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3 years ago

Simplify and solve for the unknown. Use order of operations as needed. Check your work.

Mathematics

1 answer:

antiseptic1488 [7]3 years ago

3 0

Answer:

Step-by-step explanation:

Given: 5^3– 10^2 = X(8 – 2) + 2X – 3X

Solving the equation to find the value of x.

⇒ $5^{3} -10^{2} = x(8-2)+2x-3x$

Using the distributive property of multiplication, multiplying x with 8 and -2

⇒ $125-100= 8x-2x+2x-3x$

cancelling out -2x and 2x

⇒ $25= 8x-3x$

⇒ $25= 5x$

Multiplying both side by 5

⇒ x= $\frac{25}{5}$

∴ x= 5

Hence, the value of unknown is 5.

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A laundry basket contains 8 white t-shirts and 6 black t-shirts. What is the probability of randomly picking a black t-shirt fro

MissTica

Answer:

30/182 = 15/91.

Step-by-step explanation:

<u>PROBABILITY:</u> the likelihood of an event.

There are a total of 14 shirts in the basket.

Of the 14, 8 (8/14) of them are white, and 6 (6/14) of them are black.

The probability of picking a black shirt is 6 in 14, or 6/14.

The probability of picking a white shirt is 8 in 14, or 8/14.

<u>WITHOUT REPLACING:</u> This means that you take one without putting it back. (There will be one less).

6/14 × 5/13 = 30/182.

30/182 = 15/91.

8 0

3 years ago

Debby, Ella and Unique invest $10,000 each into an oil company. Debby owns 2000 $1 common stocks, Ella owns 1000 of 5% $50 prefe

Mashutka [201]

Answer:

Ella has the greatest return in the current year.

Step-by-step explanation:

Debby would receive $0.80 for each of her 2000 common stock in the oil company,hence Debby's return on investment in the current year is $1600($0.80*2000)

Besides,Ella's return on the stock investment in the current year is computed thus:

Ella's return= 5%*1000*$50=$2,500

In addition,Unique's dollar return on the investment is computed as follows:

Unique's return on investment=4%*2000*$20=$1,600

From the above computations,Ella seems to have the highest return in the current year of $2,500 whereas the two others managed to have $1600 return each

5 0

3 years ago

6. Two observers, 7220 feet apart, observe a balloonist flying overhead between them. Their measures of the

MaRussiya [10]

Answer:

The ballonist is at a height of 3579.91 ft above the ground at 3:30pm.

Step-by-step explanation:

Let's call:

h the height of the ballonist above the ground,

a the distance between the two observers,

$a_1$ the horizontal distance between the first observer and the ballonist

$a_2$ the horizontal distance between the second observer and the ballonist

$\alpha _1$ and $\alpha _2$ the angles of elevation meassured by each observer

S the area of the triangle formed with the observers and the ballonist

So, the area of a triangle is the length of its base times its height.

$S=a*h$ (equation 1)

but we can divide the triangle in two right triangles using the height line. So the total area will be equal to the addition of each individual area.

$S=S_1+S_2$ (equation 2)

$S_1=a_1*h$

But we can write $S_1$ in terms of $\alpha _1$ , like this:

$\tan(\alpha _1)=\frac{h}{a_1} \\a_1=\frac{h}{\tan(\alpha _1)} \\S_1=\frac{h^{2} }{\tan(\alpha _1)}$

And for $S_2$ will be the same:

$S_2=\frac{h^{2} }{\tan(\alpha _2)}$

Replacing in the equation 2:

$S=\frac{h^{2} }{\tan(\alpha _1)}+\frac{h^{2} }{\tan(\alpha _2)}\\S=h^{2}*(\frac{1 }{\tan(\alpha _1)}+\frac{1}{\tan(\alpha _2)})$

And replacing in the equation 1:

$h^{2}*(\frac{1 }{\tan(\alpha _1)}+\frac{1}{\tan(\alpha _2)})=a*h\\h=\frac{a}{(\frac{1 }{\tan(\alpha _1)}+\frac{1}{\tan(\alpha _2)})}$

So, we can replace all the known data in the last equation:

$h=\frac{a}{(\frac{1 }{\tan(\alpha _1)}+\frac{1}{\tan(\alpha _2)})}\\h=\frac{7220 ft}{(\frac{1 }{\tan(35.6)}+\frac{1}{\tan(58.2)})}\\h=3579,91 ft$

Then, the ballonist is at a height of 3579.91 ft above the ground at 3:30pm.

6 0

3 years ago

Solve in simultaneou linear equation.

dangina [55]

Answer:

The bag costs 1500, while the umbrella cost 500

Step-by-step explanation:

Let the cost of the bag be b and the cost of the umbrella be u

Total cost is;

b + u = 2,000 •••••(i)

From the second part of the question;

b = 5u-1000 ••••••(ii)

Substitute ii into i

5u-1000 + u = 2000

6u = 2000 + 1000

6u = 3000

u = 3000/6

u = 500

To get b, substitute the value of u into equation ii

b = 5(500)-1000

b = 2500-1000

b = 1500

5 0

3 years ago

The mean age of 9 women in an office is 27 years old.

Veronika [31]

26 to nearest year

We require the total of the sums of ages for both groups before calculating the mean for all 16

using mean = $\frac{sum}{count}$

Women

27 = $\frac{sum }{9}$ ( cross- multiply )

sum = 9 × 27 = 243

Men

25 = $\frac{sum}{7}$ ( cross- multiply )

sum = 7 × 25 = 175

Total sum of all 16 = 243 + 175 = 418

mean = $\frac{418}{16}$ = 26 ( to nearest year )

6 0

3 years ago

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