The U.S. Bureau of Labor Statistics is a government agency that collects information about jobs in the U.S. In 2014, the Bureau reported that police officers had a median yearly salary of $52,936.

Calculate the average hourly wage for police officers. Round to the nearest cent. Assume that police officers generally work 40 hours a week. There are 52 weeks in the year.

Answer = $ per hour

The standard form of the equation of a circle is,

⇒ (x - 3)² + (y + 1)² = 13

Given that;

a circle that has a center at (3, -1) and a point on the circle at (5, 2).

Hence, The value of radius is distance between (3, - 1) and (5, 2).

So, We get;

Radius = √(5 - 3)² + (2 - (- 1))²

Radius = √4 + 9

Radius = √13

So, the standard form of the equation of a circle is,

⇒ (x - 3)² + (y + 1)² = (√13 )²

⇒ (x - 3)² + (y + 1)² = 13

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Answer:

x=68

Step-by-step explanation:

<ABD = 116 degrees

<ABC = x

<BDC = 48 degrees

<ABD = <ABC + <BDC

116 = x + 48                        Subtract 48

x = 116 - 48

x = 68

Hope this helps! ;)

Answer:

3.5 feet

Step-by-step explanation:

To determine whether you can jump a fence that is 7/6 of a yard tall, we need to convert the height to feet and compare it to your own jumping ability.

1 yard = 3 feet

So, 7/6 yards = (7/6) x 3 feet = 3.5 feet

Since a horse can jump a fence that is 4 feet tall and 4 feet is greater than 3.5 feet, it is likely that the horse can jump the fence while it may be more challenging for you to do so.

The amount of time it will take to completely fill the pool would be = 18 hours.

To determine the amount of time it will take to fill the pool, the volume of the pool is first calculated by dividing the figure to obtain two regular shapes of a trapezoidal prism and a square prism.

The volume of a trapezoidal prism = 1/2(a+b)×h×l

where;

a = 3m

b = 1m

h = 18-6 = 12m

l = 9m

Volume of the trapezoidal prism = 1/2(3+1)×12×9

= 4×12×9 = 432m³

Volume of square prism = length×width×height

where;

length = 6m

width = 9m

height = 1 m

Volume = 6×9×1 = 54m³

Therefore the volume of the pool = 432+54 = 486m³

If 4 hours = 2 m up from the deepest part

The volume filled for 4 hours = 1/2×2×12×9 = 108m³

If 4 hours = 108

X hours = 486

make X the subject of formula;

X = 4×486/108

= 1944/108

= 18 hours.

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A(n) "conjunction" is a compound inequality in which the two simple inequalities are separated by the word "AND."

Conjunctions are used in mathematics to represent the intersection of two sets, which means that the solution to the inequality must satisfy both conditions simultaneously.

For example, if we have the inequality 3x + 2 > 7 AND 5x - 3 < 17, the solution must satisfy both 3x + 2 > 7 and 5x - 3 < 17. To solve this type of inequality,

we can use algebraic methods such as isolating the variable in each simple inequality and then finding the intersection of the resulting intervals. Conjunctions are important in many areas of mathematics and are commonly used in algebra, geometry, and calculus.

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a)

The sum of the first six terms of the given geometric sequence is approximately 0.92.

b)

The sum of the first six terms of the given geometric sequence is approximately 0.92.

We have,

A.

We know that for a geometric sequence, the ratio of consecutive terms is constant.

Let's call this ratio "r".

So, we have:

a2/a1 = r

a3/a2 = r

Substituting the given values, we get:

0.7/a1 = r

0.49/0.7 = r

Simplifying the second equation:

r = 0.7/0.49 = 1.4286...

Substituting this value in the first equation:

0.7/a1 = 1.4286...

Solving for a1:

a1 = 0.7/1.4286... = 0.49

Now we can use the formula for the sum of the first n terms of a geometric sequence:

Sn = a1(1 - r^n)/(1 - r)

Substituting the values we have found, and using n = 6, we get:

S6 = 0.49(1 - 1.4286^6)/(1 - 1.4286) ≈ 0.92

B.

