The lengths of the sides of triangle XYZ are written in terms of the variable m, where m ≥ 6.

Triangle X Y Z is shown. The length of side X Y is m + 8, the length of side Y Z is 2 m + 3, the length of side Z X is m minus 3.

Which is correct regarding the angles of the triangle?

mAngleX < mAngleZ < mAngleY
mAngleY < mAngleZ < mAngleX
mAngleY < mAngleX < mAngleZ
mAngleZ < mAngleY < mAngleX

The domain is: a = -4, and b = 1 and the y = mx + b rule that makes the left (red) piece of the graph is given by y = -0.5x - 2.

The range of values that can be plugged into a function is known as its domain. In a function like f, this set represents the x values (x).

The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set. They are the values for y.

The domain of the left (red) graph is determined using the x-coordinates of the line. The x-coordinates give the input of the function of the graph, which forms the domain.

The domain is:

a = -4, and

b = 1

Hence, the domain of the function of the graph is: -4 < x <1.

The y = mx + b is the equation of the linear function where, m is the slope and b is the point where the line intersects the y-axis.

The value of m - slope is given by:

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

m = (-2.5 - 0) / (1 - (-4))

m = -2.5/ 5

m = - 0.5

The value of b from the graph is:

b= -2

Substituting the values of m and b in the equation we have:

y = mx + b

y = -0.5x - 2

Hence, the y = mx + b rule that makes the left (red) piece of the graph is given by y = -0.5x - 2.

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The total cost C of construction as a function of h is:

[tex]C = \frac{10 + 5\sqrt{2}~ h^2}{h}[/tex]

As the pen is in the shape of an isosceles right angle, one of the

angle must be 90 degrees.

Also, the two sides of the triangle are equal and the base angles

are equal.

Here, x represents the length of legs of isosceles right triangle

and h be the length of hypotenuse of isosceles right triangle

Using Pythagoras theorem,

x² + x² = h²

2x² = h²

x² = h² / 2

x = [tex]\sqrt{\frac{h^2}{2} }[/tex]

So, x = [tex]\frac{h}{\sqrt{2} }[/tex]

The fencing costs $5 per feet for the legs and $10 per feet for the hypotenuse.

So, the fencing cost for the legs would be,

= 5 × (2x)

= 10x

= [tex]10\times \frac{h}{\sqrt{2} }[/tex]

= [tex]5\sqrt{2}~ h[/tex]

And the fencing cost for the hypotenuse would be,

= 10/ h

So, the total cost of fencing C would be,

[tex]C = \frac{10}{h} + 5\sqrt{2}~ h\\\\C = \frac{10 + 5\sqrt{2}~ h^2}{h}[/tex]

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The model's graph, y = 10770/x2 - 0.37, 5 x 100 demonstrates that the resistance will be about halved when the wire's diameter is doubled. This is brought on by the inverse square relationship between wire resistance and diameter.

1. Graph the model y = 10770/x² - 0.37, 5 ≤ x ≤ 100 using a graphing utility.

2. Find the resistance when x is 5.

y = 10770/5² - 0.37 = 2104.1 ohms

3. Find the resistance when x is 10.

y = 10770/10² - 0.37 = 526 ohms

4. Divide 2104.1 by 526 to find the factor by which the resistance is changed when the diameter of the wire is doubled.

2104.1/526 = 4

The graph of the model y = 10770/x² - 0.37, 5 ≤ x ≤ 100 shows that the resistance of the wire decreases as the diameter of the wire increases. Doubling the diameter of the wire will roughly halve the resistance, as can be seen by comparing the resistance when x is 5 (2104.1 ohms) to the resistance when x is 10 (526 ohms). Thus, the resistance is changed by a factor of 4 when the diameter of the wire is doubled.

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Answer:12 fives 2 10's

Step-by-step explanation:

174 number of students must be in the 8th grade class.

A relationship between two expressions or values that are not equal to each other is called 'inequality.

Given that The eight grade class is planning a trip to Washington, D.C. this spring.

They need a minimum of 75 people to attend in order to reserve busses.

1/3 of the 8th grade class plus 17 parent chaperones have signed up and this is enough to satisfy the requirement,

We need to find the number of students must be in the 8th grade class

1/3x+17≤75

Subtract 17 on both sides

1/3x≤58

x≤174

Hence, 174 number of students must be in the 8th grade class.

