What is 9 x (46+70) 5 - 32 (40 - 219) =

It's true, any irrational number squared will result in a rational number

A real number that can NOT be made by dividing two integers (an integer has no fractional part).

"Irrational" means "no ratio", so it isn't a rational number. We aren't saying it's crazy!

Its decimal also goes on forever without repeating.

A counterpart problem in measurement would be to find the length of the diagonal of a square whose side is one unit long; there is no subdivision of the unit length that will divide evenly into the length of the diagonal. (See Sidebar: Incommensurables.) It thus became necessary, early in the history of mathematics, to extend the concept of number to include irrational numbers. Irrational numbers such as π can be expressed as an infinite decimal expansion with no regularly repeating digit or group of digits. Together the irrational and rational numbers form the real numbers.

Irrational numbers are those that cannot be expressed as a fraction of integers.

 If we square the irrational numbers then it becomes rational numbers as it can be shown as ratio of integers.

[tex]\sqrt{3}[/tex]  is a irrational number but by squaring it [tex](\sqrt{3 )^{2}[/tex] is a rational number

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A person who watches 14 hours of TV can do 21.1 sit-ups.

The regression equation is used to predict or estimate the value of the response (or dependant) variables based on an understanding of the explanatory (or predictor) variables.

A regression equation has the following general form:

y = ax + b

Here,

y = dependent variable

x = independent variable

a = intercept

b = slope

The regression equation showing the relationship between the number of sit-ups a person can accomplish (y) and the number of hours of TV viewed each day (x) is:

y = -1.284x + 39.108

Compute the number of sit-ups a person who watches 14 hours of TV can do as follows:

y = -1.284(14) + 39.108

y = -17.976 + 39.108

y = 21.132 ≈ 21.1

Thus, a person who watches 14 hours of TV can do 21.1 sit-ups.

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By dividing the integral of the function over the interval by the length of the interval, the average value of a function can be determined.

The height of the rectangle with an area equal to the area under the curve of the function is the average value of the function or its average height. The equation provides a general definition of it. 1(b−a)∫baf(x)dx.

The average, also known as the arithmetic mean, is calculated by adding a group of numbers and then dividing by their count.

The mean() function in R is used to calculate a vector's mean. The function returns the average as a number after taking a vector as its input.

The general typical equation is numerically communicated as Normal = {Sum of Observations} ÷ {Total number of Observations}.

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The age of the bones from the skeleton of a prehistoric creature is 8460 years.

The formula to be used for the calculation of age is

ln (N/N₀) = -kt

where, N/N₀ represents represents remaining time

k is constant of proportionality

t is age or time period

The remaining time is 100 - 65 = 35

Remaining time = 35% or 0.35

Keeping the values in the above formula, we have

ln (0.35) = - 0.000124 t

-1.049 = -0.000124 t

t = 8459.67 ≈ 8460 years

Thus, the age of the prehistoric creature is 8460 years.

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●(a + b)^2 = a² + 2ab + b²

●(a – b)^2 = a² - 2ab + b²

●(a - b)(a + b) = a² - b²

Define Distributive property

By applying Distributive property solve the following expression,

●(a + b)^2

= (a + b) (a + b)

= a(a + b) + b(a + b)

= a² + ab + ba + b²

= a² + 2ab + b²

●(a – b)^2

= (a - b) (a - b)

= a(a - b) - b(a - b)

= a² - ab - ba + b²

= a² - 2ab + b²

●(a - b)(a + b)

= a(a + b) - b(a + b)

= a² + ab - ba - b²

= a² - b²

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If numbers is a two-dimensional array, which of the following would give the length of row r is d. numbers[r].length

A two-dimensional array is a data structure used to store data in a tabular format, consisting of rows and columns. Each element in the array is accessed by two indices, one for the row and one for the column. The length of a row in a two-dimensional array can be determined by accessing the array at the specified row and then returning the length of that row. To do this, the expression numbers[r].length can be used, where 'numbers' is the name of the two-dimensional array, and 'r' is the index of the row whose length is being determined.

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The four types of probability sampling methods are

1. Simple random sampling

2. Stratified sampling

3. Systematic sampling

4. Cluster sampling

Probability sampling is a sampling method that involves randomly selecting a sample, or a part of the population that you want to research.

