What is the unit rate for 4543.08 km in 52.4 h? Enter your answer, as a decimal, in the box. km/h

Final answer:

The Junior Soccer League will need a total of 14 vans to transport 160 people, with 4 people left over after filling the 13th van.

Explanation:

To calculate the number of 12-person vans needed for the Junior Soccer League event, we first need to determine the total number of people that require transportation. This includes both players and coaches.

We have 146 players and 14 coaches, giving us a total of 160 people. If each van holds 12 people, the next step is to divide the total number of people by the capacity of the van.

160 ÷ 12 = 13 vans with 4 people left over because 12 vans can only carry 144 people (12 × 12), and 16 people are remaining, which requires another van to accommodate them.

So, the league will need a total of 14 vans for transportation, and there will be 4 people left over after filling the 13th van.

Final answer:

The derivative dy/dx for the equation 9y cos(x) = x² + y² is found by applying implicit differentiation. Rearranging terms after differentiation, dy/dx is obtained as the fraction (9y sin(x) + 2x) / (9 cos(x) - 2y).

Explanation:

The question asks for the derivative of dy/dx using the equation 9y cos(x) = x2 + y2. To find dy/dx, we can apply implicit differentiation, which implies taking the derivative of both sides with respect to x while treating y as a function of x (y(x)).

Let's differentiate both sides:

The left side: d/dx [9y cos(x)] = d/dx [9y] cos(x) + 9y d/dx[cos(x)] = 9(dy/dx) cos(x) - 9y sin(x)

The right side: d/dx [x2 + y2] = 2x + 2y(dy/dx)

Equating both the derivatives, we have:

9(dy/dx) cos(x) - 9y sin(x) = 2x + 2y(dy/dx)

Now, solving for dy/dx gives us:

dy/dx = (9y sin(x) + 2x) / (9 cos(x) - 2y)

The equation of parabola is y = ( x - 2 )² + 3

What is a Parabola?

A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line

The equation of the parabola is given by

( x - h )² = 4p ( y - k )

where ( h , k ) is the vertex and ( h , k + p ) is the focus

y is the directrix and y = k - p

The equation of the parabola is also given by the equation

y = ax² + bx + c

where a , b , and c are the three coefficients and the parabola is uniquely identified

Given data ,

The vertex of the parabola is given as A ( 2 , 3 )

Now ,

The equation of parabola is given by

y = a ( x - h )² + k

where the vertex of the parabola is A ( h , k )

a = 1

So , substituting the values of vertex in the equation of parabola , we get

y = ( x - 2 )² + 3

Hence , the equation of parabola is y = ( x - 2 )² + 3

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Saylor Henshaw invested $1600.

To find out how much money Saylor Henshaw invested, we can use the formula for simple interest:

Interest = Principal × Rate × Time

In this case, Saylor earned $120 in 9 months at an annual interest rate of 5%.

Let's assume the principal amount is P.

Using the formula:

120 = P × 0.05 × (9/12)

Simplifying the equation, we have:

P = 120 ÷ 0.05 × 12/9

P = $1600

So, Saylor Henshaw invested $1600.

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The solution is : n = 9

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

Explanation:

To find the answer we need to check at what point the running time of algorithm A is equal the running time of B:

1000*n*n = n*n*n*n*n  

1000 = n*n*n = n^3

n = ∛(1000) = 10  (when n equals ten A equal B)

For any integer greater than ten B > A  and for any integer smaller than ten B < A.

The greatest integer for which B < A is nine, therefore nine is our answer.  

                   A                                      B

                   1000n^2                          n^5

n = 8             64000              <             32768

n = 9             81000              <             59049

n = 10            100000            =             100000

n = 11             121000             >             161051

n = 12            144000             >             248832

therefore nine is our answer.  

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For [tex]\( n = 0, 1, 2, 3, 4, 5, 6 \)[/tex], Algorithm A (which runs in [tex]\( 2n \)[/tex] steps) beats Algorithm B (which runs in [tex]\( 5\sqrt{n} \)[/tex] steps).

To determine for which values of [tex]\( n \)[/tex] Algorithm A beats Algorithm B in terms of running time, we compare their complexities:

Algorithm A runs in [tex]\( 2n \)[/tex] steps.

Algorithm B runs in [tex]\( 5\sqrt{n} \)[/tex] steps.

Algorithm A beats Algorithm B if [tex]\( 2n < 5\sqrt{n} \)[/tex].

Let's solve this inequality step by step:

1. Square both sides to eliminate the square root (valid since [tex]\( n \geq 0 \)[/tex]):

[tex]\[ (2n)^2 < (5\sqrt{n})^2 \][/tex]

[tex]\[ 4n^2 < 25n \][/tex]

2. Bring all terms to one side to form a quadratic inequality:

[tex]\[ 4n^2 - 25n < 0 \][/tex]

3. Factorize the quadratic inequality if possible:

[tex]\[ n(4n - 25) < 0 \][/tex]

4. Find the values of [tex]\( n \)[/tex] that satisfy the inequality:

[tex]\( n(4n - 25) < 0 \)[/tex] holds when one factor is negative, and the other is positive:

[tex]\( n < 0 \)[/tex] and [tex]\( 4n - 25 > 0 \)[/tex]: No valid solutions since [tex]\( n \geq 0 \)[/tex].

[tex]\( n > 0 \)[/tex] and [tex]\( 4n - 25 < 0 \)[/tex]:

[tex]\[ 4n < 25 \Rightarrow n < \frac{25}{4} = 6.25 \][/tex]

[tex]\( n < 0 \) and \( 4n - 25 < 0 \)[/tex]: All [tex]\( n \geq 0 \)[/tex] satisfy this condition.

