a) Using the result of Exercise 7, determine the solution that satisfies the initial condition Y(0) = (x(O), y(0)) = (-1,3). (b) In the xy-phase plane, plot the solution curve associated to this solution. (e) Plot the corresponding X(t)- and y(t)-graphs.

Algebra is used to solve the mathematical problems, the total amount spent by Andy on lunches in this week is equals to $195.

Algebra is the branch of mathematics that use in the representation of problems or situations in the form of mathematical expressions. Mathematical ( arithmetic) operations say multiplication (×), division (÷), addition (+), and subtraction (−) are used to form a mathematical expression.

We have, a data of amount spent by Andy on lunches in a week. Let the total amount spent by him in this week be "x dollars". Using algebra of mathematics, we can written as x = sum of amounts spent by him in whole week so, x = $50 + $20 + $10 + $25 + $25 + $15 + $50 = $195

Hence, required total amount value is $195.

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Complete question:

Andy spent the following amounts on lunches this week,

day. amount

Sunday $50

Monday. $20

Tuesday $10

Wednesday $25

Thursday $25

Friday $15

Saturday $50

Calculate total amount he spent in this week.

Standard deviation - The value of x is 1.96.

What is standard normal distribution?

A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.

As given, for a standard normal distribution, 95% of the data points are contained in the interval [ -x , x ].

The standard normal distribution, commonly known as the z-distribution, is a unique type of normal distribution in which the mean and standard deviation are both equal to 1. By transforming its values into z-scores, any normal distribution can be standardised. Z-scores indicate how far away from the mean each number is from.

Hence, from the standard normal table, the value of x = 1.96 for 95% confidence level.

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Answer:

2640.74

Step-by-step explanation:

Circumference : π  * 2r

Area of circle : π  * \(r^{2}\)

For this particular circumference,

Circumference : π  * 58

58 = 2r

So by dividing we learn that,

r = 29

When we substitute the radius into the equation for area, we get,

Area of circle : π  * \(29^{2}\)

Area of circle : π  * 841

Area of circle : 2640.74

* I used 3.14 as π

Hope this helps ! Feel free to ask questions! : )

we can express the x coordinate as tsin(t) and the z coordinate as tcos(t). This gives us the vector parametrization of the curve: x = tsin(t), z = tcos(t).

we can express the x coordinate as tsin(t) and the z coordinate as tcos(t). This gives us the vector parametrization of the curve: x = tsin(t), z = tcos(t).

The xz-plane is the plane formed by the x-axis and the z-axis. To find a vector parametrization of a curve in this plane, we need to express the x and z coordinates of the curve as functions of a parameter t. In this case, we can express the x coordinate as tsin(t) and the z coordinate as tcos(t). This gives us the vector parametrization of the curve: x = tsin(t), z = tcos(t).

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Answer:

7

Step-by-step explanation:

when multiplying powers with the same base, add the powers

Answer:

a²×a⁵

a²⁺⁵

a⁷

OAmalOHopeO

Answer:

slope = 2 : 8 or 1:4

Step-by-step explanation:

a(-3, 4)

b(5, 6)

slope = rise / run

slope (6-4, 3+5))

slope = 2 : 8 or 1:4

Answer:

Slope =¼

Step-by-step explanation:

\((-3, 4) \: (5, 6) \\ x _{1} = - 3 , y_1 = 4 \\ x_2 = 5 \\ y_2 = 6\)

\(m = \frac{y_2 - y_1}{x_2 - x_1} \\ m = \frac{6 - 4}{5 - ( - 3)} \\ m = \frac{2}{8} = \frac{1}{4} \)

Answer:

-100

Step-by-step explanation:

8*-100=-800

Answer:

∠ W = 30°

Step-by-step explanation:

using the cosine ratio in the right triangle

cos W = \(\frac{adjacent}{hypotenuse}\) = \(\frac{WY}{WX}\) = \(\frac{2\sqrt{21} }{4\sqrt{7} }\) = \(\frac{1}{2}\) \(\sqrt{\frac{21}{7} }\) = \(\frac{\sqrt{3} }{2}\) , then

∠ W = \(cos^{-1}\) ( \(\frac{\sqrt{3} }{2}\) ) = 30°

The correct representation of the inequality -3(2x - 5) < 5(2 - x) is a number line from negative 3 to 3 in increments of 1, with an open circle at negative 5 and a bold line starting at negative 5 and pointing to the left.

