How do I combine like terms
14(x - 2)

Answer:

82-24=48

Step-by-step explanation:

Answer:

y ≤ 1/3x - 4

Step-by-step explanation:

it could not be options 3 or 4 because the y-intercept is -4, not +4

I picked a point in the shaded area to see which inequality, the first or the second, would make it true; the point I used was (3, -4)

1st option:  y ≥ 1/3x - 4        Is this true? -4 ≥ 1/3(3)  No, -4 is not GE 1

2nd option: y ≤ 1/3x - 4        Is this true? -4 ≤ 1/3(3)  Yes, -4 is LE 1  

Answer:

The area of the kite at the right is 72

\((1 - 5i)(5 + 6i) \\ = 5 + 6i - 25i - 30 {i}^{2} \\ = 5 - 19i + 30 \\ = 35 - 19i\)

I hope I helped you^_^

Answer:

35-19i

Step-by-step explanation:

(1-5i)(5+6i)

5-25i+6i-30i^2 where i^2=-1

5-25i+6i-30(-1)

5-19i+30

5+30-19i

35-19i

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The probability of a game duration of fewer than 210 minutes is 0.7486, or 74.86%.

To find the probability of a game duration of fewer than 210 minutes, we need to calculate the z-score and then use the standard normal distribution table.

First, we calculate the z-score using the formula: z = (x - mean) / standard deviation.
In this case, x = 210 minutes, mean = 180 minutes, and standard deviation = 45 minutes.

z = (210 - 180) / 45
z = 30 / 45
z = 0.67

Next, we look up the z-score of 0.67 in the standard normal distribution table. The table gives us the probability corresponding to the z-score.

From the table, we find that the probability corresponding to a z-score of 0.67 is 0.7486.

Therefore, the probability of a game duration of fewer than 210 minutes is 0.7486, or 74.86%..

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The probability of a major league baseball game lasting fewer than 210 minutes is approximately 74.86%.

The duration of major league baseball games is normally distributed with a mean of 180 minutes and a standard deviation of 45 minutes. To find the probability of a game lasting fewer than 210 minutes, we need to calculate the z-score and use the standard normal distribution table.

First, we calculate the z-score using the formula:

z = (x - mean) / standard deviation

Here, x represents the desired game duration, which is 210 minutes in this case. Plugging in the values, we get:

z = (210 - 180) / 45

z = 30 / 45

z = 0.67

Next, we look up the corresponding probability for the z-score of 0.67 in the standard normal distribution table. The table tells us that the probability associated with this z-score is 0.7486.

Therefore, the probability of a game duration of fewer than 210 minutes is 0.7486 or 74.86%.

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Answer: \(10, 31\ \text{years}\)

Step-by-step explanation:

Given

The present age of Madison's Mother is three time that of Madison

Suppose the Present age of Madison is \(x\), so age of her mother is \(3x\)

After \(6\dfrac{1}{4}\ \text{years}\), the sum of their age will be \(53\dfrac{3}{4}\ \text{years}\)

\(\therefore (x+6\dfrac{1}{4})+(3x+6\dfrac{1}{4})=53\dfrac{3}{4}\\\\\Rightarrow 4x+2\times \dfrac{25}{4}=\dfrac{53\times 4+3}{4}\\\\\Rightarrow 4x+\dfrac{50}{4}=\dfrac{215}{4}\\\\\Rightarrow 4x=\dfrac{215-50}{4}\\\\\Rightarrow x=\dfrac{165}{16}\\\\\Rightarrow x= 10.31\approx 10\)

Madison mother's age \(3x=30.93\approx 31\ \text{years}\)

Given the points (-4, -1), (-1, 3), (3, 0), and (0, -4), the parallelogram is a square.

