find x, show proofs

Answer:

6:36

this is when you time both by 2.

The ratio is equivalent to 3:18 is 7:42.

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

Ratio = 3:18

        = 1:6

1. 6:21

= 3:7

2. 5:20

= 1:4

3. 7:42

= 1:6

4. 12:2

= 6:1

Hence, the ratio is equivalent to 3:18 is 7:42.

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The arc length of the arc is (11/5)π inches, or approximately 6.926 inches (rounded to three decimal places).

We may use the following formula to determine the arc length of an arc having a radius of 18 inches and a centre angle of 22°:

(Central angle / 360°) x (2r) Equals arc length

where r denotes the arc's radius.

Inputting the values provided yields:

arc length is equal to (22°/360°) x (2x18 inches).

arc length is equal to 11/180 times 36 inches.

11.5 inches is the length of an arc.

As a result, the arc's length is (11/5) inches, or roughly 6.926 inches (rounded to three decimal places).

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Since the center of the circle lies on the y-axis, the x-coordinate of the center must be 0.

Also, since the diameter of the circle is 12 units, the radius is half of that, or 6 units.

Using the standard form of the equation of a circle, which is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius, we can substitute the values we know and simplify the equations to see which ones match.

The equations that represent circles with a diameter of 12 units and a center that lies on the y-axis are:

   x^2 + (y - 6)^2 = 36 (center is at (0, 6))

   x^2 + (y + 6)^2 = 36 (center is at (0, -6))

Therefore, the two options that represent the circles with the given properties are:

x^2 + (y - 6)^2 = 36 and x^2 + (y + 6)^2 = 36.

Thus, there is a 99% chance that the gap between Texas and New equation Yorkers' support for a new green programmed is between -0.218 and -0.114.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

a. Using the method below, we can create a 99% confidence interval for the difference between the percentages of Texas and New Yorkers who support a new green initiative:

CI is equal to[tex](p1 - p2) (p1(1-p1)/n1 + p2*(1-p2)/n1) \sqrt.[/tex]

where: 391/553 = 0.7077, where p1 is the percentage of Texans that support the measure.

462/529 = 0.8737, where p2 is the percentage of New Yorkers who support the measure.

n1 is the sample size for Texas, which is 553; n2 is the sample size for New Yorkers, which is 529; and z is the z-score, which is 2.576 at 99% confidence level.

CI is calculated as[tex](0.7077 - 0.8737) 2.576\sqrt(0.7077(1-0.7077)/553 + 0.8737*(1-0.8737)/529).[/tex]

CI = (-0.166 ± 0.052)

Thus, there is a 99% chance that the gap between Texas and New Yorkers' support for a new green programme is between -0.218 and -0.114.

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Therefore , the solution of the given problem of equation comes out to be  y = 6x + 11.

Mathematical formulas frequently use the same letter to try to impose uniformity between two claims. Many variable academic numbers are shown to be equal using mathematical equations, also known as assertions. The normalise divides 12 and b + 6 into two parts using the result y + 6 = 12 as an illustration. It is possible to determine the connection between each sign component and the number of lines. The significance of a symbol usually contradicts itself.

Here,

In slope-intercept form, the provided equation y = -1/6x - 2 has a slope of -1/6. Consequently, this line's perpendicular inclination is as follows:

=> m2 = -(1/-1/6) = 6

Now that we know the desired line's slope and the spot through which it passes (-2, -1). To determine the solution of a linear equation, we can use its point-slope form:

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

where m is the slope 6 and (x1, y1) is the position (-2, -1). By replacing these numbers, we obtain:

=> y + 1 = 6(x + 2) y + 1

=> 6x + 12 y + 1

=> 6x + 11 y - (-1)

=> 6(x - (-2))

As a result, the equation for the line passing through the position (-2, -1) and perpendicular to y = -1/6x - 2 is y = 6x + 11.

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Solving the equation by completing the square gives the solution as;

x = (6, -10)

The equation we are given to complete the square is;

x² + 4x = 60

Add half the square of half of the coefficient of x to both sides to get;

x² + 4x + (4/2)² = 60 + (4/2)²

x² + 4x + 4 = 64

Writing left hand side as a perfect square gives;

(x + 2)² = 64

Taking square root of both sides gives;

x + 2 = ±8

x = -2 ± 8

x = (6, -10)

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Since the electorate have decided that Senator Wiggins is the best candidate for the position. The  logical form of this argument is option b. Disjunctive Syllogism

The argument is presented in the form of a disjunctive syllogism, which involves a logical form that states that either one of two alternatives must be true, and one of them has been found to be true; therefore, the other must be false.

