how do you estimate mathematical models?

The process of arriving at an approximate answer to a computation such as 0.79 × 403 is called estimation.

Having an approximate estimate of something's worth, number, size, or extent is referred to as estimation in mathematics. When we are willing to accept a response that is extremely near to the true result, we utilize estimates of numbers to make mental computations simpler and faster.

The computation is approximate, or the number is rounded to the nearest place value.

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a) The distribution of sample means of 100 registered nurses in the city is approximately normal, with mean $31 and standard deviation of $0.5.

b) The probability that the average hourly rate of the 100 nurse sample exceeds $31.50 is of: 0.1587 = 15.87%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for this problem are given as follows:

[tex]\mu = 31, \sigma = 5, n = 100, s = \frac{5}{\sqrt{100}} = 0.5[/tex]

The probability that the average hourly rate of the 100 nurse sample exceeds $31.50 is one subtracted by the p-value of Z when X = 31.5, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem:

[tex]Z = \frac{X - \mu}{s}[/tex]

Z = (31.5 - 31)/0.5

Z = 1

Z = 1 has a p-value of 0.8413.

1 - 0.8413 = 0.1587 = 15.87%.

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Answer:

Step-by-step explanation:

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Answer:

0.35

Step-by-step explanation:

The correct option regarding the quotient of the two fractions is given as follows:

B. [tex]\frac{(4x^2 + 6)(x + 2)}{10x^2 + 15}[/tex], no values must be excluded.

The division of two fractions is given by the multiplication of the first fraction by the inverse of the second fraction.

The first fraction for this problem is given as follows:

(4x² + 6)/(x - 2).

The second fraction for this problem is given as follows:

(10x² + 15)/(x² - 4).

Applying the subtraction of perfect squares, we have that:

x² - 4 = (x + 2)(x - 2).

Then the division of the two fractions is given as follows:

(4x² + 6)/(x - 2) x [(x + 2)(x - 2)/(10x² + 15)]

Simplifying the x - 2 terms, we have that:

[tex]\frac{(4x^2 + 6)(x + 2)}{10x^2 + 15}[/tex]

No values must be excluded, as the denominator would be never zero, as:

10x² + 15 = 0

10x² = -15.

x² is always positive, hence 10x² will never be equals to -15.

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Answer: 464

Step-by-step explanation: 232+232 = 464

Answer:

464 is answer very easy.........

Answer:

f(1) = 7

Step-by-step explanation:

f(1) has x = 1 in the interval x < 2 with f(x) = - 2x + 9 , then

f(1) = - 2(1) + 9 = - 2 + 9 = 7

Answer:

Let's call the number of seats in the first aircraft "x", the number of seats in the second aircraft "y", and the number of seats in the third aircraft "z".

From the problem statement, we know that:

x = y + 88 (the first aircraft has 88 more seats than the second aircraft)

z = 2y - 103 (the third aircraft has 103 seats less than twice the seating capacity of the second aircraft)

x + y + z = 1909 (the total number of seats in all three aircraft is 1909)

We can substitute the first equation into the third equation to get:

y + 88 + 2y - 103 = 1909

3y = 2000

y = 666 (the number of seats in the second aircraft)

Now that we know the number of seats in the second aircraft, we can use the first and second equations to find the number of seats in the other two aircraft:

x = y + 88 = 666 + 88 = 754 (the number of seats in the first aircraft)

z = 2y - 103 = 2(666) - 103 = 1229 (the number of seats in the third aircraft)

So, the first aircraft has 754 seats, the second aircraft has 666 seats and the third aircraft has 1229 seats.

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Answer: The first aircraft has 265 seats, the second aircraft has 177 seats and the third aircraft has 248 seats.

Step-by-step explanation:

Let's call the number of seats for the first aircraft x, the number of seats for the second aircraft y, and the number of seats for the third aircraft z.

From the problem, we know the following:

x = y + 88 (the first aircraft has a capacity of 88 more seats than the second aircraft)

z = 2y - 103 (the third aircraft has 103 seats less than twice the seating capacity of the second aircraft)

x + y + z = 1909 (the total number of seats for all three aircraft is 1909)

We can use the first equation to substitute for x in the second and third equations:

y + 88 = y + 88

2y - 103 = z

Now we have a system of equations:

y + 88 + y + 2y - 103 + z = 1909

4y + z = 2000

We can use the first equation to find y:

y = (1909 - 88 - 103) / 4 = 709 / 4 = 177

Now we can substitute this value of y back into the first equation to find x:

x = y + 88 = 177 + 88 = 265

and substitute it back into the second equation to find z:

z = 2* 177 - 103 = 248

So the first aircraft has 265 seats, the second aircraft has 177 seats and the third aircraft has 248 seats.

The change between outputs found by dividing one output by its previous output is called output elasticity.

What is output elasticity?

Output elasticity is defined as the division of change in output by change in input which is the previous output.

