If 8 people consisting of 4 couples are randomly arranged in a row, find the probability that no person is next to their partner.

Answer:

3x-14=180

3x=194

x= 64 2/3

4(x-9)=180

4x-36=180

4x=216

x=54

Hope This Helps!!!

Step-by-step explanation:

(3x-14)°=180°

3x-14=180

3x=180+14

3x=194

x=64.6

[4(x-9)]°=180°

4x-36=180

4x=180+36

4x=216

x=54

The value of this continuous stream of  compound interest  after 18 years  will be \(\$2526\).

The interest  that we earn even on interest is termed as compound interest .

We know that formulae for compound interest when compounded annually will be \(A = P(1 + \dfrac{r}{n})^{nt}\)

Where A is the amount,

P is the principal.

r is the interest rate,

t is the time (in years).

On putting   the values in the formulae , we get:

\(A = 2000 ( 1 +\dfrac{1.3}{100})^{18}\)

On simplifying, we get:

 A = \(2000\times1.263\)

A = \(2526.24\)

Rounding to the nearest integer, we get:

A =\(\$2526\)

Therefore, the value of the continuous stream after 18 years will be \(\$2526.\)

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The triangle with side lengths of  48 in., 56 in., and 83 in.  is obtuse, because 832> 48² +56²

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

The side lengths of the triangles are 48 in., 56 in., and 83 in

The smallest side lengths are: 48 in., 56 in

The sum of the squares of these side lengths is

48^2+ 56^2

For the triangle to be obtuse, then the following must be true

83^2> 48² +56²

Evaluate the exponents

6889> 5440

The above inequality is true.

Hence, the triangle is obtuse, because 83^2> 48² +56²

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The lifter would need to perform approximately 27 reps of lifting a 16-lb barbell through a distance of 1.1 ft to work off 150 C.

To answer this question, we need to know the amount of work done in each rep of the lift. Work is defined as force multiplied by distance, so the work done in lifting the 16-lb barbell through a distance of 1.1 ft is:

Work = Force x Distance
Work = 16 lb x 1.1 ft
Work = 17.6 ft-lb

Now we can calculate the number of reps required to work off 150 C. One calorie is equivalent to 4.184 joules of energy, so 150 C is equal to:

150 C x 4.184 J/C = 627.6 J

We can convert this to foot-pounds of work by dividing by the conversion factor of 1.3558:

627.6 J / 1.3558 ft-lb/J = 463.3 ft-lb

To work off 463.3 ft-lb of energy, the lifter would need to perform:

463.3 ft-lb / 17.6 ft-lb/rep = 26.3 reps (rounded up to the nearest whole number)

Therefore, the lifter would need to perform approximately 27 reps of lifting a 16-lb barbell through a distance of 1.1 ft to work off 150 C.

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Answer:

a) let 's' = number of bags of snacks

b) let 's+50' = number of bags of beverages

s + s+50 = 400

Step-by-step explanation:

a) let 's' = number of bags of snacks

b) let 's+50' = number of bags of beverages

s + s+50 = 400

solve:

2s + 50 = 400

2s = 350

snacks = 175

beverages = 175+50 or 225

total = 400

The Euler equation represents the relationship between current-period consumption and future-period consumption in the optimum. It is derived from intertemporal optimization in economics.

In the context of consumption, the Euler equation can be expressed as:

u'(Ct) = β * u'(Ct+1)

where:

- u'(Ct) represents the marginal utility of consumption in the current period,

- Ct represents current-period consumption,

- β is the discount factor representing the individual's time preference,

- u'(Ct+1) represents the marginal utility of consumption in the future period.

This equation states that the marginal utility of consumption in the current period is equal to the discounted marginal utility of consumption in the future period. It implies that individuals make consumption decisions by considering the trade-off between present and future utility.

Note: The Euler equation assumes a constant discount factor and a utility function that is differentiable and strictly concave.

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Answer:

Y is the awnser

Step-by-step explanation:

The range at which Dan's car can go is 3.33 miles

A car's range is the distance it can travel with the current amount of fuel in the tank.

The vehicle calculates the range based on the amount of fuel, how the accelerator and brakes are used, and how quickly the car is travelling.

The range of a car can be measured in the unit of distance.

Therefore the range of a car can be calculated as;

R = distance per gallon/ number of gallon.

Dan's car is 40mpg and has 12 gallons in it's tank.

Therefore it's range = 40/12

= 3.33miles.

therefore the range of Dan's car is 3.33miles

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The dimensions that maximize the area are, 96cm and 84cm.

What is area?

