The perimeter of the rectangle below is 132 units. Find the length of side RS.
Write your answer without variables.
S
P
5x
R
4x + 3
Q

The answers are explained in the solution.

Considering the triangle, ABC,

BC = √AC²-AB² [Pythagoras theorem]

BC = √126.4²-126²

BC = 10 ⇒ Height of the ramp at B,

Slope = tanBC/AB = 10/126

The slope is less than 1/12, hence, it will get ADA approval,

Let θ be angle of elevation,

θ = tan⁻¹(10/126)

= 4.5° < 5°

Hence the town met the given requirement.

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Answer:

Therefore, the area of a small family farm in square feet is 9,923,640.

Step-by-step explanation:

a. To convert acres to square miles, we divide the number of acres by 640:

231 acres / 640 acres/square mile = 0.36 square miles

Therefore, the area of a small family farm in square miles is 0.36.

b. To convert acres to square feet, we first need to convert acres to square yards (since there are 9 square feet in a square yard):

231 acres x 4840 square yards/acre x 9 square feet/square yard = 9,923,640 square feet

Therefore, the area of a small family farm in square feet is 9,923,640.

If "NE" and "TE" are tangents of circle, then length of segment NE is 53 units.

We find the length of the segment "NE" by using the fact that tangents drawn to a circle from an external point are equal in length.

So, We have,

⇒ NE = TE       ...(because they are tangents to the same circle from the same external point E),

So we can set the "two-expressions" of tangent equal to each other:

We get,

⇒ 13x - 12 = 7x + 18,

⇒ 6x - 12 = 18,

⇒ 6x = 30,

⇒ x = 5,

now, we substitute the value of x in "NE", to find the length of segment NE.

We get,

⇒ NE = 13x - 12,

⇒ NE = 13(5) - 12,

⇒ NE = 65 - 12,

⇒ NE = 53.
Therefore, length of NE is = 53 units.

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The given question is incomplete, the complete question is

Given NE and TE are tangents to the circle below, what is the length of segment NE?

(b) The graph of g(x) is the graph of f(x) vertically stretched by a factor of 5.

From the question, we have the following parameters that can be used in our computation:

f(x) = x²

g(x) = (1/5x)²

The graph of g(x) is the graph of f(x) vertically stretched by a factor of 5.

To see this, we can rewrite g(x) as g(x) = (1/5)²(x²) = (1/5²)f(x).

This means that g(x) is equal to f(x) scaled vertically by a factor of 5² = 25.

Therefore, the graph of g(x) will be the same shape as the graph of f(x), but stretched vertically by a factor of 25.

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Answer:

Step-by-step explanation:

Answer: D 24 units i did the quiz

Step-by-step explanation:

Answer:

Area = 36 [tex]units^{2}[/tex]

Perimeter = 26 units

Step-by-step explanation:

Helping in the name of Jesus.

Answer:  Enterprise Alpha must declare and pay VND 1,000 million for import duty, VND 96.44 million for excise duty, and VND 80,730 million for VAT in the period.

Step-by-step explanation:

The sets that is part of Set A are:

To be able to get the set A, a set need to have the same elements as {5, 7, 11, 13, 17, 19}.  So the set that has six number is one that can be the set A.

Hence:

The set {5, 7} exclusively comprises elements present in the initial set.

Any set contains the empty set within its subsets.

The set {17} consists of a single element that is present in the initial set.

The set {5, 7, 11, 13, 17, 19} is a subset of the original set as it encompasses all of its elements.

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See text below

Select all of the following sets that could be the set A if A ⊆⊆ {5, 7, 11, 13, 17, 19}.

{5, 7}

{}

{7, 8, 9}

{17}

{5, 7, 11, 13, 17, 19}

{4, 5, 6}

Answer:

8

Step-by-step explanation:

sqrt(2x) - x = - 4

sqrt(2x) = x - 4

2x = (x - 4) ^ 2

2x = x ^ 2 - 8x + 16

o = x ^ 2 - 10x + 16

matrix 0&=& (x - 2)(x - 8) matrix )

Answer:

Step-by-step explanation:

We need to look at the graph:

The graph shows a pretty clear upward trend, so we can assume that as the years of college increases, income increases as well. Based on how well the data represents a straight line, we can assume there is a strong positive linear correlatino between these variables. But remember, correlation does not imply causation, so we cannot assume that # of years in college causes income to increase.

