Use integers to represent the values in the statement the highest elevation in a country is a mountain with an altitude of 14,240 ft the lowest elevation in the country is a valley with an altitude of 285 feet below sea level

Answer:

12

Step-by-step explanation:

y= 51 x 4 = 204

x= 3 x 4 = 12

Answer:

Step-by-step explanation:

The value of X when Y is 204 is 12

Let the relationship between X and Y be a direct proportion

If Y and X is directly proportional then;

k is the constant of proportionality

If X = 3 and Y = 51

In order to get the value of X if Y is 204, Recall;

Hence the value of X when Y is 204 is 12

\(\\ \rm\rightarrowtail \dfrac{-6}{7}\div (\dfrac{-3}{8})\)

\(\\ \rm\rightarrowtail \dfrac{-6}{7}\times \dfrac{8}{-3}\)

\(\\ \rm\rightarrowtail \dfrac{-2}{7}(8)\)

\(\\ \rm\rightarrowtail -16/7\)

\(\\ \rm\rightarrowtail -2\dfrac{2}{7}\)

Based on law of sine, the value of angle C is equal to 94.5 degree.

For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,

we have, by law of sines,

\(\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}\)

\(\dfrac{\sin(angle)}{\text{length of the side opposite to that angle}}\)

we have, by law of sines,

We will use the law of sines to find c as;

sin c                sin 97.5

--------------- = -------------

14.5                      13.7

(13.7)sin c= 14.5 sin 97.5

sin c =  14.5 sin 97.5 / (13.7)

sin c = - 0.1168

Angle c = 94.5

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Answer

Domain in the correct order: -11, -8, 0, 13

Range in the correct order: -13, 0, 8, 11

Step-by-step explanation:

Part (a)

The cost is the initial cost plus the cost per slushie multiplied by the number of slushies sold.

\(C(x)=500+1.25x\)

Part (b)

The revenue is the number of slushies sold multiplied by the amount charged per slushie.

\(R(x)=3.50x\)

The quotient rule is proved below.

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).

Given is the expression -

Q(x) = F(x)/G(x)

Quotient rule in calculus is a method used to find the derivative of any function given in the form of a quotient obtained from the result of the division of two differentiable functions. Mathematically, for a function f(x), we can write -

f'(x) = [u(x)/v(x)]' = [v(x) × u'(x) - u(x) × v'(x)]/[v(x)]²

Now, let f(x) = u(x) and g(x) = v(x).

Q(x) = u(x)/v(x)

Q(x) = u(x) v⁻¹(x)

Using the product rule -

Q'(x) = u'(x) v⁻¹(x) + u(x) {d/dx v⁻¹(x)}

Q'(x) = u'(x) v⁻¹(x) + u(x) (-1)(v(x)⁻²) v'(x)

Q'(x) = u'(x)/v(x) - u(x)v'(x)/v²(x)

Q'(x) = [v(x) × u'(x) - u(x) × v'(x)]/[v(x)]²

Therefore, the quotient rule is proved above.

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0,390 because I did a lot of test and exams on these types of questions

Answer:

The plane is 388 miles far from the airport.

Step-by-step explanation:

We know that, the angle between southeast and south directions is \(135^\circ\).

The plane travels as per the triangle as shown in the attached image.

A is the location of airport.

First it travels for 210 miles southeast from A to B and then 210 miles south from B to C.

\(\angle ABC = 135^\circ\)

To find:

Side AC = ?

Solution:

As we can see, the \(\triangle ABC\) is an isosceles triangle with sides AB = BC = 210 miles.

So, we can say that the angles opposite to the equal angles in a triangle are also equal. \(\angle A = \angle C\)

And sum of all three angles of a triangle is equal to \(180^\circ\).

\(\angle A+\angle B+\angle C = 180^\circ\\\Rightarrow \angle A+135^\circ+\angle A = 180^\circ\\\Rightarrow \angle A = \dfrac{1}{2} \times 45^\circ\\\Rightarrow \angle A =22.5^\circ\)

Now, we can use Sine Rule:

\(\dfrac{a}{sinA} = \dfrac{b}{sinB}\)

a, b are the sides opposite to the angles \(\angle A and \angle B\) respectively.

