8 1/3 × 3

porfa qué alguien me ayude :( ​

Answer:

a = -7

Step-by-step explanation:

4a – (6 – 5a) + 12 = 3a + 2(2a – 4)

Based on the given information, we can calculate the annual income for each profession using the formula: Annual income = Hourly wage * Number of hours worked per year.

Using this formula, we can calculate the annual income for each profession:

Hourly wage Annual income

Federal minimum wage $7.25 $7.25 * 2000 = $14,500

Oregon's minimum wage $8.95 $8.95 * 2000 = $17,900

Average for all occupations $23.87 $23.87 * 2000 = $47,740

Marketing managers $51.90 $51.90 * 2000 = $103,800

Family-practice doctors $82.70 $82.70 * 2000 = $165,400

Veterinary assistants $11.12 $11.12 * 2000 = $22,240

Police officers $26.57 $26.57 * 2000 = $53,140

Child-care workers $9.38 $9.38 * 2000 = $18,760

Restaurant cooks $10.59 $10.59 * 2000 = $21,180

Air-traffic controllers $58.91 $58.91 * 2000 = $117,820

Now, let's calculate the difference between each annual wage figure and both the federal poverty line and the median household income:

Difference between annual wage and federal poverty line:

Federal minimum wage: $14,500 - Federal poverty line = Negative difference (below poverty line)

Oregon's minimum wage: $17,900 - Federal poverty line = Negative difference (below poverty line)

Average for all occupations: $47,740 - Federal poverty line = Positive difference

Marketing managers: $103,800 - Federal poverty line = Positive difference

Family-practice doctors: $165,400 - Federal poverty line = Positive difference

Veterinary assistants: $22,240 - Federal poverty line = Positive difference

Police officers: $53,140 - Federal poverty line = Positive difference

Child-care workers: $18,760 - Federal poverty line = Positive difference

Restaurant cooks: $21,180 - Federal poverty line = Positive difference

Air-traffic controllers: $117,820 - Federal poverty line = Positive difference

Difference between annual wage and median household income:

Federal minimum wage: $14,500 - Median household income = Negative difference (below median)

Oregon's minimum wage: $17,900 - Median household income = Negative difference (below median)

Average for all occupations: $47,740 - Median household income = Negative difference (below median)

Marketing managers: $103,800 - Median household income = Positive difference

Family-practice doctors: $165,400 - Median household income = Positive difference

Veterinary assistants: $22,240 - Median household income = Negative difference (below median)

Police officers: $53,140 - Median household income = Positive difference

Child-care workers: $18,760 - Median household income = Negative difference (below median)

Restaurant cooks: $21,180 - Median household income = Negative difference (below median)

Air-traffic controllers: $117,820 - Median household income = Positive difference

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Answer:

41 mph

Step-by-step explanation:

122 = 3r

r = 40 2/3 mph

Answer:

2 nonreal solutions

Step-by-step explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 (a ≠ 0 )

then the nature of the roots are determined by the discriminant

b² - 4ac

• if b² - 4ac > 0 then 2 real and irrational solutions

• if b² - 4ac > 0 and a perfect square then 2 real and rational solutions

• if b² - 4ac = 0 then 2 real and equal solutions

• if b² - 4ac < 0 then no real solutions

5x² - 2x + 6 = 0 ← in standard form

with a = 5 , b = - 2 , c = 6

b² - 4ac

= (- 2)² - (4 × 5 × 6)

= 4 - 120

= - 116

since b² - 4ac < 0

then there are 2 nonreal solutions to the equation

Answer:

D

Step-by-step explanation:

that's where they cross

Answer:

Length of the side of the square is 12 cm.

Step-by-step explanation:

Given information:

\(\text{side}_1 = 8a \text{ cm (side of a rectangle)}\\\text{side}_2 = 7a \text{ cm (side of a rectangle)}\\P_\text{rec} = 42 + P_\text{sq} \text{ cm } (P_\text{rec} \text{ is perimeter of the rectangle and } \\P_\text{sq} \text{ is the perimeter of the square)}\\\text{side}_\text{sq} = 4a \text{ cm (side of a square)}\)

Our mission is to find the length of the side of the square. We know that the side of the square is 4a cm, so to be able to answer we have to find the value of a first.

Step 1: Finding the value of a

Key to finding the value of a is the perimeter of the rectangle. Notice that we can calculate the perimeter of the rectangle in two different ways.

