Darius and Matthew have three fruit bars. They are both hungry after playing football and decide to split the fruit bars evenly.

Final answer:

To simplify the ratio 18 feet to 5 yards, convert yards to feet to get 15 feet, then divide both by the greatest common divisor, 3, ending up with a simplified ratio of 6:5.

Explanation:

To express the ratio 18 feet: 5 yards in simplest form, we first need to convert either yards to feet or feet to yards so that we are comparing the same units. Since we know that 1 yard is equal to 3 feet, we can multiply the number of yards by 3 to find out how many feet it equates to.

Now, let's calculate:

5 yards × 3 feet/yard = 15 feet

So the ratio 18 feet: 5 yards can be rewritten as 18 feet: 15 feet. To simplify this ratio, we divide both numbers by their greatest common divisor (GCD), which in this case is 3.

Here is the calculation:

18 feet ÷ 3 = 6

15 feet ÷ 3 = 5

Therefore, the ratio in simplest form is 6: 5.

The flux of [tex]\vec f(x,y,z)[/tex] across S is given by the surface integral

[tex]\displaystyle \iint_S \vec f(x,y,z) \cdot d\vec s[/tex]

Join to S the disk D of radius 3 in the plane z = 2, for which we have

[tex]x^2+y^2+2=11 \implies x^2+y^2=9=3^2[/tex]

Let S' = S U D (the union of S and D). Since S' is closed, we can use divergence theorem to compute the flux of [tex]\vec f[/tex] through S' :

[tex]\displaystyle \iint_{S'} \vec f \cdot \vec s = \iiint_R \mathrm{div}\vec f \, dV[/tex]

Compute the divergence of [tex]\vec f[/tex] :

[tex]\mathrm{div}\vec f = \dfrac{\partial\left(z\tan^{-1}(y^2)\right)}{\partial x} + \dfrac{\partial\left(z^3\ln(x^2+5)\right)}{\partial y} + \dfrac{\partial(z)}{\partial z} = 1[/tex]

Compute the volume integral by converting to cylindrical coordinates. Take

[tex]\begin{cases}x=r\cos(\theta) \\ y = r\sin(\theta) \\ z = \zeta \\ dV = dx\,dy\,dz = r\,dr\,d\theta\,d\zeta\end{cases}[/tex]

Then the flux of [tex]\vec f[/tex] across S' is

[tex]\displaystyle \iint_{S'} \vec f \cdot \vec s = \int_{-3}^3 \int_{-\sqrt{9-x^2}}^{\sqrt{9-x^2}} \int_2^{11-x^2-y^2} dV = \int_0^{2\pi} \int_0^3 \int_2^{11-r^2} r \, d\zeta \, dr \, d\theta = \frac{81\pi}2[/tex]

To get the flux across S alone, we subtract from this integral the flux of [tex]\vec f[/tex] across D.

Parameterize D by the vector function

[tex]\vec\sigma(\rho,\phi) = \rho \cos(\phi) \, \vec\imath + \rho \sin(\phi) \, \vec\jmath + 2\, \vec k[/tex]

with [tex]0\le\rho\le3[/tex] and [tex]0\le\phi\le2\pi[/tex].

Get the downward-pointing normal vector to D :

[tex]\vec n = \dfrac{\partial\vec\sigma}{\partial\phi} \times \dfrac{\partial\vec\sigma}{\partial \rho} = -\rho\,\vec k[/tex]

Compute the flux across D :

[tex]\displaystyle \iint_D \vec f\cdot d\vec s = \int_0^{2\pi} \int_0^3 \vec f(\vec\sigma) \cdot \vec n \, d\rho\,d\phi = \int_0^{2\pi} \int_0^3 (-2\rho) \, d\rho \, d\phi = -18\pi[/tex]

So the flux of [tex]\vec f[/tex] across S is

[tex]\displaystyle \iint_S \vec f \cdot d \vec s = \frac{81\pi}2 - (-18\pi) = \boxed{\frac{117\pi}2}[/tex]

To find the flux of f across the part of the paraboloid that lies above the plane z = 2 and is oriented upward, we can use the formula for flux and evaluate the integral.

To find the flux of f across the part of the paraboloid that lies above the plane z = 2 and is oriented upward, we can use the formula for flux: flux = ∫∫(f•n)dA. Here, f(x,y,z) = z tan⁻¹(y²)i + z³ ln(x² + 5)j + zk.

The equation of the paraboloid is x² + y² + z = 11. Using these equations, we can set up the double integral and solve for the flux.

After evaluating the integral, we can find the flux of f across the given surface.

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Answer:

Zack can finish the 215 page book after 5 total hours of reading but Pam cannot.

Step-by-step explanation:

Pam read 126 pages of her summer reading book in 3 hours.