The inequality -3(2x - 5) < 5(2 - x) can be depicted graphically on a number line from negative 3 to 3 in increments of 1. The number line needs to include an open circle at negative 5 and a bold line starting at negative 5 and pointing to the left. This is because the inequality is less than zero, which means that all x values to the left of negative 5 are considered true, and all x values to the right of negative 5 are considered false. This is represented by the open circle, which indicates that the value of x can be any number less than negative 5. The bold line then indicates that all values of x greater than or equal to negative 5 are false. This representation accurately shows the inequality and makes it easier to understand the meaning of the inequality.

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The value of x at which the minimum value of y occurs in [0, 1] is B) 1/8

Given y = 3x^(4/3) - 2x

We are asked to determine the value of x at which the minimum value of y occurs in [0, 1].

                                    Now, dy/dx = 0

                                     4x^(1/3) - 2 = 0

                                             x^(1/3) = 1/2

                                                     x = 1/8

Here, dy/dx = 0 when x = 1/8

So calculating y at x = 0, 1/8, 1

y(x = 0) = 0

y(x = 1/8) =3 (1/8)^(4/3) - 2/8 =  -1/16

y(x = 1) = 1

Hence, y has a minimum value of -1/16 at x = 1/8

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An independent basic service set (IBSS) does not consist of any access points.

In an IBSS, devices such as laptops or smartphones connect with each other on a peer-to-peer basis, forming a temporary network. This type of network can be useful in situations where there is no existing infrastructure or when devices need to communicate with each other directly.

Since an IBSS does not involve any access points, it is not limited by the number of access points. Instead, the number of devices that can be part of an IBSS depends on the capabilities of the devices themselves and the network protocols being used.

To summarize, an IBSS does not consist of any access points. Instead, it is a network configuration where wireless devices communicate directly with each other. The number of devices that can be part of an IBSS depends on the capabilities of the devices and the network protocols being used.

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Answer:

85,700...8,570...857...85.7...8.57...0.857

Step-by-step explanation:

53.35km^2 this is the right answer

Answer:

true

Step-by-step explanation:

the equation is exactly the same on both sides but just expressed differently

By angle angle similarity ΔWYZ ≈ Δ WZX ≈ ΔZYX are similar.

Triangles with exactly similar corresponding angle configurations are said to be similar triangles. This implies that equiangular triangles are comparable. All equilateral triangles are thus interpretations of similar triangles.

In the given statements, thus the similar triangle are:

ΔWYZ ≈ Δ WZX ≈ ΔZYX

A,

∠Y is common

∠x = ∠z = 90°

Therefore, by angle angle similarity ΔWYZ ≈ Δ WZX ≈ ΔZYX are similar.

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Answer:

x=17 degrees

Step-by-step explanation:

All 3 angles = 180 degrees

So 90 + 54 + (x+19) = 180

Combine like terms

163 + x = 180

Subtract 163 from both sides

x = 180-163

x = 17

Answer:          1/2

If 2 students are drinking punch

and 2 are drinking lemonade that would mean it would be 2/4

but if you were to simplify by dividing both by 2

it would be 1/2.

The probability that three numbers are the solution of the equation is 1/27.

The total possible outcome or numbers in the is 27.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27.

total = 27

xyz = 27

(1)(3)(9) = 27

probability of the numbers whose product is 27 is calculated as follows;

p = possible numbers / total outcome

p = 1/27

Thus, the probability that three numbers are the solution of the equation is 1/27.

