which measure captures the variation in ressponses? multiple choice the frequency distribution the median the mode the standard deviation the mean

The distance from lake b to camp is 310 km and the direction of lake b to camp is 57° S of W.

Distance is a numerical value. The length between the two points is measured by distance. The face or position of an object or person can be said by direction.

There are four cardinal directions which are the main four compass directions. The four directions are North, East, West and South. North-East, North-West, South-East and South-West also come under directions.

As per the question,

With a scale of unit 1, the vector from the base camp to the lake to the vector connecting lakes a and b is graphically represented.

Therefore, 310 km is the distance from the lake b to base camp and 57.0° south of west is the direction of the plane.

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Answer:

y=ax+b

a=(y2-y1) /(x2-x1) =(-4+2)/(-4+5)=-2

The equation becomes:

y=-2x+b

Substitute (-2,-5) in the equation:

-5=-2(-2)+b

b=-9

y=-2x-9

Answer:

Below

Step-by-step explanation:

x values are the DOMAIN....for this equation 'x' can have any value :

 (- inf, + inf)

the y values that the function can have define the RANGE of the function. Due to the absolute value bars.....'y' can only be positive values or zero:

  [ 0 , + inf)

The doubles plus one fact for 7 7  is 7+7+1=15.

In layman's terms, Double Plus One Fact is a strategy for adding two consecutive numbers (numbers that are next to each other). To get the final result, simply add a smaller number to itself or double it and add 1.

Doubles fact are the numbers which are added with itself. such as 5+5=10, 3+3=6

so the doubles plus one fact are nothing but adding 1 to the result of doubles fact.

for given, doubles plus one fact for 7 7 is 7+7=14 and then adding 1 gives 14+1=15.

Hence, 7+7+1=15 is the doubles plus one fact for 7 7.

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According to the evidence, we cannot conclude that the lower proportions of drowsiness in group 1 subjects is the side effect of the subjects in group 2., at alpha equals 0.05 level of significance. Thus, the correct option is C.

It is given that in the double-blind clinical trial, children are divided into two groups.

[tex]H_0 : p1=p2\\[/tex]

[tex]H_a: p1 > p2[/tex]

Now, N1= 450 , P1=136/450=0.3022

N2=95, P2=39/95=0.410

We have to now state the null and alternative hypotheses and draw conclusions based on them.

Now, the test statistics are done as follows:

Z= [tex]p1-p2/\sqrt{p1*1-p1/n1+p2*1-p2/n2}[/tex]

Z= [tex]0.3022-0.410/\sqrt{0.3022*1-0.3022/450+0.410*1-0.410/95}[/tex]

Z= [tex]-0.10/\sqrt{4.686+0.0025}[/tex]

Z= -0.10/2.165

Z= -0.04

At the significance level of 0.05.

Decision: We will reject the null hypothesis if the value of Z is less than the critical value

Critical value at Z(0.05)= -1.645

Thus, we will not reject the null hypothesis as the value of z is greater than the critical value. Thus, in this situation, we cannot conclude that the lower proportions of drowsiness in group 1 subjects as the side effect of the subjects in group 2.

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The function that represents the number of weeks with the height of the tomato plants is 4t - 25y = -150.

When the week has started, the height of the plant in inches is 6 inches.

So, one point can be (0,6).

Now, it is said that the plants grows at a rate of 16% per inches for several months.

So, it means that the slope of the equation is 0.16.

Now, we can use the point slope form of the line.

So, the required equation of the line is,

(y-6)/(t-0) = 0.16

y-6 = 0.16t

16t - 100y = -600

4t - 25y = -150

So, the above equation of line is the function that will relate number of weeks with the height of the plant.

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The length and height of the box with a volume of 70 cubic feet to reduce construction costs is 8.572 and 3.81.

Given that,

The base of an open box must be built with the length of the base being four times more than the width of the base. If building the base costs two dollars per square foot and building the four sides costs one dollar per square foot.

We have to identify the dimensions of a box with a volume of 70 cubic feet to reduce construction costs.

We know that,

The volume =70 cubic feet

L=4w    ------>equation(1)

Volume= l×w×h

70=4w×w×h

h=70/4w²     ------>equation(2)

The construction cost is

C= 4(lw)+2(wh)+2(hl)

C=4(4w×w)+2(w×70/4w²)+2(4w×70/4w²)

C=4(4w²)+2(70/4w)+2(70/w)

C=16w²+70/2w+140/w

Now,

To determine the minimum cost,

dC/dw

16w-70/4w²-140/w²=0

16w³=1/w²(70/4+140)

16w³=1/w²(315/2)

16w³=315/2

w³=315/32

w=2.143

From equation(1)

L=4w=4×2.143=8.572

H=70/4w²=70/4(2.143)²=3.81

Therefore, The length and height of the box with a volume of 70 cubic feet to reduce construction costs is 8.572 and 3.81.

