(01.03 MC)

The Kelly school district gives awards to its schools based on overall student attendance. The data for attendance are shown in the table below, where Min represents the fewest days attended and Max represents the most days attended for a single student:

School
Min
Max
Range
Mean
Median
IQR
σ
High School M
128
180
52
141
160
55.5
41.5
High School N
131
180
49
159
154
48.5
36.5
High School P
140
180
40
153
165
32.5
31.5
Part A: If the school district wants to award the school that has the most consistent attendance among its students, which high school should it choose and why? Justify your answer mathematically. (5 points)

Part B: If the school district wants to award the school with the highest average attendance, which school should it choose and why? Justify your answer mathematically. (5 points) (10 points)

The probability that Andre, Olivia, and zack all win gift cards that are at least $25 is 1/4. Hence option C is the correct option.

What is an event?

An event is a collection of experiment results (a subset of the sample space) to which a probability is ascribed in probability theory.

The wheel consists of 8 equal sections. Each section contains the price of a gift card. 4 sections contain a $5 gift card, 2 sections contain a $5 gift card, one section contains a $25 gift card, one section contains a $50 gift card.

To win at least $5, they have to get either $25 or $50.

Thus the number of outcomes of favorable event is 2.

Total number of outcomes is 8.

The probability to win at least $25 is 2/8

Divide denominator and numerator by 2:

2/8 = 1/4

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Darnell's constant speed, as determined by the solution, is 20 miles per hour.

It covers linear transformations more broadly as well as vectors, matrices, and vector spaces. One area of mathematics is linear algebra. In comparison to other areas of mathematics that are frequently driven by innovative ideas and unresolved problems, linear algebra is a discipline that is very well understood.

Distance=8 miles

Time taken is=32 minutes

speed=distance/time

speed=15 miles/hour

Darnel has travelled a distance of 1.5x5/60=0.125 miles in under five minutes.

Hector bicycle speed = distance/time

hector speed of bike=  20 miles/hour

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A linear inequality that models the total cost of the daily rental c(m) as a function of the total miles driven, m is c(m) ≤ 45 + 0.4 m.

What is linear inequality?

In mathematics, an inequality involving a linear function is referred to as a linear inequality. One of the inequality symbols is found in a linear inequality. In graph form, it displays the non-equal data.

Given:

Nancy Stone has a small company and has negotiated a special rate for rental cars when she and other employees take business trips.

The maximum charge is $45. 00 per day plus $0. 40 per mile.

A linear inequality involves a linear function. It contains one of the symbols of inequality. It exactly looks like a linear equation, with the inequality sign replacing the equality sign.

According to the statement Nancy has negotiated a special rate and the maximum charge is $45.00 per day with the addition of $ 0.40 per mile.

So,

a linear inequality that models the total cost of the daily rental as a function of the total miles driven, m is:

c(m) ≤ 45 + 0.4m

Hence, a linear inequality that models the total cost of the daily rental c(m) as a function of the total miles driven, m is c(m) ≤ 45 + 0.4 m.

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The solution to the system of linear equations is x = 10 and y = 22.

To solve this system of linear equations, we can use the substitution method.

First, we want to isolate one of the variables in either equation. Let's start with equation 1:

3x - 2y = 14

Add 2y to both sides to isolate x:

3x = 14 + 2y

Divide both sides by 3 to solve for x:

x = (14 + 2y) / 3

Now, substitute this expression for x into equation 2:

5x + y = 32

5(14 + 2y) / 3 + y = 32

Simplify:

70 + 10y + y = 32

Combine like terms:

11y = -38

Divide both sides by 11 to solve for y:

y = -38 / 11

y = -3.45454545...

Now, substitute -3.45454545... for y in the expression for x:

x = (14 + 2(-3.45454545...)) / 3

x = (14 - 6.9090909...) / 3

x = 7.09090909... / 3

x = 2.36363636...

x = 2.4 (rounded to nearest tenth)

Now that we have both x and y, the solution to the system of linear equations is x = 2.4 and y = -3.5.

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Answer:

-30

Step-by-step explanation:

-1x/5 = 6

-x/5 = 6

-x = 30

x = -30

As per the given equation the total number of positive divisors that $6$ has is 38.

The divisors (or factors) of a positive integer are the integers that evenly divide it.

The formula for calculating the total number of divisor of a number ′n′ where n can be represent as powers of prime numbers is shown as.

If N= paqbrc

Then total number of divisors = (a+1)(b+1)(c+1).

If we want to find the positive divisors for an integer n, we just take the integers 1, 2, 3, . . . , n, divide n by each, and those that divide evenly make up the set of positive divisors for n.

The divisors (or factors) of a positive integer are the integers that evenly divide it

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He needs to make 1 and a half trips to the well to fill the barrel which has a height of 15 inches and  radius 10 inches.