General, elasticity is a concept that is used to measure the change in the aggregate quantity demanded of a good or service in relation to price movements of that good or service.

A product is considered to be elastic if the quantity demand of the product changes more than proportionally when its price increases or decreases.

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Answer: By SSS, ΔSUR ≅ ΔTVR.

Step-by-step explanation:

This might be a longer method, but still here you go.

Given, ΔSTU ≅ ΔTSV

By CPCT, we have the following.

∠TUS / ∠RUS = ∠SVT / ∠RVT  ----   1

SU = TV   ----    2

SV = TU ---- 3

∠STU / ∠STR = ∠TSV / ∠TSR

Now, in the triangle TRS,

TR = SR ( ∠TSR = ∠STR) ---- 4

SV= TU

SV - SR = TU - TR (SR= TR)

UR = VR ---- 5

Now, we can use SSS in the triangles ΔSUR and ΔTVR

SU = TV (2)

SR = TR (4)
UR = VR (5)
Therefore, by SSS, ΔSUR ≅ ΔTVR.
Cheers

As x gets very large , the function that becomes largest is y = 5x^3

An exponential function is a Mathematical function in the form f (x) = a^x, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

An exponential function is defined by the formula f(x) = a^x, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x. Where a>0 and a is not equal to 1. x is any real number.

This means that the greater the power of x , the larger the function of y.

For example, If y = 5x^n , as n increases the value of x increases and the value of y will increase also.

Therefore the largest function as x becomes large is y = 5x^3

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Answer:

12/35

Step-by-step explanation:

2/7 / 5/6

= 2/7 x 6/5
= 12/35

The value of  2(3 + 2) to the third power minus 6 is 2.187.

An expression is combination of variables, numbers and operators.

The given sentence is 2(3 + 2) to the third power minus 6

Mathematically is can be written as [tex]2(3+2)^{\frac{1}{3}-6}[/tex]

Let us solve the exponent part

1/3-6

1-18/3=-17/3

Now [tex]2(3+2)^{\frac{-17}{3}}[/tex]

[tex]10^{-5.6}[/tex]

2.187

Hence, the value of  2(3 + 2) to the third power minus 6 is 2.187.

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Answer: The probability of not taking a yellow ball can be found by using the formula:

Probability of event A = (Number of favorable outcomes) / (Total number of outcomes)

In this case, the event of not taking a yellow ball is the favorable outcome, and the total number of outcomes is the total number of balls in the bag, which is 10 yellow, 5 orange, and 5 green balls. So, the total number of outcomes is 20.

The number of balls that are not yellow is 5 orange + 5 green = 10.

So, the probability of not taking a yellow ball is

Probability of not taking a yellow ball = (Number of non-yellow balls) / (Total number of balls) = 10/20 = 1/2

So the answer is 1/2.

Step-by-step explanation:

The estimates of the area under the curve using rectangles is given as follows:

The area under a curve is approximated using the definite integral of the function that defines the curve within it's bounds.

As it is specified that the area should be approximated using rectangles, a Left Riemann Sum will be used to approximate the area.

With two rectangles, the Delta value is obtained as follows:

[tex]\Delta_x = \frac{9 - (-9)}{2}[/tex]

[tex]\Delta_x = 9[/tex]

The values of x are obtained with the rule presented as follows:

[tex]x_i = a + \Delta_x(i - 1)[/tex]

With two rectangles, the values are given as follows:

-9 and -9 + 9 = 0.

The numeric values are given as follows:

The definite integral is given as follows:

[tex]\sum_{i = 1}^n = \Delta_xf(x_i)[/tex]

Hence the result is of:

9 x 81 = 729 units squared.

With four rectangles, the Delta value is given as follows:

[tex]\Delta_x = \frac{9 - (-9)}{4} = 4.5[/tex]

Hence the values of x are:

x = -9, x = -4.5, x = 0, x = 4.5.

The numeric values are:

Hence the result of the integral is given as follows:

4.5(60.75 + 81 + 60.75) = 911.25 units squared.

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Answer:

Step-by-step explan

THATS A U PROBLEM!

Answer:18,9

Step-by-step explanation:

9x1=9 9x2=18

Answer:

The distance between two points in the coordinate plane can be found using the distance formula, which is:

distance = √((x2 - x1)^2 + (y2 - y1)^2)

In this case, the two points are (3,2) and (6,0), so we can plug in the values to get:

distance = √((6 - 3)^2 + (0 - 2)^2)

distance = √((3)^2 + (-2)^2)

distance = √(9 + 4)

distance = √13

So the distance between the two points (3,2) and (6,0) is approximately 3.61 units.

Answer:

11(c)-9

Step-by-step explanation:

The product is the result of multiplication, so the product of 11 and c looks like: 11*c or 11(c).

Nine less means subtract, so we simply subtract from the above to get:

11(c)-9 or I suppose another answer could be -9+(11(c))

The unknown side length x is 65 units.