The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Let the height of poster be h and breadth be b,

bh = 15630cm square........(1)

Height of the printed area=h-10-10 = h - 20

(decrement of 10 from top and bottom)

the breadth of the printed area b-6-6 = b-12

(decrement of 9 from both sides)

for maximum printed area:

A=(h-20)(b-12) should be maximum

\(A = (h - 20)(\frac{15360 }{h}-12)\)

From equation (1)  

\(A = 15360-12h-\frac{307200}{h} +240\)

A = 15600 - 12h - (307200/h)

differentiate with respect to h (it should be=0)

\(\frac{dA}{dh}= 0-12 + \frac{307200}{h^2}\)

\(12 = \frac{307200}{h} \\h = 160 cm\)

from equation (1),

\(bh = 15630cm^2\\b = 96cm\)

dimension of printed area,

= h - 20

= 160 - 20

= 140 cm

= b - 12

= 96 - 12

= 84 cm

Therefore, the dimensions that maximize the area are, 96cm and 84cm.

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Answer:

h(g(x))=h(3x^2+1)=2(3x^2+1)=6x^2+2

Answer: 24 inches.

Step-by-step explanation:

We can use the formula for the area of a triangle to solve for the length of the base:

A = (1/2)bh

where:

A = the area of the triangle (in this case, 72 square inches)

b = the length of the base (what we're trying to find)

h = the height of the triangle (in this case, 6 inches)

Plugging in the values we know, we get:

72 = (1/2)b(6)

72 = 3b

b = 24

Therefore, the length of the base of the triangle is 24 inches.

Answer:

about 23 villagers

Step-by-step explanation:

17 x 1.13 =19.21 + 4 =23.21

chase would have to use the equation

(n x 1.13)+4

with n being the number of towns

To maximize the amount of peaches produced by the orchard, the peach orchard owner should plant a certain number of trees per acre. The per-tree yield is given by the equation Y = 1200 - 15x, where Y represents the yield per tree and x represents the number of trees planted per acre.

To find the number of trees per acre that maximizes the crop yield, we need to determine the value of x that corresponds to the vertex of the equation. The vertex of a downward-opening parabola, represented by the given equation, occurs at the x-coordinate given by x = -b / (2a).

In this case, the coefficient of x is -15 and the constant term is 0, so b = 0 and a = -15. Substituting these values into the formula, we get x = -0 / (2 * -15) = 0.

While the mathematical calculation suggests that planting zero trees per acre would maximize the yield, this result is not practical. Therefore, the closest feasible value greater than zero would be 1 tree per acre.

For 1 tree per acre, substituting x = 1 into the equation, we find that each tree would produce a yield of Y = 1200 - 15 * 1 = 1185 peaches. Consequently, the resulting total yield would be 1185 peaches per acre.

Number of trees per acre: 1 tree per acre

Total yield: 1185 peaches per acre

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Answer:

please mark me brainlist

Step-by-step explanation:

a. Decision rule: Reject the null hypothesis if the calculated z-value is less than or equal to -1.28. b. Calculated z-value: -1.8892. c. Conclusion: Reject the null hypothesis, indicating evidence that the population mean is less than 128.

To complete parts (a) through (c), we need to perform a hypothesis test for the given hypotheses

H0: μ = 128 (null hypothesis)

HA: μ ≤ 128 (alternative hypothesis)

Given: X= 119 (sample mean)

σ = 27 (population standard deviation)

n = 46 (sample size)

α = 0.10 (significance level)

a. The decision rule is to reject the null hypothesis if the calculated value of the test statistic is less than or equal to the critical value(s) of the test statistic. Since the alternative hypothesis is one-sided (μ ≤ 128), we will use a one-sample z-test and compare the calculated z-value with the critical z-value.

To find the critical z-value, we need to determine the z-value corresponding to the significance level α = 0.10. Looking up the critical value in the standard normal distribution table, we find that the critical z-value is -1.28 (rounded to two decimal places).

b. The calculated value of the test statistic, in this case, is the z-value. We can calculate the z-value using the formula

z = (X - μ) / (σ / √n)

Substituting the given values:

z = (119 - 128) / (27 / √46) ≈ -1.8892 (rounded to two decimal places)

c. The conclusion is based on comparing the calculated value of the test statistic with the critical value. Since the calculated z-value of -1.8892 is less than the critical z-value of -1.28, we have enough evidence to reject the null hypothesis. Therefore, we conclude that the population mean is less than 128.

The conclusion statement in part (c) is inconsistent with the given alternative hypothesis and should be revised accordingly.

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If this claim is true then one percent of response times take at least \(38.077\) minutes.

In the given question,

A fire department in a rural county reports that its response time to fires is approximately normally distributed with a mean of 22 minutes and a standard deviation of 6.9 minutes.

