a study was conducted in which two types of engines, a and b, were compared. gas mileage, in miles per gallon, was measured. 50 experiments were conducted using engine type a and 75 experiments were done with engine type b. the gasoline used and other conditions were held constant. the average gas mileage was 36 miles per gallon for engine a and 42 miles per gallon for engine b. assume that the population standard deviations are 6 and 8 for engines a and b, respectively. we found a 95% confidence interval on the difference of population mean gas mileages for engines a and b is (-8.46,-3.54). how do you interpret this interval?

The Least common denominator of the given fractions is 12.

What is least common denominator?

The lowest common multiple of the denominators of a group of fractions is known as the lowest common denominator, or LCD, in mathematics. It makes adding, taking away, and comparing fractions easier.

Consider the given fraction, 3/4 and 1/6

The denominator are 4 and 6.

The multiples of 4 are, 4, 8, 12, 16, 20.

And the multiples of 6 are, 6, 12, 18, 24, 30.

From the above listed multiples of 4 and 6, 12 is the least common multiple of both the numbers.

Hence, the Least common denominator of the given fractions is 12.

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Extrapolation is the use of the regression line to estimate a mean of y-values for an x-value that is far outside the x-range of data.

What is extrapolation?

A statistical technique called extrapolation aims to understand the unknown data from the known data. It uses historical data to attempt to predict future data. For instance, using the current population size and growth rate to project the size of a population in a few years.

Predicting hypothetical values outside of a specific data set is the goal of extrapolation.

Contrary to interpolation, which typically focuses on estimating past values, extrapolation is used to predict unknown future values due to its predictive nature.

Hence, extrapolation is the use of the regression line to estimate a mean of y-values for an x-value that is far outside the x-range of data.

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Answer:

q = -4

Step-by-step explanation:

0.0009 = 9 × 10^(-4)

q = -4

We can show that these data can be modeled using a linear function in the following manner:

a) We must compute the differences in the number of high school graduates in each year in order to model the data using a linear function. For instance, the difference between the 1993 and 1994 graduation rates is 5,479 - 5,410, or 69. This pattern of differences suggests that a linear function can be used to model the data.

The annual change in the number of graduates serves as the slope for the linear function. The slope, for instance, is 69 between 1993 and 1994 and 76 between 1994 and 1995. The slope for the linear function is, in general, the difference between the number of graduates in successive years, therefore it is the slope between graduates in consecutive years.

b) Y = mx + b, where y is the number of graduates, x is the year, m is the slope, and b is the y-intercept, is the formula for a linear function that represents the data. We need to know the values of m and b in order to calculate the formula for the linear function that describes the data.

We can use the slope between any two consecutive years to get the value of m. For instance, m = 69 since the slope from 1993 to 1994 is 69. The number of graduates in the first year of the data, which is the y-intercept, can be used to determine the value of b.

For instance, if the first year of the data is 1993 and that year had 5,479 graduates, then b = 5,479. Consequently, y = 69x + 5,479 is the equation for the linear function that models the data.

c) Functional notation can be used to indicate the number of high school graduates in 1994. The formula is y = 69x + 5,479, where x is the year and y is the total number of graduates. Therefore, y = 69(1994) + 5,479 = 137,123 is the total number of graduates in 1994. We may enter the numbers of x and b into the formula from section c to obtain y = 69 (1994) + 5,479 = 137,123.

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The surface area of the prism is 166 mm² in the given figure.

The total surface area of the given prism can be expressed in terms of length (l), width (w), and height of cuboid (h) as:

Surface area of prism = 2 (lw + wh + lh) ....(i)

As per the given figure, we have

length (l) = 5 mm

width (w) = 4 mm

height (h) = 7 mm

Substitute the values in the formula, and solve

Surface area of prism = 2 (5 x 4 + 4 x 7 + 7 x 5)

Surface area of prism = 2 (20 + 28 + 35)

Surface area of prism = 2 (83)

Surface area of prism = 166 mm²

Thus, the surface area of the prism is 166 mm² in the given figure.

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Answer: 100 Hours

Step-by-step explanation:

We know the ratio is 1:1:1

So now the ratio is 100 times so that it will take 100 hours

Step-by-step explanation:

is that root 3 x..........?

There is no such a number whose absolute value is -2. This is because the absolute value of any number is its distance from 0 irrespective of the direction.

An absolute value of a number is the distance of the number from 0 on a number line irrespective of the direction.

Consider the number "x".

Then its absolute value is written as

|x| = x if x ≥ 0;

   = 0 if x = 0;

   = -x if x < 0;

For example x = -9; then its absolute value is

|(-9)| = -(-9) = 9; (Since x = -9 < 0; we applied |x| = -x)

So, we can conclude that irrespective of the direction (positive or negative), the absolute value of any number remains positive.