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

Given:

Perpendicular = 33

Base = 56

Using Pythagoras theorem

H² = P² + B²

H² = 56² + 33²

H²= 3136 + 1089

H² = 4225

H= √4225

H = 65

Hence, the unknown length is 65 units.

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Answer:

Step-by-step explanation:

Answer:

3.65

Step-by-step explanation:

3.78

1.30

___

2.48

3-1=2

7-3=4

8-0=8 -

The conclusion of the test hypothesis at the significance level of 0.05 is given as follows:

The results are statistically insignificant at the significance level of 0.05, meaning that there is insufficient evidence to conclude that the mean on the day after Thanksgiving is less than the mean on the day after Christmas.

At the null hypothesis, it is tested if the mean is not greater than 135, that is:

[tex]H_0: \mu = 135[/tex]

At the alternative hypothesis, it is tested if the mean is greater than 135, hence:

[tex]H_1: \mu > 135[/tex]

The test statistic is given by the equation presented as follows:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]\overline{x} = 147, \mu = 135[/tex]

The standard error is obtained as follows:

[tex]s = \sqrt{\left(\frac{49}{\sqrt{57}\right)^2 + \left(\frac{32}{\sqrt{55}\right)^2}}[/tex]

s = 7.79.

Hence the test statistic is of:

t = (147 - 135)/7.79

t = 1.54.

The p-value of the test is obtained considering a right-tailed test, as we are testing if the mean is greater than a value, with 57 + 55 - 2 = 110 df and t = 1.54.

Using a t-distribution calculator, the p-value is given as follows:

0.0632.

Greater than the p-value, hence the result is not significant.

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The linear inequality represented by the graph is defined as follows:

y ≥ -2x + 1.

The ordered pairs that are solutions to the inequality x < -3 are given as follows:

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which the coefficients are given as follows:

The function in this problem crosses the y-axis at y = 1, hence the intercept b is given as follows:

b = 1.

When x increases by one, y decays by two, hence the slope m is given as follows:

m = -2.

The shaded region, considering the solid line, is given by the values to the right of the line, hence the inequality is defined as follows:

y ≥ -2x + 1.

The inequality for this problem is defined as follows:

x < -3.

The ordered pairs have the following format:

(x,y).

Hence all the ordered pairs that have x < -3, no matter the coordinate of y, are solutions to the inequality.

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Gianna is 90 miles far away in 3 hours of driving.

She drove in total of 180 minutes.

The speed can be defined as the rate at which an object covers some distance. Speed can be measured as the distance traveled by a body in a given period of time. The SI unit of speed is m/s.

Given,

Gianna drives 5 miles in 10 minutes

Speed per minute = 5/10 = 0.5 miles/minute

Gianna drove in total for 3 hours

1 hour = 60 minutes

3 hours = 60 × 3 = 180 minutes

Distance Gianna drove in 180 minutes = speed per minute × time

                                                                = 0.5 × 180

                                                                = 90 miles

Hence, Gianna drove 90 miles in 3 hours, 180 minutes is total time she drove.

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Answer:

the first one is the correct answer

The two expressions in the second row and one expression in the first row will be 11t - 2u & 10t + 2u and 21t, respectively.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The three expressions in the third row are given below.

4t - 6u, 7t + 4u, and 3t - 2u

The two expressions in the second row are given as,

4t - 6u + 7t + 4u = 11t - 2u

7t + 4u + 3t - 2u = 10t + 2u

The one expression in the first row is calculated as,

11t - 2u + 10t + 2u = 21t

The two expressions in the second row and one expression in the first row will be 11t - 2u & 10t + 2u and 21t, respectively.

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Answer:

Option 2

Step-by-step explanation:

The associative property of multiplication states that you get the product of the numbers no matter what way you arrange the equation and multiply the numbers, you can begin with any two numbers and go on multiplying with the rest, you get the same product!

Answer: [tex]x=7[/tex]

Step-by-step explanation:

[tex]3^{x-5}=9\\ \\ 3^{x-5}=3^2 \\ \\ x-5=2 \\ \\ x=7[/tex]

Answer:

-3

Step-by-step explanation:

Answer:

Assasination

Step-by-step explanation:

TBH I think this is it. I did some research and this is what I got. weird huh?

Hope this helps :)

The height of the isosceles triangle OPQ is given as follows:

2.41.

An isosceles triangle is a triangle that has two equal side lengths, hence it also has two equal angle measures.

The top angle is of 45º, while the sum of the internal angles of the triangle is of 180º, hence the base angles are obtained as follows:

2x + 45 = 180.

2x = 135

x = 135/2

x = 67.5º.

Then the height is obtained considering a right triangle, in which the height is opposite to an angle of 67.5º, while the adjacent side has length of 1, which is half the base.

Applying the tangent of the angle of 67.5º, the height is obtained as follows:

tan(67.5º) = h/1

h = tan(67.5º)

h = 2.41.

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