Select that integer that matches the following situation:
I go for a hike in Colorado. The top of the mountain is , feet above sea level.

Question 4 options:

A: 144


B: 14,000


C: -14


D: -14,000

The correlation values 1 and -1 represent a perfect linear relationship between the two variables x and y.

Step to Step explanation:

Therefore, the perfect linear relationship between two variables x and y is given correlation value 1 and -1.

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a) The system of equations that represents this situation is given as follows:

b) The number of cups of regular lemonade sold is given as follows: 60.

c) The number of cups of pink lemonade sold is given as follows: 80.

The amounts are obtained with a system of equations, in which the variables are as defined in the problem.

They sell 140 cups, hence:

x + y = 140.

y = 140 - x.

They earn a total of $90, hence, considering the amount earned per cup:

0.5x + 0.75y = 90.

Replacing the first equation into the second, the variable x is obtained as follows:

0.5x + 0.75(140 - x) = 90.

0.25x = 15

x = 15/0.25

x = 60.

Then the variable y has a value of:

y = 140 - x = 140 - 60 = 80.

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Answer:

Step-by-step explanation:

4% = 4/100

4/100 x 30 = 1.2

30 + 1.2 = 31.20 (nearest cent)

Answer:

31.20

Step by step explanation: I got it from delta

The height and radius of the cup that will use the smallest amount of paper are 3.86 cm and 2.72 cm. The result is obtained by using the first derivative .

To find the height and radius of a cone for the smallest surface area, we can use the first derivative dS/dh. We then equate it to 0 for the maximum value.

The volume of a cone-shaped paper drinking cup is 30 cm³. Find the height and radius for the smallest amount of paper!

The radius of the cone can be expressed as

V = 1/3 (πr²h)

30 = 1/3 (πr²h)

90 = πr²h

r² = 90/πh

The surface area of the cone can be expressed as

S = πrs

[tex]S = \pi r \times \sqrt{h^{2} + r^{2}}[/tex]

[tex]S = \pi \sqrt{\frac{90}{\pi h}} \times \sqrt{{h^{2} + \frac{90}{\pi h}[/tex]

[tex]S = \pi \sqrt{\frac{90}{\pi h}} \times \sqrt{\frac{(\pi h^{3} + 90)}{\pi h}[/tex]

[tex]S = \sqrt{90} \times \sqrt{\frac{(\pi h^{3} + 90)}{h^{2}}[/tex]

[tex]S = \sqrt{90} \times \sqrt{\pi h + \frac{90}{h^{2}} }[/tex]

The 1st derivative is

[tex]\frac{dS}{dh} = \sqrt{90} \times (\pi - \frac{180}{h^{3}}) \times [(\pi h + \frac{90}{h^{2}})^{-\frac{1}{2} } ][/tex]

[tex]0 = \sqrt{90} \times (\pi - \frac{180}{h^{3}}) \times [(\pi h + \frac{90}{h^{2}})^{-\frac{1}{2} } ][/tex]

The height for the smallest amount of paper is

π - 180/h³ = 0

π = 180/h³

h³ = 180/π

h³ = 57.32

h = 3.86 cm

The radius for the smallest amount of paper is

r² = 90/πh

r² = 90/π(3.86)

r² = 7.42

r = 2.72 cm

Hence, the dimension of the cone-shaped paper drinking cup for the smallest amount of paper is

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The equation of the line perpendicular to 4x + 3y = -24 that passes through the point (-8, 3) is 4y = 3x + 36.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given:

4x + 3y = -24 and point (-8, 3).

Calculate the slope,

3y = -4x - 24

y = -4 / 3 x - 8

so, m = -4 / 3

The slope of the perpendicular line, M = - 1 / m

M = - 1 / -4 / 3 = 3 / 4

Calculate the equation of the line as shown below,

y - 3 = 3 / 4 [x - (-8)]

y - 3 =  3 / 4 [x + 8]

4y - 12 = 3x + 24

4y = 3x + 36

Therefore, the equation of the line perpendicular to 4x + 3y = -24 that passes through the point (-8, 3) is 4y = 3x + 36.

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The equation of best fit is y = (-22/5)x + 10.

What is an equation of a line?

The equation of a line is given by:

y = mx + c where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The following coordinates are given:

Pick two coordinates.

(0, 10) and (25, -100)

The equation of best fit.

y = mx + c

Now,

m = (-100 - 10) / (25 - 0)

m = -110 / 25

m = -22/5

Now,

(0, 10) = (x, y)

10 = (-22/5) x 0 + c

c = 10

Now,

y = mx + c

y = (-22/5)x + 10

Thus,

Using the coordinates the equation of best fit is y = (-22/5)x + 10.