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Some of the situations where we can apply parallel lines cut by transversal are mentioned below.

Transversal line is a line which cuts two or more coplanar lines. Coplanar lines are the lines which does not intersect each other.

The real life situations were we can apply parallel lines cut by transversal are:

Thus, in real life there are many situations where parallel lines cut by transversal.

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The final balance is $446.44

What is compound interest ?

Compound interest is when you add the interest you've already earned back into your principal balance, which increases your returns by compounding them. Consider that you have $1,000 in a savings account with a 5% annual interest rate. You would make $50 in the first year, giving you a new balance of $1,050.

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.

r = 5/100

r = 0.05 rate per year,

Then solve the equation for A

A = P(1 + r/n)^nt

A = 300.00(1 + 0.05/4)^(4)(8)

A = 300.00(1 + 0.0125)^(32)

A = 446.44

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The example of descriptive statistics is d) 50% of the students surveyed spend at least two hours online each day.

Given:

a survey on internet usage was conducted among a group of 200 students in the school cafeteria. it was found that 100 students spend at least two hours online every day.

Here number of possible outcomes = 200

Number of favorable outcomes = 100

Probability p = 100/200

= 1/2

= 0.5

= 0.5*100%

= 50%

Therefore  50% of the students surveyed spend at least two hours online each day.

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Full question:

A survey on Internet usage was conducted among a group of 200 students in the school cafeteria. It was found that 100 students spend at least two hours online every day.Which of these is an example of descriptive statistics?a.) 50% of the students surveyed spend at least two hours online each day.b.) 50% of the students in the school spend at least two hours online each day.c.) 50% of the students in a class spend at least two hours online each day.d.) 50% of the students in the cafeteria spend at least two hours online each day.

The HL postulate states that two triangles are congruent if the hypotenuse and leg of one right triangle are congruent with the hypotenuse and leg of another right triangle.

Hypotenuse Leg Theorem

hypotenuse theorem proof shows how a given set of right triangles is congruent when the corresponding hypotenuses and one leg are of equal length.

Statement:

Two triangles are congruent by the hypotenuse leg theorem if the hypotenuse and one leg of a right triangle are congruent with the hypotenuse and leg of another right triangle.

given: where ABC is an isosceles triangle, AB = AC, and AD is perpendicular to BC.

Proof : AD as altitude is perpendicular to BC and forms ADB and ADC as right triangles. AB and AC are the respective hypotenuses of these triangles and we know they are equal. Because AD = AD is common for both triangles.

That is, AB = AC and AD is common.

Therefore, the hypotenuse and pair of legs of the two right-angled triangles satisfy the definition of the HL theorem.

We know that angles B and C are equal (property of isosceles triangle).

We also know that the angles BAD and CAD are equal (AD bisects BC and BD equals CD).

Therefore, △ADB ≅ △ADC

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The maximum degree of f(x) g(x) will be 14 and the minimum degreee of f(x) g(x) will be 0.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Function f(x) is a polynomial of degree 7,

And, g(x) is a polynomial of degree 7.

Now,

Since, Function f(x) is a polynomial of degree 7,

And, g(x) is a polynomial of degree 7.

Hence, The maximum degree of f(x) g(x) = 7 + 7 = 14

And, The minimum degree of f(x) g(x) = 0

Thus, The maximum degree of f(x) g(x) will be 14 and the minimum degree of f(x) g(x) will be 0.

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Research or Basic research is purely thoretical in  nature as its not easy to find its application in the real world. For example consider new theorems or  Formula in mathematics, its difficult to find their practical use right away as it takes time to find the fields where they may be applicable.

Practical research is more focused on solving a known problem hence its use is already known or easy to find as it is derived from real world only.

Like Research in development of new medicine is practical in nature as we know for whic disease we are trying to cure from it.

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In general, the limit will reach infinity or negative infinity when you take a limit and the denominator is equal to zero (depending on the sign of the function).

The number zero is not a real number. It is a mathematical notion used to symbolize an extremely huge value that is theoretically impossible to obtain. Limit solutions imply that the equation you are getting the limit of will continue to go in that direction indefinitely. The graph approaches but never touches the y-axis (represented by x = 0) because you have a vertical asymptote there. g(x) = 1/(x2) will continue to rise as you approach x = 0 from the right or left. You can picture it continuing upwards after it leaves the page. In other words, because g(x) keeps increasing indefinitely as x approaches 0, its limit is infinity.

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A population proportion is estimated to be around 541.

We can use the formula for the minimal sample size required for an interval estimate of a population proportion to address the problem.

n = pq ((Z/2) / E)^2

We use the conventional p and q, which are 0.5 and 0.5, because p is not defined.

