if the textbook committee makes a histogram of the sample data and it is single-peaked with no outliers, are the conditions of randomness and normality of the population met for this test?

Given the details above, the sequence of steps below shows that ABCD is a Trapezoid.

A trapezoid, also known as a trapezium, is a closed, flat object with four straight sides and one set of parallel sides. A trapezium's parallel sides are known as the bases, while its non-parallel sides are known as the legs.

Given:

The diagonals of the quadrilateral ABCD intersect at o where AO/BO = CO/DO; which also means that

AO/CO = BO/DO the proof is given as follows:

Create line OE || DC in a way that E lies on BC.

In ΔBDC, based on the Basic Proportionality Theory,

BO/OD = BE/EC ............................1

It is also given that:

AO/CO = BO/DO   ..........................2

Hence, from Equations 1 and 2,

AO/CO = BE/EC

Thus, we can state that on the basis of the Converse of the Basic Proportionality Theorem,

OE || AB

Since AB || OE || DC, it is correct to state that ABCD is a Trapezoid.

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Work done in stretching spring from 36 cm to 38 cm is 0.333J.

The work needed to stretch a spring is given by the formula mentioned below:

[tex]W_{s}[/tex] = (1/2) K × [tex]x^{2}[/tex]

Here,  k is spring constant and x is the elongation.

So, x = [tex]x_{f} - x_{i}[/tex]

When spring is stretched from 40 cm to 34 cm

x = 40 - 34  = 6cm = 0.06 m

We need to know the spring constant so that we can calculate work.

3 = (1/2) K × [tex](0.06)^{2}[/tex]

K = 1666.67

Now, when spring is stretched from 36 cm to 38 cm

x = 38 - 36 = 2 cm = 0.02 m

[tex]W_{s}[/tex] = (1/2) × (1666.67) × [tex](0.02)^{2}[/tex]

[tex]W_{s}[/tex] = 0.333J

So, 0.333J work is done in stretching spring from 36 cm to 38 cm.

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Answer:

hii!!! z = 3, ¼

Step-by-step explanation:

Hope this helps xb

Jane decides to randomly interview 10 freshmen from each of the dorms, these people are her Sample.

What is Sample?

Sampling is the process of choosing a portion of a statistical population to estimate attributes of the entire population in statistics, quality control, and survey methods. Statisticians try to get samples that are typical of the population under consideration.

A little sample or amount of someone or something that is inspected, analyzed, or otherwise investigated to learn more about the rest.

Given: Jane wants to know what percentage of freshmen at her college purchase clothing with college logos. She decides to randomly interview 10 freshmen from each of the dorms.

Therefore, by the above information, these people are her Sample.

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After combining the like terms of the given expression -4r -2r + 5 the equivalent expression is -6r +5.

As given in the question,

Given expression is equal to :

-4r -2r + 5

Now combine the like terms to get the equivalent expression we have,

Like terms of the given expression -4r -2r + 5 are -4r and -2r

( -4r -2r) +5

= -r (4+2) +5

= -6r +5

Equivalent expression of the given expression -4r -2r + 5  is -6r +5.

Therefore, after combining the like terms of the given expression -4r -2r + 5 the equivalent expression is -6r +5.

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ANSWER

R1, R2, R3, R4, G1, G2, G3, G4. Option B.

The unit rate of gallon to mile is calculated as: 5/6 gallon per mile.

The unit rate between two variables is simply the ratio of the quantity of one variable to the quantity of the other variable, such that the the denominator of the will be equal to exactly 1.

We are given the variables gallons and miles, where 1/4 of a gallon is to 3/10 mile.

The unit rate between these two variables would be an amount of gallons per mile.

Thus, find the unit rate by dividing 1/4 by 3/10:

1/4 ÷ 3/10

= 1/4 × 10/3

= 10/12

= 5/6

The unit rate is therefore, 5/6 gallon per mile.

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It is known that 1 gallon is 3.78541 litres.

So it follows:

Hence the value of 3.5 gallons is 13.2489 litres.

