Marion buys three similar vanity cases to gift her air hostess colleagues.
She hands over $100 to the cashier. How much did each vanity cost?

The graph of x(t) can be drawn by substituting the values of C1 and C2 into the equation

The second-order linear differential equation can be written as follows:x''(t) - x'(t) = 0To verify that x(t) = C1et + C2 is a solution, we need to differentiate the given function twice and substitute the resulting values back into the equation.x(t) = C1et + C2Differentiating x(t) = C1et + C2 with respect to t once,x'(t) = C1e tDifferentiating x'(t) = C1e t with respect to t once,x''(t) = C1e tSince the resulting values for x''(t) and x'(t) are equal, we can state that x(t) = C1et + C2 is indeed a solution to x''(t) - x'(t) = 0.For x(t) = C1et + C2 to satisfy x(0) = 10 and x'(0) = 100, the following conditions must be satisfied:x(0) = C1e0 + C2 = 10⇒ C1 + C2 = 10andx'(0) = C1e0 = 100⇒ C1 = 100We can solve the two equations above to obtain C1 and C2:C1 + C2 = 10, C1 = 100∴ C2 = - 90Therefore, C1 = 100 and C2 = - 90.The graph of x(t) can be drawn by substituting the values of C1 and C2 into the equation x(t) = C1et + C2 and plotting the resulting function on a graph. This will yield a rising exponential curve that levels off as it approaches the x-axis.

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James earns 24,000 yearly.

1 year = 12 months

Total money earned yearly divided by the number of months.

\(24,000\div12\)

\(=\fbox{2000 monthly income}\)

Answer: 2,000

Step-by-step explanation: There are 12 months in one year, so do

24,000 ÷ 12 = 2,000

2.1 The volume in ml of one can of cold drink is 83 ml.

2.2 The height of the cooler bag is 18 cm.

2.3 The volume in ml of the cooler bag if the breadth of the bag is 12 cm and the length 18 cm is 3,888 ml.

2.4 The circumference of the can is 18.84 cm.

In Mathematics and Geometry, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

By substituting the given side lengths into the volume of a cylinder formula, we have the following;

Volume of can = 3.14 × (6/2)² × 8.84

Volume of can = 83.27 cm³.

Note: 1 cm³ = 1 ml

Volume of can in ml = 83.27 ≈ 83 ml.

Part 2.2.

For the height of the cooler bag, we have:

Height of cooler bag = 2 × height of can

Height of cooler bag = 2 × 8.84

Height of cooler bag = 17.68 ≈ 18 cm.

Part 2.3

Volume of cooler bag = length × breadth × height

Volume of cooler bag = 18 × 12 × 18

Volume of cooler bag = 3,888 ml.

Part 2.4

The circumference of the can is given by:

Circumference of circle = 2πr

Circumference of can = 2 × 3.14 × 3

Circumference of can = 18.84 cm.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The Mean of the sample is = 3.7

The Standard deviation of the sample is  = 0.1125

If we assume that the population mean and standard deviation of GPAs are 3.7 and 0.9, respectively, then the mean of the distribution of sample means of size 64 would also be 3.7, and the standard deviation would be:

standard deviation = population standard deviation / sqrt(sample size)

= 0.9 / sqrt(64)

= 0.1125

So the mean and standard deviation of the distribution of sample means would be approximately:

mean = 3.7

standard deviation = 0.1125

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The mode of the given data values is N/A (not applicable).Hence, the mean, median, and mode of the given data values are:Mean = 54.36Median = 55.5Mode = N/A (not applicable)

Given data values are 55, 56, 70, 61, 53, 57, 50, 73, 52, 69, and 2. We need to calculate the mean, median, and mode of this sample.So, let's first arrange the data values in ascending order:2, 50, 52, 53, 55, 56, 57, 61, 69, 70, 73

Mean:The mean is the sum of all the data values divided by the total number of data values. So, we can use the following formula to calculate the mean:

Mean = (sum of all the data values) / (total number of data values)Sum of all the data values = 55 + 56 + 70 + 61 + 53 + 57 + 50 + 73 + 52 + 69 + 2 = 598Total number of data values = 11

Therefore,Mean = (sum of all the data values) / (total number of data values) = 598 / 11 = 54.36 (rounded to two decimal places)Therefore, the mean of the given data values is 54.36.

Median:The median is the middle value of a sorted data set. Since the data set has 11 data values, the median is the average of the 6th and 7th values (counting from smallest to largest).

Therefore, the median is :Median = (55 + 56) / 2 = 55.5Therefore, the median of the given data values is 55.5.

Mode:The mode is the data value that appears most frequently in the data set. In this case, there is no data value that appears more than once. So, there is no mode.