We know that the absolute value of any number is calculated by

|x| = x if x ≥ 0;

   = 0 if x = 0;

   = -x if x < 0;

And the absolute value of any number irrespective of its direction on the number line remains positive.

So, no such number has a negative absolute value.

Hence, the answer is none for the given question.

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To write 31/25 as a decimal, we can divide 31 by 25 using long division or a calculator and we get 1.24

A decimal is a way of expressing a number as a fraction of one.

Rounding off is a mathematical process that involves replacing a number with an approximate value that is easier to work with. When you round off a number, you choose the nearest whole number, ten, hundred, etc., depending on the place value you are rounding to.

For example, if you are asked to round the number 3.6 to the nearest whole number, you would round it off to 4, because 4 is the nearest whole number to 3.6.

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The equivalent expression of the given expression is 7x³y² -3x²y² + xy -5. Second option is the correct option.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator).

What are like terms?

Similar variables and powers are referred to as like words in algebra. It is not necessary for the coefficients to agree. When two or more terms do not share the same variables or powers, they are said to be unlike terms. Unless there is a power, the variables' order is irrelevant.

Given expression is

(5x³y²−3xy+2)+(2x³y²−3x²y²+4xy−7)

Now open the brackets:

= 5x³y²−3xy+2+2x³y²−3x²y²+4xy−7

Combine like terms:

= (5x³y²+2x³y²)+ (−3xy + 4xy )+(2−7)−3x²y²

= 7x³y² + xy -5 -3x²y²

= 7x³y² -3x²y² + xy -5

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Answer:

Step-by-step explanation:

You are given the equation 8x -3 +4x +3 = 180 and asked to simplify it and solve for x.

Collecting terms, we have ...

  (8 +4)x +(-3 +3) = 180

  12x + 0 = 180

Dividing by the coefficient of x gives ...

  x = 180/12 = 15

The value of x is 15.

$100 much better off per month would the firm be if it adopted preventive maintenance.

Given that,

We have to find how much more profitable would the company be each month if it implemented preventive maintenance.

We know that,

Number of Breakdowns are 0, 1, 2, 3, 4

The problems for the breakdowns are 0.50, 0.25, 0.10, 0.10, 0.05

Cost of a breakdown is $2,000

A monthly preventive maintenance programme costs $2,000

Expected probability of breakdown:

E(x) = Σ(X × p(x))

= (0×0.5) + (1×0.25) + (2×0.10) + (3×0.10) + (4×0.05)

= 0.95

E(x) ×cost of breakdown = (0.95 × 2000) = $1900

So, Difference between breakdown and preventive maintenance

1900 - 2000 = - $100

Therefore, $100 much better off per month would the firm be if it adopted preventive maintenance.

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Answer:

Step-by-step explanation:

Rearranging:

(i) 16x2−3=(2x+5)(5x−3)

   16x^2 - 3 = 10x^2 + 19x -15

   6x^2 - 19x + 12 = 9

THIS IS QUADRATIC.

(ii) (x+2)3=x3−4

(x + 2)(x + 2)^2 = x^3 - 4

(x + 2)(x^2 + 4x + 4) = x^3 - 4

x^3 + 4x^2 + 4x + 2x^2 + 8x + 8 = x^3 - 4

6x^2 + 12x + 4 = 0.

THIS IS QUADRATIC.

(iii) x(x+1)+8=(x+2)(x−2)

x^2 + x + 8 = x^2 - 4

x + 12 = 0

THIS IS NOT QUADRATIC.

Answer:

3

Step-by-step explanation:

because it consists two side separated by equal sign and has letters in it

We can shown that the triangles are congruent by a translation of 2 units left and then a reflection over the y-axis.

Congruent triangles are triangles that have the same side lengths.

Transformations that keep  the congruence of a triangle are given as follows:

One vertex of the original triangle is given as follows:

A(8,8).

The equivalent vertex on the reflected and translated triangle is given as follows:

A'(6,-8).

Considering the reflection over the y-axis that we can see from the image, the complete rule is given as follows:

(x,y) -> (x - 2, - y).

Meaning that the translation was two units left.

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To solve this problem, we can use the standard normal distribution and the Z-score formula to find the probability that a pregnancy will last at least 300 days.

The Z-score is a measure of how many standard deviations a value is from the mean. We can use the Z-score to standardize a value, which means we can express it in terms of how many standard deviations it is from the mean of the distribution.

The Z-score formula is:

Z = (x - μ) / σ

Where x is the value we are standardizing, μ is the mean of the distribution, and σ is the standard deviation of the distribution.

To find the probability that a pregnancy will last at least 300 days, we can use the Z-score formula to standardize 300 days:

Z = (300 - 268) / 15 = 4

This means that 300 days is 4 standard deviations above the mean of 268 days.

