Tìm đạo hàm Y' = Y'(x) tại X0 = π/4 của hàm số y -= y(x) được cho bởi phương trình tham số
X= arctan t
y = ln t

Note that the notation   "∪C = {x : x ∈ for some S ∈ C} = ∪ { S:S ∈ C}" represents a mathematical statement involving sets.

∪C : This represents the  union (∪) of the sets in C.

{x : x ∈ for some S ∈ C}: This is the description or definition of the elements in the set formed by the union of sets in C.

It states that an element x belongs to the union of   sets in C if and only if x belongs to at least one set S that is an   element of the set C.

= ∪{ S:S ∈ C}   : This means that the union (∪) of sets in C is equal to the union of all sets S that belong to the set C.

In summary,  the statement is saying that the union of sets in C consists of all elements that belong to at least one set in C. It is the combined collection of elements from all sets in C.

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Answer:

D 0.89275

Step-by-step explanation:

To construct a frequency histogram based on the given temperature data, we will use the temperature ranges as the x-axis and the number of days as the y-axis.

The temperature ranges and their corresponding frequencies are as follows:

30-39: 2 days

40-49: 26 days

50-59: 28 days

60-69: 8 days

70-79: 2 days

To create the histogram, we will represent each temperature range as a bar and the height of each bar will correspond to the frequency of days.

Using an appropriate scale, we can label the x-axis with the temperature ranges (30-39, 40-49, 50-59, 60-69, 70-79) and the y-axis with the frequency values.

Now, we can draw rectangles (bars) on the graph, with the base of each rectangle corresponding to the temperature range and the height representing the frequency of days. The height of each bar will be determined by the corresponding frequency value.

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The amount of Dividends of $3,000, $5,000, $34,500, and $71,000 were distributed to the 20,000 preferred and 25,000 common shareholders of Lightfoot Inc. over the first four years of operations.

To calculate the dividend per share of the preferred and common stock of Lightfoot Inc., the total amount of dividends paid out over the first four years must first be determined. This can be done by adding the given amounts of $3,000, $5,000, $34,500, and $71,000 to get a total of $113,500. To find the dividend per share for the preferred stock, the total dividend is divided by the number of shares (20,000) which gives a dividend per share of $5.68. To find the dividend per share for the common stock, the total dividend is divided by the number of shares (25,000) which gives a dividend per share of $4.54.

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Answer:

1 24/25 or one and twenty-four twenty-fifths (in word form).

Step-by-step explanation:

This would be the answer since, we firstly have to convert the mixed fractions into improper fractions. 7/5*7/5, which equals to 49/25. In simplified form it would be 1 2/25.

1 2/5=7/5

7/5*7/5= 49/25 or 1 24/25.

Anyhow, the answer is 1 24/25

The simplified mixed fraction for the given fraction is  \(24\frac{1}{2}\)

A fraction represented with its quotient and remainder is a mixed fraction, a mixed fraction is a combination of a whole number and a proper fraction.

Given that a fraction \(1\frac{2}{5}\) × \(1\frac{2}{5}\)

We need to simply it in a mixed fraction,

\(1\frac{2}{5}\) × \(1\frac{2}{5}\)

= 7/2 × 7/2

= 49 / 2

= \(24\frac{1}{2}\)

Hence, the simplified mixed fraction for the given fraction is  \(24\frac{1}{2}\)

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The total time taken for the entire journey is 2.8 hours.

To calculate the total time taken for the entire journey, we can use the formula:

Time = Distance / Speed

For the first part of the journey, the car travels a distance of 112 km at an average speed of 70 km/h. Using the formula, the time taken for this part is:

Time1 = 112 km / 70 km/h = 1.6 hours

For the second part of the journey, the car travels a further distance of 60 km at an average speed of 50 km/h. Again, using the formula, the time taken for this part is:

Time2 = 60 km / 50 km/h = 1.2 hours

To find the total time for the entire journey, we sum up the times for both parts:

Total Time = Time1 + Time2 = 1.6 hours + 1.2 hours = 2.8 hours

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STATEMENT:

ANSWER:

STEP BY STEP EXPLANATION:

Answer:

A) \(x=-1\pm\sqrt{\frac{13}{6}}\)

Step-by-step explanation:

\(\displaystyle x=\frac{-12\pm\sqrt{12^2-4(6)(-7)}}{2(6)}\\\\x=\frac{-12\pm\sqrt{144+168}}{12}\\\\x=\frac{-12\pm\sqrt{312}}{12}\\\\x=\frac{-12\pm2\sqrt{78}}{12}\\\\x=-1\pm\frac{\sqrt{78}}{6}\\\\x=-1\pm\sqrt{\frac{78}{36}}\\\\x=-1\pm\sqrt{\frac{13}{6}}\)

The coordinates of the y-intercept are (0, 3.5) and the coordinates of the x-intercepts are (-17.5, 0). Using these coordinates, the graph of the equation is shown below.

