Whenever a sampled population is normally distributed or whenever the conditions of the central limit theorem are fulfilled, the sample mean is a(n):

The area of the isosceles triangle with sides of 13 and a base of 10 is 60 square units.

To find the area of an isosceles triangle with sides of 13 and a base of 10, we can use the formula for the area of a triangle: A = 1/2 * b * h, where b is the length of the base and h is the height of the triangle.

Since the triangle is isosceles, we know that the two sides with length 13 are equal. Let's call the height of the triangle h. We can draw an altitude from the vertex opposite the base to the midpoint of the base. This will split the isosceles triangle into two congruent right triangles.

Using the Pythagorean theorem, we can find the height of one of the right triangles:

a^2 + b^2 = c^2

where a and b are the legs of the right triangle (which are half of the base, or 5), and c is the hypotenuse (which is one of the sides with length 13):

5^2 + h^2 = 13^2

25 + h^2 = 169

h^2 = 144

h = 12

Now we can plug in the values we have into the formula for the area of a triangle:

A = 1/2 * b * h

A = 1/2 * 10 * 12

A = 60

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The solutions to the inequality are:

C) 5.6

D) 5.75

E) 6

To solve the inequality y + (-8) > -2.5, we can isolate the variable y by adding 8 to both sides:

y + (-8) + 8 > -2.5 + 8

y > 5.5

Therefore, any value of y that is greater than 5.5 will satisfy the inequality.

From the options given:

A) 5.25 is not greater than 5.5, so it is not a solution.

B) 5.5 is equal to 5.5, and we need values greater than 5.5, so it is not a solution.

C) 5.6 is greater than 5.5, so it is a solution.

D) 5.75 is greater than 5.5, so it is a solution.

E) 6 is greater than 5.5, so it is a solution.

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The closest answer to the total volume of the can is approximately 215.8 cubic inches.

To find the volume of a cylinder, we use the formula V = πr²h, where r is the radius of the base of the cylinder and h is the height.

Given that the diameter of the can is 6.2 inches, we can find the radius by dividing it by 2: r = 6.2/2 = 3.1 inches.

We also know that the height of the can is 7 inches.

Substituting these values into the formula, we get:

V = π(3.1)²(7)

V ≈ 215.8 cubic inches

When dealing with real-world measurements, it is common to have some degree of error or uncertainty in the values.

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The value of the expression (9 1/2 - 3 7/8) + (4 4/5 - 1 1/2) is 5 5/8.

To evaluate the expression (9 1/2 - 3 7/8) + (4 4/5 - 1 1/2), we need to first simplify the mixed numbers by converting them into improper fractions.

9 1/2 = 19/2

3 7/8 = 31/8

4 4/5 = 24/5

1 1/2 = 3/2

Now, we can substitute these values in the expression as:

(19/2 - 31/8) + (24/5 - 3/2)

To add or subtract fractions, we need to have a common denominator. In this case, we can use 40 as the common denominator. Therefore, we need to convert the fractions to have a denominator of 40.

(19/2 * 20/20 - 31/8 * 5/5) + (24/5 * 8/8 - 3/2 * 20/20)

Simplifying the fractions, we get:

(380/40 - 155/40) + (192/40 - 30/40)

Combining like terms, we get:

225/40

Now, we need to convert the improper fraction back to a mixed number in simplest form. We can do this by dividing the numerator by the denominator and writing the remainder as a fraction.

225 ÷ 40 = 5 with a remainder of 25

So, the mixed number in simplest form is:

5 25/40

We can simplify this fraction by dividing the numerator and denominator by 5:

5 25/40 = 5 5/8

Therefore, the value of the expression (9 1/2 - 3 7/8) + (4 4/5 - 1 1/2) is 5 5/8.

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The radius of the circle is 24 cm.

Given that, a circle has an arc length of 8π cm and a degree measure of 60°, we need to find the radius of the circle,

The arc length = central angle / 360° × π × diameter

8π = 60° / 360° × π × diameter

Diameter = 48

Radius = 48/2

= 24

Hence, the radius of the circle is 24 cm.

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The ordered pair (0, -7), (1, -4), and (2, -1) are the solution to the equation 3x - y = 7.

Given that:

Equation, 3x - y = 7

In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.

Let x = 0, then the value of 'y' is calculated as,

3 × 0 - y = 7

y = - 7

Let x = 1, then the value of 'y' is calculated as,

3 × 1 - y = 7

y = - 4

Let x = 2, then the value of 'y' is calculated as,

3 × 2 - y = 7

y = - 1

The ordered pair (0, -7), (1, -4), and (2, -1) are the solution to the equation 3x - y = 7.