A cuboid is a three-dimensional geometric shape that has six rectangular faces, three of which meet at each corner. A cuboid has three dimensions: length, width, and height. It is also commonly referred to as a rectangular prism. The formula for the volume of cuboid is [tex]V = l *w * h[/tex], where l is the length, w is the width, and h is the height. The formula for the surface area of a cuboid is [tex]2lw + 2lh + 2wh[/tex]. Cuboids are used in everyday life such as building blocks and package boxes.

The cylindrical barrel has a volume of [tex]\pi * r^2 * h = \pi * 10^2 * 15 = 1500\pi[/tex] cubic inches.

The hemisphere has a volume of [tex](2/3) * \pi * r^3 = (2/3) * \pi * 10^3 = (2000/3)\pi[/tex] cubic inches.

So, to fill the barrel, Brad must make [tex]1500\pi / (2000/3)\pi = 3/2 = 1.5[/tex] trips to the well.

In other words, he needs to make 1 and a half trips to the well to fill the barrel.

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The values for figure is  x = 2, y = 9,

GH = 8, GJ = 7,

FE = 3, GE = 7​.

A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.

The Latin words quadra, which means four, and latus, which means sides, are combined to form the English word quadrilateral. A quadrilateral does not always have to have equal lengths on each of its four sides.

Given figure shows

GH parallel to EG

GH = EG

GH = 3y - 19

EG = 8

3y - 19 = 8

3y = 27

y = 9

GH = 3y - 19 = 3(9) - 19 = 8

and GJ parallel  to JE

GJ = JE

GJ = 3x + 1

JE = 5x - 3

3x + 1 = 5x - 3

5x - 3x = 1 + 3

2x = 4

x = 2

values are,

GJ = 3x + 1 = 3(2) + 1 = 7

JE = 5x - 3 = 5(2) - 3 = 7

FE = 6x - y

substitute values,

x = 2, y = 9

FE = 6x - y = 6(2) - 9 = 12 - 9 = 3

Hence x = 2, y = 9

GH = 8, GJ = 7,

FE = 3, GE = 7​.

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I'm pretty sure the answer is 72 :))

A 9-sided shape is called a nonagon.

Therefore the answer is nonagon.

A nonagon is a polygon with nine sides and nine angles. A nonagon can be regular or irregular, depending on the lengths of its sides and angles. A regular nonagon has equal sides and angles, while an irregular nonagon has sides and angles of different lengths.

Nonagons are two-dimensional shapes, and they can be described by their number of sides, angles, and vertices. They are considered a type of polygon, which is a closed geometric figure that is made up of straight lines. In addition to nonagons, there are other types of polygons such as triangles, quadrilaterals, pentagons, hexagons, heptagons, and so on.

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Answer:

2) The estimated weight, in pounds, of the beaver on June 1.

Step-by-step explanation:

Given function:

[tex]w(t) = 29 + 0.0674t \quad t < 90[/tex]

where:

When t = 0:

[tex]\begin{aligned}\implies w(0)&=29+0.0674(0)\\&=29+0\\&=29\end{aligned}[/tex]

Therefore, the constant of the equation (29) is the estimated weight of the beaver, in pounds, when t = 0.

As t = 0 is June 1:

Answer:

y = x + 1/3

Step-by-step explanation:

We know

You drank x ounces of juice and someone drank 1/3 more than what you think

Let's y represent the total, we have the equation

y = x + 1/3

Answer: 4/3x (or 1/3 + x, since your wording's pretty odd)

Step-by-step explanation:

i can't tell if the one-third you're referring to is a third of how many ounces of juice you drank (meaning it will change if you drank 1, 2, 3 oz of juice and so on) or if it's always going to be a third of an ounce more than the amount of oz of juice you drank (in which case it'd be 1/3 + x). anyway just choose whichever answer you're looking for :3

The slope of the line is 20.

The slope represents the rate of change in the price per hour is $20.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

Two coordinates from the graph.

(1, 60) and (3, 100)

Slope.

= (100 - 60) / (3 - 1)

= 40 / 2

= 20

The slope represents the rate of change in the price per hour.

Thus,

The value of the slope is 20.

The slope denotes that the rate of charge per hour is $20.

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Answer:

1.0833333333333333333333333333333333 (repeats)

Step-by-step explanation:

use a calculator

The formula to calculate the distance:

d = √(x₂ - x₁)² + (y₂ - y₁)²

The points are:

We substitute and solve:

d = √(-5(-2))² + (-4-1)²

d = √7² + (-5)² = √49 + 25

d = √74 ====> Alternative "A"

Answer:

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

The two triangles have 2 sides marked as congruent and the included angles are congruent as vertical angles:

This gives us SAS congruence postulate.

The matching choice is B.

Answer: m = -1/10

Step-by-step explanation:

Use the slope formula to find the slope m.

m = −1/10

Answer: So the positive solution is:

ANSWER:    X = 5

(x = 5 ),  (x = - 2 )

Step-by-step explanation:

when 10 is subtracted from the square of a number the result is 3 times the number.