The reason for this is that, if we choose values for p and q that range from 0.1 to 0.9, we will see that this is the point at which pq reaches its greatest value.

The value of (Z/2) will then be determined. We may determine that (Z/2) = 2.326 with a 98% confidence level by looking at the Z-table. We now begin changing the values in the formula above.

n = (0.5)×(0.5) × (2.326/0.05)^2

n = 541.027

n ≅ 541.

So, population proportion is estimated to be around 541

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Answer:

Step-by-step explanation:

Two different fractions where lowest common denominator is 20 are 1/4 and 1/5.

What are the lowest common denominator?

For two or more fractions, if the numbers at the bottom (or denominator) by which the lowest number can be divide into, is called the lowest common denominator. It is also known as the least common denominator.

Here, 20 is the given lowest common denominator. 

Therefore, we can write: 20 = 1 × 20, 20 = 2 × 10, 20 = 4×5

Hence, two fractions for which 20 can be a lowest common denominator are 1/4 and 1/5.

Hope it helps!

Step-by-step explanation:

it depends on what the numbers are now if it's negative 10 and you're positive number is like over 10 then your number will be positive now if the negative number is more than the positive number then you know your answer is going to be negative so negative 10 - -5 is -5 so there would be your answer now if it was negative 10 - 20 that would be positive 10 does that make any sense

In this scenario, the dependent variable is the time the pencil takes to become dull and the type of pencil.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that, there are three different pencils that Monique possesses. She's interested in finding out what kind of pencil maintains its sharpness the longest. Each pencil she uses leaves an identical mark on a piece of paper.

There are often two different sorts of variables in analytics. We obtained that independent variables will have an impact on dependent variables. What occurs as a result of the independent variable is referred to as a dependent variable.

Thus, in this scenario, the dependent variable is the time the pencil takes to become dull and the type of pencil.

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Rejecting a null hypothesis that is actually true in the population results in a type I error (false-positive); failing to reject a null hypothesis that is actually untrue in the Type II errors are produced by the population (false-negative).

Given that,

We have to find what kind of error is committed if the researcher doesn't rule out the null hypothesis even though it's incorrect.

We know that,

To determine whether the provided experimental results are valid, the null hypothesis is a type of hypothesis that explains the population parameter. Depending on the viability of the given population or sample, this hypothesis is either rejected or not.

Rejecting a null hypothesis that is actually true in the population results in a type I error (false-positive); failing to reject a null hypothesis that is actually untrue in the Type II errors are produced by the population (false-negative).

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a) The critical value 90% is 1.833

b) The critical value for 98% is 2.528

c) The critical value of 90% is 1.645

d) 3.169 is the critical value of 99%.

The critical probability (p*) = 1 - (α / 2), where α equals 1 - (confidence level / 100).

Given that an independent random sample is drawn from a population with an essentially normal standard deviation.

To calculate the degrees of freedom and crucial t-value for a given sample size and confidence level.

n-1 degrees of freedom

Critical t can be obtained from the internet's t table.

a) degree of liberty = 5

The critical 90% is 1.833

b) degree of freedom is 20.

The critical value for 98% is 2.528

c) degree of freedom =28

The critical value of 90% is 1.645

d) degree of freedom =10.

3.169 is the critical value of 99%.

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The cost of 15 cups is £35 and the cost of 7 glasses is £42 after applying the concept of the linear equation.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Let the cost of 15 cups is x

3 → 7

15 → x

3/15 = 7/x

1/5 = 7/x

x = £35

The cost of 7 glasses:

= (24x7)/4

= £42

Thus, the cost of 15 cups is £35 and the cost of 7 glasses is £42 after applying the concept of the linear equation.

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The average velocity for the time period is -15 feet per second

The velocity of the ball = 31 feet / seconds

The function of the height is

y = 31t - 23t^2

Time period beginning when t = 1 and lasting .01 s, .005 s, .002 s, .001 s

The average velocity = f(1.01) - f(1) / 1.01 - 1

f(t) = 31t - 23t^2

f(1.01) = 31(1.01) - 23(1.01)^2

= 31.31 - 23.46

= 7.85 feet per second

Similarly

f(1) = 31(1) - 23(1)^2

= 31 - 23

= 8 feet per second

The average velocity =  7.85 - 8 / 1.01 - 1

= -0.15 / 0.01

= -15 feet per second

Hence, the average velocity for the time period is -15 feet per second

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Length of the actual tent is 15 feet.

Actual length is any distance between points that is not foreshortened by the view type.

Given that the scale of drawing is

1 inch : 5 feet

and length is 3 inches.

We have to find actual length of the tent.

Let us denote actual length of the tent by 'x'

We have by given data

3 inches : x = 1 inch : 5 feet

multiplying LHS by 3 we get,

3 : x = 3 : 15

By comparing both the sides

x = 15

Therefore the actual length of the tent is 15 feet.

