The width of the rectangle is 60% of its length of 40 ft. What is the area of the rectangle?

Answer:

When the plane is 2mi away from the radar station, its distance's increase rate is approximately 433mi/h.

Step-by-step explanation:

Sketch a right triangle with one leg going vertically a length of 3 miles above the station, and the other leg x going horizontally from the top of the first leg. Distance r from plane to station is related by r2 = x2 + 32. Differentiate: 2r dr/dt = 2x dx/dt, which rearranges to the desired dr/dt = x/r dx/dt. When r = 4, x2 = 42 - 9 and x = √7. So dr/dt = (√7 / 4) * 520 mph = 344 mph.

{y:y is an integer AND y>10} is a set of integers that are greater than 10. Some examples of elements that would be included in this set are 11, 12, 13, 14, and so on.

Answer:

No

Step-by-step explanation:

x > -9y-3/7 (Solve for X)

_____________________________________________________

y > -7x/9 - 1/3 (Solve for Y)

_____________________________________________________

Therefore, (-3, 2) is not a solution.

Answer:

24*X or 24X

Step-by-step explanation:

24X or 24*X or 24 multiplied by X days

The variable "X" represents the number of days.

Because AR = AQ, you have an isosceles triangle with triangle RAQ.  This also means ∠ARQ = ∠AQR.

You're also told that RT = QS, so this gives you SAS to show triangle ART = triangle  AQS.

   side: AR = AQ

   angle: ∠ART = ∠AQS

   side: TR = QS

Knowing that the two triangles are congruent gives you that the two top angles are also congruent.  

Brielle uses 1/3 of a cup of nuts for 1 cup of oatmeal.

What is unitary method?

The unitary method is a process of finding the value of a single unit, and based on this value finding the required solution.

According to the given question:

Brielle uses 2/3 cup of nuts for every 2 cups of oatmeal to make granola bars.

To find the fraction cup of nuts required for 1 cup of oatmeal, using unitary method

2 cups ----- 2/3 cup of nuts

1 cup ------- [tex]\frac{2/3}{2}[/tex] cup of nuts = 1/3 cup of nuts

Therefore Brielle uses 1/3 of a cup of nuts for 1 cup of oatmeal.

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Answer:

b

Step-by-step explanation:

4y = 2x

y = 2/4  x

y = 1/2 x               where y = kx    then k = 1/2

Answer:

Maria can buy at most 2 bottles of cranberry juice and 7 lemon-lime soda bottles.

Step-by-step explanation:

For this problem, we can set up an algebraic expression to represent the price, and this will help us solve the problem.

So firstly, let's assign the number of cranberry juice bottles to the variable  "C". We could technically represent this as the variable name "cranberry juice bottles", but "C" is a bit more easier to write when writing an algebraic expression while still making it easy to distinguish. Let's also assign the number of lemon-lime soda to the variable "L".

Now let's find a way to express the price of each. The price of buying a certain amount of items, can generally be expressed as: [tex](\text{items bought})*(\text{item price})[/tex], since you have to pay the item price for each item bought, also known as, multiplication.

Since we know that the price of a cranberry juice bottle is $3.80 then that means the total amount used towards cranberry juice can be expressed as: [tex]3.80C[/tex]. We're just multiplying the number of cranberry juice bottles times the price. Likewise, we can represent the total amount used towards lemon-lime soda as: [tex]1.40L[/tex]. The same logic is being applied here.

Now if we add both of these, we get the total amount that will be spent which is: [tex]3.80C + 1.40L = T[/tex], and in this case I just set it equal to "T" which just represents the total spent.

Now there's two more things to do. Generally we can't really solve two-variable equations and we want to express one variable in terms of the other, so that we can rewrite the equation as a one-variable equation.

There is one piece of information given that allows us to do this. "The recipe calls for 3.5 times as many bottles of lemon-lime soda as cranberry". So we can represent the numbers of lemon-lime soda bottles as 3.5 times the amount of cranberry juice bottles. We can express it as: [tex]L=3.5C[/tex]

So now let's plug this into the equation, instead of "L". This gives us: [tex]3.80C + 1.40(3.5C) = T[/tex]

let's multiply the 1.40 by the 3

[tex]3.80C + 4.9C= T[/tex]

now let's add up the values.