[tex]\texttt{Speed of Pam =}\frac{126}{3}=42page/hour[/tex]

Zack read 180 pages of his summer reading book in 4 hours. [tex]\texttt{Speed of Zack =}\frac{180}{4}=45page/hour[/tex]

Number of pages Pam read in 5 hours = 5 x 42 = 210 pages

Number of pages Zack read in 5 hours = 5 x 45 = 225 pages

We need to find will they both finish the 215 page book after 5 total hours of reading,

Here number of pages read by Zack is greater than 215 and number of pages read by Pam is less than 215.

So Zack can finish the 215 page book after 5 total hours of reading but Pam cannot.

To achieve an annual income of $18,930, the woman should invest $77,700 at the 10% rate and $62,000 at the 18% rate.

To determine how much a woman should invest at each rate to achieve an income of $18,930 per year, we can set up a system of linear equations. Assuming she invests x dollars at the 10% rate and y dollars at the 18% rate, we can use the following equations:

x + y = $139,700: This equation represents the total amount of money she has to invest.

0.10x + 0.18y = $18,930: This equation represents the annual income from the investments.

To solve:

Multiply the first equation by 0.10:

0.10x + 0.10y = $13,970

Subtract this from the second equation:

0.18y - 0.10y = $18,930 - $13,970

0.08y = $4,960

Divide by 0.08 to find y:

y = $62,000

Substitute y back into the first equation to find x:

x + $62,000 = $139,700

x = $77,700

Therefore, the woman should invest $77,700 at the 10% rate and $62,000 at the 18% rate to achieve her desired income.

The answer is [tex]\( 5^{0.75} = 5^{\frac{3}{4}} = \sqrt[4]{5^3} \)[/tex].

To solve[tex]\( 5^{0.75} \)[/tex], we first express 0.75 as a fraction in its simplest form. The number 0.75 is equivalent to [tex]\( \frac{3}{4} \)[/tex]. Therefore, [tex]\( 5^{0.75} \)[/tex] can be rewritten as [tex]\( 5^{\frac{3}{4}} \)[/tex].

Now, we can break down [tex]\( 5^{\frac{3}{4}} \)[/tex] using the properties of exponents. The exponent [tex]\( \frac{3}{4} \)[/tex] indicates that we are looking for the fourth root of 5 raised to the power of 3. Mathematically, this is expressed as [tex]\( \sqrt[4]{5^3} \)[/tex].

To find the value, we first calculate [tex]\( 5^3 \)[/tex], which is [tex]\( 5 \times 5 \times 5 = 125 \)[/tex]. Then we take the fourth root of 125. The fourth root of a number is the number that, when raised to the power of 4, gives the original number. In this case, we are looking for a number that, when raised to the power of 4, equals 125.

The fourth root of 125 is not an integer, but we can approximate it. We know that [tex]\( 2^4 = 16 \)[/tex]and [tex]\( 3^4 = 81 \)[/tex], so the fourth root of 125 must be between 2 and 3. Through calculation or using a calculator, we find that [tex]\( \sqrt[4]{125} \)[/tex] is approximately 3.3019.

Therefore, [tex]\( 5^{0.75} \)[/tex] is approximately 3.3019.

To find the length of the hypotenuse of a right triangle with legs measuring 3 cm and 4 cm, use the Pythagorean theorem formula c = √(a² + b²). Plugging in the values gives c = √(9 + 16), which results in a hypotenuse of 5 cm.

The student is asking how to find the length of the hypotenuse of a right triangle when the lengths of the other two sides are given. In this case, the legs of the triangle are 3 cm and 4 cm long. To find the hypotenuse, we use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). This can be expressed as a formula: a² + b² = c². Solving for c, we can find the hypotenuse by taking the square root of the sum of the squares of the other two sides:

c = √(a² + b²)

Plugging in the values for a and b:

c = √(3 cm)² + (4 cm)²

c = √(9 cm² + 16 cm²)

c = √25 cm²

c = 5 cm

Therefore, the length of the hypotenuse is 5 cm.

35-3 =32

32/2 = 16

there are 16 pear trees and 19 apple trees

Answer: There would be 56 tubes, 112 packets and 85 toothbrushes in the dental care bags.

Step-by-step explanation:

Since we have given that

Number of tubes of toothpaste = 56

Number of packets of floss = 112

Number of toothbrushes = 85

We need to find the greatest number of identical dental care bags that dentist can make with the least amount of items leftover.

So, we will find "H.C.F." of 56, 112, 85 which is equal to 1.

So, there would be 56 tubes, 112 packets and 85 toothbrushes in the dental care bags.

Answer:

The temperature of Savannah's liquid to the nearest degree Fahrenheit is 93.1°.

Step-by-step explanation:

Given : In science class, Savannah measures the temperature of a liquid to be 34° Celsius. Her teacher wants her to convert the temperature to degrees Fahrenheit.

To find : What is the temperature of Savannah's liquid to the nearest degree Fahrenheit?