Answer:

d=y-300

Step-by-step explanation:

The quadratic function of h (x) in vertex form will be as h(x) = (x + 2)² − 3

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

Given that the values of x and h (x) for the quadratic function is given by;

x = -3, -2, -1, 0, 1, 2, 3,

h (x) = -2, -3, -2, 1, 6, 13, 22

Consider the quadratic function as;

h (x) = ax² + bx + c

Now Substitute x = -3 and h (x) = -2 in quadratic function we get;

h (x) = ax² + bx + c

- 2 = a × (-3)² + b × -3 + c

- 2 = 9a - 3b + c

And, Plug x = -2 and h (x) = -3 in function we get;

h (x) = ax² + bx + c

- 3 = a × (-2)² + b × -2 + c

- 3 = 4a - 2b + c

And, plug x = -1 and h (x) = -2 in function we get;

h (x) = ax² + bx + c

- 2 = a × (-1)² + b × -1 + c

- 2 = a - b + c

After solving we get:

a = 1 , b = 4 and c = 1

Then

h (x) = ax² + bx + c

h (x) = 1 × x² + 4x + 1

h (x) = x² + 4x + 1

h (x) = x² + 4x + 4 - 4 + 1

h (x) = (x + 2)² - 3

Hence, The quadratic function of h (x) in vertex form will be as h(x) = (x + 2)² − 3

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The percentage of young adults who send fewer than 218 text messages is 99.87%.

For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

First, solve for the z-score using the formula below.

z-score = (x – μ) / σ

where x = individual data value = 218

μ = mean = 128

σ = standard deviation = 30

z-score = (218 - 128) / 30

z-score = 90 / 30

z-score = 3

Find the probability that corresponds to the z-score in the z-table. (see attached images)

z-score = 3

probability = 0.9987

To get the percentage, multiply the probability by 100.

percentage = probability x 100

percentage = 0.9987 x 100

percentage = 99.87%

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Based on your earnings from each of the part-time jobs, your fortnightly earnings would be $1,520

First, find out how much you earn in the first part-time job per week:
= (Number of days per week x Number of hours per day x Pay per hour)

= (3 x 6 x 20)

The find out how much you earn in the second part-time job:

= (Number of days per week x Number of hours per day x Pay per hour)

= (2 x 8 x 25)

In a fortnight (two weeks), your earnings would be:

= (2 weeks x (3 x 6 x 20)) + (2 weeks x (2 x 8 x 25))

= (2 x 360) + (2 x 400)

= 720 + 800

= $1,520

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Fortnightly earnings would be $1,520 based on previous earnings.

Two or more expressions with an Equal sign is called as Equation.

Given that there are two part time jobs.

For first part time

3 days per week I work for 6 hours each day and I earn $20.00 per hour

(3 x 6 x 20)

=360

Second part time

2 days per week, I earn $25.00 per hour, working an 8-hour day.

=2×25×8

=400

Now we need to calculate, the total fortnightly earnings.

= (2 weeks x360) + (2 weeks x 400)

= (2 x 360) + (2 x 400)

= 720 + 800

= $1,520

Hence $1520 is the fortnightly earnings.

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Okay, here we have this:

Considering the provided information, we are going to write and solve the correspondinf system of equation, so we obtain the following:

According to the information given, we obtain the following system of equations, where we take x as money spent on fruit and y as money spent on green vegetables, so we have:

Now let's solve for x in the second equation:

x+x+5=30

2x+5=30

2x=30-5

2x=25

x=25/2

x=12.5

Now from the value of x that we got, then we will plug it into the first equation to get the value of y:

Then, finally we obtain that she spend $12.5 on fruits and $17.5 on green vegetables.

The answer is very simple. .

6 + 2 (5 - 8 ) ² + 7

Firstly we solve what is inside the parenthesis

Then we solve the multiplications

Finally we solve the sums.

That is the solution.

The equation of the line for the given slope 1 is y= x + 2

Equation of the line:

An equation of the line refers the algebraic form of representing the set of points, which together form a line in a coordinate system.

