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3 years ago

14

In the past, joe got paid $229,390 annually. Since switching to a new career he has been making 10% less. How much does Joe make

now.

2 answers:

butalik [34]3 years ago

8 0

Answer:

Joe makes $206,451 annually

Step-by-step explanation:

229,390 divided by 10 = 22,939

Then Subtract 22,939 from 229,390 = 206,451

Serhud [2]3 years ago

6 0

Answer:

The answer is $206,451

Step-by-step explanation

This scenario is asking to subtract 19 percent away from 229,390 .

Step one : Divide 229,390 by 10 ( take away the zero behind the 9 )

Step 2 : Subtract 22,939 from 229,390 since we know ten percent of 229,390 is 22,939 = 206451

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Courtney must earn at least $150 to pay for broken window. She earns $10 for every car she washes.

valkas [14]

Answer:

10c ≥ 150

At least 15 cars (or c ≥ 15)

Step-by-step explanation:

If she gets $10 for every car she washes a car then 10c is the rate of her gaining money and she needs at least (greater than or equal to) $150.

This equation can be used to express the situation:

10c ≥ 150

<em>To solve you divide the 10 from both sides of the inequality to get.</em>

c ≥ 15

5 0

2 years ago

On any given day, the probability that a large local river is polluted by carbon tetrachloride is 0.12. Each day, a test is cond

babymother [125]

Answer:

a) 0.2416

b) 0.4172

c) 0.0253

Step-by-step explanation:

Since the result of the test should be independent of the time , then the that the test number of times that test proves correct is independent of the days the river is correct .

denoting event a A=the test proves correct and B=the river is polluted

a) the test indicates pollution when

- the river is polluted and the test is correct

- the river is not polluted and the test fails

then

P(test indicates pollution)= P(A)*P(B)+ (1-P(A))*(1-P(B)) = 0.12*0.84+0.88*0.16 = 0.2416

b) according to Bayes

P(A∩B)= P(A/B)*P(B) → P(A/B)=P(A∩B)/P(B)

then

P(pollution exists/test indicates pollution)=P(A∩B)/P(B) = 0.84*0.12 / 0.2416 = 0.4172

c) since

P(test indicates no pollution)= P(A)*(1-P(B))+ (1-P(A))*P(B) = 0.84*0.88+ 0.16*0.12 = 0.7584

the rate of false positives is

P(river is polluted/test indicates no pollution) = 0.12*0.16 / 0.7584 = 0.0253

4 0

3 years ago

How do you know a radical expression is in simplest form?

Diano4ka-milaya [45]

Answer: To know whether a radical expression is in simplest form or not you should put the numbers and letters inside the radical in terms of prime factors. Then, the radical expression is in the simplest form if all the numbers and letters inside the radical are prime factors with a power less than the index of the radical

Explanation:

Any prime factor raised to a power greater than the index of the root can be simplified and any factor raised to a power less than the index of the root cannot be simplified

For example simplify the following radical in its simplest form:

$\sqrt[5]{3645 a^8b^7c^3}$

1) Factor 3645 in its prime factors: 3645 = 3^6 * 5

2) Since the powr of 3 is 6, and 6 can be divided by the index of the root, 5, you can simplify in this way:

- 6 ÷ 5 = 1 with reminder 1, so 3^1 leaves the radical and 3^1 stays in the radical

3) since the factor 5 has power 1 it can not leave the radical

4) the power of a is 8, then:

8 ÷ 5 = 1 with reminder 3 => a^1 leaves the radical and a^3 stays inside the radical.

5) the power of b is 7, then:

7 ÷ 5 = 1 with reminder 2 => b^1 leaves the radical and b^2 stays inside the radical

6) the power of c is 3. Since 3 is less than 5 (the index of the radical) c^3 stays inside the radical.

7) the expression simplified to its simplest form is

$3ab \sqrt[5]{3.5.a^3b^2c^3}$

And you know it cannot be further simplified because all the numbers and letters inside the radical are prime factors with a power less than the index of the radical.

7 0

3 years ago

Read 2 more answers

16/25 in decimal form

lidiya [134]

16/25 in decimal form is 0.64

5 0

3 years ago

Read 2 more answers

The point P(7, −2) lies on the curve y = 2/(6 − x). (a) If Q is the point (x, 2/(6 − x)), use your calculator to find the slope

NARA [144]

Answer:

a) (i) $m = 2.22$ , (ii) $m = 2$ , (iii) $m = 2$ , (iv) $m = 2$ , (v) $m = 1.82$ , (vi) $m = 2$ , (vii) $m = 2$ , (viii) $m = 2$ ; b) $m \approx 2$ ; c) The equation of the tangent line to curve at P (7, -2) is $y = 2\cdot x + 12$ .

Step-by-step explanation:

a) The slope of the secant line PQ is represented by the following definition of slope:

$m = \frac{\Delta y}{\Delta x} = \frac{y_{Q}-y_{P}}{x_{Q}-x_{P}}$

(i) $x_{Q} = 6.9$ :

$y_{Q} =\frac{2}{6-6.9}$

$y_{Q} = -2.222$

$m = \frac{-2.222 + 2}{6.9-7}$

$m = 2.22$

(ii) $x_{Q} = 6.99$

$y_{Q} =\frac{2}{6-6.99}$

$y_{Q} = -2.020$

$m = \frac{-2.020 + 2}{6.99-7}$

$m = 2$

(iii) $x_{Q} = 6.999$

$y_{Q} =\frac{2}{6-6.999}$

$y_{Q} = -2.002$

$m = \frac{-2.002 + 2}{6.999-7}$

$m = 2$

(iv) $x_{Q} = 6.9999$

$y_{Q} =\frac{2}{6-6.9999}$

$y_{Q} = -2.0002$

$m = \frac{-2.0002 + 2}{6.9999-7}$

$m = 2$

(v) $x_{Q} = 7.1$

$y_{Q} =\frac{2}{6-7.1}$

$y_{Q} = -1.818$

$m = \frac{-1.818 + 2}{7.1-7}$

$m = 1.82$

(vi) $x_{Q} = 7.01$

$y_{Q} =\frac{2}{6-7.01}$

$y_{Q} = -1.980$

$m = \frac{-1.980 + 2}{7.01-7}$

$m = 2$

(vii) $x_{Q} = 7.001$

$y_{Q} =\frac{2}{6-7.001}$

$y_{Q} = -1.998$

$m = \frac{-1.998 + 2}{7.001-7}$

$m = 2$

(viii) $x_{Q} = 7.0001$

$y_{Q} =\frac{2}{6-7.0001}$

$y_{Q} = -1.9998$

$m = \frac{-1.9998 + 2}{7.0001-7}$

$m = 2$

b) The slope at P (7,-2) can be estimated by using the following average:

$m \approx \frac{f(6.9999)+f(7.0001)}{2}$

$m \approx \frac{2+2}{2}$

$m \approx 2$

The slope of the tangent line to the curve at P(7, -2) is 2.

c) The equation of the tangent line is a first-order polynomial with the following characteristics:

$y = m\cdot x + b$

Where:

$x$ - Independent variable.

$y$ - Depedent variable.

$m$ - Slope.

$b$ - x-Intercept.

The slope was found in point (b) (m = 2). Besides, the point of tangency (7,-2) is known and value of x-Intercept can be obtained after clearing the respective variable:

$-2 = 2 \cdot 7 + b$

$b = -2 + 14$

$b = 12$

The equation of the tangent line to curve at P (7, -2) is $y = 2\cdot x + 12$ .

7 0

3 years ago