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Answer:

Step-by-step explanation:

For the first Value of y set x = 4 on the equation
y = 8*4+9

y = 32+9

y = 41

To find the second value of x, set y=0

0 = 8*x + 9

-9 = 8*x

-9/8 = x

x = -9/8

To find the last value of y, set x = 3 on the equation

y = 8*3+9

y = 24+9

y = 33

Rounded to one decimal place, the volume of the prism is approximately 0.0 liters.

To find the volume of the prism, we multiply the length (l), width (b), and height (h) together.

Given:

l = 0.15

b = 40 mm

h = 20 cm

First, let's convert the measurements to the same unit for consistency. We'll convert mm to cm for the width.

b = 40 mm = 4 cm

Now, we can calculate the volume:

Volume = l * b * h

Volume = 0.15 cm * 4 cm * 20 cm

Volume = 12 cm³

To convert the volume to liters, we divide by 1000 since there are 1000 cm³ in 1 liter:

Volume = 12 cm³ / 1000 = 0.012 liters

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Answer:

Step-by-step explanation:

1/5, 4/20/ 3/15, are three fractions equilvent to 2/10.

Answer:

Second Option
[tex]\left(\dfrac{1}{6} \right)\cdot t + \left(\dfrac{1}{5} \right)\cdot t = 1[/tex]

Step-by-step explanation:

Shawna can paint the fence in 6 hours. So her rate of work is 1/6 of the fence in one hour

Kevin can paint the same fence in 5 hours so his rate of work is 1/5

Working together their combined rate
= 1/6 + 1/5

Let the time taken for both of them working together to paint the entire fence be t hours

In t hours
amount of work done by each = rate x time
For Shawna:
[tex]\dfrac{1}{6} \cdot t[/tex]

For Kevin:
[tex]\dfrac{1}{5} \cdot t[/tex]

The total work done must add up to the whole fence which can be represented as 1

Therefore the equation for computing the time taken for both of them to work together is given by

[tex]\dfrac{1}{6} \cdot t + \dfrac{1}{5} \cdot t = 1[/tex]

This is the second option

[tex]-------------------------------------------[/tex]

As an aside
While you have not been asked to solve the problem, we can still do it as an exercise:
[tex]\dfrac{1}{6} \cdot t + \dfrac{1}{5} \cdot t = 1\\\\\rightarrow \left(\dfrac{1}{6} + \dfrac{1}{5} \right) \cdot t = 1\\\\\rightarrow \dfrac{11}{30} \cdot t = 1\\\\t = \dfrac{30}{11} = 2 \dfrac{8}{11} \;hours[/tex]

Answer:

Step-by-step explanation:

The town's population in 2001, as predicted by the equation, was approximately 25446.

According to the given equation yˆ=135.23x−245,121.9, the town's population in year x can be predicted. To find the population of the town in 2001, we need to substitute x = 2001 in the equation.

yˆ = 135.23x − 245,121.9

yˆ = 135.23(2001) − 245,121.9

yˆ = 270568.23 - 245,121.9

yˆ = 25446.33

Therefore, the town's population in 2001, as predicted by the equation, was approximately 25446.33. Rounded to the nearest whole number, the population was 25446.

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Answer:

-2(-6+3y-1) = -6y+14

Step-by-step explanation:

The relation y = -x + 2 is a function because (a) yes, because it passes the vertical line test.

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

y = -x + 2

The above equation is a linear function

As a general rule of functions and relations

All linear functions are functions

This is because they pass the vertical line test

So, the true statement is (a)

Hence, the relation y = -x + 2 is a function because (a) yes, because it passes the vertical line test.

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The equations that have y-coordinate of the y-intercept as positive is 3. h(x) = (x - 1)² and 5. b(x) = (x + 1)(x + 2).

We have,

The graph's intersection with the y-axis is known as the y-intercept. Finding the intercepts for any function with the formula y = f(x) is crucial when graphing the function. An intercept can be one of two different forms for a function. The x-intercept and the y-intercept are what they are. A function's intercept is the location on the axis where the function's graph crosses it.

The y-intercept is obtained when the x-coordinate is 0.

Thus, substitute the value of x = 0:

1. f(x) = x² + 3x - 2

f(x) = 0 + 3(0) - 2

f(x) = -2

False

2. g(x) = x² - 10x

g(x) = 0 - 10(0)

g(x) = 0

3. h(x) = (x - 1)²

h(x) = (0 - 1)²

h(x) = 1

True

4. m(x) = 5x² - 3x - 5

m(x) = 5(0) - 3(0) - 5

m(x) = -5

False

5. b(x) = (x + 1)(x + 2)

b(x) = (0 + 1)(0 + 2)

b(x) = 2

True

Hence, the equations that have y-coordinate of the y-intercept as positive is 3. h(x) = (x - 1)² and 5. b(x) = (x + 1)(x + 2).