1. Simple Random Sampling: Simple random sampling gathers a random selection from the entire population, where each unit has an equal chance of selection. This is the most common way to select a random sample.

2. Stratified Sampling: Stratified sampling collects a random selection of a sample from within certain strata, or subgroups within the population. Each subgroup is separated from the others on the basis of a common characteristic.

3. Systematic Sampling: Systematic sampling draws a random sample from the target population by selecting units at regular intervals starting from a random point. This method is useful in situations where records of target population already exist.

4. Cluster Sampling: Cluster sampling is the process of dividing the target population into groups, called clusters. A randomly selected subsection of these groups then forms the sample. It usually involves existing groups that are similar to each other in some way

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The probability of a coin landing on heads 4 times in a row is 1/16 or, 6.25%, the probability of flipping a coin and it landing heads is 1/2 or, 50%, the probability that exactly four students toss heads at least 4 times each is 1/16 or, 6.25%, and the probability of getting heads both times the coin is flipped is 0.25.

There are different situations for us stated as -

(a) What is the probability of a coin landing on heads 4 times in a row?

(b) What is the probability of flipping a coin and it landing heads?

(c) What is the probability that exactly four students toss heads at least 4 times each?

(d)What is the probability of flipping a coin and getting heads both times?

We have to find out the probability of the given situations happening.

(a) It is known to us that a coin is flipped.

We have to determine the probability of this coin landing on heads 4 times in a row.

In order to get 4 heads in a row, the coin should be flipped 4 times.

For n (say) number of heads, the value of n = 0, 1, 2, 3, 4

Total number of possible outcomes = 16

It can be concluded that there is only one possible outcome that will result in the coin landing on 4 heads where each flip ends up as a head.

So, the probability = 1/16

Thus, the probability of a coin landing on heads 4 times in a row is 1/16 or, 6.25%.

(b) It is known to us that a coin is flipped.

We have to find out the probability of this flipped coin landing on heads.

When a coin is flipped in the air, there is always 50% chance of the coin landing on heads and a 50% chance of the coin landing on tails.

So, the probability = 1/2

Thus, the probability of flipping a coin and it landing heads is 1/2 or, 50%.

(c) It is known to us that exactly four students toss coins.

We have to determine the probability that exactly four students toss heads at least 4 times each.

As mentioned in the previous part of the question, there is always 50% chance of the coin landing on heads.

So, the probability of getting heads when the coin is flipped first = 1/2

=> the probability of getting two heads in a row = 1/2 * 1/2 = 1/4

=> the probability of getting three heads in a row = 1/2 * 1/4 = 1/8

=> the probability of getting four heads in a row = 1/2 * 1/8 = 1/16

Thus, the probability that exactly four students toss heads at least 4 times each is 1/16 or, 6.25%.

(d) It is known to us that a coin is flipped.

We have to find out the probability of getting heads both times.

Since, there is always 50% chance of the coin landing on heads. So, the probability of getting heads both times = 0.5 * 0.5 = 0.25

Thus, the probability of getting heads both times the coin is flipped is 0.25.

Therefore, the probability of a coin landing on heads 4 times in a row is 1/16 or, 6.25%, the probability of flipping a coin and it landing heads is 1/2 or, 50%, the probability that exactly four students toss heads at least 4 times each is 1/16 or, 6.25%, and the probability of getting heads both times the coin is flipped is 0.25.

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According to the triangle inequality theorem; D)2,3,6 can not be the lengths of the sides of a triangle

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side of that triangle  

If the two shortest sides are put end to end, they should be longer than the longest side to be able to angle up to form a triangle.

Therefore applying this theorem in this case;

A) 2,3,4: The sum of 2 and 3 = 5; which is greater than 4

B) 2,3,2: The sum of 2 and 2 = 4; which is greater than 3

C) 2,3,3: The sum of 2 and 3 = 5; which is greater than 3

D) 2,3,6: The sum of 2 and 3 = 5; which is not greater than 6; therefore according to the triangle inequality theorem these cannot be the lengths of the sides of a triangle.