Solution :

The general formula to convert Celsius into Fahrenheit is

[tex]F = (C\times \frac{9}{5}) + 32[/tex]

Substitute C=34°,

[tex]F = (34\times \frac{9}{5}) + 32[/tex]

[tex]F = (34\times 1.8) + 32[/tex]

[tex]F = 61.2+ 32[/tex]

[tex]F =93.1[/tex]

Therefore, The temperature of Savannah's liquid to the nearest degree Fahrenheit is 93.1°.

Answer:

The elevators descends at the rate of 25 feet per second or we can write the change in height of elevator is -25 feet per second, since the elevator is moving in opposite direction.  

Step-by-step explanation:

We are given the following information in the question:

The elevator descends 500 feet in 20 seconds.

Now, we know that at 0 second the lift was at 0 feet.

To calculate the change in the height of elevator per second, we use the following formula:

[tex]\text{Change in height per second} = \displaystyle\frac{y_2-y_1}{x_2-x_1}\\\\= \displaystyle\frac{500-0}{20-0} = \frac{500}{20} = 25\text{ feet per second}[/tex]

Hence, the elevators descends at the rate of 25 feet per second or we can write the change in height of elevator is -25 feet per second, since the elevator is moving in opposite direction.

The change in the elevator's height per second is -25 feet per second. This is calculated by dividing the total descent (500 ft) by the time taken (20 s). The negative value indicates a descent.

To determine the change in an object's height per second, we can use the formula for velocity, which is the displacement (change in position) divided by the time. In this case, the elevator descends 500 feet in 20 seconds. Therefore, the change in the elevator's height per second is 500 feet divided by 20 seconds.

The change in the elevator's height per second is -25 feet per second

The negative sign indicates that the elevator is descending, as opposed to ascending. It's important to note that this is an average rate of change because the question doesn't specify that the elevator's speed is constant.

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The coordinates of the x-intercept are (B/C,0)

The x-intercept of a graph is defined as the places where the graph crosses the x-axis or the locations where the coordinate of the y-axis equals 0, which are known as the x-intercept of a graph.

A graph can be defined as a pictorial representation or a diagram that represents data or values.

Consider the graph of Cx + Ay = B

Here A, B, and C are all positive constants.

To determine the coordinates of the x-intercept

⇒ Cx + Ay = B,

Substitute the value of y = 0 and solve for x

⇒ Cx + A(0) = B,

⇒ Cx = B,

Divide both sides by C

⇒ x = B/C

Hence, the coordinates of the x-intercept are (B/C,0).

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Answer: c. g may cause h

Step-by-step explanation:

Correlation: It represents the relation between any two or more than two variable.

Causation: It is a kind of correlation where one variable if affected by the other variable.

Therefore , Causation implies correlation.

But correlation does not imply causation.

Hence, if  there were a strong correlation between the variables g and h, then g may cause h.

we have

[tex]10x^{2}y+ 25x^{2}[/tex]

we know that

[tex]10=2*5\\25=5*5[/tex]

substitute

[tex](2*5)x^{2}y+ (5*5)x^{2}[/tex]

Factor [tex]5x^{2}[/tex]

[tex](5x^{2})(2y+ 5)[/tex]

therefore

the answer is

[tex](5x^{2})(2y+ 5)[/tex]

The equivalent expression of 10x^2y + 25x^2 is 5x^2(2y + 5)

Equivalent expressions are expressions that have equal values

The expression is given as:

10x^2y + 25x^2

Factor out 5x^2 from the expression

5x^2(2y + 5)

Hence, the equivalent expression of 10x^2y + 25x^2 is 5x^2(2y + 5)

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Given:

Amount of calories per 117.4 grams of Cereal X

 = 110 or 0.620068 per 1 gram of cereal X

Solution:

If there are  252.5 grams of cereal X then the amount of calories in it is computed as

0.620068 X 252.5

156.5671 or 157 (rounded off)

The equation of the tangent line to the curve y = 6x/(2 + x²) at the point (2, 2) will be y-2=(1/3)x-2.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.

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

It is given that,

f(x) = 6x/(2 + x²)

f'(x)=(6x)(2+x²)-6x(2+x²)/(2+x²)²

f'(2)=(6×2)(2+2²)-6x(2+2²)/(2+2²)²

f'(2)=1/3

The value of functions gives the slope of the equation passes through the point (2, 2).

y-y₀=m(x-x₀)

y-2=(1/3)x-2

Thus, the equation of the tangent line to the curve y = 6x/(2 + x²) at the point (2, 2) will be y-2=(1/3)x-2.

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The price of the basketball on sale is $17.50.

To calculate this:

1. Calculate 50% of $35:

  $35 x 0.50 = $17.50

2. Subtract the discount from the original price:

  $35 - $17.50 = $17.50

When an item is on sale for a percentage off, you first find what that percentage represents of the original price. In this case, 50% of $35 is $17.50. Then, you subtract that amount from the original price to find the sale price. So, the basketball, originally priced at $35, would be $17.50 when it's on sale for 50% off.

Complete question:

Find the price of a $35 basketball that is on sale for 50% off the regular price.