (IQR).

The IQR is the difference between the third quartile (Q3) and the first quartile, whereas the range is the difference between the highest and lowest values in the data set (Q1). Because it is less impacted by extreme values than the range, the IQR provides a more accurate indicator of variability.

Using the given data, we can calculate the range and IQR for each bus:

Bus 47:

Range = 28 - 4 = 24

Q1 = 10, Q3 = 22

IQR = 22 - 10 = 12

Bus 18:

Range = 22 - 6 = 16

Q1 = 9, Q3 = 25

IQR = 25 - 9 = 16

According to these findings, Bus 18 has a narrower range and a higher IQR than Bus 47. The IQR, a more accurate indicator of variability in this situation, reveals that Bus 18's trip times are less variable than those of Bus 47's. Hence, we can say that when it comes to trip times, Bus 18 is the most reliable.

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Answer:

  6 inches

Step-by-step explanation:

You want to know the radius of a cylinder with volume 72π in³ and height 2 in.

The given numbers can be put in the given formula, and the equation solved for r.

  V = πr²h

  72π in³ = πr²(2 in)

  36 in² = r²

  r = √(36 in²) = 6 in

The radius of the cylinder is 6 inches.

If the budget were to increase to $3000, allowing us to survey many more people from a simple random sample, the test statistic would likely be more accurate and reliable.

As per the given scenario,

if we have a limited budget of $500, we can only survey 50 people from a simple random sample. In order to study the relationship between social class and voting preferences, the budget must be increased to $3000.

On increasing the budget, we can survey more people from a simple random sample, which would lead to a better representation of the population.
Due to the small budget, the test statistic would be less accurate as only a small number of people are being surveyed. However, if the budget increases to $3000, it would allow for a larger sample size and therefore the test statistic would be more accurate.

This would result in a narrower confidence interval and a higher level of confidence in the accuracy of the results.
Moreover, with a larger budget, it would be possible to use more sophisticated sampling techniques such as stratified random sampling, which could further increase the accuracy of the test statistic.

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