\(\dfrac{210}{sin22.5^\circ} = \dfrac{b}{sin135^\circ}\\\Rightarrow \dfrac{210}{sin22.5^\circ} = \dfrac{b}{cos45^\circ}\\\Rightarrow b = 210\times \dfrac{1}{\sqrt2 \times 0.3826}\\\Rightarrow b = 210\times \dfrac{1}{0.54}\\\Rightarrow b \approx 388\ miles\)

So, the answer is:

The plane is 388 miles far from the airport.

Answer:

The correct answer is Part 1: The 99% confidence interval for the population proportion is approximately (0.4716, 0.5416).Part 2: With 99% confidence, the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.

Part 1:

To construct a 99% confidence interval for the population proportion, we can use the formula:

Confidence Interval = Sample Proportion ± Margin of Error

where the margin of error is determined by the level of confidence and the standard error.

First, let's calculate the sample proportion:

Sample Proportion = (Number of adults who say they have started paying bills online) / (Total number of adults surveyed)

Sample Proportion = 1436 / 2837 ≈ 0.5066 (rounded to four decimal places)

Next, we need to calculate the standard statistics error, which is the measure of the variability in the sample proportion:

Standard Error = sqrt((Sample Proportion * (1 - Sample Proportion)) / Sample Size)

Standard Error = sqrt((0.5066 * (1 - 0.5066)) / 2837) ≈ 0.0136 (rounded to four decimal places)

Now, we can calculate the margin of error:

Margin of Error = Critical Value * Standard Error

The critical value is based on the desired confidence level. For a 99% confidence level, the critical value is approximately 2.576 (obtained from a standard normal distribution table).

Margin of Error = 2.576 * 0.0136 ≈ 0.0350 (rounded to four decimal places)

Finally, we can construct the confidence interval:

Confidence Interval = Sample Proportion ± Margin of Error

Confidence Interval = 0.5066 ± 0.0350

Confidence Interval ≈ (0.4716, 0.5416) (rounded to four decimal places)

Part 2:

The correct interpretation is:

C. With 99% confidence, it can be said that the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.

This means that we are 99% confident that the true proportion of adults who have started paying bills online falls within the range of 0.4716 to 0.5416. The survey results suggest that approximately 47.16% to 54.16% of the population of adults have started paying bills online in the last year.

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Answer:

the solution to the equation -2a - 6a - 9 = -9 - 6a - 2a is all real numbers, or (-∞, +∞).

Step-by-step explanation:

To solve this equation for "a", you need to simplify and rearrange the terms so that all the "a" terms are on one side of the equation and all the constant terms are on the other side. Here are the steps:

Start by combining the "a" terms on the left side of the equation: -2a - 6a = -8a. The equation now becomes: -8a - 9 = -9 - 6a - 2a.

Combine the constant terms on the right side of the equation: -9 - 2a - 6a = -9 - 8a. The equation now becomes: -8a - 9 = -9 - 8a.

Notice that the "a" terms cancel out on both sides of the equation. This means that the equation is true for any value of "a". Therefore, the solution is all real numbers, or in interval notation: (-∞, +∞).

In summary, the solution to the equation -2a - 6a - 9 = -9 - 6a - 2a is all real numbers, or (-∞, +∞).

Step-by-step explanation:

The equation of line which passes through these points is determined by:

p(x1,y1)=(-1/2,4) p(x2,y2)=(1/2,6)

\( \frac{y - y1}{y2 - y1} = \frac{x - x1}{x2 - x1} \\ \frac{y - 4}{6 - 4} = \frac{x + \frac{ 1}{2} }{ \frac{1}{2} + \frac{1}{2} } \\ \frac{y - 4}{2} = \frac{2x + 1}{2} \\ 2(2x + 1) = 2(y - 4) \\ 4x + 2 = 2y - 8 \\ 4x - 2y + 2 + 8 = 0 \\ 4x - 2y + 10 = 0\)

Note:if you need to ask any question please let me know.

The ordered pairs of the points F, G and H are their locations on the coordinate plane

The point F is above the line 1

The ordered pairs of the points are given as:

F = (0,7)

G = (6, 2)

H = (1,6)

The line is not given; so, I will provide a general explanation.

Of all the three ordered pairs, the point with the greatest y-coordinate is the point F.

This means that the point F can be above the line 1, while the other points G and H are below the line.

