About 13 out of 24 homes have a personal computer. On a street with 96 homes, how many computers would you expect to have?

Answer:

20xπ units

Step-by-step explanation:

Use the formula for the length of an arc.

θ/360 × 2πr

The length of the arc and the central angle is already given.

18/360 × 2πr = xπ

Solve for r.

r = (xπ)/(18/360)/(2π)

r = 10x

The radius of the circle is 10x.

The circumference of a circle is 2πr.

2π(10x)

20xπ

The circumference of the circle is 20xπ units.

Gender is a clear example of a categorical variable. A categorical variable is a type of variable that can take on a limited number of values, which are typically named categories. In the case of gender, the categories are male and female.

Categorical variables are also sometimes called qualitative variables, as they are used to describe qualities or characteristics of a population or sample. In contrast, quantitative variables are used to describe numerical data, such as height, weight, or income. Gender is an important variable in many areas of research, including sociology, psychology, and health. By understanding the ways in which gender influences different aspects of life, researchers can develop interventions and policies to promote gender equity and improve outcomes for everyone. It is important to note that gender is not always a binary variable, with only two categories of male and female. Some research studies may include additional categories, such as non-binary or gender non-conforming, to better capture the diversity of gender identities and experiences. Researchers may also ask participants to self-identify their gender, rather than assuming a binary male/female distinction. Overall, the variable of gender is an important consideration in research and should be included whenever relevant to the study question. By examining gender as a variable, researchers can gain insights into how gender influences outcomes and develop strategies to promote gender equity and inclusivity.

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Answer:

2.18 I think this is the answer sorry if it's not-

Answer:

2,1044 is the correct answere

To test the hypothesis that weight gain during pregnancy is associated with infant's birth weight, Pearson's correlation coefficient (option B) would be an appropriate statistical test.

In this scenario, the goal is to examine the association between two continuous variables: weight gain during pregnancy (independent variable) and infant's birth weight (dependent variable). Pearson's correlation coefficient is used to measure the strength and direction of the linear relationship between two continuous variables.

Option A, the Chi-square test, is not appropriate as it is used to analyze categorical variables, such as comparing frequencies or proportions between different groups.

Option C, a paired t-test, is used when comparing means of a continuous variable within the same group before and after an intervention or treatment, which does not align with the current scenario.

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To evaluate the integral ∫8(t² - 4)dt, we can use trigonometric substitution. Let's follow the steps below:

Step 1: Recognize the form of the integral and choose a suitable substitution.

  The expression t² - 4 resembles the form a² - x², where a is a constant and x is the variable in the integral. In this case, we can substitute t = 2secθ.

Step 2: Determine the differential dt in terms of dθ using the substitution t = 2secθ.

  Taking the derivative of both sides with respect to θ:

  dt/dθ = 2secθtanθ

Step 3: Express √(t² - 4) in terms of θ using the substitution t = 2secθ.

  √(t² - 4) = √[4sec²θ - 4] = 2tanθ

Step 4: Substitute the expressions from Steps 2 and 3 into the integral and simplify.

  ∫8(t² - 4)dt = ∫8(4sec²θ - 4)(2secθtanθdθ) = 64∫sec²θdθ - 64∫secθtanθdθ

Step 5: Evaluate each integral separately.

  - ∫sec²θdθ = tanθ + C₁ (integral of sec²θ is tanθ plus a constant C₁)

  - ∫secθtanθdθ = (secθ)²/2 + C₂ (integral of secθtanθ is (secθ)²/2 plus a constant C₂)

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Answer:

105

Step-by-step explanation:

2x17=34

17x2.5=42.5

1.5x17=25.5

1/2x2x2x1.5=3

34+42.5+25.5+3=105

Answer Po Ba Ay 11.33?

Step-by-step explanation:

Calc

Part A; Rebecca's current balance is $2500. Part B; Rebecca can save $27 by making the purchase on the last day of the billing cycle.

Part A:

Rebecca's finance charge is calculated using the following formula:

Finance charge = APR / 12 × (Average daily balance) × Number of days in billing cycle

Rebecca's APR is 24%, her average daily balance is x + $1400 / 28, and her billing cycle is 28 days. Her finance charge is $51.