To find the probability that a pregnancy will last at least 300 days, we can use a Z-table or a calculator to find the area under the standard normal curve that is greater than or equal to 4 standard deviations.

Using a calculator or a Z-table, we find that the probability that a pregnancy will last at least 300 days is approximately 0.0165, which corresponds to answer choice D: 0.0165.

Option D (No, as there are two heights associated with the wrist circumference of 16 cm.

An illustration of a relation is a function graph. In set theory and modern mathematical foundations, a function is truly equal to its graph.

The wrist circumferences and heights of six kids in Alyssa's class are represented by a collection of points in the graph that is shown.

The height is represented by the y axis, and the wrist circumference by the x axis.

Any relation is referred to as a function if there is only one value of y for any given value of x. The graph is referred to as a function if it passes the vertical line test, which requires that a vertical line be drawn and only touch the graph once.

There are two y values (162 and 165) on the above graph for the x value of x=16.

The graph is not a function as a result.

Among the possibilities The correct response is option D, "No," since the wrist circumference of 16 cm pairs with two heights.

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Addition is used to find the sum of the number of miles lauren ran

Two or more expressions with an Equal sign is called as Equation.

Given,

Lanren ran 2.76. Miles in a track event.

Then she ran 0.4 Mile home after the event

We need to find the sum of the number of miles lauren ran.

By addition we find the sum of the number of miles lauren ran.

Two point seven six plus zero point four

2.76+0.4

Three point one six

3.16

Hence, addition is used to find the sum of the number of miles lauren ran

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Answer:

  C = (5, 4)

Step-by-step explanation:

You want the coordinates of point C, located 3/4 of the way from A(-4, -2) to B(8, 6).

That point is ...

  C = A +3/4(B -A)

  C = (-4, -2) + (3/4)((8, 6) -(-4, -2))

  C = (-4, -2) + (3/4)(8+4, 6+2) = (-4, -2) + (3/4)(12, 8) = (-4, -2) +(9, 6)

  C = (-4 +9, -2 +6)

  C = (5, 4)

__

Additional comment

Equivalently,

  C = (3B +A)/4 = (3(8, 6) +(-4, -2))/4 = (24 -4, 18 -2)/4 = (5, 4)

The method shown above may be more intuitive. The formula shown here is a result of simplifying the one used above.

When computing the weighted average of the coordinates, the nearest point (B) gets the higher weight (3/4).

-25x+800=0

-25x =-800

25x=800

x=32

Answer:

x = 32

Step-by-step explanation:

0=-25x+800

To solve for x, add 25x to each side

0+25x=-25x+800+25x

25x = 800

Divide each side by 25

25x/25 = 800/25

x = 32

Answer:

1/2 & 0.5

Step-by-step explanation:

Answer: -3/4

Step-by-step explanation:

The statistical test in which the mean difference between two groups are compared to a distribution of differences between means is (b) paired-samples t-test.

The t-test, one of the most used statistical tests, is used to ascertain whether the means of two groups are equal. The test's underlying presumption is that samples from normal distributions with similar variances were used for both groups.

The two means are equal, which is the null hypothesis; otherwise, they are not. We can calculate a t-statistic that will follow a t-distribution with n1 + n2 - 2 degrees of freedom under the null hypothesis.

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1) The percentage of the products last between 9 and 15 days is 68.26%.

2)The percent of the products last between 12 and 15 days is 34.13%.

3) The percentage of the people in line waited for more than 28 minutes 2.28%.

4) The percentage of the people wait for less than 16 minutes 15.87%

Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. As an illustration, 1% of 1,000 chickens is equal to 1/100 of 1,000, or 10 birds, and 20% of the quantity is equal to 20% of 1,000, or 200.

What is the number whose 20% is 150?

20% of 150 is 30.

1) µ = 12

sd = 3

a) P(9<X<15)=P

(\frac{9-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{15-\mu}{\sigma})

9-12\sP(\s15\s12

= P(-1 < Z < 1)

= P(Z < 1) - P(Z < -1)

= 0.8413 - 0.1587

= 0.6826

= 68.26%

b) P(12<X<15)=P

(\frac{12-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{15-\mu}{\sigma})

12 - 12\sP(\s15\s12

= P(0 < Z < 1)

= P(Z < 1) - P(Z < 0)

= 0.8413 - 0.5

= 0.3413

= 34.13%

c) P(X6) = P(frac X-mu sigma frac 6 mu sigma)

=P(Z<\frac{6-12}{3})

= P(Z < -2)

= 0.0228

= 2.28%

d) P(X>15)=P(frac X–mu–sigma>frac X–mu–sigma)

=P(Z>\frac{15-12}{3})

= P(Z > 1)

= 1 - P(Z < 1)

= 1 - 0.8413

= 0.1587

= 15.87%

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lllhl and hllll are considered different series, despite the lakers winning in 4 games in both series.The total number of possible different series is 70.