In this case, the two alternatives are:

Thus, the logical form of the argument is:

Either A or B.

Not A.

Therefore, B.

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The coordinates of the receiver are (x, y) = (10, 5), and the standard form of the hyperbola is x² - 20x + 212.5 = 0.

A hyperbola is the location of all the points on a plane whose distances from two fixed points in the plane differ by an amount that is always constant. The centre, represented by O in the above diagram as the centre of an ellipse, is where two foci are connected by a line segment when they are united by a line segment. The transverse axis of the hyperbola is the line segment that passes across both foci.

From the given situation we have,

The length of the transverse axis is 180/2 = 90 miles.

Using the distance formula between the two transmitters we have:

d1 = √((x - 5)² + y²)

d2 = √((x + 5)² + y²)

Now, the equation of d is:

|d1 - d2| = 90

Simplifying and squaring both sides, we get:

(d1 - d2)² = 8100

Substituting the expressions for d1 and d2 and expanding, we get:

[(x - 5)² + y² - (x + 5)² - y²]² = 8100

-40x² + 800x - 400 = 8100

-40x² + 800x - 8500 = 0

Dividing by -40, we get:

x² - 20x + 212.5 = 0

d1 = √((x - 5)² + y²) = √((7.5)² + y²)

d2 = √((x + 5)² + y²) = √((2.5)² + y²)

Substituting d1 - d2 = 90/2 = 45 and simplifying, we get:

y² - 50y + 450 = 0

Solving for y:

We get y = 5 or y = 45.

Since the receiver is in the first quadrant, we take y = 5.

Therefore, the coordinates of the receiver are (x, y) = (10, 5), and the standard form of the hyperbola is x² - 20x + 212.5 = 0.

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Answer:

Step-by-step explanation:

37

Answer:

Find the value of b using the formula for the equation of a line.

y = mx+b

Replace the known value of m in the slope y-intercept form of the equation.

y=(1)x+b

Replace the known value of b in the slope y-intercept form of the equation.

y=(1)x+4

Simplify the slope y-intercept form of the equation.

Remove parentheses.

y=(1)x+4

Multiply 1 by x

y=1x+4

Remove parentheses.

y=(1)x+4

Multiply x by 1

this is the answer : y=x+4

i hope this helps.

The total number of copies that the band sold is given as follows:

1.89 x 10^6 copies.

The total number of copies sold is obtained adding the number of copies of each album sold.

The amounts for each album are given as follows:

When we add two numbers in scientific notation, they must have the same exponent, hence we add the bases keeping the exponents, as follows:

(1.3 + 0.59) x 10^6 = 1.89 x 10^6 copies.

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What is Function?

Function is the relationship between inputs where each input is related to exactly one output. It is a special relationship among the inputs (i.e. the domain) and their outputs (known as the codomain) where each input has exactly one output, and the output can be traced back to its input.

"y is a function of x" (denoted y = f(x)) means that y varies according to whatever value x takes on.

How to determine

Where F(x) = 2x^4 + x^2 - 10x + 1

So, to calculate f(-10)

f(x) = y

Where x = -10

f(-10) = 2(-10)^4 + (-10)^2 -10(-10) + 1

f(-10) = 2(10000) + 100 + 100 + 1

f(-10) = 20000 + 100 + 100 + 1

f(-10) = 20201

For f(2),

f(x) = y

Where x = 2

f(2) = 2(2)^4 +2^2 -10(2) + 1

f(2) = 2(16) + 4 -20 + 1

f(2) = 32 + 4 -20 + 1

f(2) = 17

For f(3)

f(x) = y

Where x = 3

f(3) = 2(3)^4 + 3^2 -10(3) + 1

f(3) = 2(81) + 9 -30 + 1

f(3) = 162 + 9 - 30 + 1

f(3) = 142

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The simplified form of the given expression is 1. Using the trigonometric functions sin b = 7/25.