Therefore, the mode of the given data values is N/A (not applicable).Hence, the mean, median, and mode of the given data values are:Mean = 54.36Median = 55.5Mode = N/A (not applicable)

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If the MSbetween (Mean Square Between) is lower than the MSwithin (Mean Square Within), the F value will be less than 1.

The F value is calculated by dividing the variance between groups (MSbetween) by the variance within groups (MSwithin). It is used in analysis of variance (ANOVA) to test for significant differences among group means. The F value follows an F-distribution, and its magnitude determines the statistical significance of the differences between groups.

When the MSbetween is lower than the MSwithin, it indicates that the variability between groups is smaller compared to the variability within groups. This suggests that the differences observed among the group means are not substantial or meaningful. In other words, there is more similarity within the groups than between them.

Since the F value is calculated as the ratio of MSbetween to MSwithin, if the numerator (MSbetween) is smaller than the denominator (MSwithin), the F value will be less than 1.

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Answer:the answer is a

Step-by-step explanation:

Answer: I got 29

Step-by-step explanation:

You would plug in 4 in all the spots where the x's are and then solve the problem

Answer:

35.19 miles

Step-by-step explanation:

There are 35.19 miles from Greenville to Sunnyvale in southwest direction and 40 miles (64.37 kilometers) by car, following the I-30 and US-67 route.

Greenville and Sunnyvale are 49 minutes far apart, if you drive non-stop .

This is the fastest route from Greenville, TX to Sunnyvale, TX. The halfway point is Royse City, TX.

Greenville, TX and Sunnyvale, TX are in the same time zone (CDT). Current time in both locations is 9:43 pm.

Question

An octagon has a side length of 15 feet and an area of 1089.6 ft²

Find the area of a smaller octagon that has a side length of 7 feet.

Answer:

237.3ft²

Step-by-step explanation:

We are given two octagons in the above question.

Side length of larger octagon = 15 ft

Area of larger octagon = 1089.6 ft²

The area of a smaller octagon = X

Side length of smaller octagon = 7 ft.

We solve for this using scale factor

Scale factor(k) = ratio of the side length of the octagon = smaller side length/ larger side length

k = 7/15

It is important to note that

The square of the scale factor k = ratio of the areas of the octagon

Hence,

k² = X/1089.6 ft²

(7/15)² = X/1089.6 ft²

7²/15² = X/1089.6 ft²

Cross Multiply

15² × X = 7² × 1089.6ft²

X = 7² × 1089.6ft²/15²

X = 237.29066667ft²

Approximately, the area of the smaller octagon = 237.3ft²

The LP problem can be stated as follows: Minimize Cost = 25x + 18y

Subject to: 2x + y ≥ 12 2y + 3y ≥ 18 x ≥ 0, y ≥ 0

A. Decision variables:

Let x be the number of days Goldilocks spends in Mine1.

Let y be the number of days Goldilocks spends in Mine2.

B. Objective function:

We want to minimize the cost of obtaining the needed metals. The cost is calculated based on the number of days spent in each mine and the respective costs per day. The objective function is:

Cost = 25x + 18y

C. Constraints:

Gold constraint: Gold obtained from Mine1 and Mine2 combined should be at least 12lbs per month.

2x + y ≥ 12

Silver constraint: Silver obtained from Mine1 and Mine2 combined should be at least 18lbs per month.

2y + 3y ≥ 18

Non-negativity constraint: The number of days spent in each mine should be non-negative.

x ≥ 0, y ≥ 0

These constraints ensure that Goldilocks meets the minimum requirements for gold and silver while also considering the limitations on the number of days she can spend in each mine.

To summarize, the LP problem can be stated as follows:

Minimize Cost = 25x + 18y

Subject to:

2x + y ≥ 12

2y + 3y ≥ 18

x ≥ 0, y ≥ 0

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Answer:

B=28

Step-by-step explanation:

Answer:

I'm not good at math

Step-by-step explanation:

The height of the building is approximately 86.60 meters.

To find the height of the building, we can use trigonometric ratios, specifically the tangent function.

In this scenario, the angle of elevation is 60 degrees, and the distance from the foot of the building to the point where the angle is measured is 50 meters.

Let's denote the height of the building as 'h'. According to trigonometry, the tangent of an angle is equal to the ratio of the opposite side to the adjacent side.

In this case, the opposite side is the height of the building (h), and the adjacent side is the distance from the foot of the building (50 meters).

Using the tangent function, we have:

tan(60 degrees) = h/50

Simplifying this equation, we can solve for h:

h = 50 × tan(60 degrees)

Using a scientific calculator or trigonometric table, we find that tan(60 degrees) is approximately 1.732.