See attachment for the illustration of the line and the ordered pairs

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As per questions,

(3m+7)(9m²- 21m+49)

Expanding to a³±b³ formula,

→ 3m³ + 7³

→ 3³×m³ + 7³

→ 27m³ + 343

(x²-2x)(x⁴-2x³+4x²)

→ x²(x⁴-2x³+4x²)-2x(x⁴-2x³+4x²)

→ x²x⁴-2x²x³+4x²x²-2x×x⁴+2x×2x³-8x×x²

→ x⁶-2x⁵+4x⁴-2x⁵+4x⁴-8x³

(2y²-7y)(4y⁴+ 14y³+49y²)

→ 2y²×4y⁴ + 2y²×14y³ + 2y²×49y² -7y×14y³ -7y×49y²

→ 8y⁶+28y⁵+98y⁴-28y⁵-98y⁴

As \( {y}^{a} \times {y}^{b} = {y}^{a + b} \)

→ 8y⁶-343y³

Answer:

\(sin\;60 =\frac{\sqrt{3} }{2}\)

Step-by-step explanation:

The circumference of a circle is given by :

C=2πr, r is the radius of the circle

Also, 2r = D, diameter of the circle

⇒ C = πD

If the diameter of a circle is multiplied by 10, it means,

C = π(10)

⇒ C = 10π

Hence, if the diameter of a circle is multiplied by 10, then its circumference becomes 10π.

Answer:

Check below, please.

Step-by-step explanation:

Hi, there!

Since we can describe eccentricity as \(e=\frac{c}{a}\)

a) Eccentricity close to 0

An ellipsis with eccentricity whose value is 0, is in fact, a degenerate one almost a circle. An ellipse whose value is close to zero is almost a degenerate circle. The closer the eccentricity comes to zero, the more rounded gets the ellipse just like a circle. (Check picture, please)

\(\frac{x^2}{a^2} +\frac{y^2}{b^2} =1 \:(Ellipse \:formula)\\a^2=b^2+c^2 \: (Pythagorean\: Theorem)\:a=longer \:axis.\:b=shorter \:axis)\\a^2=b^2+(0)^2 \:(c\:is \:the\: distance \: the\: Foci)\\\\a^2=b^2 \\a=b\: (the \:halves \:of \:each\:axes \:measure \:the \:same)\)

b) Eccentricity =5

\(5=\frac{c}{a} \:c=5a\)

An eccentricity equal to 5 implies that the distance between the Foci has to be five (5) times larger than the half of its longer axis! In this case, there can't be an ellipse since the eccentricity must be between 0 and 1 in other words:

\(If\:e=\frac{c}{a} \:then\:c>0 , and\: c>0 \:then \:1>e>0\)

c) Eccentricity close to 1

In this case, the eccentricity close or equal to 1 We must conceive an ellipse whose measure for the half of the longer axis a and the distance between the Foci 'c' they both have the same size.

\(a=c\\\\a^2=b^2+c^2\:(In \:the\:Pythagorean\:Theorem\: we \:should\:conceive \:b=0)\)

\(Then:\\\\a=c\\e=\frac{c}{a}\therefore e=1\)

Answer:

1/2 is 1 example

Step-by-step explanation:

what

A fraction that is less than 5/8 is 4/8

The fraction is given as:

Fraction = 5/8

A fraction less than 5/8 will have the same denominator but a smaller numerator compared to 5/8

Take for instance, the numerator can be

1 to 4

So, we have;

Smaller fraction = 4/8

Hence, a fraction that is less than 5/8 is 4/8

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The regression line is yˆ = 4 + 1.891x , the coefficient of determination of two variables or the fraction of the variation in y that can be explained by the variation in the values of x is 0.51..

Here the fitted regression equation of y on x is

yˆ = 4 + 1.891x ---(*)

where, x --> Independent variable

yˆ --> predicted value of the dependent variable

Now, b₁ = slope cofficient = 1.891 ~ 1.91

(estimated from least squares method)

We have given that,

Standard deviations for X = 1.34 = sₓ say

Standard deviations for Y = 3.6 = sᵧ say

we know, b₁ = r₀( sₓ/sᵧ ) where ro is corr(X,Y)

=> 1.91 = r₀ (3.6/1.34)

=> 1.91×1.34/ 3.6 = r₀

=> r₀ = 0.71944

Defining, R² = cofficient of determination of two variables = Proportion of variation in Y , explained by the variation in the value of X, through the regression model.