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Answer:

all

Step-by-step explanation:

all of them

When given two points and asked to find the equation of the line in slope-intercept form, the correct steps, the correct order is 2 , 1 , 4 , 3.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

Given that,

given two points and asked to find the equation of the line in slope-intercept form.

Find that,

what are the correct steps? Place a number next to the step to put them in order.

Explanation:

to find the equation of the line in slope intercept form form given two points.

step 1 :

find the slope.

step 2

write equation in point slope form

step 3.

pick a point form the given points , substitue it into the point slope form

step 4.

write the equation in slope intercept form by simplifying

Final Answer.

Hence , the correct order is 2 , 1 , 4 , 3.

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The length of missing side is 39.

Pythagoras theorem is a mathematical statement that states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the two other sides (the legs).

It can be expressed as a2 + b2 = c2, where a and b are the two legs of the triangle and c is the hypotenuse. The theorem is named after the ancient Greek mathematician Pythagoras, who is believed to have discovered it.

Pythagoras theorem is an important concept in geometry, and is used to calculate the length of the hypotenuse in a right triangle when the lengths of the other two sides are known.

It can also be used to determine the lengths of the other two sides when the length of the hypotenuse is known. In addition, it can be used to find the angles of a right triangle when the lengths of the sides are known.

Pythagoras theorem has many applications in everyday life. For example, it can be used to calculate the height of a building, or the distance between two points.

It can also be used in carpentry, engineering, and architecture to measure distances and angles. In addition, it can be used in trigonometry to find the values of trigonometric functions.

Finally, it can be used in navigation to calculate distances and angles.

Let c be the length of missing side,

According to Pythagoras theorem,

a² + b² = c²

36² + 15² = c²

c = √1521

c = 39

So, the length of missing side is 39.

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The evaluation of the velocity function, v(t) = cos((π/6)·t) for the interval 0 ≤ t ≤ 12, th obtain the position and acceleration is as follows;

(a) The particle is moving to the left when 3 < t < 9

(b) The total distance is; [tex]\int\limits^6_0 {cos(\frac{\pi}{6}\cdot t) } \, dt[/tex]

(c) a(t) ≈ -0.453

(d) x(4) ≈ -0.346

Acceleration is the rate at which the velocity of the object changes.

The function for the velocity of the particle is presented as follows;

v(t) = cos((π/6)·t)

The position of the particle at time, t = 0 is x = -2

(a) When the particle is moving to the left, the velocity is negative

The value of cos(θ) is negative for π/2 < θ < 1.5·π

The range of values of θ = ((π/6)·t), for 0 ≤ t ≤ 2, are;

((π/6) × 0) ≤ θ ≤ ((π/6) × 12), from which we get;

0 ≤ θ ≤ (2·π)

When π/2 = (π/6)·t, we get;

t = (π/2)/(π/6) = 3

When 1.5·π = (π/6)·t, we get;

t = (1.5·π)/(π/6) = 9

The particle is moving to the left between time t = 3 and time t = 9, which can be expressed as follows;

(b) The total distance traveled by the particle from time t = 0 to time t  = 6 is presented using the definite integral as follows;

(c) Acceleration, a, is the rate of change of the velocity, therefore, the acceleration is the derivative of the velocity function, which can be obtained as follows;

[tex]a(t) =\frac{d}{dt} {cos(\frac{\pi}{6}\cdot t) } = -\frac{\pi}{6} \cdot sin(\frac{\pi}{6} \cdot t)[/tex]

[tex]a(t) = -\frac{\pi}{6} \cdot sin(\frac{\pi}{6} \cdot t)[/tex]

At time t = 4, we get;

[tex]a(4) = -\frac{\pi}{6} \cdot sin(\frac{\pi}{6} \times 4) = -\frac{\sqrt{3} \cdot \pi}{12}[/tex]

(d) The position of the particle at time t = 4, can be obtained by adding the the position of the particle at time t = 4 to the total distance covered between time t = 0 and time t = 4 as follows;

[tex]\int\limits^4_0 {cos(\frac{\pi}{6}\cdot t) } \, dt =[ \frac{6}{\pi}\cdot {sin(\frac{\pi}{6}\cdot t) }]^4_0[/tex]

[tex][ \frac{6}{\pi}\cdot {sin(\frac{\pi}{6}\cdot t) }]^4_0 = [ \frac{6}{\pi}\cdot {sin(\frac{\pi}{6}\times 4) }] - [ \frac{6}{\pi}\cdot {sin(\frac{\pi}{6}\times 0) }]=\frac{3\cdot \sqrt{3} }{\pi}[/tex]

[tex]\int\limits^4_0 {cos(\frac{\pi}{6}\cdot t) } \, dt = \frac{3\cdot \sqrt{3} }{\pi}[/tex]

The position of the particle at t = 4 is therefore;

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The maximum error in the volume of the cone is approximately 20π cubic centimeters.