To determine whether each parallelogram is a rectangle, rhombus, or square using the slope, midpoint, and distance formulas for the points (-4, -1), (-1, 3), (3, 0), and (0, -4), we will follow these steps below. Step 1: Identify the type of parallelogram The slope, midpoint, and distance formulas will be used to determine the nature of the given parallelogram. Since all the sides of a square are equal, all the angles are right angles, and all the diagonals are equal, the parallelogram is a square if all these conditions are met. Similarly, if a parallelogram has all sides equal and diagonal perpendicular bisectors, it is a rhombus. In addition, the parallelogram is a rectangle if any two adjacent sides are equal, and the diagonals are of equal length and perpendicular. Step 2: Calculate the distances of all sides The length of each side of the parallelogram should be calculated using the distance formula.

To calculate the length of the diagonal connecting the points (-4, -1) and (3, 0), we have: D₁ = √((3+4)²+(0+1)²) = √50To calculate the length of the diagonal connecting the points (-1, 3) and (0, -4), we have: D₂ = √((0+1)²+(-4-3)²) = √50Since the diagonals are equal, the parallelogram is either a rhombus or a square. Step 5: Determine the type of parallelogram Since all sides are equal, the slopes of opposite sides are equal, and the diagonals are equal, the parallelogram is a square.

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In a multiple regression model, the variance of the error term e is assumed to be the same for all values of the independent variable. Therefore, the correct option is C) the same for all values of the independent variable.

In multiple regression, we use several independent variables to predict the values of the dependent variable. The model estimates the relationship between the independent variables and the dependent variable by calculating the coefficients of the independent variables.

The error term e represents the difference between the predicted value of the dependent variable and the actual value of the dependent variable.

The assumption of constant variance of the error term e is known as homoscedasticity. It means that the variance of the errors is the same for all levels of the independent variables.

This assumption is important because, if the errors have different variances across the levels of the independent variable, the model may not accurately capture the relationship between the independent variables and the dependent variable, leading to biased and unreliable results. so, the correct answer is C).

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Answer:

mean = 2.25

standard deviation = 1.34

Explanation:

The mean of the distribution can be calculated as the sum of each value of x times P(x), so taking into account the table, we get that the mean is equal to

mean = 0(0.10) + 1(0.20) + 2(0.30) + 3(0.20) + 4(0.15) + 5(0.05)

mean = 0 + 0.2 + 0.6 + 0.6 + 0.6 + 0.25

mean = 2.25

Therefore, the mean is 2.25

On the other hand, the variance is equal to the square of the difference between each value and the mean multiplied by its probability, so

variance = (0 - 2.25)²(0.10) + (1 - 2.25)²(0.20) + (2 - 2.25)²(0.30)

+ (3 - 2.25)²(0.20) + (4 - 2.25)²(0.15) + (5 - 2.25)²(0.05)

variance = 0.51 + 0.31 + 0.02 + 0.11 + 0.46 + 0.38

variance = 1.79

Then, the standard deviation is equal to the square root of the variance, so

standard deviation = √1.79

standard deviation = 1.34

Therefore, the standard deviation is 1.34

The price of carrots per ounce is $0.24 .

Ounce is an unit of mass in the Imperial System. It is widely used throughout the world and is one of the oldest units of measurement to still exist. The unit ounce is derived from uncia, a unit of measurement in roman times.

The ounce(abbreviated oz) is equal to approximately 28.35 grams and 16 ounces make up a pound.

Now it is given that a 2-pound bag of carrots cost $7.68 .

Therefore price per pound of carrots=$7.68÷2

Price per pound=$ 3.84 .

Now we know that 16 ounces make up a pound.

Price of carrots per ounce=  $3.84 ÷16

Price per ounce=  $ 0.24

Therefore the price of carrots per ounce is $0.24

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Answer:

-7/5

Step-by-step explanation:

It is given that,

→ (-4/5) + (-3/5) = ?