One way was given in the question:
\(P_\text{rec} = 42 + P_\text{sq}\)

We want equations in terms of a, so we can calculate a. Perimeter of the square can be calculated as:

\(\text{perimeter}_\text{square} = 4 \times \text{side}\)

Substituting the values in equation:

\(P_\text{sq} = 4 \times 4a\\P_\text{sq} = 16a\)

Therefore the first equation for perimeter of the rectangle becomes:

\(P_\text{rec} = 42 + P_\text{sq}\\\fbox{\begin{test}P_\text{rec} = 42 + 16a\end{test}}\)

For the second way we use formula for the perimeter of rectangle which is:
\(\text{perimeter}_\text{rectangle} = 2 \times \text{width} + 2 \times \text{length}\)

Substituting the values in equation:
\(P_\text{rec} = 2 \times 7a + 2 \times 8a\\P_\text{rec} = 14a + 16a\\\fbox{\begin{test}P_\text{rec} = 30a\end{test}}\)

Now let's equate both perimeters of the rectangle.

\(P_\text{rec} = P_\text{rec}\\42+16a = 30a\\42 =14a\\3 = a\)

Step 2: Find the length of the side of the square

It's given that side of the square is 4a cm. All we have to do is substituting a with its value, which we got in the previous step.

\(\text{side}_\text{sq} = 4a\\\text{side}_\text{sq} = 4(3)\\\text{side}_\text{sq} = 12 \text{ cm}\)

The angle included by the sides line PN and line NM is < N

The term included angels refers to the angle formed when two lines meet. The angle as a result of the two lines meeting is the included angle, The angle is located at the meeting point of the two lines.

The following are deduced from the given figure

Line NN

Line NM

Line MP

Looking at the two lines in the question that is Line PN and line NM. The angle at the meeting point is < N and hence the included angle.

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Answer:

To ensure that her team will act immediately, Diana should say the message is very important, or urgent.

Step-by-step explanation:

PLEASE MARK ME AS BRAINLIEST I REALLY WANT TO LEVEL UP

Have a blessed day and remember to keep smiling! :)

Answer:

7

Step-by-step explanation:

So, substitute in your 4 for r, 2(3) + 1. Multiply 2 and 3 to get 6 and then add a to get 7. I hope this helps :)

The power series expansion of f(x) is:

f(x) = 2 - (10/11)x + (130/363)x^2 - (12870/1331)x^3 + ... (for |x/11| < 1)

We can use the binomial series to expand the function f(x) = 2(1-x/11)^(2/3) as a power series:

f(x) = 2(1-x/11)^(2/3)

= 2(1 + (-x/11))^(2/3)

= 2 ∑_(n=0)^(∞) (2/3)_n (-x/11)^n (where (a)_n denotes the Pochhammer symbol)

Using the Pochhammer symbol, we can rewrite the coefficients as:

(2/3)_n = (2/3) (5/3) (8/3) ... ((3n+2)/3)

Substituting this into the power series, we get:

f(x) = 2 ∑_(n=0)^(∞) (2/3) (5/3) (8/3) ... ((3n+2)/3) (-x/11)^n

Simplifying this expression, we can write:

f(x) = 2 ∑_(n=0)^(∞) (-1)^n (2/3) (5/3) (8/3) ... ((3n+2)/3) (x/11)^n

Therefore, the power series expansion of f(x) is:

f(x) = 2 - (10/11)x + (130/363)x^2 - (12870/1331)x^3 + ... (for |x/11| < 1)

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Answer:

x would be 58°

Step-by-step explanation:

Answer:

13.21

Step-by-step explanation:

Sin(32)=7/x

x=7/sin(32)= 13.21

There is sufficient evidence that the valve performs above the specifications.

Null Hypothesis (H0): The mean pressure of the valve is equal to 5.3 lbs/square inch

Alternative Hypothesis (H1): The mean pressure of the valve is greater than 5.3 lbs/square inch

To test whether the valve performs above the specifications, a hypothesis test can be used. The test statistic used will be a t-test since the sample size is below 30. The critical value at the 0.05 level is 1.645. The formula for the t-test is: t = (X-μ)/(s/√n) , where X is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.

Plugging in the known values, the t-test is calculated as: t = (5.5-5.3)/(0.7/√100) = 2.571. Since this value is greater than the critical value at the 0.05 level (1.645), we can reject the null hypothesis and conclude that there is sufficient evidence that the valve performs above the specifications.

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Answer:

69

Step-by-step explanation:

\(24 +45= 69\)

24 + 45=

2+4=6

4+5=9

so, 24+45=69

Hope this helps! Have a good day! :)

b). 1. is the correct option. The number of cookies remaining would be 1.

To find out how many cookies would remain if (N+6) cookies were divided equally among 8 children, we can start by determining the number of cookies each child receives when N cookies are divided equally.
Since N cookies are divided equally among 8 children and 3 remain, each child receives (N/8) + 3 cookies.
Now, let's find out how many cookies each child would receive if (N+6) cookies were divided equally among 8 children.

