Jamal is x years old. His mother is 28 years older than Jamal. Jamal's uncle is two times older than Jamal's mother. Write and simplify an expression that represents Jamal's uncle age in years

Polonium-210 is a radioactive element that decays exponentially. Its half-life is 140 days, which means that after 140 days, the amount of Polonium-210 will be reduced by half. The rate of decay is proportional to the amount at time t, which means that the more Polonium-210 there is, the faster it will decay.

Now, if we start with 200mg of Polonium-210, we can calculate how much will remain after 12 weeks. To do this, we need to convert 12 weeks into days, since the half-life of Polonium-210 is measured in days.
12 weeks is equal to 84 days (12 x 7 = 84), so we need to find out how many half-lives occur in this time period.
84 days divided by 140 days (the half-life of Polonium-210) gives us approximately 0.6 half-lives.
To calculate how much Polonium-210 remains after 0.6 half-lives, we can use the formula:
Amount remaining = initial amount x (1/2)^(number of half-lives)
Plugging in the values, we get:
Amount remaining = 200mg x (1/2)^(0.6)
Amount remaining = 111.3mg
Therefore, after 12 weeks, approximately 111.3mg of Polonium-210 will remain out of the initial 200mg.

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According to the given statement the total deposited into the employee's fund in the first year would be $7,515.

To calculate how much would be deposited into the employee's fund in the first year, we need to add the amount deducted from the worker's salary (7.7%) and the additional contribution made by the company (9%).

Step 1:

Calculate the amount deducted from the worker's salary:

7.7% of the worker's salary = (7.7/100) * 45,000

Step 2:

Calculate the additional contribution made by the company:

9% of the worker's salary = (9/100) * 45,000

Step 3:

Add the two amounts to find the total deposited into the fund:

Total deposited into the fund = Amount deducted from the worker's salary + Additional contribution made by the company

In the first year, an employee with a starting salary of $45,000 would have $3,465 deducted from their pay and deposited into their retirement fund.

Additionally, the company would contribute $4,050 to the fund.

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Answer:

See solutions below

Step-by-step explanation:

2) angle at the vertex is half that of its intercepted arc;

51 = 1/2(14x-38)

51*2 = 14x-38

102 = 14x-38

14x = 102 + 38

14x = 140

x = 140/10

x = 14

3) 9x+7 = 1/2(68)

9x + 7 = 34

9x = 34-7

9x = 27

x = 27/9

x = 3

4) 114 = 1/2(30-(8x-36+40))

114 = 1/2(360-8x+36-40)

114*2 = 356 - 8x

-8x = 228-356

-8x = -128

x = 128/8

x = 16

Answer:2

Step-by-step explanation:

51+14x-38=180

13+14x=180

14=167

X=12

Answer:

Sorry for the late answer but hopefully it helps others. The answer is A

Step-by-step explanation:

y = -x^2

The graph of a quadratic function, y=x² reflected over the x-axis will be y = -x²

Images that are reflected over each other are mirror images of each other.

Given the coordinates (x, y) reflected over the x-axis, the resulting equation will be (x, -y)

This shows that reflecting the function y = x²over the x-axis will negate the output function.

Hence the graph of a quadratic function, y=x² reflected over the x-axis will be y = -x²

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The nurse will advise the patient to take 1 ml of medication with each dose.

The physician orders medication at 400 mg po twice daily. The pharmacy supplies medication with a dosage strength of 2 grams per 5 ml.

How many milliliters does the nurse advise the patient to take with each dose?

The nurse should advise the patient to take 1 ml of medication with each dose.

To find the number of milliliters, the following formula will be used.

Dose × Volume/Strength

Given, Dose = 400 mg

Strength = 2 grams per 5 ml

Volume = ?

To convert 400 mg to grams, divide by 1000.

400 mg = 400/1000 = 0.4 g

Now, put the values in the formula,

0.4 g × Volume / 2 g/ 5 ml= 5/2 × 0.4/1= 5/2 × 0.4= 1 ml

Hence, the nurse will advise the patient to take 1 ml of medication with each dose.

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Answer:

I don't really know how to do that or I just don't remember

A leaking faucet in the S&E building lab, dripping at a rate of one drop per second, will result in a water loss of approximately 4,725 liters in one year.

To calculate the amount of water lost in one year, we need to determine the number of drops per year and then convert it to liters. Since the faucet drips at a rate of one drop per second, there are 60 drops in a minute (60 seconds), which totals to 3,600 drops in an hour (60 minutes).