Given,

The point where the graphs of two equations intersect has y-coordinate 2. One equation is y = -3x + 5.

Here we need to find the other equation if its graph has a slope of 1.

We know that, the general representation of equation of line is y= ax + b

where a is the slope and b is the y intercept.

Through the given details we know that the slope of the line is 1 and why is point where two lines intersect hence, it is the intercept.

And the intercept value is 2.

Therefore, the equation of the other line is y= x + 2

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Step-by-step explanation:

The slope-intercept form of the equation of a line that passes through (5, -4) and has a slope of 3/4 is y = (3/4)x - 31/4.

What is the slope-intercept form?

The slope-intercept form of a line is y=mx + c.

Where, x and y are coordinates. m = slope and c = y intercept.

Given, slope (m) = 3/4

Substituting the values of (x, y) as (5, -4) and m = 3/4, we get:

-4 = (3/4) × 5 + c

⇒ c = -4 - (3/4) × 5 = -4 - 15/4 = -31/4

Now, putting the value of c in the standard equation:

y = (3/4)x - 31/4

⇒ 4y = 3x - 31

⇒ 3x - 4y = 31

Answer is Option C

To solve this problem we change the structure from

1/2 + ? = 7/8

to

7/8 - 1/2 = ?

Now we need to subtract the fractions and find the difference. To do this, make the denominators (the bottom numbers on the fractions) the same.

1/2 = 4/8

then subtracts the numerator

7/8 - 4/8 = 3/8

there is your answer... 3/8

The room numbers of two adjacent classrooms are 359 and 361.

What is consecutive odd numbers?

Consecutive odd numbers are odd integers that are separated by 2 and come after one another.

Suppose the first odd number is x, then the another consecutive odd number is x + 2.

The sum of these two numbers is 720.

So,

x + (x + 2) = 720

2x + 2 = 720

2x = 718

x = 359

Therefore, the first odd number is 359 and the second add number is 361 which gives the sum 720.

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Step-by-step explanation:

12/4 = x/8

1st: cross multiply

96 = 4x

2nd: divide both sides by 4

96/4 = 4x/4

therefore x = 24

Two lines are parallel if they hay the same slope.

The slope, m, of the line that passes through the points (x1, y1) and (x2, y2) is computed as follows:

From the graph, line m passes through the points (0, 1) and (3,3), then its slope is:

Equation of a line in slope-intercept form

where m is the slope and (x1, y2) is a point on the line.

The new line has to pass through point P(1, -2). Substituting with this point and m = 2/3 into the general formula:

The function that can be used to represent the total amount that will be paid for the room is 100 + 55h.

A function simply means the expression that. an be used to show the relationship between the variables or the data given.

In this case, the interior designer charges $100 to visit a site, plus $55 to design each room.

Let the number of rooms be represented as r.

The function that represents the total amount will be:

= 100 + (55 × h)

= 100 + 55h

This illustrates the concept of functions.

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The measure of Angle A and Angle B are 54° and 122° respectively.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In triangle ABC,

The measure of angle A = (n + 20)°

The measure of angle B = (3n - 10)°

The measure of angle C = n°

Now,

The sum of all the angles of the triangle = 180°

So, we can formulate;

(n + 20)° + (3n - 10)° + n° = 180°

Solve for n as;

n + 20 + 3n - 10 + n = 180

5n + 10 = 180

5n = 180 - 10

5n = 170

Divide by 5, we get;

n = 170/5

n = 34

Thus, The measure of angle A = (n + 20)°

                                               = 34 + 20

                                               = 54°

And, The measure of angle B = (3n - 10)°

                                             = 3 x 34 + 20

                                             = 102 + 20

                                             = 122°

Therefore,

The measure of Angle A and Angle B are 54° and 122° respectively.

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The exponential equation that represents the table is given as y = 81(3)^x.

Exponent-based equations in which the exponent or a portion of the exponent is a variable are known as exponential equations.