Using the same logic, each child would receive ((N+6)/8) + 3 cookies.
To find out how many cookies remain, we subtract the number of cookies each child receives from the total number of cookies.
Therefore, the number of cookies remaining would be ((N+6)/8) + 3 - ((N/8) + 3) = (N+6)/8 - N/8 = 6/8 = 3/4.
So, the answer is 3/4 of a cookie, which is equivalent to option b. 1.

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Answer:

Step-by-step explanation:

The gradient of the line 3y-12x+7=0 is; 4.

According to the question;

We are responsible to determine the gradient of the line 3y-12x+7=0.

To do this; we must rewrite the equation 3y-12x+7=0 in the slope-intercept form as follows;

3y-12x+7=0

3y = 12x - 7

y = 4x -7/4

By comparison with; y = mx + c;

where, gradient/slope is m;

The gradient/slope of the line 3y-12x+7=0 is; 4.

Answer:

Yes 17/20 is bigger than 7/9

Step-by-step explanation:

17 divided by 20 = 0.85

7 divided by 9 = 0.778 ish

17/20 is bigger

1. Data input

P = 9500 dollars

r = 5.75% daily

A = 26100 dollars

n = 365

2. Equation

The examples of direct variation are;

equation image indicator. Option B and D

Direct variation is a type of variation such that the variables proportionally increases or decreases.

As one of the variable decreases, the other decreases and as one increases, the other increases.

From the information given, we have that;

For option B:

The equation image indicator does represent direct variation because it can be simplified to y = 2x, where the constant k is equal to 2.

Also, for option D the equation image indicator represents direct variation because it can be simplified to y = -3x, where the constant k is equal to -3.

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The area of the square base = x².

we have:l = w = x ... (2) ... And, h = V/lw = V/x² ... (3) ...

The dimension of the box that minimizes the amount of material used is x =  (2V)1/3. A(x) = x² + 4V/x, A'(x) = 2x - 4V/x², x =  (2V)1/3

The given volume of the box is 62500 cm³. We wish to find the dimensions of the box that minimize the amount of material used.

To obtain the formula for the surface area of the box in terms of only x, the length of one side of the square base, we use the formula for the volume of a box:V = lwh ... (1) ... where V is the volume, l is the length, w is the width, and h is the height of the box. Here, the base of the box is a square with side length x.

Hence, the area of the square base = x². Therefore, we have:l = w = x ... (2) ... And, h = V/lw = V/x² ... (3) ... We can substitute (2) and (3) in (1) to get the formula for V in terms of x as follows:V = x² V/x² A(x) = A(x) = x² + 4xhA(x) = x² + 4x(V/x²) = x² + 4V/x

Now, to find the derivative A'(x) of A(x), we differentiate A(x) with respect to x:A'(x) = 2x - 4V/x²  A'(x) = 0 when x =  (2V)1/3. Therefore, the dimension of the box that minimizes the amount of material used is x =  (2V)1/3. A(x) = x² + 4V/x, A'(x) = 2x - 4V/x², x =  (2V)1/3

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The  component form for the given expression for x and y respectively is <-12, 7>

Given Data

For the x component: a=2 and b=–3, so 2b-3a

Substituting our given data in the expression

2b-3a  = 2*-3-3(2)

2b-3a  = -6-6

2b-3a  = -12

For the y component: a=-1 and b=5, so 2b-3a

Substituting our given data in the expression

2b-3a  = 2*5-3(-1)

2b-3a  = 10-3

2b-3a  = 7

Now put x and y back together: <-12, 7>

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a) The average rate of change of a function over an interval is the change in the function's output (f(b) - f(a)) divided by the change in the function's input (b - a). So, to find the average rate of change of f over the interval -4 <= x <= 3, we can use the formula:

(f(3) - f(-4)) / (3 - (-4)) = (sqrt(25 - 9) - sqrt(25 - 16)) / (3 - (-4)) = (-2sqrt(7) + 4sqrt(3)) / 7

b) To find the derivative of f(x), we need to use the power rule and the chain rule. The power rule states that the derivative of x^n is nx^(n-1), and the chain rule states that the derivative of f(g(x)) is f'(g(x)) * g'(x).

So, the derivative of f(x) = sqrt 25 - x^2 is:

-2x

c) To find the equation of the line tangent to the graph of f at x = -3, we need to use the point-slope form of a line, which is:

y - y1 = m(x - x1)

where m is the slope of the line (which is f'(-3) = -6), (x1, y1) is the point on the graph where the line touches (which is (-3, f(-3)) = (-3, sqrt(25 - 9) = 2sqrt(7))

so we have: y - 2sqrt(7) = -6(x + 3)

d) To check if g(x) is continuous at x = -3, we need to check if the limit of g(x) as x approaches -3 exists and is equal to g(-3).