Substituting these values into the formula:

$51 = (24 / 12) × ((x + $1400) / 28) × 28

Solving for x:

x = $2500

Therefore, Rebecca's current balance is $2500.

Part B:

If Rebecca makes the purchase on the first day of the billing cycle, her average daily balance will be $2500 + $1400 / 28 = $267.86.

Her finance charge will then be:

(24 / 12) × ($267.86) × 28 = $78

Therefore, Rebecca can save $78 - $51 = $27 by making the purchase on the last day of the billing cycle instead of the first day.

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Answer:

3x - y = 20

a = 3, b = -1, and c = 20

Step-by-step explanation:

y + 2 = 3(x - 6) => y + 2 = 3x - 18 => 3x - y = 20

To maximize profits, the firm should produce a quantity of goods x = 5 and y = 10, based on the cost function and price constraints.

To maximize profits, the firm needs to find the quantities of goods x and y that will yield the highest profit. The profit function can be defined as the revenue minus the cost. Revenue is calculated by multiplying the quantity of each good produced with their respective prices, while the cost function is given as C(x, y) = 10x + xy + 10y.

The firm is committed to delivering a total of 15 units, which can be expressed as x + y = 15. To determine the optimal production quantities, we need to maximize the profit function subject to this constraint.

By substituting the price expressions Ps = 50 - x + y and Py = 50 - x + y into the profit function, we obtain the profit equation. To find the maximum profit, we can take the partial derivatives of the profit equation with respect to x and y, set them equal to zero, and solve the resulting system of equations.

Solving the equations, we find that the optimal production quantities are x = 5 and y = 10, which maximize the firm's profits.

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We can write a vector in the span of {u1} as a scalar multiple of u1, i.e., αu1 for some scalar α. Similarly, a vector in the span of {u2, u3, u4} can be written as a linear combination of these vectors, i.e., β1u2 + β2u3 + β3u4 for some scalars β1, β2, and β3.

To express v as the sum of two vectors, one in span {u1} and the other in span {u2, u3, u4}, we need to find α and β1, β2, β3 such that:

v = αu1 + β1u2 + β2u3 + β3u4

Let's solve for α and β1, β2, β3. We can set up a system of equations by equating the components of both sides of the equation:

45 = 1211α - 2β1 + β2 - β3

-22 = -1211α - β1 - 2β2 - 2β3

Solving this system of equations gives:

α = -1/11

β1 = -57/22

β2 = -101/22

β3 = 47/22

Therefore, we can express v as:

v = (-1/11)u1 + (-57/22)u2 + (-101/22)u3 + (47/22)u4

This expresses v as the sum of a vector in span {u1} and a vector in span {u2, u3, u4}.

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y = -1/3x + 4

Therefore, the equation of the line that is perpendicular to 4y - 12x = 20 and passes through the point (9,1) is y = -1/3x + 4.

To find the equation of a line that is perpendicular to 4y - 12x = 20, we need to first find the slope of the original line by putting it in slope-intercept form:

4y - 12x = 20
4y = 12x + 20
y = 3x + 5/2

So the slope of the original line is 3. To find the slope of a line perpendicular to this one, we need to take the negative reciprocal of 3, which is -1/3.

Now we can use the point-slope form of a line to find the equation of the perpendicular line that passes through the point (9,1):

y - y1 = m(x - x1)
y - 1 = -1/3(x - 9)
y - 1 = -1/3x + 3
y = -1/3x + 4

Therefore, the equation of the line that is perpendicular to 4y - 12x = 20 and passes through the point (9,1) is y = -1/3x + 4.

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a.) There are 635013559600 ways to break up a deck of 52 cards into four piles of 13 cards.

b.) There are approximately 1.0554516e+32 ways to break up a deck of 52 cards into three piles of eight cards and four piles of seven cards.

There are two parts to this question, so we will answer each part separately.

(a) Four piles of 13 cards:
To determine the number of ways a deck of 52 cards can be broken up into four piles of 13 cards, we can use the formula for combinations:

C(n,k) = n! / (k! * (n-k)!)