In a day, there would be 86,400 drops (24 hours * 3,600 drops). Considering a year of 365 days, the total number of drops would be approximately 31,536,000 drops (86,400 drops * 365 days). To convert the number of drops to liters, we need to multiply the total number of drops by the volume of each drop.

Given that each drop contains 0.150 milliliters, we convert it to liters by dividing by 1,000, resulting in 0.00015 liters per drop. Multiplying the total number of drops by the volume per drop, we find that the total water loss is approximately 4,725 liters (31,536,000 drops * 0.00015 liters/drop).

Therefore, in one year, the leaking faucet in the S&E building lab would result in a water loss of approximately 4,725 liters.

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The car travels 1.5 miles in one hour.

Speed is the rate at which an object moves, and is usually expressed in distance per unit of time. The standard units for speed are meters per second (m/s), kilometers per hour (km/h), miles per hour (mph), or feet per second (ft/s). Speed can be calculated as the distance traveled divided by the time taken to travel that distance. It is a scalar quantity, meaning it only has a magnitude (i.e. a value) and not a direction.

To find the speed of the car, we need to divide the distance traveled by the time taken:

Speed = Distance / Time

In this case, the car traveled 7.5 miles in 5 hours. We can use this information to find the speed:

Speed = 7.5 miles / 5 hours

Speed = 1.5 miles per hour

Therefore, the car travels 1.5 miles in one hour.

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The correct question should be:

A car is traveling at a constant speed. Find the number of miles a car travels in 1 hour if it is traveling at the given rate of 7.5 miles in 5 hours.

Answer: 38 pages per night

Step-by-step explanation:

Tori used to read an average of 40 pages per night but now she is going at a rate that is 5% slower.

To find the number of pages she is reading now, first find 5% of 40 pages:

= 5% * 40

= 2

Then subtract this figure from 40:

= 40 - 2

= 38 pages per night

By deducting 5% from the reading quantity, the person is reading at 5% less.

the mean is the center of the distribution, over-, and under-estimations of any current or future score will cancel out in the long run (add up to zero)

A sample mean is a data set average. The sample mean can be used to calculate the central tendency, standard deviation, and variance of a data set. The sample mean can be used to compute population averages, among other things.

You can use the sample mean to perform additional calculations by determining the variance of the data sample. Variance represents how widely distributed each sample item is within a data set. You find the difference between each data item and the mean to calculate variance.

Because the mean is the center of the distribution, over-, and under-estimations of any current or future score will cancel out in the long run (add up to zero)

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Therefore the solution to this equation is imaginary given by x = \(\rm \dfrac { 3 \pm \sqrt{-3}}{2}\)

A Quadratic equation is an equation that can be written in the form of

ax² +bx+c = 0

The solution of the given quadratic equation

x² -3x +3 = 0

the roots of the equation is given by

\(\dfrac { -b \pm \sqrt{b^2 -4ac}}{2a}\)

here a = 1 , b = -3 , c = 3

Substituting the values

The solution is

\(\rm \dfrac { 3 \pm \sqrt{(-3)^2 -4*1 *3}}{2}\)

Therefore the solution to this equation is imaginary

given by

x = \(\rm \dfrac { 3 \pm \sqrt{-3}}{2}\)

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A half life is the amount of time it takes for half of a radioactive substance to decay.

Yes, that is correct. The half-life of a radioactive element is the amount of time it takes for half of the initial amount of the element to decay. Therefore, the larger the initial amount of the element, the longer the half-life will be. This is because there are more atoms that need to decay in order for the half-life to occur. Conversely, if the initial amount of the element is small, the half-life will be shorter because there are fewer atoms that need to decay.

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Perpendicular lines have slopes that are opposite signs and reciprocals.

Since the line y = -1/4x + 10 has a slope of -1/4, the slope of the perpendicular line will be + 4/1 or 4.  So any line with a slope of 4 will be perpendicular to  y = -1/4x + 10.

This means A and D will be your answers.

the lowest amount of precipitation occurred in February, with a value of approximately 2.32 inches.

Why it is and how to form a graph?

To find the month with the lowest amount of precipitation, we need to find the minimum value of the quadratic equation y = –0.04088x²2 + 0.4485x + 1.862.

