Rodney collects 17 leaves and Sheila collects 23 leaves. How many leaves more leaves does Sheila collect then Rodney?

The solution for the given equation X^3 + Y^2 = 971,028. So, option A is correct.

A multiple of a number is the number whose remainder is 0 when divided by the given number.

Consider 'a' as the multiple of a number 'n'.

Then, a ÷ n = b (and remainder = 0)

It is given that,

X = largest 2-digit multiple of 3 which is not a multiple of 5

⇒ X = 99

Y = smallest 2-digit multiple of 9 which is not a multiple of 6

⇒ Y = 27

Then, substituting the values in the given equation,

= X^3 + Y^2

= (99)³ + (27)²

= 970,299 + 729

= 971,028

Therefore, the value of the given equation is 971,028.

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Answer:

249

Step-by-step explanation:

Remember:

P arenthesess

E xponent

M ultiplictaion

D ivision

A ddition

S ubtraction

So first do the parenthesess:

7^2 x 5 + 10/2-1

Then exponent:

49 x 5 + 10/2-1

Then multiplication:

245 + 10/2-1

Then divsion (Before subraction),

245 + 4

Which equals

249

Have a good day. :)

Hope this helps!

(brainliest would be appreciated)

The rigid motion that verifies the congruence of two triangles using the Side-Angle-Side (SAS) criterion is the combination of a translation and a rotation.

To establish congruence between two triangles using the SAS criterion, we need to show that the triangles have two corresponding sides and the included angle equal in measure. This can be achieved through a specific rigid motion, which preserves the shape and size of the triangles.

The first step in the rigid motion is a translation. Translation involves moving the entire triangle along a straight line without altering its shape or size. By sliding one triangle along the plane, we can place the corresponding sides of the two triangles in the same position.

The second step is a rotation. A rotation is a transformation that turns the triangle around a fixed point, called the center of rotation. By rotating one triangle around its center, we can align the corresponding angles of the two triangles. By combining the translation and rotation, we ensure that the sides and the included angle of the two triangles match, verifying their congruence using the SAS criterion.

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Answer:

B. card I'' increased by 1.2986 = 13 more than card H's

Step-by-step explanation:

Expressions B) 5 + (-3) and C) -6 + 4 have values that are greater than -3.

B) 5 + (-3) simplifies to 2, which is greater than -3.

C) -6 + 4 simplifies to -2, which is also greater than -3.

A) -8 + 3 simplifies to -5, which is less than -3.

D) 3 + (-4) simplifies to -1, which is also less than -3.

In summary, when evaluating expressions, it's important to remember that the order of operations matters, and we can simplify the expression to determine its value. In this case, expressions B and C have values that are greater than -3, while expressions A and D have values that are less than -3.

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Answer:

The inverse of x² +1 is:  

\(\sqrt{x-1},\:-\sqrt{x-1}\)

Step-by-step explanation:

Given

y = x² + 1,  x>0

We know that A function g is the inverse of a function f if for y = f(x), x = g(y)

y = x² +1

Replace x with y

x = y² + 1

solve for y

y² = x - 1

Taking square root

\(y=\:\sqrt{x-1},-\sqrt{x-1}\)

Thus, the inverse of x² +1 is:  

\(\sqrt{x-1},\:-\sqrt{x-1}\)

Answer:

Distance = \(\sqrt{(1-5)^{2} + (5-2)^{2} }\) units

               = \(\sqrt{(-4)^{2} + (3)^{2} }\) units

               =\(\sqrt{25}\) units

               = 5 units

An equivalent function of the form G(t) = ab^t is G(t) = 900(0.9^3)^t. We want to write the given function G(t) in the form of G(t) = ab^t.

We can use the laws of exponents to rewrite 0.9^3t as (0.9^3)^t:

G(t) = 900(0.9^3t) = 900((0.9^3)^t)

We can see that (0.9^3) is a constant, so we can rewrite the function as:

G(t) = a(0.9^3)^t

where a = 900(0.9^0) = 900.

Now, we can write the function in the desired form by letting b = 0.9^3:

G(t) = ab^t = 900(0.9^3)^t

Therefore, an equivalent function of the form G(t) = ab^t is G(t) = 900(0.9^3)^t.

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Answer:

N=15

Step-by-step explanation:

Simplify 1/4 (2n-8)

2n-8/4+1/4n=1/2(n+6)

Factor out the common term 2.