The Pythagorean identity is a trigonometric identity that relates the values of sine and cosine of an angle in a right triangle.

a)Given cos(b) = 24/25, we can use the Pythagorean identity to find sin(b):

sin(b) = √(1 - cos²(b))

         = √(1 - (24/25)²)

         = √(1 - 576/625)

         = √(49/625)

         = 7/25

Now we can use the definitions of the trigonometric functions to find the remaining values:

cos(b) = 24/25

sin(b) = 7/25

tan(b) = sin(b)/cos(b) = (7/25)/(24/25) = 7/24

csc(b) = 1/sin(b) = 25/7

sec(b) = 1/cos(b) = 25/24

cot(b) = 1/tan(b) = (24/7)

b) By simplifying the given expression using the identity:

[tex]tan x = sin x / cos x[/tex]

[tex]cos x+sinxtanx=cosx+sinx(sinx/cosx)[/tex]

By multiplying through by cos x,

cos² x + sin x sin x = cos² x + sin²x

Using the identity sin² x + cos² x = 1,

cos² x + sin² x = 1

cos x + sin x tan x = 1

The simplified form of the given expression is 1.

c) tan²α(csc²α-1)=1 for all values of α where csc α ≠ 0.

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Answer:

<1 and <2 - Add to 180

<1 and <3 - Equal

<3 and <4 - Add to 180

<2 and <4 - Equal

Step-by-step explanation:

No such step-by-step explanation, but we can reason with theorems.

The Vertical Angle theorem states: the opposing angles of two intersecting lines must be congruent, or identical in value.

The Linear Pair theorem states: If two angles form a linear pair, then the measures of the angles add up to 180°.

<1 and <2

<3 and <4

These angle pairs criteria make them apply to the Linear Pair theorem. Therefore, when a pair of angles are a linear pair, they add up to 180.

<1 and <3

<2 and <4

These angle pairs' criteria make them apply to the Vertical Angle Theorem. Therefore, when a pair of angles are vertical angles, they will be congruent (equal, have the same measure).

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We can state this by responding to the provided question A direct function variation function is represented by the graph of this equation, which is a straight line going through the points (0, -2) and (-4, 0).

Mathematicians research numbers, their variants, equations, associated structures, forms, and possible configurations of these. The word "function" describes the connection between a group of inputs, each of which has a corresponding output. A function is a connection between inputs and outputs where each input results in a single, distinct outcome. Each function has a domain, codomain, or scope assigned to it. Functions are usually denoted by the letter f. (x). An x is entered. On functions, one-to-one capabilities, so multiple capabilities, in capabilities, and on functions are the four main categories of accessible functions.

The coordinate plane with a line crossing between (0, -2) and (-2) is the graph that illustrates a function with direct variation (-4, 0).

If m is the line's slope and (x1, y1) is a point on the line, [tex]y - y1 = m(x - x1).[/tex]

The line's slope is as follows:

[tex]m = (y2 - y1)/(x2 - x1) = (-2 - 0)/(0 - (-4)) = 1/2[/tex]

The equation of the line going through (0, -2) and (-4, 0), expressed in point-slope form, is:

[tex]y - (-2) = 1/2(x - 0) (x - 0)[/tex]

When we simplify the equation, we obtain:

[tex]y = 1/2x - 2[/tex]

A direct variation function is represented by the graph of this equation, which is a straight line going through the points (0, -2) and (-4, 0).

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The function g(x) = 3/(x-2) + 5 is a transformation of the parent function f(x) = 1/x with a horizontal shift of 2 units to the right, a vertical stretch by a factor of 3, and a vertical shift of 5 units up.

The function g(x) = 3/(x-2) + 5 is a transformation of the parent function f(x) = 1/x.

Here are the transformations that were applied to f(x) to obtain g(x):

1. Horizontal shift: The denominator of f(x) is x, which means that the vertical asymptote is at x = 0. By subtracting 2 from x in the denominator of g(x), we are shifting the vertical asymptote to x = 2. This is a horizontal shift of 2 units to the right.

2. Vertical stretch: The coefficient 3 in front of the fraction means that the function is stretched vertically by a factor of 3 compared to f(x). This means that the distance between the horizontal asymptotes (which are at y = 0 for f(x) and y = 5 for g(x)) is three times larger for g(x) than for f(x).