Using calculus, we can find the minimum point of the quadratic function by taking its derivative and setting it equal to zero:

y' = -0.08176x + 0.4485

0 = -0.08176x + 0.4485

x = 5.484

This means that the minimum value of the function occurs at x = 5.484. Since x represents the month number (with January being 1), we can conclude that the month with the lowest amount of precipitation is February (the second month in the table).

To verify this, we can plug in x = 2 into the quadratic equation:

y = –0.04088(2)²2 + 0.4485(2) + 1.862

y = 2.31752

Therefore, the lowest amount of precipitation occurred in February, with a value of approximately 2.32 inches.

To graph the function, we can plot the points given in the table and connect them with a smooth curve. Here is a completed table with the missing values:

Month (x) Precipitation

January 1 2.27 inches

February 2 2.32 inches

March 3 2.57 inches

April 4 2.94 inches

May 5 3.43 inches

June 6 3.94 inches

July 7 2.72 inches

August 8 2.86 inches

September 9 2.59 inches

October 10 2.03 inches

November 11 1.46 inches

December 12 1.03 inches

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Answer:

D: December

The given model for precipitation in Phoenix, Arizona is y = –0.04088x2 + 0.4485x + 1.862, where x is the month number (1 for January, 2 for February, and so on) and y is the precipitation in inches. We can use this model to fill in the missing values in the table:

| Month (x) | Precipitation |

|-----------|---------------|

| January   | 2.27 inches   |

| February  | 2.27 inches   |

| March     | 2.24 inches   |

| April     | 2.18 inches   |

| May       | 2.09 inches   |

| June      | 1.98 inches   |

| July      | 1.84 inches   |

| August    | 1.68 inches   |

| September | 2.59 inches   |

| October   | 1.50 inches   |

| November  | 1.30 inches   |

| December  | 1.08 inches   |

According to the table, Phoenix received the lowest amount of precipitation in **December** with **1.08 inches** of precipitation, so the correct answer is **D. December**.

The result of (f - g)(x) is 3x^2 - 2x - 1. There are no domain restrictions for this operation.

To compute (f - g)(x), we subtract the function g(x) from f(x).

Distributing the negative sign to g(x) yields -2x^2 - x + 2. Combining like terms with f(x) = 5x^2 - 3x + 1, we subtract the corresponding coefficients.

The resulting expression is (f - g)(x) = (5x^2 - 2x^2) + (-3x - (-x)) + (1 - 2) = 3x^2 - 2x - 1.

There are no domain restrictions for this operation, as both f(x) and g(x) are defined for all real numbers.

The resulting function represents the difference between f(x) and g(x) and can be used to analyze the behavior of the two functions when subtracted from each other.

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The matrix of \(t\) relative to the basis \(b'\) is \(A' = \begin{bmatrix} -9 & 7 \\ -37 & 43 \end{bmatrix}\).

\(\textbf{To find the matrix of } t \textbf{ relative to the basis } b', \textbf{we have to follow some steps. The steps are described below:}\)

First, we have to find the images of basis vectors under the transformation \(t\). \(t(-1,1) = (-9,7)\) and \(t(1,-5) = (-37,43)\).

Represent the image vectors of the basis in the standard basis. We use these vectors as columns in the matrix of \(t\) in the basis \(b'\).

\((-9,7) = -9(1,0) + 7(0,1) = (-9,7) = -9(-1,1) + 7(1,-5)\)

\((-37,43) = -37(1,0) + 43(0,1) = (-37,43) = -37(-1,1) + 43(1,-5)\)

Hence, we can write the following equation: \(A[x]_{b'} = [x]_S\)

Where \(A[x]_{b'}\) is the main answer in the form of a matrix, and \([x]_S\) is the coordinate of \([x]_{b'}\) with respect to the standard basis.

Now, we will write the equations with the coordinates of the basis vectors of \(b'\).

\(A[1,0] = [-9, -37]\) and \(A[0,1] = [7, 43]\)

Now we will write the matrix of \(A\) as follows:

\(A = \begin{bmatrix} -9 & 7 \\ -37 & 43 \end{bmatrix}\)

Thus, the matrix of \(t\) relative to the basis \(b'\) is \(A' = \begin{bmatrix} -9 & 7 \\ -37 & 43 \end{bmatrix}\).

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Answer:

A liter is a larger unit than a milliliter, so multiply the numbers by 1000 to find the number of milliliters. Therefore, 37 liters is equal to 37,00 milliliters.

Answer:

A liter is a

Answer: larger

unit than a milliliter, so

Answer: multiply

the number of liters by

Answer: 1,000

to find the number of milliliters. Therefore, 37 liters is equal to

Answer: 3,700

milliliters.