The standard exponential form is expressed according to the formula;

y= ab^x

Using the coordinate points (2, 9) and (3, 3) from the table, we can create simultaneous equation as shown;

9 = ab^2

3 = ab^3

Divide both equations

3/9 = ab^3/ab^2

1/3 = b^3/b^2

1/3 = b

Substitute b = 1/3 into any of the equations

3 = ab^3

3 = a(1/3)^3

3 = 1/27 a

a = 81

Determine the required equation

y = ab^x

y = 81(3)^x

This gives the required equation of the function.

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Answer: 81

Step-by-step explanation: Took the test & got it right :)

Answer:

90%

Step-by-step explanation:

To find the percent of increase in the height of the tree, we need the change of the height and the original height (40 feet)

The change of height = 76 - 40 = 36 feet

Now, we need to divide the change by the original height to find the percent of increase.

36/40 = 9/10

9/10, which is then 90%.

According to the factor theorem, if "a" is any real integer and "f(x)" is a polynomial of degree n larger than or equal to 1, then (x - a) is a factor of f(x) if f(a) = 0.Finding the polynomials' n roots and factoring them are two of their principal applications.

Calculate p(x(*r(x)?

I This theorem comes in very handy when we need to determine the determinant's value in "factors" form.

p(x) =5x

r(x)  = 3x  - 7

p(x)×r(x) =

=5x(3x-7)

5x²  -  7

2×15x²-1

=  30x

p(x)*r(x)  =   30x

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Answer:

D y < 8

Step-by-step explanation:

the range is the interval or set of all valid y (functional result) values.

we can see the y values start at +8, and as the curve is only going down, clearly endlessly, every value smaller than 8 is valid.

8 itself is the be excluded, as there is a hollow point (a filled point would indicate "include").

and therefore we cannot say y <= 8.

we have to use y < 8.

Answer:

Step-by-step explanation:

x

=

−

2

x

=

−

5

Explanation:

x

2

+

7

x

+

10

=

0

We could right the equation in another form using brackets.

(

x

+

2

)

(

x

+

5

)

=

0

In order to get two numbers to multiply and give 0, at least one number has to be 0.

a stands for the first bracket and b for the second.

a x b = 0

a=0 or b=0 to make this equation valid.

Therefore x= -2 or x= -5 because -2+2=0 and -5+5=0 according to both brackets.

The coordinates of the point C on the line AB such that AC is 2/3 the length of AB is (3,6) .

In the question ,

it is given that

the coordinates of the end points of A and B is A(-1,2) and B(5,8) .

also AC = 2/3(AB)

So , AC/AB = 2/3

and given that point C is on the line AB , hence AC+CB=AC

2+CB=3

So , CB=1

hence AC/CB = 2/1

so , the point C divides the line AB in the ration 2:1 .

and we have the coordinates of end points ,

that is x₁[tex]=[/tex] -1 , y₁=2 and x₂=5 , y₂ = 8 and the ratio m=2 and n=1 .

Substituting the above values in the section formula ,

which states that the coordinate of point C will be

((m*x₂+n*x₁)/(m+n)  ,  (m*y₂+n*y₁)/(m+n))

= ((2*5+1*(-1))/(2+1) , (2*8+1*2)/(2+1))

= ((10-1)/3 , (16+2)/3)

= (9/3 , 18/3)

= (3,6)

Therefore , The coordinates of the point C on AB such that AC is 2/3 the length of AB is (3,6) .

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In linear equation, The price at which the quantity demanded equals the quantity supplied is $ 260."  option (b) is answer.

What in mathematics is a linear equation?

a.  The demand for a product is given by p+3q= 315 or, q = (315 - p)/3 and the supply for this product is given by  p-7q = 65 or, q = (p- 65)/7

The price at which the quantity demanded equals the quantity supplied is given by

              315 - p/3 = p - 65/7

         7( 315 - p ) = 3( p - 65 )

        2405 - 7p = 3p - 195

        2405 + 195 = 3p + 7p

           2600 =  10p

            p = 2600/10 = 260

Thus, the required price is $ 260.

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