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Although part of your question is missing, you might be referring to this full question: Use the exponential regression equation that best fits the data (10, 4), (12, 20), (13, 35), and (16, 300) to estimate y when x = 15.

The estimated y value at x = 15 is 147.

The exponential regression equation in general has form y = a*b^x.

And from the attached graph, it is shown that:

a ≈ 0.0038

b ≈ 2.0223

So, using the exponential regression calculator, the exponential model created by the data is:

y = a*b^x

y = 0.0038*(2.0223)^x

And when x = 15, thus:

y = 0.0038*(2.0223)^15

y ≈ 147

Hence, the estimated y value at x = 15 is 147.

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The mean of x is 1.8 and standard deviation of X is 0.98 using calculations for mean and standard deviation by given values or data.

What is mean and standard deviation?

The standard deviation is a summary measure of the differences of each  observation from the mean.

In the given que:

X         1     2     3     4

P(X)     .5   .3     .1      .1

For mean :

Mean = 1(.5) + 2(.3) + 3(.1) + 4(.1)

          = 1.8

For standard deviation :

Standard deviation = √.5(1-1.8)² + .3(2-1.8)² + .1(3-1.8)² + .1(4-1.8)²

                                = .98

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Answer:

Left shift, 6 units

Step-by-step explanation:

In the equation:

f(x)=3 |x+6| +9

the " +6 " in close to the x represents the horizontal shift. X always tells us about horizontal or right/left moves. So an adjustment to the x is a horizontal adjustment.

But Caution! It is the opposite of what you might think. A PLUS6 is a LEFT shift. (While a MINUS6 would be a right shift, not the case here).

The parent function is:

f(x) = |x|

So our equation:

f(x)=3 |x+6| +9

has two changes made to it. LEFT6 because of the

" +6 " by the x. And the +9 tacked onto the end of the equation is a vertical shift UP9.

The fraction of Josh's height which is 2/3 of Josh's current height indicates that the equation that can be used to  find Josh's height and Josh's current height are;

a. (2/3) × h 4 1/2 feet

b. 6 3/4 feet

A fraction of an item is a representation of the whole or entire of the item.

Josh's height two years ago = (2/3) × Josh's height now

Hosh's height two years ago = 4 1/2  feet

a. Josh's current height, = h

An equation is mathematical statement that joins two equivalent expressions with an equal to sign.

(2/3) of Josh's current height is equivalent to Josh's initial height of 4 1/2 feet.

The equation that can be written to solve for h is therefore;

b. h = (4 1/2)/(2/3) = (4 1/2) × 3/2

4 1/2 = 9/2

Therefore;

h = 9/2 × 3/2 = 27/4 = 6 3/4

Josh's current height, h = 6 3/4 feet

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Answer:

To solve the absolute value inequality 4x+7

3

< 8, we need to first isolate the absolute value expression on one side of the inequality. We can do this by dividing both sides of the inequality by 3, which gives us 4x+7<24.

Next, we need to consider two cases, depending on whether the quantity inside the absolute value is positive or negative. If the quantity inside the absolute value is positive, then the inequality will remain unchanged. In this case, we have 4x+7<24, which we can solve by subtracting 7 from both sides to get 4x<17, and then dividing both sides by 4 to get x<4.25.

If the quantity inside the absolute value is negative, then the inequality will be reversed. In this case, we have 4x+7>24, which we can solve by subtracting 7 from both sides to get 4x>17, and then dividing both sides by 4 to get x>4.25.

Therefore, the solution to the inequality 4x+7

3

< 8 is the set of all values of x that are less than 4.25 or greater than 4.25. We can write this solution in interval notation as (-∞,4.25)∪(4.25,∞), or as a union of two disjoint intervals: (-∞,4.25) and (4.25,∞).

Step-by-step explanation:

The amount deposited in an account that pays 3% and 7% of interest will be $225 and $775, respectively. Then the correct option is D.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

You have $1000 to put resources into two distinct records. To set aside the cash you really want for school, you really want to average a 6.1 percent premium. Assuming the two records pay a 3% and 7 % premium.