[tex]8.7C=T[/tex]

Now lastly, this represents the total amount that is going to be spent. Since Maria only has $17.40, we want this total to be less than or equal to 17.40 (assuming there is no sales tax, but this was never given). this gives us our final expression we will be using: [tex]8.7C\le 17.40[/tex]

From here solving the problem is actually pretty easy. Think of the inequality as a linear equation, we can still apply the same (for the most part) algebraic manipulations we apply to linear equations. We just divide both sides by 8.7 to isolate the C

[tex]\frac{8.7C}{8.7}\le\frac{17.40}{8.7}\\\\C\le 2[/tex]

So Maria can buy a maximum of 2 bottles of cranberry juice. From this we can actually determine the number of lemon-lime soda bottles.

So we know that:

[tex]C=2[/tex]

From this we can determine what L is, since remember the equation we set up earlier?

[tex]L = 3.5C[/tex]

Let's just plug C into the equation, and we get:

[tex]L=3.5(2)[/tex]

Multiply

[tex]L=7[/tex]

So Maria can buy at most 2 bottles of cranberry juice and 7 lemon-lime soda bottles.

Answer:

each girl scored 9 points

each boy scored 7 points

Step-by-step explanation:

41-13=28

28/2=14

14 is the number scored by boys

14/2

one boy scored 7 points

14+13=27

27 is the number scored by girls

27/3=9

each girl scored 9 points

Answer:

For the problem with the horse: 10,000 grams

For the problem with the hiker labeled 11: 2 feet

I hope these answers are of use to you!

Step-by-step explanation:

Okay, for the horse problem I understood that it was a horse eating exactly 10 kg per day. If she does, then you just convert 10 kilograms to grams. To do this, you multiply the amount of kilograms by 1,000, since that is how it works.

10 x 1,000 = 10,000 grams.

For the problem labeled 11 with the hiker, you divide 120 ft by 60 since there are 60 seconds in a minute.

120 divided by 60 = 2 feet

Mr. Dillon balance at the end of month is $809.

In a financial institution, a checking account is a deposit account that permits both deposits and withdrawals.

Money kept or held in any bank account is referred to as a deposit.

A withdrawal entails taking money out of a trust, pension, savings plan, or bank account.

As Mr. Dillon opened a checking account, so balance is $0 in starting.

When he deposits $1530, $896, $571, $472

Total deposit= $1530+$896+$571+$472

             = $ 3,469

Check is a kind of withdrawal.

He wrote check of $32 , $981 , $825 , $661 , $224

Total withdrawal= $32+$981,$825+$661+$224

                             = $2,660

Balance= Total deposit - Total withdrawal

             = $3,469 - $2,660

             = $809

Therefore, balance is $ 809.

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The simplified form of the given expression, 4(3x^2y^4)3 / (2x^3y^5) ^4, is 27/x⁶y⁸

From the question, we are to simplify the given expression

From the given information,

The expression is

4(3x^2y^4)3 / (2x^3y^5) ^4

First, we will write the given expression properly

The given expression written properly is

4(3x²y⁴)³ / (2x³y⁵)⁴

Simplifying the expression

4(3x²y⁴)³ / (2x³y⁵)⁴

4 × (3x²y⁴)³ / (2x³y⁵)⁴

4 × (3)³(x²)³(y⁴)³ / (2)⁴(x³)⁴(y⁵)⁴

4 × (3)³ × (x²)³ × (y⁴)³ / (2)⁴ × (x³)⁴ × (y⁵)⁴

4 × 27 × x⁶ × y¹² / 16 × x¹² × y²⁰

108 × x⁶ × y¹² / 16 × x¹² × y²⁰

This can be further expressed as

108/16 × x⁶/x¹² × y¹²/y²⁰

27/4 × 1/x⁶ × 1/y⁸

= 27/x⁶y⁸
Hence, the simplified expression is 27/x⁶y⁸

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The mathematical model that gives the stopping distance d in terms of speed v is

d = 1/(40 x 5280²) v²

The stopping distance when v is 59 miles per hour is 87.03 feet.

Speed is the ratio of distance and time.

It shows how fast an object is moving at a given time.