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The optimal solution for this LP model is x = 2 and y = 2, with a maximum objective function value of 10

To graph the constraints, we can rewrite each inequality in slope-intercept form:

2x + 2y < 8

y < -x + 4

3x + 2y < 12

y < -1.5x + 6

x + 0.5y < 3

y < -2x + 6

Now we can plot these three lines on a coordinate plane and shade the regions that satisfy each inequality. The feasible region is the region that satisfies all three inequalities.

To find the optimal solution, we need to evaluate the objective function at each corner point of the feasible region and choose the point that maximizes the objective function.

The corner points of the feasible region are (0,0), (0,3), (1.5,3), and (2,2).

Objective function at (0,0): 3(0) + 2(0) = 0

Objective function at (0,3): 3(0) + 2(3) = 6

Objective function at (1.5,3): 3(1.5) + 2(3) = 9

Objective function at (2,2): 3(2) + 2(2) = 10

Therefore, the optimal solution is at (2,2), which gives a maximum value of 3(2) + 2(2) = 10.

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Note that in the above scenario the significance test (z) ≈ -2.25

The right test statistic for this significance test is a z-score.

The formula is

z = (p - p0) / √(p0 (1-p0) / n)

where:

Plugging in the values, we get

z = ( 0.4 - 0.45) / √ (0.45 x0.55 / 500 )

Simplifying this expression, we get....

z = -2.24733287488

z ≈ -2.25

So we can say correctly that test statistic for this significance test is -2.25

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If the test statistic value falls within the critical region, we reject the null hypothesis (H0) at the given significance level (α).

If the test statistic value falls outside the critical region, we do not reject the null hypothesis.

To determine the decision regarding the null hypothesis based on a test statistic value and a critical region, we need to compare the test statistic value to the critical value(s) of the test.

Since the question does not provide information about the significance level or the directionality of the test, we cannot determine the critical region or make a decision about the null hypothesis based on the test statistic value alone.

More information is needed to interpret the result of the test.

At the specified significance level (), we reject the null hypothesis (H0) if the test statistic value is inside the crucial zone.

If the test statistic result is outside of the acceptable range, the null hypothesis is not rejected.

The test statistic value to the test's critical value(s) in order to decide whether to reject the null hypothesis based on a test statistic value and a crucial area.

We cannot establish the crucial area or choose the null hypothesis based only on the test statistic value since the question does not specify the significance level or directionality of the test.

To understand the test's outcome, more details are required.

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Yes, this is accurate, Evaluators must forthrightly report limitations in presented information. It is the duty of evaluators to disclose any restrictions or flaws in the data they offer. This makes it possible to guarantee which decision-makers have a thorough knowledge of the data. These are capable of making judgements based on their advantages and disadvantages.

Evaluators can also pinpoint areas for further research and advancements in data collection and processing methods by admitting shortcomings. By acknowledging limitations, evaluators can also identify areas for future research and improvement in data collection and analysis methods.

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We have expressed x as a ratio of two integers (5194.52178217821 and 99), which shows that x is a rational number.

To show that 52.4699169916991... is a rational number, we need to find a way to express it as a ratio of two integers. Let x = 52.4699169916991...

Since the repeating decimal starts after the second digit, we can multiply x by[tex]10^2[/tex] to obtain:

100x = 5246.99169916991...

Now, we can subtract x from 100x to eliminate the repeating decimal:

100x - x = 5246.99169916991... - 52.4699169916991...

Simplifying the right-hand side gives:

99x = 5194.52178217821...

Dividing both sides by 99 yields:

x = 52.4699169916991... = 5194.52178217821... / 99

Thus, we have expressed x as a ratio of two integers (5194.52178217821 and 99), which shows that x is a rational number.

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The absolute value of the t-statistic is greater than 1.977, then we can reject the null hypothesis that the coefficient is zero at the 0.05 level of significance and conclude that the coefficient is statistically significant.

To determine the critical value of t for testing the significance of each independent variable's coefficient in a regression model with 5 independent variables and 136 observations, we need to use the t-distribution with degrees of freedom equal to the residual degrees of freedom.