Therefore, h = 50 × 1.732 ≈ 86.60 meters.

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The instantaneous velocity of the object at t = 1 is 135 ft/s. The object will have an instantaneous velocity of 12 ft/s after approximately 14.2 seconds.

The height of the object at the highest point of its trajectory is 1,153.5 feet. The object will strike the ground with a speed of 135 ft/s.

a. To determine the instantaneous velocity of the object at t = 1, we need to find the derivative of the height function with respect to time (s = 153t - 9t^2). The derivative of s with respect to t gives us the instantaneous velocity. Taking the derivative, we have:

ds/dt = 153 - 18t.

Substituting t = 1 into the derivative, we get:

ds/dt = 153 - 18(1) = 153 - 18 = 135 ft/s.

Therefore, the instantaneous velocity of the object at t = 1 is 135 ft/s.

b. To find the time at which the object has an instantaneous velocity of 12 ft/s, we set ds/dt equal to 12 and solve for t:

12 = 153 - 18t.

Rearranging the equation, we have:

18t = 153 - 12,

18t = 141,

t = 141/18,

t ≈ 7.83 seconds.

Hence, the object will have an instantaneous velocity of 12 ft/s after approximately 7.83 seconds.

c. The highest point of the object's trajectory occurs when its velocity becomes zero. At this point, the instantaneous velocity is 0 ft/s. Setting ds/dt equal to 0 and solving for t, we have:

0 = 153 - 18t.

Rearranging the equation, we get:

18t = 153,

t = 153/18,

t ≈ 8.5 seconds.

To find the height at this time, we substitute t = 8.5 into the height equation:

s = 153(8.5) - 9(8.5)^2,

s ≈ 1,153.5 feet.

Therefore, the height of the object at the highest point of its trajectory is approximately 1,153.5 feet.

d. The object strikes the ground when its height (s) becomes zero. We set s equal to zero and solve for t:

0 = 153t - 9t^2.

This equation represents a quadratic equation. Solving it, we find two possible values for t: t = 0 and t = 17 seconds. Since the object is initially fired upward, we discard t = 0 as the time it takes to reach the ground. Therefore, the object strikes the ground after approximately 17 seconds.

To find the speed at which it strikes the ground, we substitute t = 17 into the derivative of s with respect to t:

ds/dt = 153 - 18(17),

ds/dt = 153 - 306,

ds/dt = -153 ft/s.

The negative sign indicates the downward direction, so the object strikes the ground with a speed of 153 ft/s.

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Answer:

Step-by-step explanation:

The probability P(Z>1.28) represents the area under the standard normal distribution curve to the right of the z-score 1.28.

Using a standard normal distribution table or a calculator, we find that the area to the right of 1.28 is approximately 0.1003.

Therefore, the answer is closest to option (b) 0.10. there is a 10% chance of obtaining a value above 1.28 in a standard normal distribution.

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Question 1: The item not included in the cost of merchandise inventory is "Purchase discounts."

2: The total cost of the merchandise is $3,332.00.

5: The company's gross margin and operating expenses, are $211,000 and $191,720.

Merchandise inventory expenses normally consist of the price paid for the inventory, deductions from the purchase price resulting from purchase returns and allowances, and freight expenses paid by the purchaser.

Although purchase discounts reduce the cost of merchandise inventory, they are not considered part of it. Instead, they are treated as a distinct discount in the accounting records.

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a. The probability that a patient experiences relief is 0.9.

b. The probability that at least 10 patients experience relief is 0.9988 (rounded to four decimal places)

c. The probability that at most 7 experience relief is 0.0007 (rounded to four decimal places)

d. The average number of patients who experience relief is 1.14 (rounded to two decimal places)

e. The probability that none of the 15 patients experience relief is 1.0E-15 (rounded to scientific notation)

a. The probability that a patient experiences relief is 0.9. The probability that all 15 experience relief is given by:

P(all 15 experience relief) = (0.9)^15 = 0.2059 (rounded to four decimal places)

b. The probability that at least 10 patients experience relief can be calculated by adding the probabilities of 10, 11, 12, 13, 14, and 15 patients experiencing relief:

P(at least 10 experience relief) = P(10) + P(11) + P(12) + P(13) + P(14) + P(15)

where P(k) represents the probability that k patients experience relief. Each P(k) can be calculated using the binomial probability formula:

P(k) = (15 choose k) * 0.9^k * 0.1^(15-k)

Using a calculator or software, we can find:

P(at least 10 experience relief) = 0.9988 (rounded to four decimal places)

c. The probability that at most 7 patients experience relief is the same as the probability that 8 or fewer patients experience relief. We can use the complement rule to calculate this probability:

P(at most 7 experience relief) = 1 - P(more than 7 experience relief)

To find P(more than 7 experience relief), we can add the probabilities of 8, 9, ..., 15 patients experiencing relief:

P(more than 7 experience relief) = P(8) + P(9) + ... + P(15)

Again, each P(k) can be calculated using the binomial probability formula. Using a calculator or software, we can find:

P(at most 7 experience relief) = 0.0007 (rounded to four decimal places)

d. The average number of patients who experience relief is given by the expected value of a binomial distribution:

E(X) = np

where X is the number of patients who experience relief, n is the sample size (15), and p is the probability of success (0.9). Thus,

E(X) = 15 * 0.9 = 13.5

The standard deviation of a binomial distribution is given by the square root of the variance:

s = sqrt(np*(1-p))

Thus,

s = sqrt(150.90.1) = 1.14 (rounded to two decimal places)

e. The probability that none of the 15 patients experience relief is given by:

P(none experience relief) = 0.1^15 = 1.0E-15 (rounded to scientific notation)

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Answer:

4th one please give me brainliest

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

The measure of two supplementary angles =  15:21

The angles are  15x , 21x

15x + 21x = 180       {Supplementary}

         36x = 180

             x = 180/36

             x = 5

Smallest angle = 15 * 5 = 75

Answer:

adult tickets  6.9

children tickets  3.9

Step-by-step explanation:

3x + y = 24.60    L1

5x + 4y = 50.10  L2

5L1 - 3L2

15x +  5y = 123

-15x - 12y = -150.3

-7y = -27,3

y = -27,3/-7

y = 3.9

3x + y = 24.60

3x + 3.9 = 24.60

3x = 24.60 - 3.9

3x = 20.7

x = 20.7 / 3

x = 6.9

Answer:

B

Step-by-step explanation:

21 inches to 7 inches

The width of the original image is B)  \(7\frac{7}{8}\) inches.

Given that: The width of the large poster is 21 inches.

Given that: The original image has dimensions that are 3/8 of the dimensions of the image in the poster.

So the width of the original image is = \(\frac{3}{8}\cdot21=\frac{63}{8}=7\frac{7}{8}\)

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The quantity of substance remains after 850 years is 8.98g if the half life of radioactive radium is 1,599 years.

The time taken by substance to reduce to its half of its initial concentration is called half life period.

We will use the half- life equation N(t)

N e^{(-0.693t) /t½}

Where,

N is the initial sample

t½ is the half life time period of the substance

t2 is the time in years.

N(t) is the reminder quantity after t years .

Given

N = 13g

t = 350 years

t½ = 1599 years

By substituting all the value, we get

N(t) = 13e^(0.693 × 50) / (1599)

= 13e^(- 0.368386)

= 13 × 0.691

= 8.98

Thus, we calculated that the quantity of substance remains after 850 years is 8.98g if the half life of radioactive radium is 1,599 years.

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The series to 10 term is

1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512

An equation that represents a sequence based on a rule is called a recurrence relation.

Finding the following term, which is dependent upon the prior phrase, is made easier (previous term). We can readily predict the following term in a series if we know the preceding term.

The term is predicted by multiplying the preceding term by 2

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Answer:

a.

Step-by-step explanation:

ME = 1/2mv² + mgh which is correct option(A)

Mechanical energy is defined as the sum of kinetic energy and potential energy.

Mechanical energy = 1/2mv² + mgh

Where, kinetic energy is 1/2mv² and potential energy is mgh

Hence, ME = 1/2mv² + mgh

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Answer:

Step-by-step explanation:

To find the volume of a Rectangular prism you have to do W*H*L

L=1/5

W=4/5

H=3/5

So just multiply them all and you get .0096 cm^3

Answer:£11,854.11

Step-by-step explanation:

By applying the Pythagorean theorem (c² = a² + b²) to the right triangle formed by the ladder, ground, and house height, the height of the house is calculated as approximately 156.9 inches.

To determine the height of the house when the ladder extends to a length of 158 inches, you need to use the Pythagorean Theorem which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides (legs).

The ladder represents the hypotenuse of the right triangle formed by the ladder, the ground, and the height of the house. Thus, you can use the formula c² = a² + b², where c is the length of the ladder, and a and b are the length and height of the house, respectively. Rearranging the formula to solve for b, you get b = √(c² - a²).

Substituting c = 158 inches and a = 24 inches (assuming the ladder touches the ground at a distance of 24 inches from the base of the house), you get b = √(158² - 24²) = √(24644) = 156.9 inches, rounded to the nearest hundredth of an inch.

Therefore, the height of the house is 156.9 inches when the ladder extends to a length of 158 inches.

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