We have,

The stopping distance d is directly proportional to the square of the speed v.

This can be written as,

d ∝ v²

Now,

Converting 40 miles into feet.

1 mile = 5280 feet

40 miles = 40 x  5280 feet

40 miles = 211200 feet

Now,

40 feet ∝ 211200 feet per

Now,

The stopping distance is 40 feet when the speed is 40 miles per hour

d = 40 and v = (40 x 5280) feet per hour

d = k v²

k = d/v²

k = 40/(40 x 5280)²

k = 1/(40 x 5280²)

The mathematical model that gives the stopping distance d in terms of speed v is

d = 1/(40 x 5280²) v²

The stopping distance when v is 59 miles per hour

v = (59 x 5280) feet per hour

d = 1/(40 x 5280²) x (59 x 5280)²

d = (59 x 59) / 40

d = 87.03 feet

Thus,

The mathematical model that gives the stopping distance d in terms of speed v is

d = 1/(40 x 5280²) v²

The stopping distance when v is 59 miles per hour is 87.03 feet.

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The equation of inequality for the given graph will be;

⇒ y < - 4/3x + 5

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The graph is shown in figure.

Now,

Take two points on the graph as;

⇒ (0, 5) and (3, 1)

Hence, The equation of line will be;

⇒ y - 5 = (1 - 5) / (3 - 0)  (x - 0)

⇒ y - 5 = - 4/3x

⇒ y = - 4/3x  + 5

Since, The inequality is shown in figure.

Hence, We get;

⇒ y < - 4/3x + 5

Thus, The equation of inequality for the given graph will be;

⇒ y < - 4/3x + 5

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By using linear inequation it can be calculated that-

The shaded region right of the y axis and above the x axis gives all possible solution.

The required linear inequation is

1310g + 20s < 900

What is linear inequation?

Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by >, <, ≥, ≤

A one degree inequation is known as linear inequation

Let the alloy has g ounces of gold and s ounces of silver

An ounce of gold costs $1310 and an ounce of silver costs $20.

Cost of the alloy should be less than $900

The required linear inequation is

1310g + 20s < 900

The graph has been attached

The shaded region right of the y axis and above the x axis gives all possible solution.

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According to the given information The 50 child tickets and 64 adult tickets were sold that day.

The area of mathematics concerned with the characteristics and use of numbers a field of study that concentrates on multiplying, dividing, adding, and subtracting numbers. Mathematical simplifications are made using fractions, decimals, percentages, fractions, square roots, exponents, and other arithmetic operations.

child admission (c)= $5.70

adult admission (a)= $9.80

5.70c + 9.80a = 912.20      (i)

a + c = 114                            (ii)

Set up the equation:

5.70(114 - a) + 9.80a = 912.20

649.8 - 5.7a + 9.80a = 912.20

4.1a = 262.4

a = 64

adult tickets = 64  

Put the value of a in equation (ii) we get,

64 + c = 114

c = 114 - 64

c = 50

child tickets = 50

Therefore , the 50 child tickets and 64 adult tickets were sold that day.

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Answer:

  c  The first two hours cost $4, between two hours and six hours cost $2 per hour, and all hours after that cost $1.

Step-by-step explanation:

You want an interpretation of the graph that is a constant 4 up to x=2, has a slope of 2 for 2 ≤ x < 6, and a slope of 1 for x ≥ 6. The vertical axis is labeled dollars, and the horizontal axis is labeled hours.

The constant value of y = 4 for x < 2 means the cost of parking is $4 for the first two hours.

The slope of 2 from x=2 to x=6 means the cost of parking is $2 per hour between 2 and 6 hours.

The slope of 2 for x ≥ 6 means the cost of parking is $1 per hour for more than 6 hours.

The description of c applies.

__

Additional comment

The slope, or "unit rate", is the ratio of "rise" to "run". It can be simpler to choose a "run" of 1 and look at the corresponding "rise".

From x=2 to x=3, the cost rises from $4 to $6, a rise of 2 for the run of 1. That is why we say the slope is 2, or the "unit rate" in dollars per hour is $2 per hour.

A sampling method is simple random sampling.