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Answer:

x=11

Step-by-step explanation:

we need to change 3/2 to have a denominator of 6

3x3/2x3

9/6

Now we set x-2 equal to 9

x-2=9

 +2 +2

x=11

Hopes this helps please mark brainliest

Answer:

[tex]\huge\boxed{\sf x = 11}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{x-2}{6} = \frac{3}{2} \\\\Cross \ Multiply\\\\2(x-2)=3 \times 6\\\\Distribute\\\\2x - 4 = 18\\\\Add \ 4 \ to \ both \ sides\\\\2x = 18+4\\\\2x = 22\\\\Divide \ 2 \ to \ both \ sides\\\\x = 11\\\\\rule[225]{225}{2}[/tex]

In the Binary method's complement method, positive integers are represented as they would in in sign-and-magnitude format. the leftmost bit is still reserved as the sign bit. a negative integer is just the complement of the positive integer, with a 1 in the leftmost spot to represent the negative sign

The method of complements is a technique to encode a symmetric range of positive and negative integers in a way that they can use the same algorithm for addition and subtraction throughout the whole range

Changing the sign of any number is encoded by generating its complement, which is usually done by a very simple and efficient algorithm

Therefore, In the Binary method's complement method, positive integers are represented as they would in in sign-and-magnitude format.

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The required Cost of the bench will be $475

Let the cost of a garden table be $x

And the cost of a bench be  $y

Now, according to the question

Combined cost of garden table and bench are $1023

Therefore, we can write

x + y = 1023……….(i)

Now, again the cost of garden table is $73 more than that the cost of the bench

Therefore, we can write

x - y = 73………..(ii)

Subtracting equation (i) and (ii) we get

2x = 1096

x = 1096/2 = 548

x = 548

Putting the value of x in equation in (i) we get

y = 1023 - 548 = 475

Cost of garden table is $x = $548

Cost of bench is $y = $475

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True , In any random sample drawn from a population, the sample mean is an unbiased estimator of the population mean.

What is the central limit theorem formula?

The central limit theorem gives a formula for the sample mean and the sample standard deviation when the population mean and standard deviation are known. This is given as follows: Sample mean = Population mean = μ μ Sample standard deviation = (Population standard deviation) / √n = σ / √n.

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the rectangular coordinates of the point whose spherical coordinates are given. (3, 0, 0) are (0.0.3)

What is spherical coordinates?

The coordinate system that is most frequently employed in three-dimensional systems is called spherical coordinates of the system, represented as (r,Ф,∅ ). The surface area in three dimensions is calculated using the spherical coordinate system. Radial distance, polar angles, and azimuthal angle are the three numbers that these coordinates indicate. Additionally known as spherical polar coordinates.

Given (r,Ф,∅ ) = (3,0,0)

x = rsin∅ cosФ = 3 * sin0 *cos0 = 0

y =  rsin∅ sinФ = 3*0*0 = 0

z = rcos∅ = 3*1 = 3'

SO (x,y,y) = (0,0,3)

Hence the rectangular coordinates of the point whose spherical coordinates are given. (3, 0, 0) are (0.0.3)

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The measure of the angle of elevation of the sun to the nearest degree is 35 degrees.

Given:

A 50 foot tall tree casts a 72 foot shadow.

Here tree height is opposite to angle of elevation and shadow is adjacent to angle of elevation.

Let E be the angle of elevation.

tan(E) = opposite side / adjacent side

= 50/72

= 25/36

= 0.694

E = tan^-1(0.694)

= 34.99 degrees

≈ 35 degrees.

Therefore The measure of the angle of elevation of the sun to the nearest degree is 35 degrees.

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The lengths of the three sides are 15 inches , 19 inches and 25 inches respectively.

Let a represent the length of the shortest side.

Let b represent the length of the mid-length side.

Let c represent the length of the longest side.

From the question, we have

The perimeter of a triangle is 59 in.

a + b + c = 59

The shortest side is 10 in. less than the longest side.

a = c-10

The middle side is 21 in. less than the combined lengths of the shortest and longest sides.

b=(a+c)-21

b=(59-b)-21

2b = 38

b = 19 inches

substituting the value  we get

a+c = 40................(i)

a-c = -10................(ii)

Solving, we get

2a = 30

a = 15 inches

c=25 inches

The lengths of the three sides are 15 inches , 19 inches and 25 inches respectively.

Addition:

The act of combining two or more items is known as addition. The process of computing the sum of two or more numbers in mathematics is called addition. It is a fundamental mathematical procedure that is frequently used in daily life. When we work with money, figure out our food bills, or figure out the time, we frequently employ addition. One-digit numbers can be added simply for solving addition problems, however for bigger numbers, we divide the numbers into columns using their corresponding place values, such as ones, tens, hundreds, thousands, and so on.

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