We can rewrite the formula for the sum of the first n terms of a geometric sequence using rational exponents as:

Sn = a1(1 - r^n)/(1 - r^(1/n))

Substituting the values we have found, and using n = 6, we get:

S6 = 0.49(1 - 1.4286^6)/(1 - 1.4286^(1/6))^(6)

Simplifying the expression using a calculator, we get:

S6 ≈ 0.92

Therefore,

The sum of the first six terms of the given geometric sequence is approximately 0.92.

The sum of the first six terms of the given geometric sequence is approximately 0.92.

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Answer: x = [tex]-\frac{1}{3}[/tex]

Step-by-step explanation:

       To show your work for this problem, you will write out every step that you take to solve for x.

Given:

     3x - 5 = x + 2 - 10 - 7x

Combine like terms:

     3x - 5 = - 6x - 8

Add 5 and 6x to both sides of the equation:

     9x  = - 3

Divide both sides of the equation by 9 and simplify the fraction:

     x = [tex]-\frac{3}{9}=-\frac{1}{3}[/tex]

Based on the given probability values, Mark is likely to have studied the most hours overall, and Amy is likely to have studied the least hours overall when selecting 10 Sundays from the school year at random.

The expected number of hours for each person is determined by multiplying the probability of studying on a Sunday by the average number of hours of studying.

Amy: 0.23 * 2.5 = 0.575

Susan: 0.31 * 1.5 = 0.465

Mark: 0.17 * 3 = 0.51

Nina: 0.19 * 2 = 0.38

Jeff: 0.1 * 4.5 = 0.45

From the calculations, we can see that Mark is likely to have studied the most hours overall with an expected value of 0.51. Amy is likely to have studied the least hours overall with an expected value of 0.575.

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The number of hours they can play video games before the weekend, then the inequality that represents the situation will be:

8 - a ≤ 4

Noted that inequality is a mathematical statement that compares two quantities or expressions that are not equal using the inequality signs such as:

Given that Trini is allowed to play video games no more than 4 hours over the weekend.

A number of hours to be played during the weekend is given as, at least 4 hours. This means the number of hours to play at the weekend can be 4 hours or more.

If a represents the number of hours they can play video games before the weekend, then the inequality that represents the situation will be:

8 - a ≤ 4

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a. The concentration would be 0.5 mg/L at approximately t = 40 hours.

b. The table representing the concentration of the drug in the bloodstream, t hours after administration is shown below.

c. A reasonable domain for this function is t ≥ 0.

d. The patient should receive the next intravenous dose of the drug in order to maintain a concentration above 1 mg/L and below 8 mg/L at t = 1.25 hour.

e. The concentration of the oral drug and the concentration of the intravenous drug would keep increasing over the first 20 hours after it is administered.

In order to determine the time when the concentration would be 0.5 mg/L, we would substitute the value of the concentration and then solve the quadratic function for time (t);

c(t) = 20t/(t² + 4)

0.5 = 20t/(t² + 4)

0.5(t² + 4) = 20t

0.5t² + 2 = 20t

0.5t² + 2 - 20t = 0

t² + 4 - 40t = 0

t² - 40t + 4 = 0

Time, t = 38.8998 ≈ 40 hours.

Part b.

In this context, we would complete the table of values at various time (t) as follows;

t        0    2      4     6       8           10        12        14     16        18      20

c(t)    0    5      4      3     2.35      1.92     1.62     1.4    1.23     1.10    1.00

Part c.

Since the concentration of the drug at time, t = 0 is equal to 0 mg/L and the concentration actually never becomes zero (0) for any value of time (t), we can reasonably infer and logically deduce that a reasonable domain for this quadratic function is t ≥ 0 or {0, ∞}.

Part d and e.

Furthermore, the intravenous drug must be administered to the patient between the time interval 1.25 ≤ t ≤ 20 in order to maintain a concentration above 1 mg/L and below 8 mg/L.

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The domain of the function is all real numbers (x ∈ R) and the range is all positive real numbers (y > 0).

The set of all values of the independent variable for which the function is defined is known as domain.

The function is defined for all real values of x so domain is R.

Domain: x ∈ R

The range of a function is the set of all values of the dependent variable (usually denoted as 'y') that the function can take as x varies over its domain.

For this function, the base of the exponent is 2, which means that the function grows exponentially as x increases.

