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2 years ago

PLS HELP ME ASAP!! WILL MARK BRAINLIEST

Mathematics

2 answers:

SIZIF [17.4K]2 years ago

7 0

Answer: 10

Step-by-step explanation:

Lana71 [14]2 years ago

3 0

Answer:

Step-by-step explanation:

The sqrt of 81 equals to 9, the sqrt of 100 equals to 10

So, sqrt of 92 is between 9 and 10, but closer to 10

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A worker was paid a salary of $10,500 in 1985. Each year, a salary increase of 6% of the previous year's salary was awarded. How

Mazyrski [523]

Note that 6% converted to a decimal number is 6/100=0.06. Also note that 6% of a certain quantity x is 0.06x.

Here is how much the worker earned each year:

In the year 1985 the worker earned <span>$10,500.

</span>In the year 1986 the worker earned $10,500 + 0.06($10,500). Factorizing $10,500, we can write this sum as:

$10,500(1+0.06).

In the year 1987 the worker earned

$10,500(1+0.06) + 0.06[$10,500(1+0.06)].

Now we can factorize $10,500(1+0.06) and write the earnings as:

$10,500(1+0.06) [1+0.06]= $$10,500(1.06)^2$ .

Similarly we can check that in the year 1987 the worker earned $$10,500(1.06)^3$ , which makes the pattern clear.

We can count that from the year 1985 to 1987 we had 2+1 salaries, so from 1985 to 2010 there are 2010-1985+1=26 salaries. This means that the total paid salaries are:

$10,500+10,500(1.06)^1+10,500(1.06)^2+10,500(1.06)^3...10,500(1.06)^{26}$ .

Factorizing, we have

$=10,500[1+1.06+(1.06)^2+(1.06)^3+...+(1.06)^{26}]=10,500\cdot[1+1.06+(1.06)^2+(1.06)^3+...+(1.06)^{26}]$

We recognize the sum as the geometric sum with first term 1 and common ratio 1.06, applying the formula

$\sum_{i=1}^{n} a_i= a(\frac{1-r^n}{1-r})$ (where a is the first term and r is the common ratio) we have:

$\sum_{i=1}^{26} a_i= 1(\frac{1-(1.06)^{26}}{1-1.06})= \frac{1-4.55}{-0.06}= 59.17$ .

Finally, multiplying 10,500 by 59.17 we have 621.285 ($).

The answer we found is very close to D. The difference can be explained by the accuracy of the values used in calculation, most important, in calculating $(1.06)^{26}$ .

Answer: D

4 0

2 years ago

Furniture store is having a sale where everything is 40% off.Write a function that represents the amount of discount d on an ite

Vladimir79 [104]

Answer:

d = .4p

Step-by-step explanation:

Discount = original price * discount rate

We know the discount rate is 40%

original price is p

discount = d

d = p*40%

Changing this to decimal form

d = .4p

6 0

3 years ago

mr martin has 36 calculators in a box. The ratio of the ordinary calculators to the scientific 5:1. How many of each calculator

andre [41]

Answer:

180 calculators.

Step-by-step explanation:

She has 180 calculators because if you were to un - simplify 5:1 you would get 180:5 and you would use the first number. So, you have 180 calculators.

Sorry if this is wrong I tried my best.

8 0

3 years ago

HELPP I NEED TO TURN THIS IN 5 Mins!!!!!

zaharov [31]

Answer:

3. The vertex form of the function, f(x) = x² - 4·x - 17 is f(x) = (x - 2)² - 21

4. The solutions are, x = -2 + √10 and x = -2 - √10

5. The quadratic equation with vertex (3, 1) and a = 1 in standard form is given as follows;

f(x) = x² - 6·x + 10

Step-by-step explanation:

3. The function given in standard form is f(x) = x² - 4·x - 17, which is the form, f(x) = a·x² + b·x + c

The vertex form of the of a quadratic function can be presented based on the above standard form as follows;

f(x) = a(x - h)² + k

Where;

(h, k) = The coordinate of the vertex

h = -b/2a

k = f(h)

Comparing with the given equation, we have;

f(x) = a·x² + b·x + c = x² - 4·x - 17

a = 1

b = -4

c = -17

∴ h = -(-4)/(2 × 1) = 2

h = 2

k = f(h) = f(2) = 2² - 4 × 2 - 17 = -21

k = -21

The vertex form of the function, f(x) = x² - 4·x - 17 is therefore, given as follows;

f(x) = (x - 2)² - 21

4. The given equation for which we need to solve by completing the square is 2·x² + 8·x = 12

Dividing the given equation by 2 gives;

x² + 4·x = 6

Which is of the form, x² + b·x = c

Where;

a = 1

b = 4

c = 6

From which we add (b/2)² to both sides to get x² + b·x + (b/2)² = c + (b/2)²

Adding (b/2)² = (4/2)² to both sides of x² + 4·x = 6 gives;

x² + 4·x + 4 = 6 + 4

(x + 2)² = 10

x + 2 = ±√10

x = -2 ± √10

The solution are, x = -2 + √10 and x = -2 - √10

5. Given that the value of the vertex = (3, 1), and a = 1, we have;

The vertex, (h, k) = (3, 1)

h = 3, k = 1

Therefore, h = 3 = -b/(2 × a) = -b/(2 × 1)

∴ -b = 2 × 3 = 6

b = -6

k = f(h) = a·h² + b·h + c, by substitution, we have;

k = f(3) = 1 × 3² + (-6) × 3 + c = 1

∴ c = 1 - (1 × 3² + (-6) × 3) = 10

c = 10

The quadratic equation with vertex (3, 1) and a = 1 in standard form, f(x) a·x² + b·x + c is therefor;

f(x) = x² - 6·x + 10

4 0

3 years ago

a dart board has 10 equally sized slices numbered from 1-10. some are grey and some are white. the slices numbered 1,2,3,4,5,6,8

mr_godi [17]

Answer:

We have 10 sections, we can assume that the probability of hitting each of one of them is the same.

we have 9 grey slices and 1 white slice, then the probability of landing in a grey slice is equal to the number of grey slices divided by the total number of slices:

P(X) = 9/10 = 0.90

The probability of not landing in a grey slice is equal to the probability of landing in the white slice, this is:

P(not X) = 1/10 = 0.10

Also, when you have only two events, you can calculate this as:

P(not X) = 1 - P(X) = 1 - 0.90 = 0.10

6 0

3 years ago