Find the positive solution.

Let:   x = number

Let x^2 = square of a number.

x^2 - 10x = 3x transpose

x^2  -  3x - 10 = 0

Apply Factoring: Fractions of  10  are   5  and 2

( - 5)(2)  =   - 10

- 5  + 2  =  - 3

( x - 5 )(x + 2) = 0

x - 5 = 0      x + 2 = 0

x = 5             x   =  - 2

So the positive solution is:

ANSWER:    X = 5

I hope that helps!!!!

Answer:

16c9

Step-by-step explanation:

First, we will add up the number of different car possibilities. This is:

6 + 7 + 3 = 16.

Then, we need to take 9 of these 16 cars, giving us 16c9.

Hope this helped!

Answer:

4,151,347,200

Step-by-step explanation:

From given circle, Measure of arc FG = 23πr/45 and ∠FHG = 92°.

The distance between the two locations along a segment of a curve is known as the arc length. Any portion of the circumference is an arc in a circle. The angle that an arc occupies at any given point is the angle created by the two line segments that connect that point to the arc's endpoints.

Length of an Arc = r, where is in radians, is the formula used to express the arc length of this arc OP.

The measure of ∠FHG = 2 × 46° [As Angle at center equals twice at circumference]

So, ∠FHG = 92°

Measure of the arc FG = 2πr(θ/360°)

FG = 2πr(92/360)

FG = 23πr/45

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It’s angle 1 and angle 8

The pair of angles that are formed on the other side of the pearl lines, but on the opposite side of the transversal

goodluck

Answer:

x = 5/3, y = 2/3

Step-by-step explanation:

x + 1/3 = 2 equ 2

Answer:

no

Step-by-step explanation:

the one equation has variables and numbers go in for the variable and the other equation just equals 11

The measure that would be most useful to determine if the people can safely use the elevator is B. Mean

The most useful measure to determine if the people can safely use the elevator would be the mean weight of the people, as it would give an idea of the average weight of the group and if it is below 4,500 pounds.

The mode is the most common value in a set of data and does not give information about the weight of the entire group. The interquartile range is a measure of the spread of the middle 50% of the data and does not give information about the average.

In conclusion, the correct option is B.

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The nature of roots of quadratic equation 5x² = 4x - 1 is imaginary roots.

The standard form of a quadratic equation is:

ax² + bx + c = 0

The discriminant is defined as:

D = b² - 4ac

Using  the value of discriminant, we can determine the nature of roots of a quadratic equation.

If:

D > 0, the quadratic equation has two distinct real roots or the roots are real and distinct.

D = 0, the quadratic equation has 1 real equal roots or the roots are unique

D < 0, the quadratic equation has complex conjugate roots or the roots are imaginary.

In this case, the quadratic equation is:

5x² = 4x - 1

transform it into the standard form:

5x² - 4x + 1 = 0

Calculate the discriminant:

D = (-4)²  - 4 (5)(1)

  = 16 - 20 = -4

Since D < 0, the roots are imaginary.

Your question is incomplete, but most probably your question was:

What is the nature of roots of quadratic equation 5x² = 4x - 1?

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Answer:

No

Step-by-step explanation:

Since [tex]2^2+3^2 \neq 5^2[/tex], the side lengths do not satisfy the Pythagorean theorem.

Answer:

No, the point isn't in the shaded area

Step-by-step explanation:

We can use the sin (), and cos () functions in C programming to find the sine and cosine values of any problem.

sin( ), cos( ) and tan( ) functions in C are used to find sine, cosine and tangent values.

sinh( ), cosh( ) and tanh( ) functions are used to find hyperbolic sine, cosine and tangent values.

exp( ) function is used to find the exponential “e” to the xth power. log( ) function is used to find the natural logarithm and the log10( ) function is used to find the base 10 logarithms.

The” math.h” header file supports all these functions in the C language.

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Therefore , the solution of the given problem of ratio is Because of this, at a 95% confidence level, (a,b) = ($65.57, $74.43).

A ratio or fraction in math displays how many times one number is contained in another. For instance, the proportion of oranges to lemons in a bowl of fruit is eight to six if there are eight oranges and six lemons (that is, 8:6, which is equivalent to the ratio 4:3 or decimal 1.333).

Here,

Confidence intervals are defined as a range of values with a known chance that a parameter's value falls inside them.

A statistical data's confidence interval can be expressed as.

=> x+/-zr/√n

=> Knowing that;

Average Sample x = $70.00

$17.50 is the standard deviation.

n = 60 samples were used.

95% confidence interval

95% confidence interval for z = 1.96

substituting our current values;

$70.00+/-1.96($17.50/√60)

$70.00+/-1.96($2.259240285287)

$70.00+/-$4.428110959163

$70.00+/-$4.43

= ( $65.57, $74.43)

Therefore , the solution of the given problem of ratio is Because of this, at a 95% confidence level, (a,b) = ($65.57, $74.43).

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