Thus, looking at our answer choices, the answer is e

The value of the vector from initial point P₁ to terminal point P₂ is,

⇒ V = 3i - 10j

We have to given that;

Points are,

P₁ = (-5, 3)

P₂ = (-2, -7)

Hence, The value of the vector from initial point P₁ to terminal point P₂ is,

⇒ V = (x₂ - x₁) i + (y₂ - y₁)j

⇒ V = (- 2 + 5) i + (- 7 - 3) j

⇒ V = 3i - 10j

Thus, The value of the vector from initial point P₁ to terminal point P₂ is,

⇒ V = 3i - 10j

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Answer:

The image you provided appears to be a rectangular prism. To find the surface area of a rectangular prism, we need to add up the areas of all of its faces.

The rectangular prism has dimensions of 4 cm x 6 cm x 8 cm.

Each face of the rectangular prism is a rectangle, so the area of each face can be found by multiplying the length by the width.

The surface area of the rectangular prism is:

2(4 cm x 6 cm) + 2(4 cm x 8 cm) + 2(6 cm x 8 cm)

= 48 cm^2 + 64 cm^2 + 96 cm^2

= 208 cm^2

Therefore, the surface area of the rectangular prism is 208 square centimeters.

have a good day and stay safe

Answer:

Step-by-step explanation:

To solve this problem, we can use the simple interest formula:

I = P*r*t

where I is the interest earned, P is the principal (the initial investment), r is the interest rate (as a decimal), and t is the time (in years).

Here, we want to find P, so we'll rearrange the formula:

P = I/(r*t)

We know that the final value of the investment (including interest) is $15,500, and the time is 10 months (or 10/12 years). We can plug in the numbers:

I = $15,500 - P

r = 0.02

t = 10/12

P = (15,500 - P)/(0.02*(10/12))

P = (15,500 - P)/(0.1667)

P = 93,000 - 6P

7P = 93,000

P = $13,285.71

Therefore, you should pay $13,285.71 for the note if you want to earn 2% annual simple interest and have it be worth $15,500 in 10 months.

Hope that helps :)

a z-test for the proportional difference is the proper hypothesis test.

A hypothesis test can be used to find whether the deviation in proportions impacts the medication's effectivity. We may compare the secondary hypothesis—that the proportions are different—to the null hypothesis.

which states that the dimension of patients who show cut down blood pressure is the same for the two doses of the drug (50 mg and 100 mg).

Popular test statistics like the z-test can be applied to this hypothesis test and other statistical analyses.

[tex]z = (p1 - p2) / SE[/tex]

where p1 and p2, for the 50 mg and 100 mg doses, respectively, are the sample proportions of patients who show fallen blood pressure, and SE is the standard error of the difference between the proportions.

the samples are assumed to be independent or dependent, impacts the SE formula. The samples in this instance are presumed to be independent because they came from various patients. Consequently, the equation for SE is:

[tex]SE = \sqrt(p1 \times (1 - p1)/n1 + p2 *\times(1 - p2)/n2)[/tex]

here, the sample sizes for two doses is n1 and n2.

We can compute the z-test statistic based on the sample sizes and proportions and compare the result to a critical value or p-value to decide whether to accept or reject the null hypothesis.

Therefore, a z-test for the proportional difference is the proper hypothesis test.

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Length of the curve is e² - 1 .

In arithmetic, a function from a group X to a group Y assigns to every part of X precisely one part of Y. The set X is termed the domain of the function and therefore the set Y is termed the codomain of the function

Main body:

A parametric curve is a function expressed in components form, such that;

x = f(t) , y = g(t).

The length of a parametric curve on the interval a ≤ t ≤ b is given by the definite integral :

L =  [tex]\int\limits^a_b {\sqrt{\frac{dx}{dt}^2 + {\frac{dy}{dt}^2 } } } \, dx[/tex]

Let's begin by getting the first derivative of the components of the function with respect to the variable t.

x = e^t - t  

dx / dt = e^t−1

And, y = 4 e^t/2

dy /dt = 2 e^t/2

Substitute the derivatives into the following definite integral which computes the length of the parametric curve on the interval

[a,b]=[0,2].

