A region satisfies the inequalities 1 ≤ x ≤ 5 and 2 ≤ y ≤a. What value of a would give the region an area of 24 square units?​

Answer:

a. To find the equation for the median-fit line, we need to first determine the slope (m) and the y-intercept (b) of the line. We can use the following formulas to calculate these values:

m = (nΣxy - ΣxΣy) / (nΣx^2 - (Σx)^2)

b = median y - m(median x)

Where n is the number of data points, x is the independent variable (year), y is the dependent variable (number of students learning English), Σ means to sum, and xy represents the product of x and y.

For this dataset, we have 5 data points, so n = 5.

x = 2003, 2004, 2005, 2006, 2007

y = 1.600, 1.599, 1.592, 1.570, 1.560

Σx = 10,015

Σy = 7,966

Σxy = 31,948

Σx^2 = 40,307

m = (531948 - 100157966)/(5*40307 - 10015^2) = -0.007

median x = 2005

median y = 1592

b = 1592 - -0.007 * 2005 = 1597.014

The equation for the median-fit line is:

y = -0.007x + 1597.014

b. To predict the number of students who were learning English in California in 2001, we can substitute 2001 for x in the median-fit line equation:

y = -0.007(2001) + 1597.014 = 1600.087

c. To predict the number of students who were learning English in California in 2010, we can substitute 2010 for x in the median-fit line equation:

y = -0.007(2010) + 1597.014 = 1590.028

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The possible percentage of the marks the students will have is (D) 83%.

A percentage, often known as percent, is a division by 100.

Percentage, which means "per 100," designates a portion of a total sum.

45 out of 100 is represented by 45%, for instance.

Finding the percentage of a whole in terms of 100 is what percentage calculation is.

Both manual calculation and the use of internet calculators are options.

So, we know that:

When we find the percentage, after division, we multiply the answer by 100 to get the answer in percentage.

Similarly,

0.83 * 100 = 83%

Therefore, the possible percentage of the marks the students will have is (D) 83%.

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Complete question:
A student added all her grades together and then divided by the total points possible to figure out her grade, as her instructor had said to do, and the result was 0.83. What percent of the possible points does she have?

a) 8.3%

b) 0.83%

c) Can't tell, but she has 83 total points.

d) 83%

The requried value of given expression when a = 7 and b = 28 is 125.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

here,
Given expression,
(a + b)² = a² + b² + 2ab
We have,
a = 7 and b = 28
(7 + 28)² = 7² + 28² + 2 × 7 × 28
35² = 49 + 786+ 392
125 = 125

Thus, the requried value of given expression when a = 7 and b = 28 is 125.

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No, the conditions for inference have not been met. The two samples must be independent, meaning that the individuals in the college sample should not also be in the high school sample. Without independent samples, it is not possible to construct a 95% confidence interval for the true mean difference.

1. Collect data from the two samples of seniors in high school and college.

2. Calculate the mean difference in the number of hours of sleep for the two samples.

3. Calculate the standard deviation of the differences in hours of sleep for the two samples.

4. Calculate the standard error of the mean difference.

5. Calculate the critical value for a 95% confidence interval.

6. Calculate the lower and upper bounds of the confidence interval by

adding and subtracting the critical value from the mean difference.

7. Interpret the confidence interval to determine the true mean difference in the number of hours of sleep for seniors in high school and colleg

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The provided statement indicates that the regression line's equation is[tex]\hat{Y}[/tex] =  -0.06392X + 3.42231. Hence the formula for predicting the anticipated sepal size of a floral with panicle length 6.39 is [tex]\hat{Y}[/tex] = 3.01

More specifically, the nature and degree of the correlation between a variable y and a number of different independent variables are assessed using linear regression. It aids in the creation of models for making predictions, such as projecting the stock price of a corporation.

