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3 years ago

In a certain clothing store, 4 shirts and 6 ties cost $70, and 2 shirts and 4 ties cost $42. What is the cost of each tie?

Mathematics

1 answer:

Oksanka [162]3 years ago

3 0

Answer:

Step-by-step explanation:

Your two equations are ...

4s +6t = 70
2s +4t = 42

Double the second equation and subtract the first:

2(2s +4t) -(4s +6t) = 2(42) -(70)

2t = 14 . . . . . simplify

t = 7 . . . . . . . divide by 2

The cost of each tie is $7.

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Two groups of staff at a store are making flowers to decorate the entrance. If Group A were to do it alone, it would take them 1

Tcecarenko [31]

Answer:

$\dfrac{6750}{7}$

Step-by-step explanation:

Let x be the number of flowers. If Group A were to make x flowers alone, it would take them 10 hours to complete the task, then they make $\dfrac{x}{10}$ flowers in an hour. If Group B were to make x flowers alone, it would take them 15 hours to complete the task, then they make $\dfrac{x}{15}$ flowers in an hour.

The groups decided to work together. They can make $\dfrac{x}{10}+\dfrac{x}{15}=\dfrac{x}{6}$ together in an hour and it takes them $\dfrac{x}{\frac{x}{6}}=6$ hours. Group B took a break for 1 hour and 40 minutes ( $1\dfrac{2}{3}$ hour), then Group B works

$6-1\dfrac{2}{3}=4\dfrac{1}{3}$ hours.

Thus,

$\dfrac{x}{10}\cdot 6-\dfrac{x}{15}\cdot 4\dfrac{1}{3}=300,\\ \\\dfrac{3x}{5}-\dfrac{13x}{45}=300,\\ \\14x=300\cdot 45=13500,\\ \\x=\dfrac{13500}{14}=\dfrac{6750}{7}.$

6 0

2 years ago

The six seventh grade classes held a fundraiser where they sold candy bars. The school's principal award a $1000 prize to be div

Gelneren [198K]

Answer:

8200/1000 = 8.2 so each time a class selss 8.2 bars, they receive 1 dollar.

If a class sold 16 bars, the class receives 2 dollars, if it sold 82 bars, it receives 10 dollars and so on.

6 0

2 years ago

A cube has a lateral area of 676 square feet.<br> What is the side length of the cube?

sp2606 [1]

Answer:

13 ft.

Step-by-step explanation:

Lateral Surface area of a cube is the area of 4 sides, front side, back side, left side face and right side face.

It can be seen seen from the attached figure as well.

Each face in a cube is a square. And each side in the cube is equal.

So, Lateral surface area is nothing but 4 $\times$ area of a square.

And we know that area of a square = $side^{2}$ .

Hence, Lateral surface area = $4 \times side^{2}$

As per question:

$4 \times side^{2}$ = 676

$side^2 = 169 \\\Rightarrow side = 13$

Hence, side length of cube = 13 feet.

7 0

3 years ago

Find the following integral

ololo11 [35]

There's nothing preventing us from computing one integral at a time:

$\displaystyle \int_0^{2-x} xyz \,\mathrm dz = \frac12xyz^2\bigg|_{z=0}^{z=2-x} \\\\ = \frac12xy(2-x)^2$

$\displaystyle \int_0^{1-x}\int_0^{2-x}xyz\,\mathrm dz\,\mathrm dy = \frac12\int_0^{1-x}xy(2-x)^2\,\mathrm dy \\\\ = \frac14xy^2(2-x)^2\bigg|_{y=0}^{y=1-x} \\\\= \frac14x(1-x)^2(2-x)^2$

$\displaystyle\int_0^1\int_0^{1-x}\int_0^{2-x}xyz\,\mathrm dz\,\mathrm dy\,\mathrm dx = \frac14\int_0^1x(1-x)^2(2-x)^2\,\mathrm dx$

Expand the integrand completely:

$x(1-x)^2(2-x)^2 = x^5-6x^4+13x^3-12x^2+4x$

Then

$\displaystyle\frac14\int_0^1x(1-x)^2(2-x)^2\,\mathrm dx = \left(\frac16x^6-\frac65x^5+\frac{13}4x^4-4x^3+2x^2\right)\bigg|_{x=0}^{x=1} \\\\ = \boxed{\frac{13}{240}}$

4 0

2 years ago

4. Evan took an exam that had 50 questions. He got 38 of the questions correct. What percentage did he

Natasha2012 [34]

Answer:76%

Step-by-step explanation:38 out of 50 equals 76%

5 0

2 years ago