The residual degrees of freedom in a regression model with k independent variables and n observations is given by:

residual degrees of freedom = n - k - 1

k = 5 and n = 136, so the residual degrees of freedom are:

residual degrees of freedom = 136 - 5 - 1 = 130

The critical value of t for a two-tailed test with a significance level of 0.05 and 130 degrees of freedom is approximately 1.977 (using a t-distribution table or calculator).

For each independent variable's coefficient, we can test its significance by computing its t-statistic as:

t-statistic = (coefficient estimate - 0) / standard error of the estimate

and comparing it to the critical value of t of 1.977.

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The solutions to the trigonometry equation tan(2x) = x are x = -5.41, -3.80, -2.14, 0, 2.14, 3.80, and 5.41

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

tan(2x) = x

To solve the above equation graphically, we start by splitting the above equation/function as follows

y = tan(2x)

y = x

Next, we plot the graphs of y = tan(2x) and y = x on the same coordinate plane

And finally, we then write out the points of intersection

Using the above as a guide, we have the following:

x = -5.41, -3.80, -2.14, 0, 2.14, 3.80, and 5.41

Hence, the solutions to the equation tan(2x) = x are x = -5.41, -3.80, -2.14, 0, 2.14, 3.80, and 5.41

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Answer:

Solution for What is the percentage increase/decrease from 3000 to 70:

(70-3000):3000*100 =

(70:3000-1)*100 =

2.3333333333333-100 = -97.67

Now we have: What is the percentage increase/decrease from 3000 to 70 = -97.67

Step-by-step explanation:

pls mark brainliest

Answer:

-97.67

Step-by-step explanation:

If x>5, then x+3 is also greater than 5+3=8. Therefore, |x+3| simplifies to x+3. Thus, |x+3| = x+3, if x>5.

The absolute value of a number is its distance from zero on the number line, and it is always a non-negative value. Therefore, if we are given the expression |x+3| and asked to simplify it for x>5, we can use the fact that x+3 is greater than 5+3=8 when x is greater than 5.

Thus, since the absolute value of a number is its distance from zero, we know that |x+3| must be positive when x>5, so we can write:

|x+3| = x+3, if x>5

For values of x less than or equal to 5, |x+3| would have a different simplified form, which would involve a negative sign due to the fact that x+3 would be less than or equal to zero.

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The final temperature of the liquid is 4°C.

Remember that two real numbers are called opposites if their sum is equal to zero, so, A and B are opposites if:

A + B = 0

And neither A or B are zero.

Here the initial tempreatuire is -4°C and the final temperature is T, and it is the opposite of the initial one, then we can write:

-4°C + T = 0

T = 4°C

That is the final temperature.

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Answer:

y = mx + b

Step-by-step explanation:

so you first put the points on the graph and connect them with a slanted line.

Next, for your equation start of with y =

then, your going to find your slope, after you find it put it in front of x (slope x) (Ex; if the slope was 3 then it would look like this 3x)

finally you write + and the y intercept (at which point the line goes through the y axis)

the equation together should look like y = slope x + y intercept

The maximum force, in Newton's, that can safely be applied to the rectangular tile is  735 (N/m²).

We have,

Pressure is defined as a force applied perpendicular to an object's surface per unit area. P = F/A, where P denotes pressure, F denotes force, and A denotes area.

Pressure is indeed a scalar quantity, meaning it has only magnitude and no dimensional vector properties.

For the given question;

A rectangular floor tile has dimensions are given to the nearest 0.1 metres; 1.6m x 2.3m.

The pressure applied of the tile floor is 200 Newton's per square metre (N/m²).

The formula for calculating the pressure is ;

Pressure = Force/area

Thus,

Force = Pressure × area

Force  = 200 × 1.6 × 2.3

Force = 736 (N/m²).

Force = 735 (N/m²) nearest to 5 N/m².

Thus, the maximum force, in Newton's, that can safely be applied to the tile is  735 (N/m²).

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complete question:

A rectangular floor tile is shown.

Its dimensions are given to the nearest 0.1 metres.

1.6m

The tile is only able to sustain a maximum pressure

of 200 Newtons per square metre (N/m²),

correct to the nearest 5 N/m².

Force

Given that Pressure =

Area

work out the maximum force, in Newtons, that can safely be applied to the tile.

2.3m

The given statement " If A and B are n x n and invertible, then A⁻¹B⁻¹ is the inverse of AB." is true because  A and B are invertible matrices, it means that they both have an inverse (A⁻¹and B⁻¹, respectively). The product of A and B, represented by AB, is also an n x n matrix.