Let X represent the sepal's length, and Y represent its breadth. Next, we have the information below:

Cov (X, Y) = -0.0438254

[tex]$$\begin{aligned}& \bar{Y}=3.04966 \\& \sigma_Y=0.445429 \\& \bar{X}=5.829932 \\& \sigma_X=0.828054\end{aligned}$$[/tex]

The following provides the least squares estimates of the intercept and regression coefficient:

[tex]\hat{\beta_0}=\bar{Y}-\hat{\beta_1} \bar{X}[/tex]

[tex]$\hat{\beta_1}$[/tex] = Cov (X, Y)/[tex]$\sigma_X^2$[/tex]

[tex]\begin{aligned}& \hat{\beta}_1=\frac{-0.0438254}{0.828054^2} \\& \hat{\beta}_1=-0.06392\end{aligned}[/tex]

and,

[tex]$$\begin{aligned}& \hat{\beta_0}=3.04966-(-0.06392) *(5.829932) \\& \Rightarrow \hat{\beta}_0=3.42231\end{aligned}$$[/tex]

Thus, the regression line's equation is as follows:

[tex]\hat{Y}[/tex] =  -0.06392X + 3.42231

With a sepal length of 6.39, the following formula predicts the sepal breadth of a flower:

[tex]$$\begin{aligned}\hat{Y} & =-0.06392 * 6.39+3.42231 \\\Rightarrow \hat{Y} & =3.0138612 \simeq 3.01\end{aligned}$$[/tex]

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The complete question is-

The famous iris dataset (the first sheet of the spreadsheet linked above) Was first published in 1936 by Ronald Fisher. The dataset contains 50 samples from 3 iris species. setosa, virgiria, and versicolor. Four features are measured, all in cm sepal length, sepal with, petal length, and petal width.

What is the equation tor the least,square regressian line where the independen; or predictor variabie is pelat Iength and the dependent of response variable is petal width for iris versicolar?

What is the predicted petal width for iris versicolor for a flower with a pelal length of 4.1?

The definition of sequence is an ordered list of objects.

The term ordered list is known as the way to uses numbers or some sort of notation that indicates a series of items.

in math the term sequence is defined as an arrangement of numbers in a particular order.

Where as which is also known as a series is defined as the sum of the elements of a sequence.

in the sequence the listed of objects are an arrangement of two or more things in a successive order and the successive order of two or more things which means that they are in chronological sequence.

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The probability that the flight would be delayed when it is not raining is 12.46%.

Probability is a branch of math which deals with finding out the likelihood of the occurrence of an event. Probability measures the chance of an event happening and is equal to the number of favorable events divided by the total number of events. The value of probability ranges between 0 and 1, where 0 denotes uncertainty and 1 denotes certainty.

To determine what is the probability that the flight would be delayed when it is not raining, the following calculation must be performed:

Probability that it will not rain = 1 - probability that it will rain

X = 1 - 0.11

X = 0.89

Probability that the flight would be delayed when it is not raining = probability that it is not raining x probability that the flight will be delayed

X = 0.89 x 0.14

X = 0.1246

0.1246 x 100 = 12.46

Therefore, the probability that the flight would be delayed when it is not raining is 12.46%.

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The numbers that are potential roots of the function given above are:
Option B-D. That is -  ±1, ±2, and ±12.

It is correct to state that in mathematics, a root of an equation is a value that, when substituted into the equation, makes the equation true.

To obtain the potential roots of the expression p(x) = x⁴ + 22x² - 16x - 12:

Note that from the rational root theorem, all the possible roots of the function are in the form of a rational number.

x =  ± p/q

x = ± (Factors of the constant term)/ (Factors of leading coefficient)

Thus, according to the polynomial above,  we know that

Factors of 1 are ±1.

Thus, according to the theorem of rational root, the potential roots of the function are ±1, ±2, ±3, ±4, ±6, ±12.

Therefore, the potential roots of the function from the options listed are: are ±1, ±2, and ±12.