In this problem we must estimate the maximum error in the volume of the cone, based on uncertainties in radius and height of a circular cone. The volume formula for a circular cone is:

V = (π / 3) · R² · h

Where:

And the maximum error formula (ΔV), in cubic centimeters, is found by total differentials:

ΔV = (dV / dR) · ΔR + (dV / dh) · Δh

Where:

All first derivatives are shown below:

dV / dR = (2π / 3) · R · h

dV / dh = (π / 3) · R²

If we know that R = 10 cm, h = 25 cm, ΔR = 0.1 cm and Δh = 0.1 cm, then the maximum error in volume of circular cylinder is:

dV / dR = (2π / 3) · (10 cm) · (25 cm)

dV / dR = 500π / 3 cm²

dV / dh = (π / 3) · (10 cm)²

dV / dh = 100π / 3 cm²

ΔV = (500π / 3 cm²) · (0.1 cm) + (100π / 3 cm²) · (0.1 cm)

ΔV = 20π cm³

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To find the percentile, we need to calculate what percentage of the data falls below the $78 thousand dollars wage.

To find the percentile, we sort the data in ascending order and find the percentage of the data that falls below $78 thousand dollars. Here's one way to do this:

69 58 43 43 43 51 57 57 62 68 69 75 76 78 78 80 91 97 102 124 130 135 144 157 185 217

Out of 28 observations, 22 of them are below $78 thousand dollars. So, the percentile for someone who earns $78 thousand dollars is 22/28 * 100 = 78.5714.

In this context, the value of the percentile represents the percentage of the population of full-time employed people who hold at least a Bachelor's degree and earn less than $78 thousand dollars. So, someone who earns $78 thousand dollars is in the 78.5714th percentile of this population.

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Answer: In order to solve for x, we will have to use the logarithmic properties to isolate x.

f(x) = 3 - 4 In (x-2)

To solve for x, we will have to get x alone on one side of the equation by using the logarithmic property that logb(a^c) = c*logb(a).

4 In (x-2) = 3

In (x-2) = 3/4

To find x, we will raise e to the power of both sides

x-2 = e^(3/4)

x = e^(3/4) + 2

So the solution of x is e^(3/4) + 2

It's important to notice that the natural logarithm (ln) and log base e (In) are same and the solution is valid for both.

Step-by-step explanation:

By equation for the graph y = 2 cos (x − π 12)  this  we get  

x            f (x)

π /2        2

π            0

3π / 2     -2

2π           0

5π / 2      2.

y = 2 cos (x − π 12)

Find the parameters necessary to calculate the amplitude, period, phase shift, and vertical shift using the formula a cos (b x c ) + d.

a = 2

b= 1

c = π /2

d = 0

locate | a |'s amplitude.

Dimension: 2

Calculate the duration of 2 cos (x 2 ).

2 | b | can be used to determine the period of the function.

2π / |b|

In the formula for the period, swap out b for 1.

2π  /  |1 |

What separates a number from zero is its absolute value. 0 to 1 are separated by a distance of 1 and 2 units.

1

Subtract 2 from 1 to get 2.

Use the cb formula to get the phase shift.

From c b, one may get the phase shift of the function.

c b: Phase Shift

The equation for phase shift should have the values of c and b changed.

Changing phases: 2 1

Take 2 and divide it by 1.

Shift in Phase: 2

Name the trigonometric function's attributes.

Two-second period with amplitude two

Phase Change: 2 (rightward by 2).

Vertical Shift: null

To graph, choose a few points.

To continue, tap the screen.

x          f ( x )

π /2         2

π             0

3π /2      − 2

2 π           0

5π / 2       2

Amplitude, period, vertical shift, phase shift, and points can all be used to graph the trig function.

Dimension: 2

Two (2) years

Phase Change: 2 (rightward by 2).