As such, the range of this function is all positive real numbers.

Range: y > 0

Therefore, the domain of the function is all real numbers (x ∈ R) and the range is all positive real numbers (y > 0).

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Answer:

[tex]\sin\beta=\dfrac{8}{17}[/tex]

[tex]\cos\beta=\dfrac{15}{17}[/tex]

[tex]tan\beta=\dfrac{8}{15}[/tex]

[tex]\csc\beta=\dfrac{17}{8}[/tex]

[tex]\cot\beta=\dfrac{15}{8}[/tex]

Step-by-step explanation:

The secant ratio is the reciprocal of the cosine ratio.

[tex]\sec \beta= \dfrac{1}{\cos \beta}[/tex]

Therefore, if sec β = 17/15 then:

[tex]\dfrac{1}{\cos \beta}=\dfrac{17}{15}[/tex]

[tex]\cos \beta=\dfrac{15}{17}[/tex]

The cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse of a right triangle:

[tex]\cos\beta= \sf \dfrac{adjacent}{hypotenuse}[/tex]

Therefore, the length of the side adjacent angle θ is 15 and the length of the hypotenuse is 17.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]

We can use Pythagoras Theorem to calculate the length of the side opposite angle β:

[tex]15^2+O^2=17^2[/tex]

[tex]O^2=17^2-15^2[/tex]

[tex]O=\sqrt{17^2-15^2}[/tex]

[tex]O=\sqrt{64}[/tex]

[tex]O=8[/tex]

Therefore, the length of the side opposite angle β is 8.

Now we have the lengths of the three sides of the right triangle, we can find the other trigonometric function of angle β.

[tex]\boxed{\begin{minipage}{8cm}\underline{Trigonometric functions}\\\\$\sf \sin\beta=\dfrac{O}{H}\quad\cos\beta=\dfrac{A}{H}\quad\tan\beta=\dfrac{O}{A}$\\\\\\$\sf\csc\beta=\dfrac{H}{O}\quad\sec\beta=\dfrac{H}{A}\quad\cot\beta=\dfrac{A}{O}$\\\\\\where:\\\phantom{ww}$\bullet$ $\beta$ is the angle.\\\phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle.\\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse.\\\end{minipage}}[/tex]

Given values:

Substitute these values into the six trigonometric functions:

[tex]\sin\beta=\dfrac{O}{H}=\dfrac{8}{17}[/tex]

[tex]\cos\beta=\dfrac{A}{H}=\dfrac{15}{17}[/tex]

[tex]tan\beta=\dfrac{O}{A}=\dfrac{8}{15}[/tex]

[tex]\csc\beta=\dfrac{H}{O}=\dfrac{17}{8}[/tex]

[tex]\sec\beta=\dfrac{H}{A}=\dfrac{17}{15}[/tex]

[tex]\cot\beta=\dfrac{A}{O}=\dfrac{15}{8}[/tex]

The descriptions that represent a categorical data set are: Color of chewing gum brands sold at Store A, Best selling chewing gum flavors, Names of stores that carry Brand X of chewing gum.

We know that,

A data set is a collection of data, usually presented in tabular form, that can be analyzed to draw conclusions or make decisions. It can be numerical or categorical and can come from various sources such as surveys, experiments, or observations.

A data set typically contains individual data points or observations, each representing a unit or subject being studied. The size of a data set can range from small (e.g., a few observations) to large (e.g., millions of observations).

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If the dilation is centered at the origin, the vertices of polygon A′B′C′D′ are: D. A′(−2.4, 3.6), B′(−1.2, 1.2), C′(2.4, −1.2), D′(2.4, 2.4).

In Geometry, dilation refers to a type of transformation which typically changes the size of a geometric object, but not its shape.

Next, we would have to dilate the coordinates of the preimage by using a scale factor of 3/5 centered at the origin as follows:

Ordered pair A (-4, 6) → Ordered pair A' (-4 × 3/5, 6 × 3/5) = Ordered pair A' (-2.4, 3.6).

Ordered pair B (-2, 2) → Ordered pair B' (-2 × 3/5, 2 × 3/5) = Ordered pair B' (-1.2, 1.2).