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Full Question:

Which of the number(s) below are potential roots of the function? p(x) = x⁴ + 22x² - 16x - 12?

± 5
±1

±2

±12

±17

Answer:2

Step-by-step explanation:

No, it does not mean all real numbers. No solution means that there is no value of the variable that satisfies the equation.

No solution means that there is no value of the variable that satisfies the equation. This means that no matter what value is assigned to the variable, the equation will not be true. Therefore, no solution does not mean all real numbers.

No solution means that there is no value of the variable that satisfies the equation. The equation might be a linear, quadratic, or some other type of equation, but no matter what value is assigned to the variable, the equation will not be true. Therefore, no solution does not mean all real numbers since all real numbers would include the value that would make the equation true. It is possible that all real numbers would be a solution, but no solution does not mean that all real numbers are a solution.

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The absolute value of a number is always positive or zero because it represents the distance of a number from zero on a number line, and the distance between two points can never be negative.

The absolute value of a number is defined as the distance of that number from zero, regardless of its sign. For example, the absolute value of -5 is 5 and the absolute value of 5 is also 5. When we apply the absolute value function to a number, the result is always positive or zero.

Additionally, the definition of absolute value is |x| = { x if x >=0, -x if x<0 }

if x is greater or equal to 0, the absolute value of x is x, otherwise is -x, which is positive.

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The table that shows the value of the input and output values of g(x) is shown below where x is for the input values and the output values is g(x)

x       g(x)

2       4

1        2

0        0

1         2

2         4

The values are solved by substituting the values of f(x) in the formula as shown in the problem, the formula is

g (x) = 2f (x)

The values of f(x) which is the input values for g(x) are

2 1 0 1 2

this values are substituted in to the function g (x) = 2f (x) to get

4 2 0 2 4

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Answer:3.41

Step-by-step explanation:it is pie

A. Johnny's biweekly gross pay is $2,595.23.

B. Johnny's Social Security deduction is 6.2% of his gross pay is $160.90.

C. Johnny's Medicare deduction is 1.45% of his gross pay, which is $37.63.

D. Johnny's new annual salary with a 14.5% raise is $71,179.93.

A. Johnny's biweekly gross pay is $62,285.50 / 24

= $2,595.23.

B. Johnny's Social Security deduction is 6.2% of his gross pay, which is $2,595.23 * 6.2% = $160.90.

C. Johnny's Medicare deduction is 1.45% of his gross pay, which is $2,595.23 * 1.45% = $37.63.

D. Johnny's new annual salary with a 14.5% raise is $62,285.50 * 1.145 = $71,179.93.

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Answer:

distance from beginning is 225 and the change is -65 per hour

Step-by-step explanation:

Answer:

Coupon A

Step-by-step explanation:

Coupon A takes 40% off

51 x .40= $20.40

Coupon B only gives a rebate for $18

Coupon A is $2.40 less than the price with coupon B

A chord is a combination of three or more tones (notes) played together.

To determine the notes in a chord, we need to calculate the intervals between the notes. An interval is the distance between two notes. Intervals are measured in half steps (or semitones). A half step corresponds to the interval between two adjacent keys of a piano.

In a major chord, the formula for determining the intervals is 1-3-5. This means the root note (1st note) is a major third (4 half steps) away from the 3rd note and a perfect fifth (7 half steps) away from the 5th note.

For example, if the root note is C, the 3rd note is E and the 5th note is G. The intervals in this chord are C to E (4 half steps) and C to G (7 half steps). Therefore, the chord is a C major chord.

In a minor chord, the formula for determining the intervals is 1-b3-5. This means the root note is a minor third (3 half steps) away from the 3rd note and a perfect fifth (7 half steps) away from the 5th note.

For example, if the root note is F, the 3rd note is Ab and the 5th note is C. The intervals in this chord are F to Ab (3 half steps) and F to C (7 half steps). Therefore, the chord is a F minor chord.