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The prove the SAS congruence rule,  two sides and one angles between the includes sides of the triangle and the two sides and one angles between the includes sides of the another triangle should be equal

The SAS congruence rule is used to prove the congruence of the one triangle angle and another triangle.

SAS congruence rule stands for the side-angle-side congruence rule of triangles.

Side-angle-side rule of congruence states that if two sides and one angles between the includes sides of the triangle is equal to the two sides and one angles between the includes sides of the another triangle, then the both the triangles are congruent

Therefore, to prove the SAS congruence rule two sides and one angle of both triangle should be equal

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Answer:

79°

Step-by-step explanation:

All three of the angles form a straight line = 180°

28 + x + 73 = 180

x = 79°

Answer:x=79

Step-by-step explanation:

As calculated with the help of Pythagorean theorem, The ladder will reach 19.36 feet high on the building.

What is Pythagorean theorem?

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a fundamental Euclidean geometry relationship between the three sides of a right triangle. The square whose side is the hypotenuse, or the side across from the right angle, has an area equal to the sum of the areas of the squares on its other two sides. The Pythagorean equation, which connects the lengths of the sides B, P, and the hypotenuse H, can be used to express this theorem.

H² = B² + P²

As given in the question,

the length of the ladder is 20 ft. which will work as a hypotenuse of a right angled triangle,

The base is 5 ft.

we need to find the perpendicular line to the base.

Applying Pythagorean theorem.

H² = B² + P²

20² = 5² + P²

400 = 25 + P²

400 - 25 = P²

P = 19.36 ft.

Therefore, the ladder will go 19.36 ft. high on the building.

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Answer:

3072, -12288, 49152

Step-by-step explanation:

[tex]-3*-4=12\\12*-4=-48\\-48*-4=192\\192*-4=-768\\-768*-4=3072\\3072*-4=-12288\\-12288*-4=49152\\\\Answer= -3,12,-48,192,-768,3072,-12288,49152[/tex]

The equation of a line passes through (6,1) is 3x - 2y = 16.

Here we have to find the equation of a line.

Data given:

Point = (6,1)

The equation of another line is 2x + 3y = 18

From the given equation we can find the slope;

So we have

3y = -2x + 18

y = -2/3x + 18/3

So the slope is -2/3

As the line is perpendicular, so the slope of the line perpendicular to it will be 3/2

The general formula of the line is:

(y - y1) = m(x-x1)

(x1, y1) is the point

The point is (6,1 ) and the slope is 3/2

Now put that in the equation we get:

(y - 1) = 3/2(x - 6)

2y - 2 = 3x - 18

3x - 2y = 16

Therefore the equation is 3x - 2y = 16.

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Answer x=1/2

Step-by-step explanation:

6x+2=4x+3

2x+2=3

2x=1

x=1/2

Answer:

x= 1/2

Step-by-step explanation:

x=1/2

6x+2=4x+3

-4x     -4x

2x+2=3

-2   -2

2x=1

/2 /2

x=1/2

The probability that their sum will be 6 is 1/6.

What is probability?

The proportion of favorable cases to all possible cases is used to determine how likely an event is to occur.

Here are all rolls of the dice, the sample space,

which contains 36 elements:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

If one face shows a 2, then there are 6 possible faces on the other die.

Only one of those is a 4 which would make the sum of 6.

Hence,  the probability that their sum will be 6 is 1/6.

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The dimensions such as length is 18 and width is 16 or length is 32 and width is 9 will produce an enclosed area of 288ft.

We know that,

P = l + 2w

50 = l + 2w

50 - 2w = l

A = l x w

288 = (50 - 2w)w

288 = 50w -2w²

2w² - 50w + 288

By dividing throughout by 2

w² - 25w + 144

This is in quadratic equation form.

By applying quadratic formula,

w = (-(-25) ± [tex]\sqrt{(-25)^{2}-4*1*144[/tex]) / 2

w = (-(-25) ± 7)/2

w1 =  (-(-25) + 7)/2

w1 = (25 + 7) / 2

w1 = 16

w2 =  (-(-25) - 7)/2

w2 = (25 - 7) / 2

w2 = 9

By substituting the values in eq1,

A = l x w

if w = 16

288 = l x 16

l = 288/16

l = 18

if w = 9

288 = l x 9

l = 288/9

l = 32

The dimensions will be length is 18 and width is 16 or length is 32 and width is 9.