Let 'x' be the amount deposited in an account that pays 3% of interest. Then the amount deposited in another account that pays 7% of interest is (1000 - x). Then the equation is given as,

0.03x + 0.07(1000 - x) = 0.061 × 1000

Simplify the equation, then we have

0.03x + 0.07(1000 - x) = 0.061 × 1000

0.03x + 70 - 0.07x = 61

-0.04x + 70 = 61

0.04x = 70 - 61

0.04x = 9

x = 9 / 0.04

x = $225

Then the amount in the second account will be given as,

⇒ $1000 - $225

⇒ $775

The amount deposited in an account that pays 3% and 7% of interest will be $225 and $775, respectively. Then the correct option is D.

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The histogram that represents the data-set in this problem is given by the image shown at the end of the answer.

An histogram is a graph that shows the number of times each element of x was observed.

For this problem, the elements are divided in ranges, hence the histogram will give the number of elements in each range that was observed.

The ranges for this histogram are given as follows:

The number of elements in each range is given as follows:

Meaning that the third histogram, from the top down, is the correct option.

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The 95% confidence interval for difference in mean drying times of two type of paints is (4.90, 17.50). This suggests that Type A takes between 4.90 and 17.50 hours more to dry than type B paint.

Given that,

A paint's formula was altered by the manufacturer to hasten drying time. 11 cans of type A (the original paint) and 9 cans of type B (the modified paint) were randomly chosen at random and applied on comparable surfaces. The drying periods were measured in hours. The following are the statistics in brief.

Type A                 Type B

Sample-1             Sample-2

x₁ = 76.3 hrs        x₂ = 65.1 hrs

s₁ = 4.5 hrs          s₂ = 5.1 hrs

n₁ = 11                   n₂ = 9

We have to create a 98% confidence interval for the range 1–2, which represents the difference in the average drying time for paint cans of types A and B.

We know that,

Consider about Type A, which is the original paint, and Type B, which is the changed paint.

The difference between the mean drying time for paint cans of type A and the mean drying time for paint cans of type is within a 98% confidence interval, and it is as follows:

4.90 < μ₁ - μ₂ < 17.50

Therefore, The 95% confidence interval for difference in mean drying times of two type of paints is (4.90, 17.50). This suggests that Type A takes between 4.90 and 17.50 hours more to dry than type B paint.

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The length of each Plan A workout will be 1.25 hours and the length of each Plan B workout will be 1.25 hours.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Let 'x' be the number of hours of plan A and 'y' be the number of hours of plan B. Then the equations are given as,

2x + 6y = 10

x + 3y = 5            ...1

5x + 3y = 10        ...2

Subtract equation 1 from equation 2, then we have

5x - x = 10 - 5

4x = 5

x = 1.25 hours

Then the value of 'y' is calculated as,

1.25 + 3y = 5

3y = 3.75

y = 1.25

The length of each Plan An exercise will be 1.25 hours and the length of each Plan B exercise will be 1.25 hours.

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The value of x in the diagram is 80°

What is an isosceles triangle?

Isosceles triangles are those triangles that have at least two sides of equal measure. We know that triangles are three-sided enclosed polygons and they are classified as equilateral, isosceles, and scalene, based on the length of their sides. In this article, we will learn about the definition of an isosceles triangle and its properties.

The body of the calculation is attached in a document.

In conclusion the value of x is 80°

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The greatest quotient is 292 and the least quotient will be equal to 45.8.

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per the given information in the question,

The greatest quotient will be,

3 ) 876 (

= 292 and,

The smallest quotient will be,

8) 367 (

= 45.8

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When the net is folded into the rectangular prism

A rectangular prism is a polyhedron in geometry that has two parallel and congruent bases. Another name for it is a cuboid.

Applying science of vision to see technical details in the prism, seeing letter B on the top means that D will be on the bottom.

the side we face will be C while the bac will be A

on the other side, the left end not showing is E and this make up all the part of the prism

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Yes, it is possible that one-to-one function and its inverse are true. If f(f(x)) = x then function and its inverse coincide.

If each x-value corresponds to exactly one y-value, the function is said to be one-to-one.  Inverse function graphs are reflections of the y = x line. This indicates that there can be only one y-value for each x-value. One-to-one functions are those that fit this description.

Inverse of function is represented by [tex]f^{-1} (x)[/tex].