5. Determine the integer values of [tex]\( n \)[/tex]:

Since [tex]\( n \)[/tex] must be non-negative, the integer values of [tex]\( n \)[/tex] that satisfy [tex]\( 4n^2 - 25n < 0 \)[/tex] are [tex]\( n = 0, 1, 2, 3, 4, 5, 6 \)[/tex].

Each bag contained 1.375 cups of sugar.

To find out how many cups of sugar were in each bag that Latrell bought, we need to divide the total amount of sugar by the number of bags. Latrell has a total of 5 1/2 cups of sugar, which is the same as 5.5 cups when converted to a decimal. He bought 4 bags of sugar. Therefore, the calculation we need to perform is:

5.5 cups / 4 bags = 1.375 cups per bag

So, each bag contained 1.375 cups of sugar.

To deliver 2 grams of a drug with a concentration of 350 mg per 10 mL, convert 2 grams to milligrams (2000 mg), and then divide this value by the concentration in mg/mL (350 mg/10 mL) to find the volume in milliliters. After calculation, this results in approximately 6 milliliters, when rounded to the nearest milliliter.

To calculate how many milliliters are needed to deliver 2 grams of the drug when the concentration is 350 mg per 10 mL, we start with the conversion of grams to milligrams since the concentration is provided in milligrams. Remember, 1 gram equals 1000 milligrams:

Therefore, approximately 6 milliliters of the drug are needed to deliver a dose of 2 grams.

Answer:

when the tension is 72 pounds , the frequency is 900 hertz

Step-by-step explanation:

Hello, I think I can help you with this.

you can easily solve this by using a rule of three.

According to the question data:

the pitch, or frequency, of a vibrating string varies directly with the square root of the tension.in mathematical terms it is:

f ∝ √T

where f is the pitch or frequency and T is the tension

Step 1

if a string vibrates at a frequency of 300 hertz due to a tension of 8 pounds

300 hertz  ∝ √8 pounds

300⇔√8

what is the frequency when the tension is 72 pounds

x⇔√72

Step 2

Let

300⇔√8

x⇔√72

the relation is

[tex]\frac{300}{\sqrt{8} } =\frac{x}{\sqrt{72} }\\\\ Now, solve\ for\ x\\\\\\\frac{300*\sqrt{72} }{\sqrt{8} } =x\\x=\frac{300*\sqrt{72} }{\sqrt{8} } \\x=\frac{300*\sqrt{8*9}}{\sqrt{8}} \\x=\frac{300*\sqrt{8}*\sqrt{9}}{\sqrt{8}} \\x=300*\sqrt{9}\\x=300*3\\x=900[/tex]

when the tension is 72 pounds , the frequency is 900 hertz

have a good day.

Answer:

12 ways

Step-by-step explanation:

We know that,

When the cube is rolled,

Possible ways = 6 ( i.e. 1, 2, 3, 4, 5 or 6 ),

While, when a penny is flipped,

Possible ways = 2  ( i.e. head or tail ),

Thus, when the cube and penny flipped one time,

Total possible ways = 6 × 2 = 12

( i.e, 1H, 2H, 3H, 4H, 5H, 6H, 1T, 2T, 3T, 4T, 5T or 6T )

The distributive property is used to multiply 7 by each term inside the parentheses (4n, -5m, -2) resulting in the expression 28n - 35m - 14.

To apply the distributive property to the expression 7(4n-5m-2), you multiply each term inside the parentheses by 7. The distributive property allows us to multiply a single term outside a parenthesis with each term inside the parenthesis, effectively distributing the multiplication.

Therefore, the product written as a sum, using the distributive property, is 28n - 35m - 14.

The answer is; c.) checks!

Take the limit as x approaches 8 to get the answer of 9.

To find the limit of (x² - 64) / (x² - 8x) as x approaches 8, we can simplify the expression by factoring and cancelling common factors.

First, we factor in the numerator and denominator:

x² - 64 = (x + 8)(x - 8) and x² - 8x = x(x - 8).

Now we can cancel the common factor of x - 8 to simplify the expression: (x + 8)/(x).

Now, we can take the limit as x approaches 8:

Lim(x→8) (x + 8)/(x) = 8 + 8/8

                             = 9.

So the limit of the given expression as x approaches 8 is 9.

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To convert [tex]7.085 * 10^-{14}[/tex] to an ordinary number, move the decimal point 14 places to the left, resulting in 0.00000000000007085.

To write [tex]7.085 * 10^-{14}[/tex] as an ordinary number, you need to move the decimal point 14 places to the left because the exponent is negative. This means the number is very small. The process is similar to changing other numbers from scientific to standard notation, for example, changing [tex]7.5 x 10^{-3}[/tex] to 0.0075 by moving the decimal point three places to the left.

For [tex]7.085 * 10^-{14}[/tex], you will end up with 0.00000000000007085. The number has thirteen zeros after the decimal point and before the 7085 because we move the decimal 14 places.

Answer:

the Answer is. A 1/7

Step-by-step explanation:

i did the test

Final answer:

To model the situation, use the rule t = 12 + 8(n - 1), where n is the number of trucks. Applying this rule, 7 trucks can carry a total of 60 tons of dirt.

Explanation:

The student should write a rule to model the situation where the first truck carries 12 tons of dirt and each subsequent truck carries 8 tons. The rule can be defined as t = 12 + 8(n - 1), where n represents the number of trucks and t represents the total tons of dirt carried. For 7 trucks, we can plug in the value of n into the equation:

t = 12 + 8(7 - 1)

t = 12 + 8(6)

t = 12 + 48

t = 60 tons

Therefore, 7 trucks can carry a total of 60 tons of dirt.