L =  [tex]\int\limits^a_b {\sqrt{\frac{dx}{dt}^2 + {\frac{dy}{dt}^2 } } } \, dx[/tex]

L=  [tex]\int\limits^2_0 {\sqrt{\ (e^t - 1)^2 + ({\(2e^{t/2}) ^2 } } } \, dx[/tex]

L = [tex]\int\limits^2_0 {e^t - 1} \, dx[/tex]

Evaluate the solution at the limits of integration to get the length.

L = (e² - 1 )- (e⁰ - 1)

L = e² - 1 - 1 + 1

L= e² - 1

Hence , length of the curve is e² - 1 .

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Answer:

Last number line

Step-by-step explanation:

Solving |d| > 3,

d^2 > 9

d = +-3

Using the graph y=x^2,

d < -3, d > 3

Hence, it's the last number line i.e. the one with blank dots.

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Answer:

Two lines that are in general position divide a plane into four regions or parts.

When two lines intersect at a point, they divide the plane into four distinct regions, called quadrants. However, if the two lines are parallel, they do not intersect, and the plane is divided into only two regions, called half-planes.

In general position, two lines in a plane have different slopes and different y-intercepts, which means that they are neither parallel nor coincident. Therefore, the two lines must intersect at a point, dividing the plane into four regions.

Hope this helps!

Answer:

Step-by-step explanation:

False.

The correct identity is:

cos^2(x/3) = 1/2[1+cos(2x/3)]

To see why, use the double angle formula for cosine:

cos(2x/3) = 2cos^2(x/3) - 1

Substitute this into the original equation:

cos(x/3)cos(x/3) = 1/2[1+2cos^2(x/3)-1]

Simplify:

cos^2(x/3) = 1/2[1+cos(2x/3)]

Answer:

Statement is true!

Step-by-step explanation:

Required to Prove:

[tex]\Large \textsf{$\cos \left(\frac{x}{3}\right)\cos \left(\frac{x}{3} \right)=\frac{1}{2} \left[1+\cos(\frac{2x}{3})\right]$}[/tex]

This is a special property, used in integral calculus, that can be derived and hence proved, from the double angle formula of cosine.

[tex]\large \textsf{Given that cos(A+B) = cosA\,cosB $-$ sinA\,sinB,}\\ \\\large \textsf{Hence cos(A+A) = cosA\,cosA $-$ sinA\,sinA}\\ \\\large \textsf{$\therefore$ cos2A = cos$^2$A $-$ sin$^2$A}\\ \large \textsf{$\rm \phantom{\therefore cos^2A}=$ 1 $-$ 2sin$^2$A}\\ \large \textsf{$\rm \phantom{\therefore cos^2A}=$ 2cos$^2$A $-$ 1 (using Pythagorean Identity $\Rightarrow cos^2A+sin^2A = 1$)}[/tex]

This property, can be quoted in exams and only has to be derived, not proved. Now using the Cos2A property, we can manipulate the formula:

[tex]\large \textsf{$\cos2\rm A = \cos^2A - \sin^2A$}\\ \\ \large \textsf{$\rm \phantom{\cos 2A}=2\cos^2A-1$}\\ \\ \large \textsf{$\rm \therefore \cos2A+1 = 2\cos^2A$}\\ \\ \large \textsf{$\rm \cos^2A=\frac{\cos2A+1}{2}$}\\ \\ \large \textsf{$\rm \phantom{\cos^2A}=\frac{1}{2}(\cos2A+1)$}\\ \\ \large \textsf{$\rm \phantom{\cos^2A}=\frac{1}{2}(1+\cos2A)$}[/tex]

And since:

[tex]\large \textsf{$\cos \left(\frac{x}{3}\right)\cos\left(\frac{x}{3}\right)=\cos^2\left(\frac{x}{3}\right)$}[/tex]

Therefore, inputting the value of A = [tex]\Large \textsf{$\frac{x}{3}$}[/tex] into the formula we derived above, hence:

[tex]\Large \boxed{\boxed{\textsf{$\cos \left(\frac{x}{3}\right)\cos \left(\frac{x}{3} \right)=\frac{1}{2} \left[1+\cos(\frac{2x}{3})\right]$}}} \Large \textsf{ , as required}[/tex]

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The answer for the above expression is 16/9.