A collection of similar items or occasions occurring in close proximity to one another over time or space. a series of concerts. The corridor led to a string of compact rooms. a group of often broadcast television shows, each of which stands alone as a complete program. the shown sum of a typically endless series of...

Sequence and series types

arithmetic progressions

Sequences in geometry.

Harmonic patterns.

a fibonacci sequence.

We have to clculate nuber of series in which lakers win:

if lakers win the champion ship they must win the last game played

if there are n games played, the lakers must win the nth game and 3 games before the nth game.

since the outcome of the nth game is fixed

lakers can win 3 games out of the first n-1 in (n-1C3) ways .

if n games are played lakers can win the championship in  (n-1C3) ways  

n can vary from 4 to 7

no of series in which lakers can win =(3C3)+(4C3)+(5C3)+(6C3)=35

The total number of possible different series =2x25= 70.

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( g - 14)² is factor of equation .

What is factor ?

A number that divides another number by itself with no residual is known as a factor.The factors of 8 are the numbers that divide 8 exactly without leaving any remainder. There are four factors of 8, they are 1, 2, 4, and 8.

             In other words, if multiplying two whole numbers results in a product, the numbers we are multiplying are factors of the product since the product is divisible by them. Since the numbers we are multiplying are divisible by the product, they are factors of the product.

g2 − 28g + 196

= g² - 14g - 14g + 196

= g( g- 14 ) - 14( g - 14 )

= ( g - 14) ( g - 14)

= ( g - 14)²

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The complete question is -

One of the factors of g2 -28g + 196 is a. g-7 b. g-14 c. g+14 d. g+7

The solution is Option D.

The equation of line that passes through the point P ( 4 , -3 ) and the point Q ( 0 , -2 ) is y = ( -1/4 )x - 2

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the first point be P = P ( 4 , -3 )

Let the second point be Q = Q ( 0 , -2 )

Now , the slope of the line passing through the points is calculated from the formula slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( -2 - ( -3 ) ) / ( 0 - 4 )

Slope m = ( -2 + 3 ) / -4

Slope m = -1/4

Now , the equation of line is given by

y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - ( -3 ) = ( -1/4 ) ( x - 4 )

On simplifying the equation , we get

y + 3 = ( -1/4 )x + 1

Subtracting 3 on both sides of the equation , we get

y = ( -1/4 )x - 2

Therefore , the value of A is y = ( -1/4 )x - 2

Hence , the equation of line is y = ( -1/4 )x - 2

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Answer:

$3.90

Step-by-step explanation:

3.65 / 3 = 1.22

1.22 x 3.2 = 3.90

Answer:

The day before, Mike had 34 apples. Today, he had 24 times as much as the apples that he had the day before. How many apples did he have today?

Step-by-step explanation:

1st, gather information: The day before, Mike had 34 apples, Today, he had 24 times as much as the apples that he had the day before

2nd, plan to solve: I will do 34 x 24.

3rd, Solve: 34 x 24= 816.

4th, is it resonable? : Yes. 816/34=24.

Therefore, the probability that the lifetime X of the first component exceeds 5 is 0.006737, based on process.

Probability theory examines numerical illustrations of the probability that an event will happen or that a statement is true. An event's probability is expressed as a number between 0 and 1, with 1 generally denoting certainty and 0 generally denoting impossibility.

Here,

f(x,y) =[tex]xe^{-x(1+y)}[/tex]

Took the double integral of the equation above, first the integral with respect to y (from 0 to infinity) and then with respect to x (from 5 to infinity).

therefore the integration,

[tex]\int\limits^ {infinity}_0{xe^{-x(1+y)} } \, dx[/tex]

[tex]\left \{ {{y=infinity} \atop {x=0}} \right. \frac{-x}{y+1} e^{-x(y+1)} + \frac{1}{y+1} \int\limits^{infinity} _0{ e^{-x(y+1)} \, dx[/tex]

[tex]=\frac{1}{(y+1)^2}[/tex]

[tex]fX(x)[/tex] is easier with:fX(x) =[tex]\int\limits^{infinity}_0 {x}e^{-(x(y+1))} \, dy[/tex]=[tex]xe^{-x} \int\limits^{infinity}_0 x {e^{-xy} } \, dy=e^{-x}[/tex]

We get

We used u substitution to end up with    [tex]e^{-x(1+y)}[/tex] which is needed to evaluate from 0 to infinity, which left me with [tex]e^{-x}[/tex]

Then the integral with respect to x from 5 to infinity which left with an answer of [tex]e^{-5}[/tex]

So the probability that the lifetime X of the first component exceeds 5 is 0.006737, based on my process.

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