From the question, we are to graph the given linear equation.

To graph the equation,

We will determine the coordinates of the x-intercepts and y-intercepts.

When x = 0

y = 1/5x + 3.5

y = 1/5(0) + 3.5

y = 3.5

(0, 3.5)

When y = 0

y = 1/5x + 3.5

0 = 1/5x + 3.5

Multiply through by 5

0 = x + 17.5

x = -17.5

(-17.5, 0)

Using the coordinates of the x-axis and y-axis, the graph of the equation is shown below.

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We were told that the recipe uses 6 cups of flour to 1 1/10 cups of milk. Converting 1 1/10 to improper fraction, it becomes 11/10

Let x represent the number of cups of milk that would be used for 2 cups of flour. The equations would be as shown below

11/10 = 6

x = 2

By cross multiplying, we have

2 * 11/10 = 6 * x

6x = 22/10 = 11/5

x = (11/5) / 6

If we flip 6 such that it becomes 1/6, the division sign changes to multiplication. Thus, we have

x = 11/5 * 1/6 = 11/30

Thus, 11/30 cup of milk should be used

According to the Empirical Rule, 99.7% of the measures fall within 3 standard deviations of the mean in the normal distribution.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:

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nswer: The perimeter is approximately equal to 43.7 ft.

Step-by-step explanation:



since we are working with a square, we know all the sides tend to have equal measurements including the side which acts as a hypotenuse to the triangle. Therefore, if we somehow find the measurement of the hypotenuse we'll be able to get the measurement of all sides of the square which we could add in to the two other sides of the triangle to get the perimeter.

Joshua calculated the hypotenuse wrong. The correct calculation is:

hypotenuse² = 7² + 7²

hypotenuse = √( 7² + 7²)

hypotenuse = √( 49 + 49)

hypotenuse = √( 98)

hypotenuse = 7√2

now it's going to be easy doing further calculation. We will three sides of square add them to two other sides of the triangle and get the perimeter.

Perimeter of Pentagon :

perimeter = 7√2 + 7√2 + 7√2 + 7 + 7

perimeter = 43.6984848098

perimeter ≈ 43.7 ft ANSWER

hope that helps...

The answer of the slope or Gradient of the line is 2

Given statement solution is :- It takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

To determine the number of months it takes to pay off the credit card and the total amount paid, including interest, we can follow these steps:

Step 1: Calculate the monthly interest rate.

The APR (Annual Percentage Rate) is given as 9.5%. To find the monthly interest rate, we divide this by 12 (the number of months in a year):

Monthly interest rate = 9.5% / 12 = 0.0079167

Step 2: Determine the monthly payment.

The monthly payment is given as $400.

Step 3: Calculate the interest and principal paid each month.

The interest paid each month can be calculated by multiplying the monthly interest rate by the current balance.

Principal paid = Monthly payment - Interest paid

Step 4: Track the remaining balance each month.

Starting with the initial balance of $1,367.90, subtract the principal paid each month to determine the new balance.

Step 5: Repeat Steps 3 and 4 until the balance reaches zero.

Continue calculating the interest and principal paid each month, updating the balance, until the remaining balance becomes zero.

Step 6: Determine the total number of months and the total amount paid.

Count the number of months it takes to reach a balance of zero. Multiply the number of months by the monthly payment ($400) to find the total amount paid.

Let's calculate the number of months and the total amount paid, including interest:

Month 1:

Interest paid = 0.0079167 * $1,367.90 = $10.84

Principal paid = $400 - $10.84 = $389.16

New balance = $1,367.90 - $389.16 = $978.74

Month 2:

Interest paid = 0.0079167 * $978.74 = $7.75

Principal paid = $400 - $7.75 = $392.25

New balance = $978.74 - $392.25 = $586.49

Month 3:

Interest paid = 0.0079167 * $586.49 = $4.64

Principal paid = $400 - $4.64 = $395.36

New balance = $586.49 - $395.36 = $191.13

Month 4:

Interest paid = 0.0079167 * $191.13 = $1.51

Principal paid = $400 - $1.51 = $398.49

New balance = $191.13 - $398.49 = -$207.36 (Paid off)

It takes 4 months to pay off the credit card. Now, let's calculate the total amount paid, including interest:

Total amount paid = 4 * $400 = $1600

Therefore, it takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

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Answer:

Correct answer is D 146°

Step-by-step explanation:

x= 90° +56° ( Exterior angle of a triangle is equal to the two opposite interior angles)

x= 146°

Answer:

let the no be x ..then,

10% of x =80,000

10x=80,000*100

x=80,00,000/10

x=8,00,000

hence 10%of 8,00,000 is 80,000

The required value of x if -8/39

Given the equation 4/5x+9 1/0=5 1/5, we are to get the value of "x"

4/5 x = 5 1/5 -  9 1/10

4/5 x = 26/5 - 91/10

4/5 x = 2(26)-91/10

4/5 x = (52-91)/10

4/5 x = -39/10

Cross multiply

5x * -39 = 4 * 10

-195x = 40

x = -40/195

x = -8/39

Hence the required value of x if -8/39

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The equation of a circle with diameter endpoints of (13, -1) and (15, 9) will be x² + y² - 28x - 8y + 186 = 0.

Given that:

Endpoints of diameter, (13, -1) and (15, 9)

The equation of the circle when endpoints of diameter are given is written as,

(x - x₁)(x - x₂) + (y - y₁)(y - y₂) = 0

The equation of the circle is calculated as,

(x - 13)(x - 15) + (y + 1)(y - 9) = 0

x² - 28x + 195 + y² - 8y - 9 = 0

x² + y² - 28x - 8y + 186 = 0

The equation of a circle with diameter endpoints of (13, -1) and (15, 9) will be x² + y² - 28x - 8y + 186 = 0.

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a. It will take 7 months to pay off the credit card.

b. it will take 4 months to pay off the credit card.

Since, APR stands for Annual Percentage Rate. It is the interest rate charged on a loan or credit card, expressed as a yearly percentage rate. The APR takes into account not only the interest rate, but also any fees or charges associated with the loan or credit card.

a. If you put half of the available money each month toward the credit card, then you are paying $150.00 per month towards the credit card balance.

We can use the formula for the present value of an annuity to find how many months it will take to pay off the credit card:

PV = PMT × ((1 - (1 + r)⁻ⁿ) / r)

where:

PV is the present value of the debt

PMT is the payment amount per period

r is the monthly interest rate

n is the number of periods

Substituting the values, we get:

754.43 = 150 × ((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)

Simplifying and solving for n, we get:

n = log(1 + (PV ×r / PMT)) / log(1 + r)

n = log(1 + (754.43×0.011333 / 150)) / log(1 + 0.011333)

n = 6.18

Therefore, it will take 7 months to pay off the credit card if you put half of the available money each month toward the credit card.

b. If you put all of the available money each month toward the credit card, then you are paying $300.00 per month towards the credit card balance.

754.43 = 300 ×((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)

Simplifying and solving for n, we get:

n = log(1 + (PV × r / PMT)) / log(1 + r)

n = log(1 + (754.43× 0.011333 / 300)) / log(1 + 0.011333)

n = 3.43

Therefore, it will take 4 months to pay off the credit card if you put all of the available money each month toward the credit card.

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Answer:

53

Step-by-step explanation:

bc it is

62 square yards is the area of the figure.

Area is the measure of a region's size on a surface and the area of a plane region or plane area refers to the area of a shape

In the given figure there are three rectangle in that two are smaller rectangles squares.

The rectangle has length of 10 yd and width of 5 yd.

Area of rectangle (Large)=10×5

=50 square yds

The side length of smaller rectangle is 3 yards and width is 2 yd

Area of rectangle (small)=3×2

6 square yds.

As there are two smaller rectangles, then area will be 2(6)=12 yards.

Now total area = 50+12

=62 square yards.

Hence, the area of the figure is 62 square yards.

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The pipeline has a rate of 1 inch to one foot. 20 yards are equivalent to 20*3 = 60 ft. To find the drop (x) we can use the next proportion:

Solving for x:

The drop is 3 inches

Number of seats in each row is 51 given that a rectangular auditorium seats 2244 people and number of seats in each row exceeds the number of rows by 7. This can be obtained by assuming the value of number of seats in each row, forming quadratic equation and using quadratic formula to find root.

Here in the question it is given that,

We have to find the number of seats in each row.

Let us assume that the number of seats in each row be x.