In this case, n = 52 (the number of cards in the deck) and k = 13 (the number of cards in each pile). Plugging these values into the formula gives us:

C(52,13) = 52! / (13! * (52-13)!)
C(52,13) = 52! / (13! * 39!)
C(52,13) = 635013559600



(b) Three piles of eight cards and four piles of seven cards:
To determine the number of ways a deck of 52 cards can be broken up into three piles of eight cards and four piles of seven cards, we can use the same formula for combinations, but we need to do it multiple times for each pile size:

C(52,8) = 52! / (8! * (52-8)!)
C(52,8) = 752538150

C(44,8) = 44! / (8! * (44-8)!)
C(44,8) = 26259678350

C(36,8) = 36! / (8! * (36-8)!)
C(36,8) = 30260340

C(28,7) = 28! / (7! * (28-7)!)
C(28,7) = 1184040

C(21,7) = 21! / (7! * (21-7)!)
C(21,7) = 116280

C(14,7) = 14! / (7! * (14-7)!)
C(14,7) = 3432

C(7,7) = 7! / (7! * (7-7)!)
C(7,7) = 1

Multiplying all of these combinations together gives us the total number of ways to break up the deck into the desired piles:

752538150 * 26259678350 * 30260340 * 1184040 * 116280 * 3432 * 1 = 1.0554516e+32

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By percentage, a passive home construction is typically around 50% more expensive compared to a conventional home construction.

A passive home construction is generally more expensive compared to a conventional home construction due to several factors. Passive homes are designed to meet stringent energy efficiency standards, requiring specialized materials, insulation, ventilation systems, and high-performance windows and doors. These energy-saving features contribute to the increased cost of construction. Additionally, passive homes often incorporate advanced technologies like heat recovery systems and solar panels, further adding to the expenses.

However, it's important to note that while the initial construction costs of a passive home may be higher, the long-term energy savings and reduced operating costs can offset the higher upfront investment. Passive homes offer improved energy efficiency, better indoor comfort, and reduced environmental impact, making them a viable choice for those seeking sustainable and energy-efficient housing solutions.

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x = -11

Thus, the solution is the ordered pair (-11, 8). To solve the system of equations 5x + 9y = 17 and x + 2y = 5, we can use substitution method.

Solving x + 2y = 5 for x, we get x = 5 - 2y.

Substituting x = 5 - 2y into the first equation, we get:

5(5-2y) + 9y = 17

25 - 10y + 9y = 17

-y = -8

y = 8

Now, substituting y = 8 into x = 5 - 2y, we get:

x = 5 - 2(8)

x = -11

Therefore, the solution to the system of equations is (-11, 8).
To solve the system of equations using substitution or elimination, first, we need to write the given equations clearly:

1) 5x + 9y = 17
2) x + 2y = 5

We'll use the substitution method. From equation (2), we can isolate x:

x = 5 - 2y

Now, substitute this expression for x in equation (1):

5(5 - 2y) + 9y = 17

Expand and simplify the equation:

25 - 10y + 9y = 17

Combine like terms:

-1y = -8

Now, divide by -1:

y = 8

Next, plug the value of y back into the x equation:

x = 5 - 2(8)

x = 5 - 16

x = -11

Thus, the solution is the ordered pair (-11, 8).

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Answer:

x=20

Step-by-step explanation:

x=20 because (4x+3)=77 so you take out of parnetheses

Answer:

x=20

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Step-by-step explanation:

Given that,

The bag of skittles has 3 parts red skittles, 5 parts yellow skittles and 7 parts orange skittle.

Ratio notation is= 3:5:7

Frction notation,

Red skittle\(=\dfrac{3}{3+5+7}=\dfrac{1}{5}\)

Yellow skittle \(=\dfrac{5}{3+5+7}=\dfrac{1}{3}\)

Orange skittle \(=\frac{7}{3+5+7}=\dfrac{7}{15}\)

Hence, this is the required solution.

Answer:

Step-by-step explanation:

It’s not c

The expression that represents the total amount spent as a function of the number of points earned is y = 25 + 0.5x This function is only valid for 25 or plus points since that is the minimum amount one can have after purchase.