An expression is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, division, exponentiation, and root extraction, that represents a mathematical quantity or a mathematical statement. An expression can be as simple as a single number or variable, or it can be a complex combination of several numbers, variables, and operations.

According to the given information:

The expression "[tex](\frac{3}{4} )^{2}[/tex]" represents the fraction "3/4" raised to the power of "-2". In mathematical notation, this is written as "[tex](\frac{3}{4} )^{-2}[/tex]".

To calculate this value, we can use the rule that a negative exponent is equivalent to taking the reciprocal of the base raised to the positive exponent. Therefore, "[tex](\frac{3}{4} )^{-2}[/tex]" is equal to the reciprocal of "3/4" raised to the power of "2", or "[tex]\frac{1}{(\frac{3}{4} )^{2}}[/tex]".

Evaluating this expression, we get:

[tex](\frac{3}{4} )^{-2}[/tex]= [tex]\frac{1}{(\frac{3}{4} )^{2}}[/tex] = [tex]\frac{1}{(\frac{9}{6})^{2} }[/tex]= 16/9

So, "[tex](\frac{3}{4} )^{-2}[/tex]" is equal to 16/9.

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The volume of the of box is derived to be 12 cubic inches, which makes option B correct.

The volume of the box also known as a cuboid can be calculated using the formula:

V = l x w x h

where:

V is the volume of the cuboid

l is the length of the cuboid

w is the width of the cuboid

h is the height of the cuboid

We shall evaluate for the volume of the box as follows:

Volume of the box = 3 in × 2 in × 2 in

Volume of the box = 12 in²

Therefore, the volume of the of box is derived to be 12 cubic inches.

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The volume of the of box is derived to be 12 cubic inches, which makes option B correct.

The volume of the box also known as a cuboid can be calculated using the formula:

V = l x w x h

where:

V is the volume of the cuboid

l is the length of the cuboid

w is the width of the cuboid

h is the height of the cuboid

We shall evaluate for the volume of the box as follows:

Volume of the box = 3 in × 2 in × 2 in

Volume of the box = 12 in²

Therefore, the volume of the of box is derived to be 12 cubic inches.

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Answer: Angle EGF

Step-by-step explanation: Angle EGF is complementary to FGA because the two angles add up to 90 degrees, which is what it means to be complementary.

The approximate average number of miles she put on a rental car each day is C. 42.

The average is the quotient of the total value divided by the number of data items.

The average is also described as the mean data value.

The mean is one of the basic centers of measurement.

The total number of miles driven by Jackie's car for the five days = 209.1 miles

The number of days of driving undertaken by Jackie = 5 days

The average miles per day = 41.81 (209.1 ÷ 5)

41.81 miles per day is approximately = 42 miles per day

Thus, we can confidently conclude that Jackie's car drove 42 miles dai on the average.

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The probability that the number of times Luke will hit the inner ring of the target out of the 5 attempts is less than the mean of X is 0.951.

A discrete random variable with a countable number of potential values is said to have a discrete probability distribution. Each possible value of the random variable is given a probability by the probability distribution, and the sum of these probabilities is 1. The number of heads you get while flipping a coin or the number of cars that pass through a specific crossroads in a given hour are both examples of discrete random variables.

The mean that Luke will hit the inner ring is given as:

E(X) = np

Now, n = 5 and p = 0.90.

So, E(X) = 5 x 0.90 = 4.5

Now, the probability of less than 4.5 is given as:

P(X < 4.5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

P(X < 4.5) = 0.0005 + 0.0144 + 0.1361 + 0.4095 + 0.3915

P(X < 4.5) = 0.951

Hence, the probability that the number of times Luke will hit the inner ring of the target out of the 5 attempts is less than the mean of X is 0.951.

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The amount spent on advertising that will yield a monthly profit of $9,000 is $8.57.