2(n-4)/4+1/3n=1/2(n+6)

Simplify  2(n-4)/4 to n-4/2

n-4/2+n/3=1/2(n+6)

Simplify  1/3n to n/3

n-4/2+n/3=1/2(n+6)

Simplify 1/2(n+6) to n+6/2

n-4/2+n/3=n+6/2

Multiply both sides by 6 (the LCM of 2, 3,).

3(n−4)+2n=3(n+6)

7 Expand.

3n−12+2n=3n+18

Simplify  3n-12+2n to  5n-12

5n−12=3n+18

Add 12 to both sides.

5n=3n+18+12

Simplify  3n+18+12  to  3n+30

5n=3n+30

Subtract 3n from both sides.

5n-3n=30

Simplify  5n-3n to 2n.

2n=30

Divide both sides by 22

n= 30/2

Simplify 30/2 to 15.

n=15

n=15

Brainliest

Answer:

n = 15

Explanation :

1/4(2n-8) + 1/3n = 1/2(n+6)                 Distribute

1/2n -2  + 1/3n = 1/2(n+6)                    Combine like terms

5/6n -2 = 1/2(n+6)                               Distribute

5/6n -2 = 1/2n +3                                 Pass 1/2n  to the other side

5/6n - 1/2n -2 = 3                                Combine like terms

1/3n  -2 = 3                                            Pass -2 to the other side

1/3n = 3+2                                           Combine like terms

1/3n = 5                                                 Divide both sides by 1/3

n = 15                                                     and then you will get your answer .

to solve for surface area find the area of all sides and add them together, start with the the triangles. Half of 10 is 5 so do 5x14 to get 70, since this is a triangle you would half it but because we only solved one side of the triangle we would keep 70 for the combined area of both. Now multiply 70 by 4 since there are 4 sides of the triangle and get 280. To find the bottom do 10x10 to get 100 and add that to 280. The total surface area should be 380in squared

Answer:

380

Step-by-step explanation:

s= B + 1/2 P (slant height)

B is area of base which is 10x10 which is 100

P is perimeter of base which is 10+10+10+10 = 40

100+1/2 (40)(14)

100+ 20(14)

100+280 = 380

Answer: No

Explanation: According to me, if you use the pythagorean formula which includes the formula of a right triangle. If you hold 7 and 14then the resulted length should have been 15. And if you place different positions like that, then none of the length comes the same so we can conclude that none of the sides have a right angle. However there is a possibility to have a right angle in a scalene triangle but it is unlikely here or most probably no.

The statements about the system of linear equations represented by the tables should be described below:

The equation representing the left table is y = 1.5x – 6

The equation representing the right table is y = –4x + 6.1

The solution to the system of equations is (2.2, –2.7)

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

The left table

The slope is calculated as:

\(m=\frac{y_{2}-y_{1}}{ x_{2}-x_{1} }\)

Using the points on the table, we have:

m=(-4.5-(-6))/(1-0)=1.5

So, the equation is calculated using

\(y=m(x-x_{1})+y_{1}\)

This gives

y=1.5(x-0)-6

Open bracket

y = 1.5x – 6

The right table

Using the points on the table, we have:

m=-4

So, the equation is calculated using

\(y=m(x-x_{1})+y_{1}\)

This gives

y= -4(x-0)+6.1

Open bracket

y = –4x + 6.1

The solution

We have:

y = 1.5x – 6

y = –4x + 6.1

Equate both equations as follows

1.5x – 6=–4x + 6.1

On simplifying, x=2.2

Substitute 2.2 for x in y = 1.5x – 6

y= -2.7

Hence, the solution to the system of equations is (2.2,-2.7)

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a) The sequence (un) is strictly increasing for u0 ≥ 0 and strictly decreasing for u0 < 0. b) The limit of the sequence (un) is 0.

In the given sequence, each term un+1 is defined in terms of the previous term un using the equation un+1 = √(u\(n^2\)+ un+1). To study the monotony of the sequence, we can examine the behavior of the terms based on the initial term u0. If u0 is non-negative, the sequence is strictly increasing. This is because the square root of a non-negative number is always non-negative, and therefore, each subsequent term will be greater than the previous one. On the other hand, if u0 is negative, the sequence is strictly decreasing. This is because the square root of a negative number is undefined in the real numbers, and therefore, each subsequent term will be smaller than the previous one.

Regarding the limit of the sequence, as the terms are either increasing or decreasing, we can observe that the sequence approaches a certain value. By analyzing the equation un+1 = √(u\(n^2\) + un+1), we can see that as n approaches infinity, the term un+1 approaches 0. This is because the square root of a sum of squares will always be smaller than the sum itself. Hence, the limit of the sequence (un) is 0.