A function in mathematics set up a relatioship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.

We will first calculate the function that relates the number of points earned and the total spent x. This is given by:

y = f(x) = 25 + x/2

In order to calculate the function that represents the total spent as a function of points earned we need to isolate the variable x, in the expression above. We have:

y = 25+ x/2

y = 25 + 0.5x

The expression representing the total amount spent as a function of the number of points earned is y = 25 + 0.5x This function is only valid for 25 or plus points since that is the minimum amount of points one can have after purchase.

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Answer:

55

Step-by-step explanation:

bedcause if you add 50 and 5 then it makes yes

The number of papers checked by both becomes equal in 10 hours.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Teacher Malone is reviewing papers in the educators' parlor. She has previously gotten done with reviewing 20 tasks and is evaluating 5 additional tasks each hour. Her showing colleague just came in to help her. He can grade at a pace of 7 tasks consistently.

Let 'x' be the number of hours and 'y' be the number of assignments. Then the equations are given as,

y = 5x + 20        ...1

y = 7x                ...2

At some point, they will be finished and will have graded the same number of papers. Then from equations 1 and 2, we have

7x = 5x + 20

7x - 5x = 20

2x = 20

x = 20 / 2

x = 10

The number of papers checked by both becomes equal in 10 hours.

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Answer:

259.5

Step-by-step explanation:

8.1*12=97.2
Area of trapiezium = 1/2(b+a)h
(2.8+8.1)=10.9
10.9*3/2=16.35
16.35*2=32.7
2.8*12=33.6
33.6+32.7+97.2=163.5
4*12*2=96
163.5+96=259.5

Let's solve your equation step-by-step.

(3x−2)(x+6)−(x−1)(2x)=103

Step 1: Simplify both sides of the equation.

x2+18x−12=103

Step 2: Subtract 103 from both sides.

x2+18x−12−103=103−103

x2+18x−115=0

Step 3: Factor left side of equation.

(x−5)(x+23)=0

Step 4: Set factors equal to 0.

x−5=0 or x+23=0

x=5 or x=−23

Answer:

x=5 or x=−23

If the force is changed to 40 N,  the acceleration of the object will be 4 m/s².

The given parameters are;

The acting force ∝ The acceleration of the object.

The acceleration given by an amount of force, F, of 30 N = 3 m/s²

According to Newton's Second Law of motion, we have;

F = m·a

Where;

m = The mass of the object

Therefore, we have;

mass = force/ acceleration

From the conditions, F = 30 N, when a = 3 m/s², we have, the mass of the given object is given as follows;

m = F/a

m = 30/3 = 10kg

If the force is changed to 40N, the acceleartion will be

acceleration = force/ mass

a = 40/10

a = 4 m/s²

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Answer:

\(2(3m + 6n) + 3(5m - 2n) + 5( - 6m + n) \\ \)

open the brackets:

\( = (6m + 12n) + (15m - 6n) + ( - 30m + 5n) \\ \)

group the coefficients of m and n in their brackets:

\( = (6 + 15 - 30)m + (12 - 6 + 5)n \\ \)

then operate the brackets:

\( = - 9m + 11n\)

Answer:

Change in Y over change in X. So down 8 and over 2. Simplified it would be 4/1

The distance between the medic and the shelter is 626.3 feet.

A helicopter was hovering over a shelter and was 900 ft above the ground. A medic was on the ground and was looking up at an angle of 55 degrees to the helicopter.

The medic’s eyes were 5.5 feet off the ground when looking at this right angle of elevation.

This situation forms a right angle triangle. Therefore, the distance of the medic to the shelter can be found as follows:

Hence,

tan 55 = opposite / adjacent

tan 55 = 900 - 5.5 / a

cross multiply

a tan 55° = 894.5

divide both sides by tan 55°

a =  894.5 / 1.42814800674

a = 626.335645885

a = 626.3 feet

Hence,

distance between medic and shelter = 626.3 feet

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The chores overshadowed the joy of our Reunion, learned a valuable lesson about managing time and prioritizing obligations

Embarking on a bike ride to visit a friend who lives 3 miles away, little did I know that a looming sense of forgotten chores would soon disrupt my plans. Determined to fulfill my obligations, I mustered the strength to continue riding towards my friend's house, albeit with a heavy heart.