= (r₀)² = (0.71944)² = 0.505442

R² = 0.505442 ~ 0.51 (in two decimals)

Hence, the cofficient of determination is 0.51..

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Complete question:

Using your favorite statistics software package, you generate a scatter plot which displays a linear form. You find a regression equation and the standard deviation for both variables. The standard deviation for x is 1.34 , and the standard deviation for y is 3.6 . The regression equation is reported as y = 4 + 1.891x . What fraction of the variation in y can be explained by the variation in the values of x? (Enter your answer as a decimal between 1 and 2.)

Answer:

B. -2x + 5

Step-by-step explanation:

First, distribute the 3 and 2 to the parentheses:

3(2x + 1) - 2(4x - 1)

6x + 3 - 8x + 2

Add like terms:

-2x + 5

So, the simplified expression is -2x + 5

B is the correct answer

Answer:

it is B

Step-by-step explanation:

3*2x=6x

2*4x=8x

1*3=3

1*2=2

6x-8x= -2x

3+2=5

i got the +2 because there are two negative signs and that makes it positive

Molina jumped the greatest distance at a long jump competition which is 9.601 feet

Decimal: A decimal is a number that consists of a whole and a fractional part. Decimal numbers lie between integers and represent numerical value for quantities that are whole plus some part of a whole.

Given in the question that, the distance each of four students jumped a long jump competition

Student Distance

Aleena  9.46 feet

Susan    9.068 feet

Molina   9.601 feet

Anna      9.04 feet

let us compare the feet jumped by the  students

write them in ascending order to get the highest feet based on decimal values

9.04, 9.068, 9.46, 9.601

by checking the order we can confirm that 9.601 feet is the highest

9.601 feet long jump was done by Molina

so we can conclude that Molina jumped the greatest distance

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Answer:

The last one of commutative property of addition since there is no swapping of numbers related with addition.  

Answer:

nice

Step-by-step explanation:

whats the rest of the problem or is it just that she rolled a dice

The homeowner should go with option 1 for his budget of $40,200 to use complete budget.

Any equation that can be rearranged in the standard form as is referred to as a quadratic equation (from the Latin quadratus, "square").

ax² + bx + c = 0

where x is a value that is unknown, a, b, and c are numbers that are known, and a is a negative number. The numbers a, b, and c are the equation's coefficients; they are referred to as the constant or free term, the quadratic coefficient, and the linear coefficient, respectively.

Solutions of the equation and roots or zeros of the expression on its left-hand side are the values of x that satisfy the equation. There can only be two solutions to a quadratic equation. One suggests that there is only one solution, which is a double root.

Given a rectangular pool of  35-foot by 20-foot

area of pool = 35 x 20 = 700 sq. foot

and to built a patio around pool of equal width,

budget of patio of $40,200 all amount to be used,

Option 1: Surround the pool with a concrete band of equal width on all sides. The concrete costs $50 per square foot.

the area covered by amount is 40200/50 = 804

let width of patio be x

new length = 35 + x and new breadth = 20 + x

area covered by patio = new area including width - area of pool

new area including width = area covered by patio +  area of pool

new area including width = 804 + 700 = 1504

1504 =  (35 + x)(20 + x )

1504 = x² + 35x + 20x + 700

x² + 55x - 804 = 0

solving the equation by quadratic formula

x = (-b ± \(\sqrt{b^{2} - 4ac }\))/ 2a

where a = 1, b = 55, and c = -804

x = (-55 ± \(\sqrt{(55)^{2} - 4*1*(-804) }\))/2

x = (-55 ± √(3025 + 3216))/2

x = (-55 ± 79)/2

taking positive values

x = (-55 + 79)/2 = 12

new length = 35 + 12 = 47 foot

new breadth = 20 + 12 = 32 foot

area covered by patio = (47x32) - (35x20)

area covered by patio = 804 sq. foot

and cost will be 804 x 50 = $40,200

for option 2:  Surround the pool with a tile band of equal width on all sides. The tile costs $80 for each square foot tile.

area for patio = 40200/80 = 502.5

since the area is in fraction the cost will come in approximation.

Hence the homeowner should go with option 1 for complete use of budget.

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