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The probability of selecting 2 men and 2 women from a group of 9 women and 7 men is 11%.

The probability of selecting 2 men and 2 women from a group of 9 women and 7 men is [tex]$\frac{{7 \choose 2}{9 \choose 2}}{{16 \choose 4}}$[/tex] which simplifies to[tex]$\frac{63}{220}$[/tex] or approximately 28.6%. The probability of selecting 2 men and 2 women from a group of 9 women and 7 men is 11%.

The probability of selecting 2 men and 2 women from a group of 9 women and 7 men can be calculated by using the formula for combination, nCr. In this case, we would be selecting 4 people from 16 individuals, so n = 16 and r = 4. The formula is nCr = n!/(r!(n-r)!). This can be simplified to 16C4 = 16!/ (4!(12!)). The answer is 1820/21168, which can be simplified to 86/792, or approximately 11%. Therefore, the probability of selecting 2 men and 2 women from a group of 9 women and 7 men is 11%.

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Answer:

money. you need to know how to count your money so nobody cheat you out of it

Answer:

y-1=3(x-2)

Step-by-step explanation:

This is the equation you have to fill in y-y1=m(x-x1) to fill in this you have to lable the points (2,1)

x,y

A. 73.91% of respondents were under the age of 30 and did not snore.

B. Data show that snoring is not age-independent as most snorers are over 30 years of age.

A. The first step is to convert all percentage population groups into numbers. This helps make things clearer.

Total number of adults surveyed = 995 adults

Number of adults over the age of 30 = 81.5% of 995

                                                              = 81.5/100 × 995

                                                              = 810.925

                                    ≈ 811(part of the population can be counted).

Number of adults under 30 = 995 - 811 = 184 adults.

Number of all adults who snore = 36.8% of 995

= 36.8/100 × 995 ≈ 366 adults who snore

Of the total 995, 32% of the snorers were over 30 was.

Number of snorers over 30 × 995 ≈ 318 adults

Snorers under 30 = 366 - 318 = 48 adults

Number of under 30s recorded 30 - under 30 snorers

= 184 - 48 = 136

Converting this to percentage: 136/184× 100 = 73.91%

so 73

B. From the data, snoring is not independent of age as most of the people that snored were above 30 years. Snoring is related to the age. This is because that the most of the younger adults did not snore, while more of the older adults snored.

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The absolute value of a negative number will always be a positive number.

As discussed above, regarding the absolute number, therefore, the absolute value of a negative number will always be a positive number.

for example, |-24| = 24

The absolute value of any number will always be a positive number.

As discussed above, regarding the absolute number, therefore, the absolute value of any number will always be a positive number.

for example, |-24| = 24

Positive numbers will always have a higher absolute value than negative numbers.

As discussed above, regarding the absolute number. therefore, the absolute value of any number will always be a positive number, which will be equal in value.

for example, |-24| = 24

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Answer:

[tex]y \: = | \: x - 5| + 1[/tex]

On solving the provided question, we can say that  the slope of the line measured is 33m/s

A line's slope determines how steep it is. A mathematical equation for the gradient is called "gradient overflow" (the change in y divided by the change in x). The slope is the ratio of the vertical change (rise) between two points to the horizontal change (run) between those same two spots. When a straight line's equation is written as y = mx + b, the slope-intercept form of an equation is employed to express it. The y-intercept is located at a location where the line's slope is m, b is b, and (0, b). For instance, the slope of the equation y = 3x - 7 and the y-intercept (0, 7).The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).

rise of line = 600m

run of line = 3mins

Slope = rise/run

Slope = 600/180

Slope = 3.33 m/sec

, the slope of the line measured is 3.33

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Assume that x represents the window's rectangular portion's width and y represents the window's rectangular portion's height. The width of the rectangular component of the window is equal to the diameter of the semicircle portion since the semicircle with diameter d is atop the window, or x = d.

x = circle diameter = window width

r = x/2 and y = window height

We'll now solve for the window's perimeter. The top section of the rectangular window is not included since it is continuous with the semicircular component of the window, therefore the perimeter of the rectangle portion is x + 2y, and the perimeter of the circular portion is x/2 (which is half the circumference of a circle).

hence:

P = x2y + πx/2 = 2r + 2y + πr

We will now find a solution for the light that passes through the window. Assuming that transparent glass transmits one light per square inch, tinted glass transmits just one light per square inch.