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Using percentages, we know that 83 students more are needed to vote for the vending machine.

Additionally, "pct," "pct," and occasionally "pc" are used. A % is a number without dimensions and without a standard measurement.

For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

So, 65% of the school population is:

650/100 * 65

422.5

Rounding off: 423

Students voted for vending machines is 340.

A number of more votes/asks for the vending machine  will be:

423 - 340

83

Therefore, using percentages, we know that 83 students more are needed to vote for the vending machine.

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A confidence interval estimate of the population mean rating for Miami is:

Confidence interval:

(Mean - E) ≤ μ ≤ (mean + E)

(7.52 - 0.6578) ≤ μ ≤ (7.52 + 0.6578)

6.8622 ≤μ≤ 8.1778

Now, According to the question:

Given the data:

2 6 7 8 9 9 9 10 10 10 10 9 4 5 6 6 8 7 9 10 9

6 5 7 6 8 4 2 10 9 9 10 10 9 8 7 5 9 9 3 6 2 9

7 10 7 9 9 9 9

Assume a confidence interval of 95%

Using calculator :

The mean of the distribution (m) = 7.52

Standard deviation (s) = 2.314

Sample size),

Obtaining the t score ;

Degree of freedom (df) = (n-1) = 50 - 1 = 49

t(1-α/2), 49 = t(0.025, 49) = 2.01 ( t distribution table)

Margin of Error :

2.01 * s/√n = 2.01 * 2.314/7.0710678

Margin of Error (E) = 0.6578

Confidence interval:

(Mean - E) ≤ μ ≤ (mean + E)

(7.52 - 0.6578) ≤ μ ≤ (7.52 + 0.6578)

6.8622 ≤μ≤ 8.1778

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The complete question is this:

The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample of business travelers is selected and each traveler is asked to provide a rating for the Miami International Airport. The ratings obtained from the sample of business travelers follow.

2 6 7 8 9 9 9 10 10 10 10 9 4 5 6 6 8 7 9 10 9

6 5 7 6 8 4 2 10 9 9 10 10 9 8 7 5 9 9 3 6 2 9

7 10 7 9 9 9 9

Required:

Develop a confidence interval estimate of the population mean rating for Miami.

Using simple unitary method, the time taken to take the length of the football field is 25min.

The system for naming or representing numbers is known as the number system or numeral system. We are aware that a number is a mathematical value that aids in the measurement and counting of items as well as in several mathematical operations.

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

Loth travels 60 ft in 5 min.

Loth travels 1 ft in 5/60 min.

Loth travels 300 ft in 5/60 * 300 min.

=1/12 * 30

=25min

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The solution to this problem is , we reject null hypothesis  R H0 at  p value =0.005 .

The likelihood of rejecting the null hypothesis when it is true is the significance level, often known as alpha or. A significance level of 0.05, for instance, represents a 5% likelihood of drawing the incorrect conclusion that a difference exists when there isn't one.

Given that Hippocrates magazine states that 35 percent of all Americans take multiple vitamins regularly.

Persons surveyed = 750

Of those survived no of persons who took multiple vitamin = 296

Sample proportion = p =0.395

q =1-p = 0.605

[tex]H_{0}\\[/tex] : p= 0.35

[tex]H_{A}[/tex] : p ≠ 0.35

(Two tailed test)

Assuming H0 is true standard error = [tex]\sqrt{(0.35 * 0.65)/750}[/tex]

=>0.0174

p difference = 0.045

Test statistic = 0.045/0.0174

=>2.58

p value = 0.005 for right tailed

Reject H0:

Therefore , we reject  R H0 at  p value =0.005 .

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The equation of the parallel to y = 7/8x + 9 will be y = 7/8x+11, 7x - 8y = 3, and (y-6) = 7/8(x-1).

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given that the equation of the line is y = 7/8x+9. For the equation to be parallel the slope of the line must be the same.

The equations having the same slope of the line as that of y = 7/8x + 9 are,

y = 7/8x+11,

7x - 8y = 3,

(y-6) = 7/8(x-1)

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The Laplace transformation in the given function is = 5 - 8e⁻⁷ˣ/ x

Rewrite f in terms of the unit step function:

[tex]f(t) \left \{ {{y=5} for 0\leq t \leq 7\atop {x=-3}} \rightfor t\leq 7[/tex]

⇒ f(t) = 5{u(t) -u(t -7) - 3u (t -7)}

        = 5u(t) - 8u (t-7)

Recall the time-shifting property of the Laplace transform:

L I u(t - c)f(t -c) I

= e⁻ᵃˣ L[f(t)]

and the Laplace transform of a constant function,

L(K) = [tex]\frac{k}{a}[/tex]

So we have

L{f(t)} = 5u(t) - 8u (t-7)

        = 5 L[1] - 8e⁻⁷ˣ

        = 5 - 8e⁻⁷ˣ/ x

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Using exponential function, the annual rate of change in the school is 1.74%

Exponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function)

In this problem, the annual rate of change can be calculated as

A = P(1 + r)ˣ

Let's substitute the values into the equation and solve;

305 = 275(1 + r)⁶

r = 0.0174

r = 0.0174 * 100

r = 1.74%

The annual rate of change is 1.74%

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Thus, the distribution will be approximately normal when the sample size is large.

According to the central limit theorem, even if a population isn't normally distributed, if you take sufficiently big samples from it, the sample means will be.

Here,

the central limit theorem say about the shape of the distribution of the sample means because

If the sample size is big, the solution will be when the distribution is roughly normal.

thus, the distribution will be approximately normal when the sample size is large.

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The completed two-column table to prove that ABCD is a rectangle is presented as follows;

Step     Statement                      [tex]{}[/tex]      Reason

1   [tex]{}[/tex]       ΔABD ≅ ΔDCA                     Given

[tex]{}[/tex]            [tex]\overline{AD}[/tex] ≅ [tex]\overline{BC}[/tex]                            

2.         [tex]\overline{BD}[/tex] ≅ [tex]\overline{BD}[/tex]                             Reflexive property

3.         [tex]\overline{CA}[/tex] ≅ [tex]\overline{CA}[/tex]                [tex]{}[/tex]              Reflexive property

4. [tex]{}[/tex]      ∠CAD ≅ ∠BDA                       CPCTC

5.  [tex]{}[/tex]       [tex]\overline{AE}[/tex] ≅ [tex]\overline{ED}[/tex]                 Side length of isosceles triangle ΔAED

6.     [tex]{}[/tex]    [tex]\overline{AB}[/tex] ≅ [tex]\overline{ED}[/tex]                              CPCTC

7.  [tex]{}[/tex]       ΔABD ≅ ΔBCD                     SSS

8.        ΔDCA ≅ ΔABC         [tex]{}[/tex]             SSS

9.      ∠B ≅ ∠C ≅ ∠D ≅ ∠A   [tex]{}[/tex]          CPCTC

10.   [tex]{}[/tex] ∠B = ∠C = ∠D = ∠A [tex]{}[/tex]                Definition of congruency

11.   [tex]{}[/tex] ∠B + ∠C + ∠D + ∠A = 360°   [tex]{}[/tex]   Angles in quadrilateral

12.  [tex]{}[/tex] 4·∠B = 360°                              Substitution property

13.   [tex]{}[/tex] ∠B = ∠C = ∠D = ∠A = 90°       Substitution property

14.  [tex]{}[/tex]ABCD is a rectangle                 Definition of a rectangle

A rectangle is a quadrilateral that has four interior angles that are right angles (90°) each and in which the length of the adjacent sides are different.

The details of the reasons used to prove that ABCD is a rectangle are presented as follows;

Reflexive property

The reflexive property of congruency states that a part is congruent to itself

CPCTC

CPCTC is an acronym for Corresponding Parts of Congruent Triangles are Congruent

Isosceles triangle

An isosceles triangle is a triangle with a pair of congruent sides and a pair of congruent base angles

SSS

The Side-Side-Side (SSS) congruency postulate states that two triangles are congruent if the three sides of one triangle are congruent to the three sides of the other triangle

Definition of congruency

A geometric shape is congruent to another geometric figure if they have the same measurement

Angles in a quadrilateral

The sum of the interior angles in a quadrilateral is 360°

Substitution property

The substitution property of equality states that if a = b then b can substitute a in equations and expressions, without changing their value

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The category has an error in the table is A. breakfast.

A survey in human subjects research is a set of questions designed to elicit specific information from a specific group of people. Surveys can be conducted by phone, mail, or the internet, as well as on street corners or in shopping malls.

Historically, survey research has included large amounts of population-based data collection.

The primary goal of this type of survey research was to quickly obtain information describing the characteristics of a large sample of individuals of interest.

The category has an error in the table is breakfast. In this case, the children should be 45 and not 30.

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Domain of square root is not all real numbers.

Domain of a function:

The domain of a function is the set of input values (x) for which it produces an output value.

Like if we consider a function y = f(x)

then input inside function that is x is know as domain of function.