From the given statement, number of seats in each row exceeds the number of rows by 7, we can write that,

Number of seats in one row = Number of rows + 7

x = Number of rows + 7

⇒ Number of rows = x - 7

Total number of seats in the auditorium can be written as,

⇒ (Number of seats in one row)(Number of rows) = Total number of seats

(x)(x - 7) = 2244

x² - 7x = 2244

⇒ x² - 7x - 2244 = 0

By using quadratic formula we can find the root,

x = (-b ± √b² - 4ac)/2a

here in the question, a = 1, b = -7, c = -2244

√b² - 4ac = √(-7)² - 4(1)(-2244)

√b² - 4ac = √49 + 8976

√b² - 4ac = √9025

√b² - 4ac = 95

x = (-b ± √b² - 4ac)/2a

x = (7 ± 95)/2

x = 102/2 or x = -88/2

⇒ x  = 51 or x = -44

Hence number of seats in each row is 51 given that a rectangular auditorium seats 2244 people and number of seats in each row exceeds the number of rows by 7.

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Answer:

\(3 {x}^{2} - 5x + 4x = 3 {x}^{2} - 5 {x}^{2} + 9x \\ 3 {x}^{2} - x = - 2 {x}^{2} + 9x \\ 3 {x}^{2} + 2{x}^{2} = 9x + x \\5 {x}^{2} = 10x \\ 5x = 10 \\ x = \frac{10}{5} = 2 \\ x = 2 \\ thank \: you\)

Answer:

\( \rm x = 2\)

Step-by-step explanation:

\( \rm 3x ^ { 2 } -5x+4x=3x ^ { 2 } -5x ^ { 2 } +9x\)

\( \rm 3x^{2}-x=3x^{2}-5x^{2}+9x \)

\( \rm 3x^{2}-x=-2x^{2}+9x \)

\( \rm 3x^{2}-x+2x^{2}=9x \)

\( \rm 5x^{2}-x=9x \)

\( \rm 5x^{2}-x-9x=0 \)

\( \rm 5x^{2}-10x=0 \)

\( \rm 5x -10 =0 \)

\( \rm x = 10 \div 5 \)

\( \bold{x = 2}\)

Answer: your answer is -4 1/6

Step-by-step explanation:

Answer:

lower quartile: 19

upper quartile: 38

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

Step-by-step explanation:

At least 9 means more than 9 and includes 9

x ≥ 9     and    [9,  +∞)

At most 9 means numbers less than 9

x≤9       and  (-∞, 9]

more than 9 means bigger than 9 but not including 9

x > 9     and    (9,  +∞)

fewer than 9 means less than 9 but not including 9

x<9       and  (-∞, 9)

strictly between 7 and 9   means between 7 and 9 but not including

7<x<9      and    (7,9)       (This is the only one I'm unsure of.  Strictly, not sure if it includes or doesn't include, usually it just says include or doesn't include)

between 7 and 7 inclusive.   means it's just =7  There's no boundaries

x=7

no more than 7 means less than 7 and includes 7

x ≤ 7   and   (-∞, 7]

Answer:

  D

Step-by-step explanation:

You want to know a procedure to show that sides satisfying the Pythagorean relation will form a right triangle.

The converse of the Pythagorean theorem tells you that side lengths satisfying the relation a² +b² = c² will form a right triangle. In order to show this, we must first have three lengths that satisfy this relation. (Eliminates choices A and C.)

The right angle in a right triangle is the largest angle, so must be opposite the longest side. (Eliminates choice B.)

The only useful procedure for the desired demonstration is that of choice D.

__

Additional comment

The second attachment shows that a side of length 12 is too long for the third side of a triangle with sides 5 and 9 that have a right angle between them. (reference choice A)

Answer:

-12,1

(-12î, 1j)

is the ans

Answer:

The answer is, (-12î, 1j)

Step-by-step explanation:

The ordered pair that describes the changes in the x- and y-values is the component form of a vector. the ordered pair that describes the changes is \((x_{2} -x_{1} ,y_{2} -y_{1} )\).

According, to the question:

= (-11-1),(-2+3)

= -12,1

= (-12î, 1j)

The component form are (-12î, 1j)

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Approximately 17.65% of Ana's salary is withheld for taxes.

To calculate the percentage of Ana's salary that is withheld for taxes, we need to determine the amount of tax withheld and then express it as a percentage of her net salary.

Number of hours worked per week (H) = 25 hours

Hourly wage (W) = $10

Net salary (S) = $212.50

Calculate the total earnings before taxes:

Total earnings = Hours worked * Hourly wage

Total earnings = 25 hours * $10/hour

Total earnings = $250

Determine the amount of tax withheld:

Tax withheld = Total earnings - Net salary

Tax withheld = $250 - $212.50

Tax withheld = $37.50

Calculate the percentage of salary withheld for taxes:

Percentage withheld = (Tax withheld / Net salary) * 100

Percentage withheld = ($37.50 / $212.50) * 100

Percentage withheld ≈ 17.65%

Therefore, approximately 17.65% of Ana's salary is withheld for taxes.

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