Vertical Shift: null

x            f (x)

π /2        2

π            0

3π / 2     -2

2π           0

5π / 2      2.

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Answer:

E = 36

Step-by-step explanation:

1. Add 7 to both sides of the equation

3e - 7 = 101

    +7     +7

------------------

3e = 108

2. Isolate the variable e by dividing by 3 on both sides

[tex]\frac{3e}{3} = \frac{108}{3}[/tex]

3. Simipfy the equation

[tex]e = 36[/tex]

Answer:

no solution

Step-by-step explanation:

5(100)<12

500<12 false

has no solution

Answer:

Step-by-step explanation:

A. (AUBUC)' = {}

B. (A UBUC)' is the empty set.

Both options A and B express that the complement of the union of the sets A, B, and C is the empty set. The complement of a set is the set of all elements that are not in that set. The union of sets is the set of all elements that are in at least one of the sets.

When taking the union of A, B, and C all the elements in U are included, so there is no element that is not in the set, making the complement of the union of A,B,C is an empty set.

a) The bigger the value, each box plot is spread out. The ages of the top 50% of customers are more varied than 50% of lower consumers. Hence, each plot is slanted to the right.

b) The BMW 3 series is likely to have an outlier. It has the longest whisker.

c) When comparing median age, younger people are likely to purchase the BMW 3 series and while older people are more likely to purchase the BMW 7 series. However, because each data set is so dissimilar, this is not a rule.

d) The spread is the smallest in the second quarter of the box. The difference between the first quartile and the median seems to be barely three years.

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The complete question is:

A survey was conducted of 130 purchasers of new BMW 3 series cars, 130 purchasers of new BMW 5 series cars, and 130 purchasers of new BMW 7 series cars. In it, people were asked the age they were when they purchased their car. The following box plots display the results.

a. In complete sentences, describe what the shape of each box plot implies about the distribution of the data collected for that car series.

b. Which group is most likely to have an outlier? Explain how you determined that.

c. Compare the three box plots. What do they imply about the age of purchasing a BMW from the series when compared to each other?

d. Look at the BMW 5 series. Which quarter has the smallest spread of data? What is the spread?

The limit will be ,lim x→2 [f(x) + g(x)] = 2 + 0 = 2

In Mathematics, a limit is defined as a value that a function approaches the output for the given input values. Limits are important in calculus and mathematical analysis and used to define integrals, derivatives, and continuity. It is used in the analysis process, and it always concerns about the behaviour of the function at a particular point. The limit of a sequence is further generalized in the concept of the limit of a topological net and related to the limit and direct limit in theory category. Generally, the integrals are classified into two types namely, definite and indefinite integrals. For definite integrals, the upper limit and lower limits are defined properly. Whereas in indefinite the integrals are expressed without limits, and it will have an arbitrary constant while integrating the function.

lim x→2 means what is the value of y as x approaches 2 from the left side and the right side - they must be the same value for the limit to exist.  "Approaches" is the operative word - it does not have to exist at that y-value, as in example a.   lim x→1 [g(x)] = DNE because (left side of 1) lim x→1- [g(x)] = 2 and (right side of 1) lim x→1+ [g(x)] = 1

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Time cross-sectional data is data collected from a sample of subjects at a single point in time.

This data can be used to measure the characteristics of a population at a given point in time. For example, a population can be surveyed to measure the percentage of people who own a car, the median age of the population, or the percentage of people who have a college education.

Time series data is data collected from the same sample of subjects over a period of time. This data can be used to measure the changes in a population over time. For example, a population can be surveyed to measure the percentage of people who own a car over a five-year period, the median age of the population over the same five-year period, or the percentage of people who have a college education over the same five-year period.

Time controlled data is data collected from the same sample of subjects at different points in time but with a controlled variable. For example, a survey can be conducted to measure the percentage of people who own a car at the start of the school year, the median age of the population at the start of the school year, and the percentage of people who have a college education at the start of the school year in different cities.

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The correct answer is qualitative data, quantitative data.

Qualitative data is a type of data that describes the characteristics or attributes of a phenomenon but does not involve numbers or measurements. It is used to describe or understand the characteristics of a particular group or phenomenon.

This type of data is often used in the social sciences, such as sociology, anthropology, and psychology, but can also be used in other fields such as marketing and advertising.

Qualitative data can be analyzed in different ways, such as content analysis, thematic analysis, discourse analysis, and interpretive analysis.