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The drag force on the spherical particle with a diameter of 0.25 in. falling through oil at 50 degrees F and a velocity of 0.1 ft/s would be approximately 0.0685 lbs.

The Pi terms suitable to describe this problem are:

Pi1 = Fd/(u*V^2*d^2)
Pi2 = V/(d*u)

To use the non-dimensional correlation, we need to find the values of Pi1 and Pi2 for the initial experiment:

Pi1 = 3/(2.04x10^-5*2^2*3^2) = 4.6296
Pi2 = 2/(3*2.04x10^-5) = 49382.3529

Now we can use these values to find the non-dimensional correlation:

Pi1 = (Fd2/(u2*V2^2*d2^2))/(Fd1/(u1*V1^2*d1^2)) = (Fd2/(3.10X10^-3*0.1^2*0.25^2))/(3/(2.04x10^-5*2^2*3^2))
Pi2 = (V2/(d2*u2))/(V1/(d1*u1)) = (0.1/(0.25*3.10X10^-3))/(2/(3*2.04x10^-5))

Solving for Fd2, we get:

Fd2 = Pi1*Fd1*(u2*V2^2*d2^2)/(u1*V1^2*d1^2) = 4.6296*3*(3.10X10^-3*0.1^2*0.25^2)/(2.04x10^-5*2^2*3^2) = 0.0685 lbs

Therefore, the drag force on the spherical particle with a diameter of 0.25 in. falling through oil at 50 degrees F and a velocity of 0.1 ft/s would be approximately 0.0685 lbs.

To determine the Pi term(s) for this problem using dimensional analysis, we'll use the Buckingham Pi Theorem. We have three variables (d, V, u) and three dimensions (length L, mass M, and time T).

Dimensions:
- d: L
- V: L/T
- u: M/(LT)

We have 3 variables and 3 dimensions, so we should have n-r = 3-3 = 0 non-dimensional Pi terms.

However, Fd itself is a force and has dimensions ML/T^2. To create a non-dimensional term, we can divide Fd by a force with the same dimensions:

Force with the same dimensions: uVd
Dimensions: (M/(LT))(L/T)L = ML/T^2

Now we have the non-dimensional term:
Pi_1 = Fd/(uVd)

For the given experiment values, we can find the value of Pi_1:

Pi_1 = (3 lbs) / (2.04 x 10^-5 lbs*s/ft^2 * 2 ft/s * 3 in.)

Now, we have to find the drag force (Fd') on the smaller spherical particle in oil. We'll use the same Pi_1 value since it's dimensionless and correlates both scenarios:

Fd' = Pi_1 * (u'V'd')

Plug in the given values:

Fd' = Pi_1 * (3.10 x 10^-3 lbs*s/ft^2 * 0.1 ft/s * 0.25 in)

Solve for Fd' using the Pi_1 value calculated earlier.

Remember to convert inches to feet before calculating, as 1 inch = 1/12 ft.

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Answer:

50

Step-by-step explanation:

Step 1

10×4÷2−5×(−6)

40÷2−5×(−6)

Step 2

40÷2−5×(−6)

20−5×(−6)

Step 3

20−5×(−6)

20+30

Step 4

20+30

50

I hope this helped! Like I mentioned before, you need to do multiplication/division from left to right first before subtraction/addition from left to right. This is why in step 3 we do −5×(−6).

Answer:

70 degrees

Step-by-step explanation:

The angle opposite x and x itself are vertical angles, meaning that they have the same angle measure. Since the sum of the interior angles of a triangle is 180 degrees:

x+55+55=180

x+110=180

x=180-110=70

Hope this helps!

Answer:

You have to combine like terms (2x+5+3x-2)

Step-by-step explanation:

X=7 should be the answer.

Answer:

x = 1 , y = 4

Step-by-step explanation:

I am assuming you're looking for what x and y are? If so, then we know that

DC and AB equal each other, so

4x + y = 8

CB and AD equal each other, so

2x + y = 6

We have two equations that cannot be solved on their own, so we must solve them as a system of equations. One process to solve is elimination.

4x + y = 8

2x + y = 6

we can multiply the second equation all by -1 to make the y's cancel out and give us x. so,

4x + y = 8

-1(2x + y) = 6

4x + y = 8

-2x -y = -6

now solve them vertically. we get:

2x = 2

and so x = 1.

Now that we found x, we must find y. Using any of the two equations froom above, we can substitue our x value of 1 into it to find y. I will use the first one.