First we write square root function as y =

So inside root negative numbers are not allowed so value of x should be positive numbers  means x>=0.

So domain of square root function [0, ∞).

Domain of square root function is positive real numbers.

Not all real numbers because in all real numbers both positive and negative real numbers come.

Negative real numbers can not be input for square root function.

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The answer to this Question based on ages is 20 years and 30 years

What is age?

The age is measure of how old the person is. It also gives us idea about how many years before he was born This data is used at various places in application forms medical form etc

Let age of Tom be x and age of George be y

given 1st condition george is 3 times as old as Tom

hence we can write y = 3x

After 15 years age of tom = x + 15 and age of George be y + 15

according to 2nd condition

x + 15 = 2/3(y + 15)

3x + 45 = 2y + 30

2y - 3x = 15

put y = 3x here

2(3x) - 3x = 15

3x = 15

x = 5

and y = 3(5)

y = 15

present age of tom = 5 years and after 15 years he will be 20 years old

present age of george = 15 tears and after 15 years he will be 30 years old

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The point is on the line that passes through point h and is perpendicular to line fg is  (-6, 10).

You can get the equation of the blue line and then determine which point is on the perpendicular line to that blue line, but you can alternatively work this out physically simply by examining the points.

The slope of the perpendicular lines is negative reciprocals.

So if FG is 3/4, it would be -4/3.

The slope is calculated as m = (y2-y1)/(x2-x1).

So, in order to acquire the solution, we will enter these values (6,6) till we reach the following result: -4/3

m= (10-(-6)/(-6-6) (-6-6)

m = 16/-12

m= -4/3

As a result, the ultimate answer to this question is A) (-6, 10)

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Answer:

The point is on the line that passes through point h and is perpendicular to line fg is  (-6, 10).You can get the equation of the blue line and then determine which point is on the perpendicular line to that blue line, but you can alternatively work this out physically simply by examining the points. The slope of the perpendicular lines is negative reciprocals.So if FG is 3/4, it would be -4/3.The slope is calculated as m = (y2-y1)/(x2-x1).So, in order to acquire the solution, we will enter these values (6,6) till we reach the following result: -4/3m= (10-(-6)/(-6-6) (-6-6)m = 16/-12m= -4/3As a result, the ultimate answer to this question is

Step-by-step explanation:

The point is on the line that passes through point h and is perpendicular to line fg is  (-6, 10).You can get the equation of the blue line and then determine which point is on the perpendicular line to that blue line, but you can alternatively work this out physically simply by examining the points. The slope of the perpendicular lines is negative reciprocals.So if FG is 3/4, it would be -4/3.The slope is calculated as m = (y2-y1)/(x2-x1).So, in order to acquire the solution, we will enter these values (6,6) till we reach the following result: -4/3m= (10-(-6)/(-6-6) (-6-6)m = 16/-12m= -4/3As a result, the ultimate answer to this question is

The recursive equation for f( n ) is  f( n-1 ) + 3.75

Any term of a sequence in terms of its preceding terms is a recursive equation. The equation can be defined as a mathematical statement made up of expressions. For example, b (n )  = 2b ( n-1 ) + 4 is a recursive equation.

As per the question,

As we know,

⇒   f ( n )   =   total cost

                =   g × n + c

    f ( n )   =   3.75 ( n ) + 2.55

Replace n with n - 1,

⇒   f ( n - 1 )   =   3.75 ( n - 1 )  +  2.55

⇒   f ( n - 1 )   =   3.75 n  -  3.75  +  2.55

⇒   f ( n - 1 )   =   3.75 n  +  2.55  -  3.75

⇒   f ( n - 1 )   =   f ( n )  -  3.75

⇒   f ( n )   =   f ( n - 1 )  +  3.75

Therefore, f( n-1 ) + 3.75 is the recursive equation for f ( n ).

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The equation of cost of taxi payed by cal is,

y=1. 3x+2

here , y --> total cost of taxi

x --> distance travelled by him

Cofficient of x i.e., 1.3 represents the cost/rate of taxi per mile .

We have given a equation of total cost pay by Cal on ordering a taxi from online taxi service. The equation is

y = 1.3x+2

where, y represents the total cost in dollars

x represents the number of miles he travels ; 2 is fixed charge

Since, x represents the number of miles he travels then the cofficient of x is representing the taxi rate or cost per mile . So, that when we multiply 1.3 with number of miles he travel(i.e x ) we get the total cost on travelling x distance.

After adding the total cost of travelling with fixed charge of taxi we get total cost of journey.

Hence, 1.3 represents the cost per mile.

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