Since g(x) = f(x) for -5 <= x <= -3 and g(x) = x + 7 for -3 <= x <= 5, we have:

g(-3) = f(-3) = sqrt(25 - 9) = 2sqrt(7)

and the limit of g(x) as x approaches -3 is:

lim x->-3 g(x) = lim x->-3 (x + 7) = -3 + 7 = 4

Since g(-3) = 2sqrt(7) and lim x->-3 g(x) = 4, g(x) is not continuous at x = -3.

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(a) The mean of Z in case (a) is -60 and the variance is 400.

(b) The mean of Z in case (b) is 280 and the variance is 3600.

(c) The mean of Z in case (c) is 60 and the variance is 65.

(d) The mean of Z in case (d) is -20 and the variance is 65.

(e) The mean of Z in case (e) is 80 and the variance is 505.

To find the mean and variance of the random variable Z for each case, we can use the properties of means and variances.

(a) Z = 40 - 5X

Mean of Z:

E(Z) = E(40 - 5X) = 40 - 5E(X) = 40 - 5 * 20 = 40 - 100 = -60

Variance of Z:

Var(Z) = Var(40 - 5X) = Var(-5X) = (-5)² * Var(X) = 25 * Var(X) = 25 * (4)² = 25 * 16 = 400

Therefore, the mean of Z in case (a) is -60 and the variance is 400.

(b) Z = 15X - 20

Mean of Z:

E(Z) = E(15X - 20) = 15E(X) - 20 = 15 * 20 - 20 = 300 - 20 = 280

Variance of Z:

Var(Z) = Var(15X - 20) = Var(15X) = (15)² * Var(X) = 225 * Var(X) = 225 * (4)² = 225 * 16 = 3600

Therefore, the mean of Z in case (b) is 280 and the variance is 3600.

(c) Z = X + Y

Mean of Z:

E(Z) = E(X + Y) = E(X) + E(Y) = 20 + 40 = 60

Variance of Z:

Var(Z) = Var(X + Y) = Var(X) + Var(Y) = (4)² + (7)² = 16 + 49 = 65

Therefore, the mean of Z in case (c) is 60 and the variance is 65.

(d) Z = X - Y

Mean of Z:

E(Z) = E(X - Y) = E(X) - E(Y) = 20 - 40 = -20

Variance of Z:

Var(Z) = Var(X - Y) = Var(X) + Var(Y) = (4)² + (7)² = 16 + 49 = 65

Therefore, the mean of Z in case (d) is -20 and the variance is 65.

(e) Z = -2X + 3Y

Mean of Z:

E(Z) = E(-2X + 3Y) = -2E(X) + 3E(Y) = -2 * 20 + 3 * 40 = -40 + 120 = 80

Variance of Z:

Var(Z) = Var(-2X + 3Y) = (-2)² * Var(X) + (3)² * Var(Y) = 4 * 16 + 9 * 49 = 64 + 441 = 505

Therefore, the mean of Z in case (e) is 80 and the variance is 505.

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Step-by-step explanation:

a = 16

b = 3

because only the factor 3 gets repeatedly added every year (x).

the rest (the starting value that gets tripled and then tripled and then tripled ... every year) is constant.

f(x) = 16×3^x

as you know, exponents have the higher priority to multiplications.

if you want to be save you can use brackets like

f(x) = 16×(3^x)

Answer:

-69

Step-by-step explanation:

Answer:

0.8 is the probability that a single detection system will detect a missile attack.

Step-by-step explanation:

The total revenue from the sale of the first 17 calculators is $195.50.

To find the total revenue from the sale of the first 17 calculators, we need to integrate the rate of change of revenue function R'(x) = (x+3) ln(x+3) with respect to x. The antiderivative of (x+3) ln(x+3) can be written as [(x+3)²/2] + C, where C is the constant of integration. Now, we can calculate the total revenue by evaluating the antiderivative at the upper and lower limits of integration: Total revenue = [(x+3)²/2] evaluated from x = 0 to x = 17

Substituting the upper and lower limits into the antiderivative expression:

Total revenue = [(17+3)²/2] - [(0+3)²/2]

Total revenue = [20²/2] - [3²/2]

Total revenue = [400/2] - [9/2]

Total revenue = 200 - 4.5

Total revenue = 195.5

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Answer:

275 km

Step-by-step explanation:

5.5 x 1   cm: 5.5 x 50 km

5.5 km : 275 km

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