Quantitative data is a type of data that involves numbers or measurements. It is used to describe or understand the characteristics of a particular group or phenomenon using numerical values or statistics.

This type of data is often used in the natural sciences, such as physics, chemistry, and biology, but can also be used in other fields such as economics, business, and engineering.

Therefore, The correct answer is qualitative data, quantitative data.

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The given tax rates are as follows: Drew’s tax due is 4,519.50 and his effective tax rate is 11.6%. Option A is correct.

You will determine your total taxable income based on your tax slab by subtracting all eligible deductions from the gross taxable income. Senior citizens pay a different slab rate.

An income tax system's tax base is referred to as taxable income. That is, the amount of income that was subject to taxation by the government. In most cases, some or all of the income is included, and expenses and other deductions reduce it.

                      Single Taxpayers: Income Brackets

Tax Income                  Rate Bracket             Tax Owed              

0 to 9,525                       10%                     10% of taxable income

9,526 to38,700               12%        $952.50 plus 12% of  38,700 the excess                                                                                        over

$38,701 to 82,500          22 %                $4,453.50 plus 22% of 38,701                                                                                     the excess over

82,501 to 157,500          24%      $14,089.50 plus 24% of the excess over

                                                                                                         157,500

157,501 to  200,000       32%      $ 32089.50  plus 32% of the excess over

200,001 to   500,000     35%      45,689.50 plus 35% of excess over

500,000 >                        37%      $150,689.50 plus 37% of 500,000 of the    

                                                             excess over

The taxable income lies in the tax rate range of   $38,701 to 82,500.

Therefore the tax would be  :

                                  $4,453.50 + 22% of (39,000-38,701=299)

                                           = $4,453.50 + 22% of 299

                                                  =  $4,453.50 + 65.78

                                                  = $ 4519.28

The taxable income lies in the tax rate range of  $38,701 to 82,500. Due and effective tax rate is $4,453.50 plus 22% of 38,701 the excess over.

The calculated tax is $ 4519.28

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The statement given is showing a condition for a contrapositive statement.

Conditional statements are those statements where a hypothesis is followed by a conclusion.

Given that, If Darell is going to take music lessons, then he needs a trumpet. If Darell is not going to take music lessons, then he does not need a trumpet.

So, this is a structure of, If A then B ⇒ If not A then not B.

Which is a structure for contrapositive conditional statements.

Hence, the statement given is showing a condition for a contrapositive statement.

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Hey there!

Is this all one complex equation or it this representing multiple? Reason I ask is it's a little hard to understand above.

A Pareto diagram assists a team in focusing its efforts on the variables that have the biggest influence by separating the important few from the unimportant many. Additionally, it facilitates the team's ability to explain why specific areas are important.

The following situations call for the use of scatter plots.

In the case of paired numerical data

when more than one value of the dependent variable is associated with a particular value of the independent variable

When determining the relationships between variables, it might be helpful to look for potential problem-solving causes, see if two products that seem connected both have the same root cause, and so on.

A histogram is a graphic depiction of a frequency distribution with continuous classes that has been grouped. A series of rectangles with bases equal to the distances between class boundaries and areas proportional to frequencies in the associated classes make up the area diagram. Since the base in such representations spans the spaces between class boundaries, every rectangle is neighbouring. Rectangle heights are inversely correlated with comparable frequencies for similar classes, and inversely correlated with frequency densities for other class.

A run chart, also known as a run-sequence plot is a graph that displays observed data in a time sequence. Often, the data displayed represent some aspect of the output or performance of a manufacturing or other business process. It is therefore a form of line chart.

The complete question is :-

Which of the following charts would be best to justify focusing on a few large problems and ignoring many smaller ones?

1) run chart  (2) pareto diagram  

(3) histogram (4) scatter plot

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Between 5:15 pm to 6:30 pm, Beth is decreasing her distance from home. Hence option c is the correct answer.

Distance between two points or objects can sometimes be measured qualitatively and sometimes quantitatively.

In physics, the concept of distance can refer to a physical length or, more commonly, to an approximation based on several other considerations.

The term is frequently used metaphorically to denote a measure of the degree of separation or statistical distance between two similar objects (such as edit distance between strings of text or distance between probability distributions), given that spatial cognition is a rich source of probability metaphors in human thought (as exemplified by distance between people in a social network).

Most of these literal and figurative concepts of distance are defined in terms of a mathematical idea called a metric space.