3. Vertical shift: The constant 5 added to the fraction means that the entire function is shifted vertically by 5 units compared to f(x). This means that the horizontal asymptote of g(x) is at y = 5 instead of y = 0.

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Therefore , the solution of the given problem of interest comes out to be $630 ,   $659.15 ,  $638.89 and  $345.57 .

To determine simple interest, divide the sum by the cost of borrowing, the amount of time left, and other factors. Principal plus interest plus hours is the straightforward return strategy in marketing. The simplest approach to calculate interest is to use this method. The most popular method of calculating revenue is as a fraction of the principal amount.

Method 1: A basic interest rate of $2.50 per month for a year equals

=> $2.50 x 12 = $30 in interest.

The balance after a year equals $600 plus $30, or $630.

Response: $630

Step 2: Divide the monthly interest rate by 12 to get 0.4167%

Amount after a year:

=> $600 multiplied by (1 + 0.004167)/12 to arrive at $659.15

Response: $659.15

Option 3: $50 per month in deposits

Interest rate per month: 5% divided by 12 Equals 0.4167%

Surplus at the end of the year is equal to

=> $50 x (((1 + 0.004167)12 - 1) / 0.004167) x (1 + 0.004167) = $638.89

Response: $638.89

Method 4: Initial investment of $300, subsequent deposits of $25, and an interest rate of 5% divided by 12 equals 0.4167%.

Amount at the end of the year equals

=> $300 x (1 + 0.004167)12 + $25 x (((1 + 0.004167)12 - 1) / 0.004167) x (1 + 0.004167) = $345.57

Response: $345.57

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Answer:

b.40.3 ft2 is the answer hope it helps u u u BRAINLIST

Answer:

D. 41.7 ft.^2

Step-by-step explanation:

rectangle area: 5.2 x 6= 31.2

triangle area: (6 x 3.5)/2=10.5

31.2+10.5= 41.7

Answer:

Step-by-step explanation:

[tex]A=\pi r^2\\[/tex]

  [tex]=\pi \times 9^2[/tex]   (radius = 9 feet)

  [tex]=81\pi[/tex]

  [tex]\approx 254.47[/tex] feet

Answer:

Step-by-step explanation:

Angle sum of a triangle = 180°. So we get:

[tex]62+69+(4x+5)=180[/tex]

[tex]136+4x=180[/tex]

[tex]4x=44[/tex]

[tex]x=11[/tex]°

Answer:

x = 11

Step-by-step explanation:

We know that the sum of the interior angles in a triangle is added up to 180°.

Accordingly,

62 + 69 + 4x + 5 = 180

Combine like terms.

136 + 4x = 180

Subtract 136 from both sides.

4x = 180 - 136

4x = 44

Divide both sides by 4.

x = 11

The difference between the 92% confidence interval and the 98% confidence interval is that the 98% confidence interval for the population mean is wider than the 92% confidence interval for the population mean.

The bounds of the confidence interval are given by the rule presented as follows:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

The margin of error is given as follows:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

Increasing the confidence level, the value of z is increased, hence the margin of error is also increased and thus the 98% confidence interval for the population mean is wider than the 92% confidence interval for the population mean.

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Answer:10

Step-by-step explanation:3x2=6 and 4x1=4 4+6=10

Answer:

See below

Step-by-step explanation:

Perimeter = (7x2) + (2x2) = 18

Area (L x W) = Square + rectangle

= (3x2) + (4x1) = 6 + 4 = 10

The probability for this problem is an Empirical probability, as it is taken from an experiment.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

Empirical probability is based on observations or experimental data, for example, observing the number of students in a cafeteria and obtaining the percentage of male students and female students, as is done for this problem.

Theoretical probability, on the other hand, is based on mathematical analysis and is calculated using the principles of probability theory. It is the probability that an event will occur based on all possible outcomes. For example, a fair coin is equally as likely to be heads or tails.