We have to assuming that the claim is true and finding that one percent of response times take at least how many minutes.

From the question,

Mean \(\mu=22\) minutes

Standard deviation \(\sigma=6.9\) minutes.

Since the given percentage is \(1\%\) and percentage means division of \(100\) so we can write \(1\%=1/100=0.01\)

So the one percent of response times take at least how many minutes is

\(P(x\geq a)=0.01\)

\(P(x\geq \frac{a-\mu}{\sigma})=0.01\)

As we know the all values. SO putting the values in the formula

\(P(x\geq \frac{a-22}{6.9})=0.01\dots\dots\)Equation 1

From the z table

\(P(z\geq 2.33)=0.01\dots\dots\)Equation 2

Now from Equation 1 and Equation 2

\(\frac{a-22}{6.9}=2.33\)

Multiply by \(6.9\) on both side

\(\frac{a-22}{6.9}\times6.9=2.33\times6.9\)

Simplifying

\(a-22=2.33\times6.9\)

\(a-22=16.077\)

Add \(22\) on both side

\(a-22+22=16.077+22\)

\(a=38.077\)

Hence, if this claim is true then one percent of response times take at least \(38.077\) minutes.

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The measure of angle Z is 34°, side length of YZ is 34.1, and the side length of XZ is 41.1. The correct option is the third option ∠Z = 34°, YZ = 34.1, XZ = 41.1

From the question, we are to determine the angles measures of and the side measures of the given triangle XYZ

From the given information,

∠Y = 90°

XY = 23

∠X = 56°

First, we will determine the measure of angle Z

m ∠X + m ∠Y + m ∠Z = 180° (Sum of angles in triangle)

56° + 90° + m ∠Z = 180°

m ∠Z = 180° - 56° - 90°

m ∠Z = 34°

Now, since the measure of one of the angles is 90°, ΔXYZ is a right triangle.

Thus,

From SOH CAH TOA, we can write that

tan X = |YZ| / |XY|

∴ tan 56° = |YZ| / 23

|YZ| = 23 × tan 56°

|YZ| = 34.0989

|YZ| ≈ 34.1

Also,

cos X = |XY| / |XZ|

cos 56° = 23 / |XZ|

|XZ| = 23 ÷ cos 56°

|XZ| = 41.1307

|XZ| ≈ 41.1

Hence, ∠Z = 34°, |YZ| = 34.1, and |XZ| = 41.1

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Answer:

5280

Step-by-step explanation:

Take the amount of miles, multiply it by 1760, and you should get the approximate amount of yards.

Answer:

4+(64x1/8)=4+8=12

\(4 \times (4 + ( {2}^{6} \times {2}^{ - 3})) = \)

\(4 \times (4 + ( {2}^{6 - 3})) = \)

\(4 \times (4 + ( {2}^{3} )) = \)

\(4 \times (4 + (8)) = \)

\(4 \times (4 + 8) = \)

\(4 \times (12) = 48\)

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The correct answer is (( A )) .

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9514 1404 393

Answer:

  y > 1/2x + 2

Step-by-step explanation:

The points shown on the line are separated by a "rise" of 1 unit vertically, and a "run" of 2 units horizontally. Its slope is rise/run = 1/2.

The line crosses the y-axis at y=2, so the y-intercept is 2.

The boundary line is then ...

  y = mx + b . . . . . . . where the slope is m and the y-intercept is b

  y = 1/2x + 2 . . . . . . the equation of the boundary line

__

The line is dashed, and the shaded area is above the line, where y-values are greater than the y-value on the line. Then the y-values on the line are NOT included in the solution set. The inequality is ...

  y > 1/2x + 2

Answer:

The correct answer is $75,900.

Step-by-step explanation:

The percent sales tax of the camera that has a price with tax of $27.30 is 5 %.

Percent Sales tax is an amount of money, calculated as a percentage, that is added to the cost of a product or service when purchased by a consumer at a retail location.

To calculate the percent of sales tax, we use the formula below.

Formula:

Where:

Substitute these values into equation 1

Hence, the percent sales tax is 5 %.

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Answer:

the third circle.

Step-by-step explanation:

Answer:

if it works like the dollar 53p

Answer:

53p

Step-by-step explanation:

£1 = 100p

=> Change = 100p - 47p = 53p

Answer:

-17/10 as a simplified fraction or -1 7/10 as a normal fraction

Step-by-step explanation:

Hi there! Your answer is going to be 1 7/10.