In statistical analysis, sampling is the procedure by which researchers choose a specific number of observations from a larger population. The sample strategy will depend on the sort of study being done, although it may involve systematic sampling or just plain random sampling.

A selection of participants from a population are chosen at random by the researcher using simple random sampling, a sort of probability sampling. Every person in the population has the same probability of getting chosen. Then, data are gathered from as much of this randomly selected subgroup as feasible.

Since it only uses one random pick and is very simple, this method is the easiest of all the probability sampling techniques.

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The length of the JU would be 60 units.

What is the Basic Proportionality Theorem?

The basic Proportionality Theorem (can be abbreviated as BPT) states that, if a line is parallel to a side of a triangle that intersects the other sides into two distinct points, then the line divides those sides in proportion.

In the given figure side TU is parallel to side LK

If JK = 64 and JU = -4 + 4x

then UK = JK - JU

              = 64 - (-4 + 4x)

               =68 - 4x

Similarly,if JL = 72 and JT = 27

then TL = JL - JT

             = 72 - 27

             = 45

Now by using the property of the basic proportionality theorem, we can write

              [tex]\frac{JT}{TL} =\frac{JU}{UK}\\\\ \frac{27}{45} =\frac{-4+4x}{68 - 4x}\\\\\frac{3}{5} = \frac{-4+4x}{68 - 4x}\\\\3(68-4x) = 5(-4+4x)\\\\204 - 12x=-20+2x\\\\204+20=14x\\\\x=\frac{224}{14}\\\\x=16[/tex]

Now we can calculate the length of JU = -4 + 4x

                                                                 = -4 + 4(16)

                                                                 = -4 + 64 = 60

Hence, the length of the JU would be 60 units.

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The measure of the arc length of the sector will be 1.047 units. Then the correct option is A.

Let r is the radius of the sector and θ be the angle subtended by the sector at the center. Then the arc length of the sector of the circle will be

Arc = (θ/2π) 2πr

The radius of the sector is 1 unit and the central angle is π/3. Then the measure of the arc length of the sector will be given as,

Arc = [(π/3)/2π] 2π(1)

Simplify the equation, then we have

Arc = [(π/3)/2π] 2π(1)

Arc = (1/6) × 2π

Arc = π/3

Arc = 1.047 units

The proportion of the circular segment length of the area will be 1.047 units. Then, at that point, the right choice is A.

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Answer:

2.0 acres

Step-by-step explanation:

C(x) = 270 ln(x+1) + 1900 = 2200

270 ln(x+1) = 300

ln(x+1) = 10/9

x+1 = e^(10/9)

x = e^(10/9) - 1 = 2.0377

Answer:

Step-by-step explanation:

I think its 40

The triangle is isosceles so the left and right side are equal in length.

you would equal 4x+4=6x-14 and solve, getting 18=2x the 9=x

Hence, the point on the ray is [tex]x > 2[/tex].

What is the number line?

A number line is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides

Here given that,

Use the number line to represent the solution to [tex]x + 3 > 5.[/tex]

i.e.,

[tex]x+3 > 5\\\\x > 5-3\\\\x > 2[/tex]

Hence, the point on the ray is [tex]x > 2[/tex].

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Z-tests are closely related to t-tests, but t-tests are best performed when the data consists of a small sample size, i.e., less than 30. The given statement is true.

Does critical value depend on sample size?

The sample size and the crucial value that the researcher employed must be connected. The variations in critical values between the t-distribution and the normal-shaped sampling distribution, however, are minimal for sample sizes bigger than 30.

Z-tests and t-tests are closely related, but t-tests work best with small sample sizes of data, or those with fewer than 30 participants. Additionally, whereas z-tests assume that the standard deviation is known, t-tests assume that it is unknown.

You must use the t-distribution table when working problems when the population standard deviation (σ) is not known and the sample size is small (n<30). General Correct Rule: If σ is not known, then using t-distribution is correct.

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1. The volume of the cylinder is 942 m³.

2. The volume of the cone is 33.16 mm.

3. The volume of the sphere is 33.50 in³.

4. The volume of the cuboid is 672 in³.

Volume is defined as how much of a three-dimensional object occupies

a space.

We know the volume of a cylinder is πr²h.

∴ The volume of the given cylinder is = π(5)²×12 m³ = 942 m³.