I pedaled towards my destination, the weight of my impending chores grew heavier with each passing moment. Thoughts of unfinished tasks occupied my mind, and I knew that I couldn't stay for long once I reached my friend's place. However, in my haste, a newfound urgency propelled me forward, and I found myself pedaling at a speed 5 mph faster than my initial journey.

With this increased velocity, the return trip promised to be swifter, yet time was slipping away. My mind raced as I calculated the implications of my predicament. The total round trip, comprising both the journey to my friend's house and the hurried return, needed to be accomplished within a tight time frame of 30 minutes.

As I approached my friend's house, I realized that I had no choice but to deliver my news swiftly and immediately turn back around. The momentary joy of reunion would be overshadowed by the pressing chores that awaited me. Regrettably, I bid my friend a hasty farewell, explaining the circumstances that compelled my premature departure.

Once on my bike again, I kicked up the pace, utilizing the extra speed to my advantage. The wind rushed past my face as I hurriedly retraced my path, pushing myself to complete the return trip as swiftly as possible. The seconds ticked away relentlessly, as the pressure mounted to make it back within the allocated timeframe.

In a flurry of determination, I managed to reach home just in the nick of time, fulfilling my duties and responsibilities. Exhausted but relieved, I contemplated the whirlwind of events that had transpired within the span of this half-hour adventure.

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Note the question be like :

A company is hosting a team-building event and has allocated a total of 4 hours for various activities. If Activity A takes 1 hour, Activity B takes 2 hours, and Activity C takes 45 minutes, what is the maximum amount of time that can be dedicated to Activity D while still staying within the allocated 4-hour timeframe?

(a) The bird watcher's displacement is approximately 3.34 km.

(b) The bird watcher's average velocity is approximately 2.61 km/h in a direction 46.9 degrees north of east.

To determine the bird watcher's displacement, we need to find the straight-line distance from the starting point to the ending point. This can be calculated by treating the east and south components as negative and the north of west component as positive. Using vector addition, we can find the resultant vector which represents the displacement. The magnitude of the resultant vector gives us the displacement, which is approximately 3.34 km.

To find the average velocity, we divide the displacement by the time taken. The direction of the average velocity can be found by calculating the angle with respect to the positive x-axis. By using trigonometry, we can determine the angle to be approximately 46.9 degrees north of east. The magnitude of the average velocity is the displacement divided by the time, giving us approximately 2.61 km/h.

Therefore, the bird watcher's displacement is approximately 3.34 km, and their average velocity is approximately 2.61 km/h in a direction 46.9 degrees north of east.

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Answer:

Substitute P=7500, r=0.053 and t=1 in equation (1). Therefore, the balance of the loan be after one year is $7897.5

Answer:

P = 8

Step-by-step explanation:

Given that P varies inversely with x then the equation relating them is

P = \(\frac{k}{x}\) ← k is the constant of variation

To find k use the condition P = 7 when x = 8 , then

7 = \(\frac{k}{8}\) ( multiply both sides by 8 )

56 = k

P = \(\frac{56}{x}\) ← equation of variation

When x = 7 , then

P = \(\frac{56}{7}\) = 8

The value of P when x = 7 is 7 and can be determined by using the arithmetic operations and given data.

Given :

The following steps can be used to determine the value of P when (x = 7):

Step 1 - Given that P varies inversely with x. That is:

\(\rm P \;\alpha \;\dfrac{1}{x}\)

Step 2 - The above expression can be written as:

Px = K   ---- (1)

where K is the proportionality constant.

Step 3 - Now, it is given that P = 7 when x = 8. Put the value of P and x in the above equation.

\(\rm 7\times 8 = K\)

56 = K

Step 4 - Put the value of K = 56 and x = 7 in the equation (1).

\(\rm P \times 8=56\)

P = 7

So, when x = 7 the value of P is 7.

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