Step-by-step explanation:

Answer:

21.17 to 2d.p.

Step-by-step explanation:

Using Pythagoras rearrage to find b c^2-a^2 = b^2

c= hypothenuse

32^2 = 1024 and 24^2 = 576

1024 -576 = 448

\(\sqrt{448}\) = 21.1660105

21.17 to 2d.p.

Answer:

7

Step-by-step explanation:

42/6=7

Answer:

-8/4 or -2

Step-by-step explanation:

First of all notice the graph is negative. Meaning that this will be a negative slope.

Now we can use rise over run, counting up 8 spaces, and to the left 4.

Since the graph is negative make the rise negative. -8/4.

To simplify this fraction divide -8 by 4, and receive an answer of -2.

-Hope this helped

1/7 of the animals in the zoo are male monkeys.

To find the fraction of animals in the zoo that are male monkeys, we have to calculate the product of the fractions representing the proportion of monkeys and the proportion of male monkeys among them.

Given that 1/5 of the animals in the zoo are monkeys, we will then represent this as:

= 1/5

= 5/25.

And 5/7 of the monkeys are male which is written as 5/7.

To get fraction of male monkeys, we will multiply these two fractions:

= (5/25) * (5/7)

= 25/175

= 1/7.

Full question:

1/5 of the animals in the zoo are monkeys 5/7 of the monkeys are male. What fraction of the animals in the zoo are male monkeys?

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Hence the formula of \(a ^2 + b^ 2 + c^ 2\) is \(( a + b + c )^ 2 - 2 ( ab + bc + ca ) .\)

Formulas are equations that compute values from your spreadsheet. A formula always starts with the equal sign (=).

Using a calculating operator and a constant, you can make a straightforward formula.

For instance, the equation =5+2*3 multiplies two numbers before adding one more to the outcome.

A formula is a rule or relationship in mathematics that utilizes letters to indicate amounts that might change; these amounts are known as variables. For instance, the triangular area calculation formula.

The word "formula" is pluralized to "formulas." A list of elements that are employed in various concoctions and potions is referred to as a formula, which can also refer to a specific mathematical calculation.

Because English might be erratic at times, newborns can also be fed formula.

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Answer:

128 <33

Step-by-step explanation:

6 ÷ 3 + 32 • 4 - 2 = 128

▪︎▪︎▪︎▪︎▪︎▪︎

After the formation of the European Union (EU), it eliminated all tariffs among its member countries. This means that there are no import taxes or duties imposed on goods traded between EU member countries.

One of the key objectives of the European Union is to create a single market among its member countries, fostering economic integration and facilitating the free movement of goods, services, capital, and people. As part of this goal, the EU implemented the elimination of tariffs among its member countries. Tariffs are taxes or duties imposed on imported goods, which can increase their cost and hinder trade.

By removing tariffs, the EU promotes the free flow of goods within its borders. This has significant benefits for businesses and consumers within the EU, as it allows for increased trade, competition, and access to a wider range of products. Eliminating tariffs encourages economic cooperation and integration among EU member countries, creating a more seamless and efficient trading environment.

Option a is incorrect because the EU does not bar imports of specific products or favor domestic companies. Option c is incorrect because the EU aims to promote trade and economic activity among its member countries rather than decreasing imports and exports. Option d is incorrect because the North American Free Trade Agreement (NAFTA) is a trade agreement between the United States, Canada, and Mexico and is not directly related to the European Union.

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Answer:

No solution.

Step-by-step explanation:

Step 1: Write equation

-17(y - 2) = -17y + 64

Step 2: Solve for y

Here we see that we get y = no solution. You could also think about it as 2 parallel lines; they have the same slope but different y-intercepts so therefore there will be no intersection/no solution.

Answer:

C

Step-by-step explanation:

Answer: i think its c

Step-by-step explanation:

The length of the third side (b) of the right triangle is 8 units.

We can use the Pythagorean theorem to find the length of the third side of the right triangle.

a^2 + b^2 = c^2

Where a, b, and c are the lengths of the sides of the right triangle, with c being the hypotenuse (the side opposite the right angle).

Substituting the given values a = 15 and c = 17 into this equation, we get:

15^2 + b^2 = 17^2

So, we have

b^2 = 289 - 225

b^2 = 289 - 225

b^2 = 64

This givrs

b = 8

Hence, the length of the third side (b) is 8 units.

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