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As a result, the equation in point-slope form for the line passing through the point (-3, -1) with a slope of -1/3 is: y - (-1) = (-1/3)(x - (-3)) or y + 1 = (-1/3)(x + 3)

Slope is a mathematical term that describes how steep a path is. The ratio of the vertical shift (rise) to the horizontal transition (run) between any two points on a line is more precisely known as the slope of a line. A line's inclination can be zero, positive, negative, or undefinable. A line that has a positive slope is rising as it travels from left to right, whereas a line that has a negative slope is falling as it moves in the opposite direction. A line has a slope of zero if it is straight, and a slope of infinity if it is vertical.

given

The linear equation's point-slope form is:

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

where (x1, y1) is a spot on the line and m denotes the angle of the line's slope. The equation of the line can be expressed as follows using the provided point (-3, -1) and slope of -1/3:

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

Streamlining the right side:

y + 1 = (-1/3)(x + 3)

Increasing the right side:

y + 1 = (-1/3)x - 1

Taking away 1 from both sides:

y = (-1/3)x - 2

As a result, the equation in point-slope form for the line passing through the point (-3, -1) with a slope of -1/3 is: y - (-1) = (-1/3)(x - (-3)) or y + 1 = (-1/3)(x + 3)

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When two lines intersect each other, then the opposite angles, formed due to intersection are called vertical angles or vertically opposite angles. A pair of vertically opposite angles are always equal to each other.

Step-by-step explanation:

To calculate the future value of a loan with simple interest, we can use the formula:

A = P(1 + rt)

where A is the future value or total amount due, P is the principal, r is the interest rate, and t is the time period in years.

In this case, we have:

P = $1000

r = 5.0% = 0.05 (expressed as a decimal)

t = 6 months = 0.5 years (since there are 12 months in a year)

Plugging these values into the formula, we get:

A = $1000(1 + 0.05 x 0.5)

A = $1000(1.025)

A = $1025

Therefore, the future value or total amount due on the loan after 6 months is $1025.

The slope of the given line is  [tex]m = \dfrac{1}{2}\\[/tex].

A line's slope is calculated as the tangent of the angle it makes with the x-axis. A straight line's slope remains constant throughout. Y = mx + b can be used to calculate a straight line's slope-intercept form.

Given that the line is passing through the points ( 0,1) and (-2, 0 ). The slope of the line is calculated by the application of the formula given below,

[tex]m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]

The slope of the line is  calculated by substituting the values of the coordinates in the formula,

[tex]m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m = \dfrac{1 - 0}{0 + 2 }[/tex]

[tex]m = \dfrac{1}{2}[/tex]

Therefore, the slope of the line will be  [tex]m = \dfrac{1}{2}\\[/tex].

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The cash discount is $353.20 and the net amount due is $17,306.80.

Conditions of sale are the rules that govern a business transaction, including the cost, the method of payment, the delivery, and any other pertinent information. Normally, they are specified in a sales contract or invoice and acknowledged in advance of the transaction. The conditions of sale might alter based on the type of products or services being exchanged, the volume and complexity of the deal, and other elements.

We know that,

Cash discount = amount x discount rate

Net amount due = amount - cash discount

For 2/10:

Cash discount = $17,660 x 2% = $353.20

Net amount due = $17,660 - $353.20 = $17,306.80

Hence, the cash discount is $353.20 and the net amount due is $17,306.80.

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The p value is calculated as 0.116

Null u = 70

alternate u ≠ 70

The alternate is a two tailed test

the test statistic calculation

t = x - u / s/√n

x = 85 + 77 + 82 + 68 + 72 + 69 / 6

= 75.5

standard deviation s = [tex]\sqrt{\frac{(85- 75.5)^2+(77- 75.5)^2+...(69- 75.5)^2}{6-1} }[/tex]

= 7.01

Test stat = (75.5 - 70) / 7.01/√6

= 1.92

degree of freedom = 6 - 1 = 5

this is 2 tailed

p value using excel = tdist( 1.8, 5 , 2)

= 0.116

We fail to reject the null hypothesis because it is greater than the level of significance

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Answer:

D

Step-by-step explanation:

2ft×6ft=12ft

12ft÷2=6

6×2=12ft for the two triangles

6×4=24ft for the rectangle

24ft+12ft= 36 square feet

so it's D 36 square feet

Answer:

[tex]\huge\boxed{\sf 36 \ ft.\²}[/tex]

Step-by-step explanation:

Given that,

Base = 2 + 4 = 6 ft.

Height = 6 ft.

= Base × Height

= 6 × 6

[tex]\rule[225]{225}{2}[/tex]