Let's solve the problem,

→ (-4/5) + (-3/5)

→ (-4/5) - (3/5)

→ (-4 - 3)/5 = -7/5

Thus, the answer is -7/5.

check below for labels,

Answer:

(2, 5)

Step-by-step explanation:

The x coordinate is the number inside the parentheses, but with the opposite sign, 2

The y coordinate is the number at the end

Answer:

vertex: (2, 5)

Step-by-step explanation:

y=3(x−2)2+5

this is a parabola because of one variable squared and the other one is not so now write it in the standard form of parabolas which it is = to

______

Vertical :

(x−h)2=4p(y−k)

Horizontal:

(y−k)2=4p(x−h)2

vertex = (h, k)

______

this y=3(x−2)2+5 equation is vertical since x is squared

subtract 5 from both sides:

y−5=3(x−2)2

divide both sides by 3:

(y−5)13=(x−2)2

vertex:

(2,5)

we have the equation

step 1

Convert mixed number to an improper fraction

so

8 1/2=8+1/2=17/2

substitute

Multiply by 2 both sides

17x=102

Divide by 17 both sides

x=102/17

1x=02/17=6

therefore

If lidocaine is injected intra-arterially, it can quickly lead to systemic toxicity. The first signs of toxicity may include circumoral numbness and tongue paresthesia, but these symptoms may be followed by more severe manifestations such as dizziness, seizures, and cardiac arrest.

The systemic effects of lidocaine are dose-dependent, meaning that the higher the dose, the more severe the symptoms.

Lidocaine is a local anesthetic that is commonly used for minor surgical procedures or dental work. It works by blocking the nerve signals that transmit pain to the brain. However, if it is injected into an artery, it can rapidly spread throughout the body and affect other organs, leading to potentially life-threatening complications.

If you suspect that a patient has been injected with lidocaine intra-arterially, it is important to act quickly. The first step is to stop the injection and monitor the patient closely for signs of toxicity. If the patient is experiencing severe symptoms, such as seizures or cardiac arrest, emergency treatment should be initiated immediately. Treatment may include administering medications to counteract the effects of the lidocaine or performing cardio-pulmonary resuscitation (CPR) if necessary.

In conclusion, the first signs of lidocaine toxicity may include circumoral numbness and tongue paresthesia, but more severe symptoms may follow, such as dizziness, seizures, and cardiac arrest. If you suspect that a patient has been injected with lidocaine intra-arterially, it is important to act quickly to prevent potentially life-threatening complications.

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The radius of the circle is approximately 10.17 units (rounded to two decimal places).

To find the radius of the circle, we need to use the formula that relates the central angle to the length of the arc and the radius of the circle. The formula is given as:

arc length = radius x central angle

In this case, the arc length is given as 24.4 and the central angle is given as 2.4 radians. Substituting these values in the formula, we get:

24.4 = r x 2.4

Solving for r, we get:

r = 24.4 / 2.4

r ≈ 10.17

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Answer:

They all make a shape and the perimeters are the same but being doubled each time. They can make parallelograms. As a triangle is added they have at least one parallel side.

Step-by-step explanation:

you'd have to multiply them each. then add them all together when your done. like this, 5x5x3=75

Given:

Initial value = $800 per acre

Growth rate = 3% per year

To find:

How long will it be before the land is worth $1000 per acre.

Solution:

The exponential growth model is:

\(y=a(1+r)^t\)

Where, y is the new value, a is the initial value, r is the growth rate in decimal and t is the number of years.

Putting \(y=1000, a=800, r=0.03\), we get

\(1000=800(1+0.03)^t\)

\(\dfrac{1000}{800}=(1.03)^t\)

\(1.25=(1.03)^t\)

Taking log both sides, we get

\(\log 1.25=\log (1.03)^t\)

\(0.09691=t\log (1.03)\)

\(0.09691=0.012837t\)

Isolating the variable t, we get

\(\dfrac{0.09691}{0.012837}=t\)

\(7.54927=t\)

\(t\approx 7.55\)

Therefore, the land is worth $1000 per acre after 7.55 years.

Mean reversion is the tendency of prices or variables to return to their average level. The mean-reverting level, x1, is calculated using statistical methods and indicates potential future decreases or increases.