Ordered pair C (4, -2) → Ordered pair C' (4 × 3/5, -2 × 3/5) = Ordered pair C' (2.4, -1.2).

Ordered pair D (4, 4) → Ordered pair D' (4 × 3/5, 4 × 3/5) = Ordered pair D' (2.4, 2.4).

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The percent increase in the average height of the corn plants during this one-week period is approximately 50%.

To calculate the percent increase in the average height of the corn plants, we need to find the difference between the final height and the initial height, and then express that difference as a percentage of the initial height.

Initial height = 16 1/2 in.

Final height = 24 7/10 in.

To find the difference, we subtract the initial height from the final height:

Difference = Final height - Initial height

Difference = 24 7/10 - 16 1/2

To perform the subtraction, let's convert the heights to a common denominator, which is 10:

Difference = (24 * 10 + 7) / 10 - (16 * 10 + 5) / 2

Difference = (240 + 7) / 10 - (160 + 5) / 10

Difference = (247 / 10) - (165 / 10)

Difference = 82 / 10

Difference = 8.2 in.

Now, let's calculate the percent increase:

Percent increase = (Difference / Initial height) * 100

Percent increase = (8.2 / 16.5) * 100

Percent increase ≈ 49.70

Rounding to the nearest whole percent, the percent increase in the average height of the corn plants during this one-week period is approximately 50%.

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Two times a number c when subtracted from 6 times the number is equal to 4

Algebraic expressions are defined as expressions that are composed of terms, coefficients, variables, constants and factors.

These algebraic expressions are also made up of mathematical or arithmetic operations.

These arithmetic operations are;

From the information given, we have that;

6c - 2c = 4

The variables are c

The coefficient are 6 and 2

The constant is 4

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Answer:

Step-by-step explanation:

[tex]y=29\times2^x\\put~x=x+1\\y1=29\times2^{x+1}=29\times2^x\times2=y\times 2\\y_{n+1} =2y_{n}[/tex]

Answer:

Slope that is perpendicular to y=-2/3x+5: 3/2

y-11=3/2(x-2)

Step-by-step explanation:

have a great day and thx for your inquiry :)

Answer:

x > 0

Step-by-step explanation:

To solve the inequality x/1 + 5 > 5, we first need to isolate the variable on one side of the inequality.

Subtracting 5 from both sides gives:

x/1 > 0

Multiplying both sides by 1 gives:

x > 0

Therefore, the solution to the inequality is x > 0.

Step-by-step explanation:

what is the question that you are asking?

According to Naomi's Quilt Shoppe's contribution margin income statement, she had a net income of $12,176 for the month of February.

For the month of February, Naomi's Quilt Shoppe's contribution margin income statement is as follows:

Revenue from Sales: 95 x $490 = 46,550

Cost of Goods Sold: 95 x $290 = $27,550

Gross profit: $27,550 - $46,550 = $19,000.

Variable expenses :

Revenue Commission: 8% × $46,550 = $3,724

Costs for all variables: $3,724

Contribution Margin: $19,000 - $3,724 = $15,276

Fixed expenses :

Rent: $1,300

Cost of payroll: $1,800

Total Fixed Costs: $3,100

Net Income: $15,276 - $3,100 = $12,176

Therefore, According to Naomi's Quilt Shoppe's contribution margin income statement, she had a net income of $12,176 for the month of February.

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Answer:

Step-by-step explanation:

[tex]\frac{n}{n-1}+\frac{2}{n+1} = 2\\\frac{n^2+n + 2n-2}{n^2-1} = 2\\ n^2+3n-2 = 2n^2-2\\n^2=3n\\n^2-3n= 0\\n(n-3) = 0\\n = 0 \\or\\ n = 3[/tex]

There are 3125 different ways the nursing student can be assigned to different floors during a 5-day work week.

To determine the number of different ways a nursing student can be assigned to one of five different floors each day during a 5-day work week, we need to calculate the total number of possibilities.

Since the student can be assigned to any of the five floors each day, there are 5 options for each day. Since there are 5 days in a work week, we multiply the number of options for each day together:

Total number of possibilities = 5 options per day × 5 options per day × 5 options per day × 5 options per day × 5 options per day

Total number of possibilities = [tex]5^5[/tex] = 3125

Calculating this value, we find that there are 3125 different ways the nursing student can be assigned to different floors during a 5-day work week.