Test to check inverse function: If and only if no horizontal line intersects the graph of f at more than one location, then the function f is one-to-one and possesses an inverse function.

Example: f(x) = 5-x

f(f(x))= 5- (5-x) = x

So above function is one to one and inverse of itself.

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Answer:

c

Step-by-step explanation:

In the ellipse, the center is (-3/2,5/2) semi-major axis is 2√3 and the semi-minor axis is 2.

What is ellipse?

In addition to being drawn outside the ellipse, the directrix of the ellipse is parallel to its latus rectum. There are two directions on the ellipse that are parallel to its principal axis. The ratio of distances between any point on an ellipse and its foci, as well as the directrix of the ellipse, is used to define an ellipse's eccentricity, and it is less than 1.

6x^(2)+2y^(2)+18x-10y+2=0

[tex]\frac{\left(x-\left(-\frac{3}{2}\right)\right)^2}{2^2}+\frac{\left(y-\frac{5}{2}\right)^2}{\left(2\sqrt{3}\right)^2}=1[/tex]

[tex]\left(h,\:k\right)=\left(-\frac{3}{2},\:\frac{5}{2}\right),\:a=2,\:b=2\sqrt{3}[/tex]

[tex]\mathrm{Ellipse\:with\:center}\:\left(h,\:k\right)=\left(-\frac{3}{2},\:\frac{5}{2}\right),\:\:b=2\sqrt{3},\:\:a=2[/tex]

Hence, In the ellipse, the center is (-3/2,5/2) semi-major axis is 2√3 and the semi-minor axis is 2.

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Answer: $37.80

Step-by-step explanation: To calculate the percentage of the discount, we should recall the formula:

Percent = whole number * part percent / 10

So, now we should plug in the numbers

42 * 10 / 100

so 42 * 10 = 420

So, 420 / 100 = 4.2

Now, we subtract 4.20 from 42 and get $37.80. We don't need to worry about tax, because It isn't listed and it said "the price BEFORE tax." I hope this helped.

If a decision maker wishes to reduce the margin of error associated with a confidence interval estimate for a population mean, she can decrease the sample size. So the option a is correct.

If a decision maker wishes to reduce the margin of error associated with a confidence interval estimate for a population mean, then we have to explain what she can:

decrease the sample size.

increase the confidence level.

increase the sample size.

increase the sample size.

As we know that;

The formula of Margin of Error is;

ME = Z(α)× √σ^2/n

where; ME = margin of error

α = confidence level

z(α) = quantile

σ = standard deviation

n = sample size

So as we can see that Margin of Error is inversely proportion to sample size.

So, if a decision maker wishes to reduce the margin of error associated with a confidence interval estimate for a population mean, she can decrease the sample size. So the option a is correct.

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The equation of the transformed function is f(x) = -3(x + 4) + 4

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

g(x) = x² -- parent function

The parent function is represented by the blue line

From the graph, we can see that:

Mathematically, this can be represented as

f(x) = -3g(x + 4) + 4

Substitute the known values in the above equation, so, we have the following representation

g'(x) = -3(x + 4) + 4

So, we have

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

Hence, the transformed function is f(x) = -(x + 4) + 4

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Answer:

  x = √41

Step-by-step explanation:

Given a right trapezoid with bases 10 and 14, and height 5, you want the length of the angled side, x.

The length x is the hypotenuse of a right triangle with one leg 5 units and the other leg (14 -10) = 4 units. It can be found using the Pythagorean relation:

  c² = a² +b²

  x² = 5² +4² = 25 +16 = 41

  x = √41 . . . . . take the square root

Answer: 84 feet and 10 ¼ inches

Step-by-step explanation:

The percent increase in the cost to Deb, to fly from Boston to Hartford is  25%

If the airline charges an additional $50 baggage fee then the percent increase would be 41.67%

The percent increase to Deb to fly from Boston to Hartford can be found by the formula:

= ( Cost to fly now - Cost to fly two weeks ago ) / Cost to fly two weeks ago

= ( 375 - 300 ) / 300

= 0. 25

= 25%

If an  additional​ $50 baggage fee is added to the new price, the percent increase is:

= ( (375 + 50 ) - 300 ) / 300

= 41.67%

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