Mean reversion refers to the tendency of asset prices or economic variables to move back to their average or mean level over time. The mean-reverting level, x1, for a time series can be calculated using statistical methods like moving averages or exponential smoothing. These techniques estimate the average value or trend of the data.



The interpretation of x1 depends on the context. If the current value is above x1, it suggests a potential future decrease, reverting back to x1. Conversely, if the current value is below x1, it indicates a potential future increase, also reverting back to x1. The deviation from x1 provides insights into the strength or speed of the mean reversion process.



Therefore, Mean reversion is the tendency of prices or variables to return to their average level. The mean-reverting level, x1, is calculated using statistical methods and indicates potential future decreases or increases.

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Answer:

To calculate the net profit for each of the listed stocks, you can use the formula:

Net Profit = (Current Price - Purchase Price) * Number of Shares

Assuming you invested $500 in each stock 5 years ago, the purchase prices would be as follows:

Chipotle: $649.85 (based on the current price of $1,708.29)

Nike: $71.45 (based on the current price of $122.64)

Amazon: $45.60 (based on the current price of $103.29)

Snap Inc.: $15.49 (based on the current price of $11.21)

To calculate the number of shares you would have purchased at the time, you would divide $500 by the purchase price. For example, for Chipotle:

Number of Shares = $500 / $649.85 = 0.769 shares

Using this formula, the net profit for each stock would be:

Chipotle: (1,708.29 - 649.85) * 0.769 = $764.28

Nike: (122.64 - 71.45) * 7.006 = $359.62

Amazon: (103.29 - 45.60) * 10.920 = $630.58

Snap Inc.: (11.21 - 15.49) * 32.281 = -$137.31 (assuming you bought fractional shares)

Therefore, your total net profit would be $1,616.17.

Note that this calculation does not take into account any transaction fees or taxes that may be incurred in buying and selling the stocks.

I made a long explanation because you wanted me to explain step by step.

For Nike:

1.5 years ago the stock was at 63.59 USD, so buying $500 of Nike stock would give me 7.85 stocks (Purchase amount/stock price) or (500/63.59:7.85).

Stock is now valued at $122.64 USD, so I own $963.78 in stock (Stock price x Stock owned) or (7.85 X 122.64 = $963.78).

Net profit is $463.78 (Total of current owned stock - initial investment) or ($963.78 - $500 = $463.78).

For Amazon:

1.5 years ago the stock was at $1,765.13 USD, so buying $500 of Amazon stock would give me 0.283 stocks (Purchase amount/stock price) or (500/1,765.13:0.283).

Stock is now valued at $3,369.19 USD, so I own $953.63 in stock (Stock price x Stock owned) or (0.283 X 3,369.19 = $953.63).

Net profit is $453.63 (Total of current owned stock - initial investment) or ($953.63 - $500 = $453.63).

For Snap Inc.:

1.5 years ago the stock was at $17.46 USD, so buying $500 of Snap Inc. stock would give me 28.63 stocks (Purchase amount/stock price) or (500/17.46:28.63).

Stock is now valued at $11.21 USD, so I own $321.36 in stock (Stock price x Stock owned) or (28.63 X 11.21 = $321.36).

Net loss is $178.64 (Total of current owned stock - initial investment) or ($321.36 - $500 = -$178.64).

Based on the net profit, Chipotle and Amazon have performed well over the past 5 years, with net profits of $1,230.51 and $453.63 respectively. Nike has also performed well with a net profit of $463.78. However, Snap Inc. has decreased in price over the past 5 years and resulted in a net loss of $178.64.

Answer:

\(2\frac{7}{16}\)  inches

Step-by-step explanation:

Since 1 mi = 5,280 ft., to convert miles to feet, multiply by 5,280.

96 mi. = 96(5,280 ft.)

96 mi. = 506,880 ft.

Since 1 ft. = 12 in., to convert feet to inches, multiply by 12.

506,,800 ft. = 506,880(12 in.)