Step-by-step explanation: You have to remove the negative sign, then convert the positive decimal number to a positive fraction. Apply the negative sign to the fraction answer. Rewrite the decimal number as a fraction with 1 in the denominator. Multiply to remove 1 decimal places. Here, you multiply top and bottom by 10^1 = 10 1.7/1×10/10=17/10.

Hope this helps! Have a good day!

Answer:

36x+4

Step-by-step explanation:

4*1+4*9x

Calculating this expression will give us the amount the farmer needs to save annually over the 8-year period.

Given:

Payment required at the end of each year: P50,000

Number of years until the daughter starts college: 8

Interest rate: 7% (compounded annually)

We can calculate the annual savings using the formula for the present value of an ordinary annuity:

P = \dfrac{PMT \times (1 - (1 + r)^{-n}{r}

Where:

P = Present value (amount to be saved annually)

PMT = Payment amount (P50,000)

r = Interest rate per period (7% or 0.07)

n = Number of periods (8)

Let's substitute the given values into the formula:

\[ P = \dfrac{50,000 \times (1 - (1 + 0.07)^{-8}{0.07} \]

Calculating this expression will give us the amount the farmer needs to save annually over the 8-year period.

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In the given set of statements, various conditions and properties related to functions and sets are mentioned.

The statements discuss concepts such as derivatives, concavity, convexity, and increasing functions. The relationships between functions and sets are explored, including the conditions for a function to be strictly concave or convex, the properties of strictly increasing functions, and the impact of differentiability on the existence of maximum values.

(4) The statement mentions the function g and its derivative g'. It states that if g'(x²) = 0, then g is a constant function over D, where D is a set.

(5) The statement introduces three points A, B, and C, and states that if ACB is true, then A is a midpoint between B and C.

(6) This statement introduces two functions f and g. It states that if f is twice differentiable and f and its derivative f' have the same sign, then g is an increasing function.

(7) This statement discusses a function g and its properties. It states that if g is strictly concave over D, a closed interval [s₁, t], and g is differentiable for all x in D, then there exists a point a in D such that g(a) is the maximum value of g over D. Additionally, if g is continuously differentiable and strictly increasing, then the set B is convex.

The statements touch upon concepts related to functions, derivatives, concavity, convexity, and increasing functions. They present various conditions and relationships between functions and sets, exploring properties such as differentiability, monotonicity, and the existence of maximum values.

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(a)The amount of water in the tank is increasing.

(b)Evaluate  \(\int\limits^{18}_0(W(t) - R(t)) dt\) to get the number of gallons of water in the tank at t = 18.

(c)Solve part (b) to get the absolute minimum from the critical points.

(d)The equation can be set up as   \(\int\limits^k_{18}-R(t) dt = 1200\) and solve this equation to find the value of k.

What is the absolute value of a number?

The absolute value of a number is its distance from zero on the number line. It represents the magnitude or size of a real number without considering its sign.

To solve the given problems, we need to integrate the given rates of water flow to determine the amount of water in the tank at various times. Let's go through each part step by step:

a)To determine if the amount of water in the tank is increasing at time t = 15, we need to compare the rate of water being pumped in with the rate of water being removed.

At t = 15, the rate of water being pumped in is given by \(W(t) = 95Vt sin^2(\frac{t}{6})\) gallons per hour. The rate of water being removed is \(R(t) = 275 sin^2(\frac{1}{3})\) gallons per hour.

Evaluate both rates at t = 15 and compare them. If the rate of water being pumped in is greater than the rate of water being removed, then the amount of water in the tank is increasing. Otherwise, it is decreasing.

b) To find the number of gallons of water in the tank at time t = 18, we need to integrate the net rate of water flow from t = 0 to t = 18. The net rate of water flow is given by the difference between the rate of water being pumped in and the rate of water being removed. So the integral to find the total amount of water in the tank at t = 18 is:

\(\int\limits^{18}_0(W(t) - R(t)) dt\)

Evaluate this integral to get the number of gallons of water in the tank at t = 18.

c)To find the time t when the amount of water in the tank is at an absolute minimum, we need to find the minimum of the function that represents the total amount of water in the tank. The total amount of water in the tank is obtained by integrating the net rate of water flow over the interval [0, 18] as mentioned in part b. Find the critical points and determine the absolute minimum from those points.

d. For t > 18, no water is pumped into the tank, but water continues to be removed at the rate R(t) until the tank becomes empty. To find the value of k, we need to set up an equation involving an integral expression that represents the remaining water in the tank after time t = 18. This equation will represent the condition for the tank to become empty.

The equation can be set up as:

\(\int\limits^k_{18}-R(t) dt = 1200\)

Here, k represents the time at which the tank becomes empty, and the integral represents the cumulative removal of water from t = 18 to t = k. Solve this equation to find the value of k.

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