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Answer:

que

Step-by-step explanation:

no Tengo carnitas yo quero sopes

The probability that an orange weighs more than 17 oz is 0.1587.

The probability that an orange weighs more than 17 oz is 0.1587. This value can be calculated using the Z-score formula, which is used to calculate the probability of an event occurring. The formula is as follows:

Z = (x - μ) / σ

where x is the data point, μ is the mean, and σ is the standard deviation.

In this case, the Z-score is (17 - 14) / 2 or 1.5. We can find the probability using the Z-score table, which gives us 0.1587, the probability that an orange weighs more than 17 oz.

The Z-score formula is useful for determining the probability of an event occurring when the data follows a normal distribution. Knowing the mean and standard deviation, we can calculate the likelihood of a certain outcome occurring. In this case, the probability that an orange weighs more than 17 oz is 0.1587.

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The probability that Edward’s monthly tip income exceeds $2,350 is 0.8413.

Given that Edward works as a waiter, where his monthly tip income is normally distributed with a mean of $2,000 and a standard deviation of $350.

The z score formula is given by;`z = (x - μ) / σ`

Where; x is the raw scoreμ the mean of the populationσ is the standard deviation of the population.

The probability that Edward’s monthly tip income exceeds $2,350 is to be found.`z = (x - μ) / σ``z = (2350 - 2000) / 350``z = 1`

The value of z is 1.

To find the area in the right tail, use the standard normal distribution table.

The table value for z = 1.0 is 0.8413.

Therefore, the probability that Edward’s monthly tip income exceeds $2,350 is 0.8413.

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Based on the given information, you can borrow approximately $89,227.46 for the purchase of your first home if you can afford to make monthly payments of $500 with a 6% annual interest rate on a 30-year mortgage.

APR = \((FV / PV)^1^/^n\) - 1

Where:

APR = Annual Percentage Rate

FV = Future Value ($2,500,000)

PV = Present Value or initial investment ($800,000)

n = number of years (10 years)

Plugging in the values, we have: APR = \(($2,500,000 / $800,000)^1^/^1^0\) - 1

Calculating this expression, we find: APR ≈ 0.1153 or 11.53%

Therefore, the annual percentage rate of return on your investment in the cattle ranch is approximately 11.53%.

Regarding your question about how much you can borrow for the purchase of your first home, given that you can afford to make monthly payments of $500 and the annual interest rate is 6% on a 30-year mortgage, we can use the formula for loan amount calculation:

Loan Amount = (Monthly Payment / Monthly Interest Rate) * (1 - \((1 + Monthly Interest Rate)^-^N^u^m^b^e^r^ o^f^ M^o^n^t^h^s\))

Where:

Monthly Payment = $500

Annual Interest Rate = 6% or 0.06

Monthly Interest Rate = Annual Interest Rate / 12

Number of Months = 30 years * 12 months

Plugging in the values, we have:

Loan Amount = ($500 / (0.06 / 12)) * (1 - (1 + \((0.06 / 12))^-^3^0^ *^ 1^2\))

Calculating this expression, we find: Loan Amount ≈ $89,227.46

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The angle coterminal with -252° between 0° and 360° is 108°.

To find the angle between 0° and 360° that is coterminal with the -252° angle, we can add or subtract multiples of 360° until we get an angle within the desired range.

Since the given angle is negative, we can add 360° to it repeatedly until we get a positive angle:

-252° + 360° = 108°

Therefore, the angle between 0° and 360° that is coterminal with the -252° angle is 108°.

Coterminal angles are angles that have the same initial and terminal sides but may differ in the number of complete revolutions made. In this case, by adding 360° to the given angle, we obtain an angle that falls within the desired range.

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yes, because the midpoints (a+c) = b

Given that the line's equation is y=x.

B and C are the two points on this line.

( a+ c, b) is the midpoint of B and C.