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The choice between the two depends on the specific problem and desired model characteristics.  The lasso penalty may be preferred when the goal is to identify a small number of important predictors, while the ridge penalty may be preferred when the goal is to retain all predictors in the model but reduce their impact.

The lasso penalty and the ridge penalty are two different approaches to shrinkage models in which the goal is to reduce the complexity of a model by shrinking the coefficients towards zero. The main difference between the lasso penalty and the ridge penalty is in the way they perform this shrinking.
The lasso penalty uses an L1 norm, which encourages sparsity by driving some coefficients to exactly zero. This means that the lasso penalty is able to perform variable selection by completely eliminating some predictors from the model. In contrast, the ridge penalty uses an L2 norm, which does not drive coefficients to exactly zero, but rather shrinks them towards zero. This means that the ridge penalty is not able to perform variable selection in the same way as the lasso penalty.
The effect of this difference on the estimated coefficient is that the lasso penalty tends to produce more sparse models with fewer non-zero coefficients, while the ridge penalty tends to produce models with more non-zero coefficients. The lasso penalty may be preferred when the goal is to identify a small number of important predictors, while the ridge penalty may be preferred when the goal is to retain all predictors in the model but reduce their impact.

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1. The velocity of P after 3 seconds is -15i - 5j m·s⁻¹

1b. To one decimal place, the speed is  15.8 m·s⁻¹

2. The displacement of the particle after 4 seconds is -20i + 8j meters

2b. The distance is 21.5 meters.

In kinematics, the velocity of an object at a given time can be calculated by V = U + at

V = U + at

V = (-3i - 8j) + 3×(-4i + j)

V = (-3i - 8j) + (-12i + 3j)

V = (-3-12)i + (-8+3)j

V = -15i - 5j m/s

Speed = √((velocity in i)² + (velocity in j)²)

Speed = √((-15)² + (-5)²)

Speed = √(225 + 25)

Speed = √(250)

= 15.8 m/s.

In kinematics, the displacement of an object at any given time can be calculated by

s = ut + 1/2at²

s = (i + 6j)4 + 1/2(-3i - 2j)×4²

s = (4i + 24j) + (-24i - 16j)

s = (4-24)i + (24-16)j

s = -20i + 8j m

using the Pythagorean theorem

Distance = sqrt((displacement in i)² + (displacement in j)²)

Distance = √(-20)² + 8²)

Distance =√(400 + 64)

Distance = √464

=  21.5 meters

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There are 6,000,000 different license plates possible given the given conditions of 2 letters followed by 5 Digits, with the first letter being C, F, J, or K, and the first digit being less than 7.

The number of different license plates possible given the given conditions, we need to consider the choices available for each position.

For the first letter, we are given that it must be either C, F, J, or K. So, we have 4 options for the first letter.

For the second letter, any letter can be chosen except the one already used in the first position. Since repetition is not permitted, we have 25 options for the second letter (26 letters in the alphabet minus 1 used in the first position).

For the first digit, it must be less than 7. So, we have 6 options (0, 1, 2, 3, 4, 5).

For the second digit, we have 10 options (0-9).

For the third digit, we also have 10 options.

Similarly, for the fourth and fifth digits, we have 10 options each.

the total number of possible license plates, we need to multiply the number of choices for each position.

Total number of license plates = Number of choices for the first letter * Number of choices for the second letter * Number of choices for the first digit * Number of choices for the second digit * Number of choices for the third digit * Number of choices for the fourth digit * Number of choices for the fifth digit

Total number of license plates = 4 * 25 * 6 * 10 * 10 * 10 * 10 = 6,000,000

Therefore, there are 6,000,000 different license plates possible given the given conditions of 2 letters followed by 5 digits, with the first letter being C, F, J, or K, and the first digit being less than 7.

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Answer:

3.5 y + 1.25 x = 30

Step-by-step explanation:

she can buy x number of fly tapes and y number of ant traps. this amount has to be less or equal to the $30 that she has brought along.

3.5 y + 1.25 x ≤ 30

this is an equality.

since it asks for an equation, 3.5 y + 1.25x = 30