We know the volume of a cone is = (1/3)πr²h.

∴ The volume of the given cone is = (1/3)π(2)²×8 mm³ = 33.16 mm.

We know the volume of a sphere is (4/3)π×r³.

∴ The volume of the given sphere is = (4/3)×π×(r³) in³ = 33.50 in³.

We know the volume of a cuboid is = (length×width×height).

∴ The volume of the given cuboid is = (7×8×12) in³ = 672 in³.

The volume of the object in figure 8 is the sum of the volume of a cuboid and a pyramid.

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The value of [tex]\angle[/tex]ABC=6° was found with the help of the law of cosines.

What is the law of cosines of a triangle?

The lengths of a triangle's sides are correlated with the cosine of one of its angles according to the law of cosines. We can now determine values for distances and angles that are impossible to measure without the aid of trigonometry. When calculating the third side of a triangle given two sides and their enclosed angle, as well as when calculating the angles of a triangle if we know all three sides, the law of cosines is used.

Given values are AB = c = 36 units, BC = a = 42 units, and [tex]\angle[/tex]BCA = 31°.

Now let AB = b, we find b using the law of cosines and quadratic equation:

[tex]c^2 = a^2 + b^2 - 2a b \cos C \\36^2 = 42^2 + b^2 - 2 \cdot \ 42 \cdot \ b \cdot \ \cos 31\degree \\ b > 0 \\ b = 7.22[/tex]

Now, we calculate [tex]\angle[/tex]ABC using the law of cosines:

[tex]\angle ABC=arc cos(\frac{a^{2}+c^{2}-b^{2} }{2ac}) \\\angle ABC=arc cos(\frac{42^{2}+36^{2}-7.22^{2} }{2.42.36}) \\\angle ABC=5.55[/tex]

[tex]\angle[/tex]ABC=6°

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The expression which defines the nth term of the given sequence, in terms of n as required in the task content is; T (n) = 1 + 7(n - 1).

It follows from the task content that the expression which represents the nth term of the given sequence be determined.

According to the task content, the first term, a of the sequence is; 1.

Also, since; 8 - 1 = 15 - 8 = 22 - 15 = 29 - 22 = Common difference, d = 7.

Consequently, the required expression is an arithmetic sequence which can be modelled by;

T (n) = a + d (n - 1)

Since the constant common difference of consecutive terms in the sequence is; 7,

Ultimately, The required expression for the nth term of the expression is;

nth = 1 + 7(n -1)

On this note, the nth term of the arithmetic sequence is given by the expression; T (n) = 1 + 7 (n -1).

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Answer: He sold 19/40 of his pies or 0.475% of his pies

Step-by-step explanation: There are 40 total slices of pie and if he sold 19, then the fraction is 19/40. Additionally the fraction 19/40 as a decimal is 0.475 so it would be 0.475% of the pies.

(a) The system of equations that could be used to find the weight (in kilograms) of each type of box is

3x + 5y = 116  

9x + 7y = 238

(b)

Weight of each large box: 15.75 kilograms

Weight of each small box: 13.75 kilograms

What is a system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

Given that, the weight of 3 large boxes and 5 small boxes is 116 kilograms.

The weight of 9 large boxes and 7 small boxes is 238 kilograms.

Let x be the weight (in kilograms) of each large box.

Then the weight of 3 large boxes is 3x kilograms.

Then the weight of 9 large boxes is 9x kilograms.

Let y be the weight (in kilograms) of each small box.

Then the weight of 5 large boxes is 5y kilograms.

Then the weight of 7 large boxes is 7y kilograms.

The weight of 3 large boxes and 5 small boxes is 3x + 5y kilograms.

The weight of 9 large boxes and 7 small boxes is 9x + 7y kilograms.

Therefore,

3x + 5y = 116  .....(i)

9x + 7y = 238  .....(ii)

Solve equation by using elimination method:

Multiplying equation(i) by 3  and subtract equation (ii) from it:

9x + 15y = 348

9x + 7y = 238

(-)  (-)       (-)

_____________

       8y = 110

       y = 13.75

Putting  y = 13.75 in equation (i)

3x + 5×(13.75) = 116

3x = 47.25

x = 15.75

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