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tekilochka [14]

2 years ago

8

Vanessa is a caterer. She made several batches of appetizers last weekend for an event. This weekend, Vanessa made 4 times as ma

ny batches. She made a total of 25 batches of appetizers for the two weekends. Determine the number of batches
Vanessa made last weekend and the number of batches she made this weekend.
Let b = the number of batches of appetizers Vanessa made last weekend.

2 answers:

galina1969 [7]2 years ago

8 0

Answer:

100 x 13/16 x 25b = 4

18 3/4 = 25b/4

b=25/4

b= 6.25

Step-by-step explanation:

25/4 = 6 1/4 last weekend and 18 3/4 this weekend.

katrin2010 [14]2 years ago

3 0

Answer: Vanessa made 5 batches last weekend and 20 batches this weekend.

Step-by-step explanation:

We have that Vanessa made b batches last weekend, and we know that this weekend she made 4 times as many as the past weekend, so this weekend she made 4*b batches.

In the two weekends, she made a total of 25 batches: this means that:

b + 4*b = 25

5*b = 25

b = 25/5 = 5

then Vanessa made 5 batches last weekend, and 4*5 = 20 batches this weekend.

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It is 4.7 km from Lighthouse A to Port B. The bearing of the port from the lighthouse is N73°E. A ship has sailed due west from

Gennadij [26K]

Answer:

correct option is C. 3.7 km

Step-by-step explanation:

given data

A to Port B = 4.7 km

lighthouse = N73°E

lighthouse = N31°E

solution

we get here first $\angle$ B and

here

$\angle$ A = 90 - 73 = 17°

$\angle$ B = 73 - 31 = 42°

and

sum of all angle 180° so

$\angle$ A +

17° + 42° + $\angle$ C = 180°

solve it we get

$\angle$ C = 121°

Now we use here sin law that is

$\frac{b}{sinB} = \frac{c}{sinC}$ ........................2

put here value and we get

$\frac{b}{sin42} = \frac{4.7}{sin121}$

solve it we get

b = 3,7 km

so correct option is C. 3.7 km

7 0

2 years ago

19. Bella is putting down patches of sod

Fofino [41]

Answer:

The dimensions of the two different rectangular regions are;

1st Arrangement:

W = 4 yards and L = 5 yards or W = 5 yards and L = 4 yards

2nd Arrangement:

W = 2 yards and L = 10 yards or W = 10 yards and L = 2 yards

The perimeter of the two different rectangular regions are;

1st Arrangement:

P₁ = 18 yards

2nd Arrangement:

P₂ = 24 yards

Step-by-step explanation:

Bella is putting down patches of sod to start a new lawn.

She has 20 square yards of sod.

We are asked to provide the dimensions of two different rectangular regions that she can cover with the sod.

Recall that a rectangle has an area given by

Area = W*L

Where W is the width of the rectangle and and L is the length of the rectangle.

Since Bella has 20 square yards of sod,

20 = W*L

There are more than two such possible rectangular arrangements.

Out of them, two different possible arrangements are;

1st Arrangement:

20 = (4)*(5) = (5)*(4)

Width is 4 yards and length is 5 yards or width is 5 yards and length is 4 yards

2nd Arrangement:

20 = (2)*(10) = (10)*(2)

Width is 2 yards and length is 10 yards or width is 10 yards and length is 2 yards

Therefore, the dimensions of two different rectangular regions are;

1st Arrangement:

W = 4 yards and L = 5 yards or W = 5 yards and L = 4 yards

2nd Arrangement:

W = 2 yards and L = 10 yards or W = 10 yards and L = 2 yards

What is the perimeter of each region?

The perimeter of a rectangular shape is given by

P = 2(W + L)

Where W is the width of the rectangle and and L is the length of the rectangle.

The perimeter of the 1st arrangement is

P₁ = 2(4 + 5)

P₁ = 2(9)

P₁ = 18 yards

The perimeter of the 2nd arrangement is

P₂ = 2(2 + 10)

P₂ = 2(12)

P₂ = 24 yards

So the perimeter of the 1st arrangement is 18 yards and the perimeter of the 2nd arrangement is 24 yards.

Note:

Another possible arrangement is,

20 = (1)*(20) = (20)*(1)

Width is 1 yard and length is 20 yards or width is 20 yards and length is 1 yard.

3 0

1 year ago

Ashley invests $9,720 in a one-month money market account paying 3.16% simple annual interest and $8,140 in a two-year CD yieldi

tester [92]

For the first investment. A = P(1 + rt); where p = 9,720, r = 0.0316 and t = 1/12
A = 9720(1 + 0.0316/12) = 9720(1.0026) = $9,746

For the second investment,
A = 8140(1 + 0.0323 x 2) = 8140(1.0646) = $8,666

Total amount she had = $9,746 + $8,666 = $18,412

5 0

2 years ago

Read 2 more answers

Let P and Q be polynomials with positive coefficients. Consider the limit below. lim x→[infinity] P(x) Q(x) (a) Find the limit i

jenyasd209 [6]

Answer:

If the limit that you want to find is $\lim_{x\to \infty}\dfrac{P(x)}{Q(x)}$ then you can use the following proof.