To show that A⁻¹B⁻¹is the inverse of AB, we must demonstrate that the product of (AB) and (A⁻¹B⁻¹) results in the identity matrix, which is an n x n matrix with 1s along the diagonal and 0s elsewhere.
To verify this, we'll multiply (AB) with (A⁻¹B⁻¹) and check if the result is the identity matrix:
(AB)(A⁻¹B⁻¹) = A(BA⁻¹)B⁻¹ (associative property of matrix multiplication)
Since B and A^-1 are inverses of each other, their product equals the identity matrix:

A(BA⁻¹)B⁻¹= AI B⁻¹(where I is the identity matrix)
Multiplying A and I doesn't change A:
AI B⁻¹= A B⁻¹
Now, A and B⁻¹are inverses of each other as well, so their product also equals the identity matrix:
A B⁻¹= I
Thus, A⁻¹B⁻¹ is indeed the inverse of AB, as the product of (AB) and (A⁻¹B⁻¹) results in the identity matrix.

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The ratio of the number of large marker boxes to small marker boxes could be 3:8, 6:16, 9:24, or 12:32, depending on how we choose to express it.

The ratio of the number of large marker boxes to small marker boxes in order from the store can be represented by the fraction:

3/8

This fraction comes from the fact that the store orders 3 large marker boxes for every 8 small marker boxes.

To express this ratio in a different form, we can multiply both the numerator and denominator by the same factor, such as 2, 3, or 4. For example:

3/8 = (3x2)/(8x2) = 6/16

3/8 = (3x3)/(8x3) = 9/24

3/8 = (3x4)/(8x4) = 12/32

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The electric monorail slows down by 124 ft between t = 1 and t = 5 seconds. To find the change in the rate of slowing down for the electric monorail transport between t = 1 and t = 5 seconds, we need to calculate the difference in its deceleration at these two points in time.

Given the deceleration formula: 2t + 25 ft/s², let's find the deceleration rates at t = 1 and t = 5:

Deceleration at t = 1:
2(1) + 25 = 2 + 25 = 27 ft/s²

Deceleration at t = 5:
2(5) + 25 = 10 + 25 = 35 ft/s²

Now, we will find the difference in deceleration between these two points in time:

Difference = Deceleration at t = 5 - Deceleration at t = 1
Difference = 35 ft/s² - 27 ft/s²
Difference = 8 ft/s²

The electric monorail slows down by 8 ft/s² between t = 1 and t = 5 seconds. However, this is not listed as one of your options. If you meant to ask how many feet it slows down in total between t = 1 and t = 5 seconds, we can calculate the integral of the deceleration formula:

∫(2t + 25)dt from t = 1 to t = 5

The integral of (2t + 25) is t² + 25t + C. Now, we can evaluate it:

(5² + 25*5) - (1² + 25*1) = (25 + 125) - (1 + 25) = 150 - 26 = 124 ft

So, the electric monorail slows down by 124 ft between t = 1 and t = 5 seconds. Your answer: 124 ft/sec.

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The rate of change of the angle between the ground and the ladder is given by dθ/dt = [rcos(θ)]/[-rsin(θ) + h], θ is the angle between the ladder and the ground, r is the rate at which the top of the ladder is sliding down the wall, and h is the distance from the top of the ladder to the ground.

Let's consider a right triangle formed by the ladder, the wall, and the ground, where the ladder is the hypotenuse of the triangle.

Let's call the angle between the ladder and the ground θ.

To find dθ/dt, the rate of change of θ with respect to time.

The Pythagorean theorem to relate the length of the ladder, the distance the top of the ladder is sliding down the wall, and the distance from the bottom of the ladder to the ground.

We have:

(ladder)² = (wall)² + (ground + sliding distance)²

Differentiating with respect to time, we get:

2ladder(dladder/dt) = 2wall(dwall/dt) + 2 × (ground + sliding distance) × (d(ground+sliding distance)/dt)

Simplifying, we get:

ladder × (dladder/dt) = wall × (dwall/dt) + (ground + sliding distance) × (d(ground+sliding distance)/dt)

Now, we can use similar triangles to relate the angle θ to the lengths of the ladder, the wall, and the ground. Specifically, we have:

tan(θ) = wall/ground

Differentiating with respect to time, we get:

(sec)²(θ) × (dθ/dt) = (dwall/dt) ×ground/ (ground)²

Substituting wall = laddercos(θ) and ground

= laddersin(θ), we get:

(sec)²(θ) ×(dθ/dt) = (dladder/dt)cos(θ) - (laddersin(θ) × (dθ/dt))/(ground)

Simplifying and solving for dθ/dt, we get:

dθ/dt = [rcos(θ)]/[-rsin(θ) + h]

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