We can see from this that using the midpoint formula

a + c = \(\frac{x1+x2}{2}\)

b=\(\frac{y1+y2}{2}\)

Because both points are on y=x, we get

x1=y1, x2=y2.

As a result, x1 = a+c and 2y1 = 2b or y1 =b.

Because x1=y1, we have a+c =b.

In other words, the coordinates of the midpoint satisfy the equation y=x.

Thus, the answer is

because (a+c) = b

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The family who spends more to run these appliances in a given 30 day period is given by: Option A: The reed family spends $13.80 more than the merrill family.

Suppose that there are two positive integer numbers( numbers like 1,2,3,.. ) as a and b

Then, their multiplication can be interpreted as:

\(a \times b = a + a + ... + a \: \text{(b times)}\\\\a \times b = b + b +... + b \: \text{(a times)}\)

For example,

\(5 \times 2 = 10 = 2 + 2 + 2 + 2 + 2 \: \text{(Added 2 five times)}\\or\\5 \times 2 = 10 = 5 + 5 \: \text{(Added 5 two times)}\)

For this case, the missing table for expenses of both families is:

Reed Family                                                   Appliances                

Gas range                                                  5 cents per day            

Gas dryer                                                   1 load per day-10 cents per load

Electric water heater                                90 cents per day

Typical later model refrigerator               16 cents per day

Total cost per day                                      5+10+90+16= 166 cents = $1.21

Merrill Family                                                Appliances

Electric range                                            13 cents per day

Gas dryer -                                                 1 load per day 10 cents per load

Gas water heater                                      40 cents per day

Energy Star-labeled refrigerator              12 cents per day

Total cost per day                                    13+10+40+12 = 75 cents = $0.75

Since each of them used these appliances for 30 days, so we get:

Expense in 30 days = \(30 \times\) expense per day

Expense in 30 days = \(30 \times 1.21 = \$36.3\)

Expense in 30 days = \(30 \times\) expense per day

Expense in 30 days = \(30 \times 0.75 = \$22.5\)

So, Reed family spent more.

The difference is $36.3 - $22.5 = $13.80

Thus, the family who spends more to run these appliances in a given 30 day period is given by: Option A: The reed family spends $13.80 more than the merrill family.

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Answer:

regular price

Step-by-step explanation:

regular price

Answer:

P represents the usual price of a sandwich

The constant (1.5) represents the discount

Step-by-step explanation:

Sarah's chocolate cake has 300 calories and 15 grams of fat. the percentage of calories from fat in Sarah's chocolate cake is 45%.

To calculate the percentage of calories that come from fat, we need to divide the number of fat calories by the total number of calories and then multiply by 100.

Since we know that 1 gram of fat contains 9 calories, we can calculate the number of fat calories by multiplying the number of grams of fat by 9.

Number of fat calories = 15 grams of fat * 9 calories/gram = 135 calories

Percentage of calories from fat = (Number of fat calories / Total calories) * 100

Total calories = 300 calories

Percentage of calories from fat = (135 calories / 300 calories) * 100

Percentage of calories from fat = 45%

Therefore, the percentage of calories from fat in Sarah's chocolate cake is 45%.

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The percentage of calories from fat in Sarah's chocolate cake is 45%. This calculation is based on the ratio of fat calories to total calories.

To find out the percentage of calories from fat in her cake, we need to divide the amount of total fat calories (15g x 9 calories/gram = 135 calories) by the total amount of calories in the cake (300 calories). We then multiply this ratio (135/300) by 100, which gives us the answer of 45%. Generally, it is recommended that a person's diet should not have more than 25-35% of its total calories from fat.

Therefore, Sarah's chocolate cake is too high in fat to be a part of a well- balanced diet. To reduce the amount of fat in her cake, she should either opt for a different cake recipe or use reduced-fat or low-fat ingredients when baking.

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the answer would be 5 because 5*5 or 5 squared (5^2) is equal to 25, hope this helps!