4x + y = 8

4(1) + y = 8

4 + y = 8

y = 8 - 4

y = 4

so our x is 1 and y is 4.

hope this helps! (:

Answer:

A fraction bar separates the numerator and denominator of a fraction. It indicates that a division of the numerator by the denominator will be performed.

Step-by-step explanation:

In math, a fraction bar can be defined as a visual representation of fractions that helps in comparing fractions and carrying out operations with fractions. Fraction bars or fraction strips are a part-to-whole representational model. Each part of a fraction bar represents one unit out of a whole.

Answer:To separate the top and bottom numbers.

Step-by-step explanation:In math, a fraction bar can be defined as a visual representation of fractions that helps in comparing fractions and carrying out operations with fractions.

To find the consumer's surplus at the market equilibrium point, we need to determine the equilibrium price and quantity by setting the demand and supply functions equal to each other. Then, we can calculate the area of the triangle below the demand curve and above the equilibrium price.

The equilibrium occurs when the quantity demanded equals the quantity supplied. By setting the demand and supply functions equal to each other, we can solve for the equilibrium price:

100 - 18x = a + 2

Simplifying the equation, we have:

18x = 98 - a

x = (98 - a)/18

Substituting this value of x into either the demand or supply function will give us the equilibrium price. Let's use the demand function:

p = 100 - 18x

p = 100 - 18((98 - a)/18)

p = 100 - (98 - a)

p = 2 + a

So, the equilibrium price is 2 + a.

To calculate the consumer's surplus, we need to find the area of the triangle below the demand curve and above the equilibrium price. The formula for the area of a triangle is 0.5 * base * height. In this case, the base is the quantity and the height is the difference between the equilibrium price and the price given by the demand function. Thus, the consumer's surplus is given by:

Consumer's Surplus = 0.5 * (98 - a) * [(100 - 2) - (2 + a)]

Simplifying further, we get the expression for the consumer's surplus at the market equilibrium point.

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The graph of the scenario of the inequality 8x + 5y ≤ 100 is added as an attachment

From the question, the given parameters are:

Also, we have the inequality of the possible combinations to be

8x + 5y ≤ 100

Such that

The next step is to plot the graph of the inequality

This can be done by the use of a graphing tool

So, we enter the inequality on the graphing tool and attach the graph

Recall that the inequality is given as

8x + 5y ≤ 100

See attachment for the graph of the inequality 8x + 5y ≤ 100

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Answer:

2(2/5x+2)=4x/5+4

Step-by-step explanation:

2(2/5x+2)=4x/5+4

4x/5 +4=4x/5 +4

Answer:

100 - 15 = 85

816 = 85%

now work out 1%.

85/85 = 1% do the same to the other side

816/85 = 9.6

9.6 = 1%

now find 100%

1 X 100= 100%

9.6 X 100=960

regular price $960

The weighted-average unit contribution margin is $46.20.

The weighted-average unit contribution margin can be calculated by multiplying the unit contribution margin of each model by its respective sales mix percentage, and then summing up the results.

To find the weighted-average unit contribution margin, we first calculate the unit contribution margin for each model by subtracting the unit variable costs from the selling price:

For Model A12:

Unit contribution margin = Selling price - Unit variable cost

                     = $60 - $42

                     = $18

For Model B22:

Unit contribution margin = Selling price - Unit variable cost

                     = $120 - $84

                     = $36

For Model C124:

Unit contribution margin = Selling price - Unit variable cost

                     = $480 - $360

                     = $120

Next, we multiply each unit contribution margin by its respective sales mix percentage:

Weighted contribution margin for Model A12 = 60% * $18 = $10.80

Weighted contribution margin for Model B22 = 15% * $36 = $5.40

Weighted contribution margin for Model C124 = 25% * $120 = $30.00

Finally, we sum up the weighted contribution margins:

Weighted-average unit contribution margin = $10.80 + $5.40 + $30.00 = $46.20. Therefore, the weighted-average unit contribution margin is $46.20.

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Answer:

11.7

Step-by-step explanation:

a = 1/2bh

93.6 = 1/2(16)h

93.6 = 8h  Divide both sides by 8

11.7 = h

Answer:

\(c= 11.7 \text{ mi}\)

Step-by-step explanation:

To solve for c, we can construct an equation using the triangle area formula.