506,880 ft. = 6,082,560 in.

The map scale is 1 in. represents 2,500,000 in.

\(\frac{6,082,560}{2,500,00} = 2.4330...\)  

The distance on the map between Nanaimo and Campbell River is approximately \(2\frac{7}{16}\)

The quotient of 4 and \(\frac{1}{3}\) is equal to 12.

In Mathematics, quotient is a mathematical expression that is simply used to represent division i.e the division of a number by another number.

Translating the word problem into an equation, we have:

The quotient of 4 and \(\frac{1}{3}\) ;

\(\frac{4}{\frac{1}{3} }\)

Simplifying further, we have:

\(4 \times \frac{3}{1} = 12\)

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Answer:

Step-by-step explanation:

3x² - 33x + 54 = 0

Divide the whole equation by 3

x²- 11x + 18 = 0

Sum = -11

Product = 18

Factors = -9 , -2              { - 9 + (-2) = -11  ; (-9) *(-2) = 18}

x² - 2x - 9x  + -9 * -2 = 0

x(x - 2) - 9(x - 2) = 0

(x-2)(x-9) = 0

x - 2 = 0   ; x - 9 = 0

x = 2  ;x = 9

Lesser x = 2

greater x = 9

Answer:

lesser x = 2

greater x = 9

Step-by-step explanation:

3x² - 33x + 54 = 0

Divide both side of the equation by 3

x² - 11 x + 18 = 0

x² - 2x - 9x + 18 = 0

x ( x - 2 ) - 9 ( x - 2 ) = 0

( x - 9 ) ( x - 2) = 0

x - 2= 0 ; x - 9 = 0

solve for x

x = 2 ; x = 9

lesser x = 2

greater x = 9

Answer:

D. \( 5,\: 5\sqrt 3\)

Step-by-step explanation:

According to the 30°-60°-90° triangle theorem:

Side opposite to 30° is half of hypotenuse and side opposite to 60° is \( \frac{\sqrt 3}{2} \) times of hypotenuse.

In the given figure:

side s is opposite to 30° angle.

\( \therefore s = \frac{1}{2} \times 10= 5\\\)

side q is opposite to 60° angle.

\( \therefore q =\frac{\sqrt 3}{2} \times 10= 5\sqrt 3\\\)

Answer:

C: {−5, 1)

Step-by-step explanation:

Starting with −2|−2x−4|=−12, divide both sides by -2:

|−2x−4| =  6

Reduce this by dividing all terms by 2:

|-x - 2| = 3

This is equivalent to   x + 2 = 3  and  x + 2 = - 3

Solving thse two equations, we get x = 1 and x = -5

And so the solution set is  C: {−5, 1)

Answer:

abc i need to put a real answer

Step-by-step explanation:

The expression that is equivalent to (-2)^4/(-2)^2 is (-2)^6/(-2)^4

The expression is given as:

(-2)^4/(-2)^2

Apply the law of indices

(-2)^4/(-2)^2 = (-2)^(4 -2)

4 - 2 has the same value as 6 - 4

So, we have:

(-2)^4/(-2)^2 = (-2)^(6-4)

Apply the law of indices

(-2)^4/(-2)^2 = (-2)^6/(-2)^4

Hence, the expression that is equivalent to (-2)^4/(-2)^2 is (-2)^6/(-2)^4

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Answer:

The answer is 6x² - 21x.

Step-by-step explanation:

You have to substitute the expressions inro the formula :

\(A = length \times width\)

\(let \: l = 2x - 7,w = 3x\)

\(A = (2x - 7) \times 3x\)

\(A = 3x(2x - 7)\)

\(A = 6 {x}^{2} - 21x\)

The area of the rectangular garden is 6x² - 21x.

We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.

We know, The area of a rectangle is (length×width).

Given, The rectangular garden has a length of (2x - 7) and a width of 3x.

Therefore, The area of the garden is,

= (2x - 7)×3x.

= 6x² - 21x.

= x(6x - 21).

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