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The equation that represents the quotient of -100 and twice 10 equal to -5 is; -100 ÷ 2(10) = -5

The quotient of an algebraic operation is defined as a result that is obtained by dividing one quantity by another.

We are told that the quotient of -100 and twice 10 is equal to -5. Thus, we can express the given expression as;

-100 ÷ 2(10) = -5

This is because quotient means answer that is produced from dividing 2 numbers and since the product is a whole number and not a proper fraction, then it means that the larger number will be the numerator while the smaller number will be the denominator.

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As per the given ratio Mina's age is 12 years old.

Ratio in math is defined as shows how many times one number contains another.

Here we have given ratio information as written as

=> Lev's age : Mina's age = 1 : 2

And the ratio between is written as

=> Mina's age : Naomi's age = 3 : 4

Here we have given the condition that the sum of all three ages is written as,

=> Lev + Mina + Naomi = 30 to 50

Here let us consider Lev's age as L, Mina's age as M and Naomi's age as N

Then the ratio is calculated as,

=> L = 1/2M

=> N = 4/3M

And the sum of all value is written as

=> L + M + N = 30 to 50

When we apply the values on it, then we get,

1/2M + M + 4/3M = 30 to 50

When we simplify it by multiply all by 6, then we get

=> 3M + 6M + 8M = 180 to 300

=> 17M = 180 to 300

Therefore, here we have to find a number between 180 and 300 that divisible by 17 and 6.

So let us consider that that number is 204.

Then the value of M is calculated as,

=> 17M = 204

=> M = 12

Complete question:

Let us consider that suppose the ratio of lev's age to mina's age is 1 : 2 and the ratio of mina's age to Naomi's age is 3 : 4. if the sum of all three ages is between 30 and 50, then how old is mina?

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Answer:

A line that is perpendicular to the line y=-2x+1 will have a slope that is the negative reciprocal of -2, which is 1/2.

The equation of a line in point-slope form is:

y - y1 = m(x - x1)

Where m is the slope of the line, and (x1, y1) is a point on the line.

Given that the point (-4,3) lies on the line, we can substitute those values for x1 and y1:

y - 3 = 1/2(x + 4)

Which is the equation of a line that is perpendicular to y=-2x+1 that passes through the point (-4,3).

Alternatively, you can also write the equation of a line in slope-intercept form y = mx + b,

The slope of a line perpendicular to y=-2x+1 is 1/2, therefore m = 1/2

We can substitute the point (-4,3) in the equation y = mx + b,

3 = (1/2)(-4) + b

b = 3.5

Therefore the equation of the line is y = 1/2x + 3.5

A one-sample z-test for a population proportion requires that n po > 10 and n(1-Po) > 10 for both the sample and population proportions, Po. Additionally, each sample proportion must be less than or equal to 0.5, the sample size must be more than 10 times the population size, and the population size must be more than 10 times the sample size.

1. Calculate the sample size, n, needed for the test.

2. Check that npo > 10 and n(1 - Po) > 10 for both the sample and population proportions, Po.

3. Check that each sample proportion is less than or equal to 0.5.

4. Check that the sample size is more than 10 times the population size.

5. Check that the population size is more than 10 times the sample size.

6. Check that the population distribution is approximately normal.

A one-sample z-test for a population proportion is used to evaluate the difference between a sample proportion and a population proportion. Before conducting the test, it is important to check for independence, which is done by ensuring that certain conditions are met. First, npo > 10 and n(1-Po) > 10 must be true for both the sample and population proportions, Po. Additionally, each sample proportion must be less than or equal to 0.5, the sample size must be more than 10 times the population size, and the population size must be more than 10 times the sample size. Lastly, the population distribution must be approximately normal. These conditions must be met in order for the test to be valid and reliable. If any of these conditions are not met, the test results may be inaccurate.

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The length of the side should be 45 inches.

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.

In triangle XYZ,

As lengths of two sides XYZ are 23 and 48 inches

The range of the third side can be computed when we already know the two sides of the triangle.

If subtracting 48 - 23, the 3rd side would have to be more than 25. Else 3rd side can not be made as two smaller legs will not meet.

and If adding 48 + 23 , the 3rd side would have to be less than 61. Else 3rd side will reach further than the other two sides could reach.

Therefore, the length of side XZ should be greater than 25 and lesser than 61.

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