\(\text{area} = \dfrac{1}{2} \times \text{base} \times \text{height}\)

↓ plugging in the given measurements

\(\text{base} = 16 \text{ mi}\)     \(\text{area} = 93.6 \text{ mi}^2\)

\(93.6 \text{ mi}^2 = \dfrac{1}{2} \times 16 \text{ mi} \times \text{height}\)

↓ replacing height with c

\(93.6 \text{ mi}^2 = \dfrac{1}{2} \times 16 \text{ mi} \times c\)

↓ executing multiplication

\(93.6 \text{ mi}^2 = 8 \text{ mi} \times c\)

↓ dividing both sides by 8 mi

\(\dfrac{93.6 \text{ mi}^2}{8 \text{ mi}} = \dfrac{8\text{ mi} \times c}{8 \text{ mi}}\)

\(11.7 \text{ mi} = c\)

A leaking faucet in the S&E building lab, dripping at a rate of one drop per second, will result in a water loss of approximately 4,725 liters in one year.

To calculate the amount of water lost in one year, we need to determine the number of drops per year and then convert it to liters. Since the faucet drips at a rate of one drop per second, there are 60 drops in a minute (60 seconds), which totals to 3,600 drops in an hour (60 minutes).

In a day, there would be 86,400 drops (24 hours * 3,600 drops). Considering a year of 365 days, the total number of drops would be approximately 31,536,000 drops (86,400 drops * 365 days). To convert the number of drops to liters, we need to multiply the total number of drops by the volume of each drop.

Given that each drop contains 0.150 milliliters, we convert it to liters by dividing by 1,000, resulting in 0.00015 liters per drop. Multiplying the total number of drops by the volume per drop, we find that the total water loss is approximately 4,725 liters (31,536,000 drops * 0.00015 liters/drop).

Therefore, in one year, the leaking faucet in the S&E building lab would result in a water loss of approximately 4,725 liters.

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The process to find w involves using the fact that the angles around a point add up to 360°, and substituting expressions for the angles in terms of w to solve for it. , w = 102°

Let the angles formed by the three intersecting lines be A, B, and C as shown below:

A

/

B--C

We can see that A + B + C = 180° (since they form a straight line) and A + B = 76° (since that's the given angle).

Substituting A + B in terms of 76° in the first equation, we get:

A + B + C = 180°

76° + C = 180°

C = 104°

So, the equation that represents the relationship between the angles is: A + B + C = 180°.

To find w, we need to use the fact that the angles around a point add up to 360°.

Looking at the diagram below, we can see that the angles w, 76°, and x form a straight line, so we have:

w + 76° + x = 180°

We also know that the angles w, y, and 76° form a straight line, so we have:

w + y + 76° = 180°

Finally, we know that the angles x, y, and z form a straight line, so we have:

x + y + z = 180°

To solve for w, we can substitute x and y in terms of w using the first two equations:

x = 180° - 76° - w = 104° - w

y = 180° - 76° - w = 104° - w

Substituting these expressions in the third equation and solving for z, we get:

x + y + z = 180°

(104° - w) + (104° - w) + z = 180°

z = 2w - 128°

Now, we can substitute x, y, and z in terms of w in the first equation and solve for w:

w + (76°) + (104° - w) + (104° - w) + (2w - 128°) = 360°

4w - 48° = 360°

4w = 408°

w = 102°

Therefore, the process to find w involves using the fact that the angles around a point add up to 360°, and substituting expressions for the angles in terms of w to solve for it.

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The radius of the circle is \(\sqrt{\frac{9}{4} }\) = 3/2.

To find the radius of the circle with the equation \(x^2\) + \(y^2\) - 6y = 0, we can rewrite the equation in standard form.

The standard form for the equation of a circle is \((x-h)^{2}\) + \((y-k)^{2}\) =\(r^2\), where (h, k) is the center of the circle and r is the radius.

To convert the equation \(x^2\) + \(y^2\) - 6y = 0 to standard form, we can complete the square.

First, we can rewrite the equation as \(x^2\) + \(y^2\) - 6y = 0.

To complete the square, we need to add and subtract the square of half of the coefficient of the y term. In this case, we add and subtract $(-3/2)^2 = 9/4$.

So the equation becomes \(x^2\) +\(y^2\) - 6y + \(\frac{9}{4}\) - \(\frac{9}{4}\) = 0, which simplifies to \(x^2\)+ \((y-\frac{3}{2}) ^{2}\) = \(\frac{9}{4}\).

Therefore, the radius of the circle is \(\sqrt{\frac{9}{4} }\) =\(\frac{3}{2}\).

The complete question is:-

What is the radius of the circle x² +y² -6y =0?

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