The area of the rectangle component multiplied by the clear glass light constant, or 1*2ry = 2ry, will determine the rectangular light. The semicircular component will be equal to (1/4)*r2/2, which is the tinted glass light constant multiplied by half the area of a circle. Hence,

L = 2ry + πr2/8

Isolating y from the perimeter equation now will allow us to enter that value of y into the light equation.

L = r(P - r(2 + )) + r2/8 y = (P - r(2 + ))/2

P is a constant, hence the only variables in the light equation are  We can differentiate L with respect to r (i.e. dL/dr) and solve for when dL/dr = 0 to find the point at which the light transmitted is at a maximum.

dL/dr = P - 2r(2 + π) + πr/4

0 = P - 2r(2 + π) + πr/4

r = 4P/(16 + 7π)

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Quadrilateral LMNP has four vertices at the coordinates: L(-4,3), M(2,7), N(9,3), and P(-3,-5).

These vertices can be plotted on to  a Cartesian coordinate plane in order  to form a quadrilateral shape. The shape of the quadrilateral which  can be determined by the relative positions of its one of vertices, such as whether to check  it is a rectangle, square, parallelogram, or any other type of quadrilateral as such . However, without more information or proper data , it is not possible to determine whether the quadrilateral is having  the exact shape of quadrilateral LMNP from just its vertices or not .It is a type of polygon which contains  4 sides, 4 vertices and 4 angles. To make a one  quadrilateral and contains four non-collinear points which  are joined and the sum of all the interior angles and exterior angles is always equal to 360 degrees as we know . The word ‘Quadrilateral’ was initiated  from Latin words ‘Quadra’ and ‘Latus’ which meant four and sides respectively.

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Answer: (0, -1/3)

Step-by-step explanation: The answer is: (0, -1/3)

y=mx+b

Slope being "m"
And the y intercept being "b"

I think it's (0, -1/3)

......

..

The lowest temperature recorded in International Falls is - 40°.

Addition is also known as the sum, subtraction is also known as the difference, multiplication is also known as the product, and division is also known as the factor.

Given, The lowest temperature in Fraser, Colorado is - 54°, and the difference between the lowest temperature in Fraser, Colorado, and the lowest temperature in International Falls, Minnesota is 14°.

There the lowest temperature recorded in International Falls is,

- 54° + 14°.  (as stated warmer we put a positive sign)

= - 40°.

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Answer: [tex]110^{\circ}[/tex]

Step-by-step explanation:

[tex]\angle ACB \cong \angle HFB[/tex] by the corresponding angles theorem.

The FG slope is 1/5 and the HJ slope is -2. Because slopes are not connected to one another, they are neither parallel nor perpendicular.

The slope or gradient of a line in mathematics is a quantity that specifies both the direction and the steepness of the line. The slope of a line indicates its steepness. Slope is computed mathematically as "rise over run" (change in y divided by change in x). A slope is the steepness of a hill. The same is true for a line's steepness. The slope is defined as the ratio of the vertical change between two places, known as the rise, to the horizontal change between those same two points, known as the run.

Here,

F(3, 1), G( 8, 2), H(2, 4), and J(1, 6)

a. FG=2-1/8-3

=1/5

HJ=6-4/1-2

=-2

b. Since slopes are not related to each other it is neither parallel nor perpendicular.

The slope of FG is 1/5 and slope of HJ is -2. Since slopes are not related to each other it is neither parallel nor perpendicular.

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