Step-by-step explanation:

Let $P(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots+a_{1}x+a_{0}$ and $Q(x)=b_{m}x^{m}+b_{m-1}x^{n-1}+\cdots+b_{1}x+b_{0}$ be the given polinomials. Then

$\dfrac{P(x)}{Q(x)}=\dfrac{x^{n}(a_{n}+a_{n-1}x^{-1}+a_{n-2}x^{-2}+\cdots +a_{2}x^{-(n-2)}+a_{1}x^{-(n-1)}+a_{0}x^{-n})}{x^{m}(b_{m}+b_{m-1}x^{-1}+b_{n-2}x^{-2}+\cdots+b_{2}x^{-(m-2)}+b_{1}x^{-(m-1)}+b_{0}x^{-m})}=x^{n-m}\dfrac{a_{n}+a_{n-1}x^{-1}+a_{n-2}x^{-2}+\cdots +a_{2}x^{-(n-2)}+a_{1}x^{-(n-1)})+a_{0}x^{-n}}{b_{m}+b_{m-1}x^{-1}+b_{n-2}x^{-2}+\cdots+b_{2}x^{-(m-2)}+b_{1}x^{-(m-1)}+b_{0}x^{-m}}$

Observe that

$\lim_{x\to \infty}\dfrac{a_{n}+a_{n-1}x^{-1}+a_{n-2}x^{-2}+\cdots +a_{2}x^{-(n-2)}+a_{1}x^{-(n-1)})+a_{0}x^{-n}}{b_{m}+b_{m-1}x^{-1}+b_{n-2}x^{-2}+\cdots+b_{2}x^{-(m-2)}+b_{1}x^{-(m-1)}+b_{0}x^{-m}}=\dfrac{a_{n}}{b_{m}}$

and

$\lim_{x\to \infty} x^{n-m}=\begin{cases}0& \text{if}\,\, nm\end{cases}$

Then

$\lim_{x\to \infty}=\lim_{x\to \infty}x^{n-m}\dfrac{a_{n}+a_{n-1}x^{-1}+a_{n-2}x^{-2}+\cdots +a_{2}x^{-(n-2)}+a_{1}x^{-(n-1)}+a_{0}x^{-n}}{b_{m}+b_{m-1}x^{-1}+b_{n-2}x^{-2}+\cdots+b_{2}x^{-(m-2)}+b_{1}x^{-(m-1)}+b_{0}x^{-m}}=\begin{cases}0 & \text{if}\,\, nm \end{cases}$

3 0

2 years ago

What is the final amount if 784 is decreased by 1% followed by a 4% increase?

Iteru [2.4K]

Answer:

The final amount if 784 is decreased by 1% followed by a 4% increase is 807.52.

Step-by-step explanation:

General Formula

<em>A way to solve this problem is as follows</em>:

The general formula for this is taking into account that:

$\\ percent\;change = \frac{change}{starting\;point}$

The <em>starting point</em> is number 784.

The most important key is the solution for this answer is that:

$\\ change = starting\;point - x$

Where <em>x</em> is a number that we need to find. Then

$\\ percent\;change = \frac{starting\;point - x}{starting\;point}$ [1]

Is 784 increased or decreased after all?

We also need to evaluate the following: if a quantity decreases a percentage, and then increases in another percentage, what is the final percentage? In this case, we have first that 784 decreases by 1% and then increases by 4%. As a result 784 will +4% - 1% = +3%, that is, 784 will increase in 3%.

Finding the result

If 784 increases by 3%, we have:

$\\ 3\% = \frac{784 - x}{784}$

Which is equal to

$\\ 0.03 = \frac{784 - x}{784}$

Solving for <em>x</em>, we first multiply by 784 to both sides of the previous formula:

$\\ 0.03 * 784 = \frac{784 - x}{784}*784$

$\\ 0.03 * 784 = (784 - x)*\frac{784}{784}$

$\\ 0.03 * 784 = (784 - x)*1$

$\\ 0.03 * 784 = (784 - x)$

Remember that if we add, subtract, multiply, divide... to both sides of the equation, we do not "alter" this equation.

Subtracting 784 to both sides:

$\\ (0.03 * 784) - 784 = (784 - 784 - x)$

$\\ (0.03 * 784) - 784 = (0 - x)$

$\\ (0.03 * 784) - 784 = - x$

$\\ 23.52 - 784 = - x$

$\\ -760.48 = - x$

Multiplying by -1 to both sides:

$\\ -1 * (-760.48) = -1 * (-x)$

We have to remember that:

$\\ +*+ = +; - * - = +; - * + = -; + * - = -$

$\\ 760.48 = x$

Then

$\\ x = 760.48$

Therefore, using formula [1], an increase of 3% is

$\\ 3\% = \frac{784 - 760.48}{784}$

$\\ change = 784 - 760.48$

$\\ change = 23.52$

Since an increase of 3% is 23.52, we have to add this to the starting point 784, and finally the amount is 784 + 23.52 = 807.52.

As a result, the final amount if 784 is decreased by 1% followed by a 4% increase is 807.52.

In a more <em>terse way</em> of solving this problem, we can say that:

Increase of 4% = 784 * 0.04 = 31.36.

Decrease of 1% = 784 * 0.01 = 7.84.

Difference = 31.36 - 7.84 = 23.52.

Then, we need to add this value to 784, and 784 + 23.52 = 807.52 (the same result).

5 0

1 year ago