Profit is the amount of money or financial gain that a business or an individual makes after deducting all the expenses and costs associated with producing or providing a product or service.

According to the model, the profit P (in dollars) is dependent on the sum x (in dollars) that the business invests in advertising:

P = 130x² - 550

We want to find the amount spent on advertising that will yield a monthly profit of $9,000. In other words, we want to solve for x when P = 9000:

130x² - 550 = 9000

Adding 550 to both sides, we get:

130x² = 9550

Dividing both sides by 130, we get:

x² = 73.46

x = ±8.57

Since we are dealing with a real-world scenario, the amount spent on advertising must be a positive value. Therefore, we take the positive root:

x = 8.57

Therefore, the amount spent on advertising that will yield a monthly profit of $9,000 is $8.57.

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The value of k in the given wave equation is determined as 1/2.

The value of k in the given wave equation is calculated as follows;

The wave equation; y = a sin (bθ)

where;

when y = 24/25, the value of k is calculated as follows;

24/25 = 2 x sinbθ

sin bθ = 24/50

bθ = sin⁻¹ (24/50)

bθ = 0.5

bθ  = ¹/₂

Thus, the value of k in the given wave equation corresponds to value of b and it is determined as 1/2.

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The equation for its altitude h​ (in m) as a function of time t is h(t) = h₀ x 1000 - rt and the graph of the equation is illustrated below.

Let's begin by defining our variables. We know that the initial altitude of the airplane is given as h₀, which is in km. We also know that the rate at which the altitude decreases is given as r, which is in m/min. Our objective is to determine the altitude h of the airplane at any given time t, in minutes, during the descent.

To find the equation for the altitude of the airplane, we need to first convert the initial altitude from km to m. This can be done by multiplying h₀ by 1000. Therefore, the initial altitude in meters is h₀ × 1000.

Finally, we can find the equation for the altitude of the airplane by subtracting the amount that the altitude has decreased from the initial altitude. This gives us the following equation:

h(t) = h₀ × 1000 - rt

where h(t) is the altitude of the airplane at time t, h₀ is the initial altitude in km, r is the rate of descent in m/min, and t is the time in minutes.

To sketch the graph of this equation, we can plot altitude on the y-axis and time on the x-axis.  Then we get the graph like the following.

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Answer:

i can only answer 1 but the first one is c

Step-by-step explanation:

The work required to pump the oil out through a hole to the top of the tank is approximately 6,476,160π/3 foot-pounds.

We can find the work required to pump the oil out of the tank by using the formula:

W = ∫[V1, V2]ρgh dV

Where

First, we need to find the density of the oil. We are told that the oil weighs 50 pounds per cubic foot, so:

ρ = 50 lb/ft^3

Next, we need to find the height of the oil column being pumped. The tank is half full, so the height of the oil column is:

h = r - (r/2) = r/2 = 8/2 = 4 feet

Now, we need to find the volume of oil being pumped. Since the tank is half full, the volume of oil is:

V = (1/2)(4/3)πr^3 = (1/2)(4/3)π(8)^3 = 1,024π/3 cubic feet

Finally, we can integrate the work formula to find the total work required:

W = ∫[V1, V2]ρgh dV

W = ∫[0, 1,024π/3] (50 lb/ft^3)(32.2 ft/s^2)(4 ft) dV

W = (6,476,160π/3) ft-lb

Therefore, the work required to pump the oil out through a hole to the top of the tank is approximately 6,476,160π/3 foot-pounds.

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Answer:

To calculate the area of a sector, we can use the formula:

A = (θ/2) * r^2

where:

A is the area of the sector,

θ is the central angle of the sector in radians, and

r is the radius of the sector.

Given:

r = 2 (radius)

θ = 1.75 radians (central angle)

Plugging in the given values into the formula:

A = (1.75/2) * 2^2

A = 0.875 * 4

A = 3.5

So, the area of the se

The real distance between City X and City Y is 17 miles.

We know that the scale of the drawing is:

1 inch = 17 miles.

Now, if you look at the diagram for cities X and Y, you can see that the distance between City X and City Y is exactly 1 inch.

And we know that 1 inch is equivalent to 17 miles, then we can conclude that the actual distance between the two cities is exactly 17 miles.

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