Find the exact value of sin(x/2) if sec(x) = 7/3 and 400° < x < 430°

The amount of tea that is left after the student has drank is; ⁴/₅d mL

In word problems on fractions, what we do is that we will solve different types of problems on multiplication of fractional numbers and division of fractional numbers.

For example;

4/7 of a number is 84. Find the number.

Since 4/7 of a number = 84

The, the Number = 84 × 7/4

Number = 147

Now, in this question, we are given;

Quantity of tea in cup = d ml

Amount of tea a student takes out to drink = ¹/₅ of the quantity in the cup.

Thus;

Amount of tea left = d - ¹/₅d

Amount of tea left = ⁴/₅d

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The scale factor is 4/5.

In mathematics, a fraction represents a part of a whole. A fraction consists of two numbers separated by a horizontal line called a fraction bar or a division sign. The number above the bar is called the numerator, and the number below the bar is called the denominator.

The numerator represents the number of parts being considered, while the denominator represents the total number of parts in the whole. For example, in the fraction 3/4, 3 is the numerator and 4 is the denominator. This fraction represents three parts out of a total of four equal parts.

Fractions can be written in different forms, such as proper fractions, improper fractions, and mixed numbers.

A proper fraction has a smaller numerator than the denominator, such as 2/3 or 5/8.

An improper fraction has a numerator that is equal to or greater than the denominator, such as 7/4 or 11/6.

A mixed number consists of a whole number and a proper fraction, such as 2 1/3 or 3 2/5.

Fractions are used in many real-life situations, such as cooking, measuring, and financial calculations. They are also an essential part of mathematics and are used in operations such as addition, subtraction, multiplication, and division.

To find the scale factor, we can compare the ratios of the corresponding side lengths of the congruent triangles.

Scale factor = (corresponding side length in triangle FQX) / (corresponding side length in triangle CVI)

Let's first identify the pairs of congruent angles:

Angle FQX = angle CVI (both are right angles)

Angle XQF = angle ICV (corresponding angles)

Angle FXQ = angle CVI (corresponding angles)

Now let's write the ratios of the corresponding side lengths in a proportion:

FQ / CV = QX / VI = XF / IC

Substituting the given values, we have:

28 / 35 = 36 / 45 = 24 / 30

Simplifying each fraction, we get:

4 / 5 = 4 / 5 = 4 / 5

Therefore, the scale factor is 4/5.

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Let's denote the amount Jolene invested at 3 percent interest as 'x' dollars. Since she put twice as much in the lower-yielding account, the amount she invested at 9 percent interest would be '2x' dollars.

To calculate the interest earned from each account, we'll use the formula: Interest = Principal × Rate × Time.

For the 3 percent interest account:

Interest_3_percent = x × 0.03

For the 9 percent interest account:

Interest_9_percent = 2x × 0.09

We know that the total annual interest is $3120, so we can set up the equation:

Interest_3_percent + Interest_9_percent = 3120

Substituting the above equations, we have:

x × 0.03 + 2x × 0.09 = 3120

Simplifying the equation:

0.03x + 0.18x = 3120

0.21x = 3120

Dividing both sides of the equation by 0.21:

x = 3120 / 0.21

x = 14857.14

Therefore, Jolene invested approximately $14,857.14 at 3 percent interest and twice that amount, $29,714.29, at 9 percent interest.

Answer:

Step-by-step explanation:

X is the amount invested at 6%

Y is the amount invested at 9%

0.06X + 0.09Y = 4998

X = 2Y

0.06(2Y) + 0.09Y  = 4998

.12Y + 0.09Y = 4998

0.21Y = 4998

21Y = 499800

Y = 499800/21 = 23800

So X = 2*23800 = 47600

$47,600 is invested at 6% and $23800 is invested at 9%

Answer:

Step by step explanation:

well this is simble you just do it

The value of the n is 1

In a direct variation, the relationship between two variables is of the form y = kx, where k is a constant of proportionality.

To find the constant of proportionality k in this problem, we can use the fact that the given points satisfy the equation for direct variation.

(2,18) is one of the given points, so we can substitute these values into the equation y = kx and solve for k:

18 = k(2)

k = 18/2

k = 9

Now that we have found the value of k, we can use it to find n when y = 9:

9 = 9n

n = 1

Therefore, the value of n is 1.

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Answer:

75cm2 is right I think

Step-by-step explanation:

Hope this helps

The value of measure of x in the triangle is,

⇒ x = 4√3 units

We have to given that,

A triangle is shown in image.

Now, WE can formulate by trigonometry formula we get;

⇒ tan 30° = Opposite / Base

⇒ tan 30° = 4 / x

⇒ 1/√3 = 4/x

⇒ x = 4√3 units

Thus, The value of measure of x in the triangle is,

⇒ x = 4√3 units

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Answer:

a c

Step-by-step explanation:

Answer:

(a) 44%

(b) 32%

Step-by-step explanation:

(a) In order to find the percentage of students that prefer comedies, we can add up divide the sum of the total number of students who prefer comedies (Twice/month or less + Thrice/month or more) by the total number of students.  

Then, we can multiply this number by 100 to find the percentage:

\((\frac{45+21}{150})*100\\ (\frac{66}{150})*100\\ 44\)

(b) To find the percentage of students who visit the movies three times a month or more, we can divide the sum of the total number of students who visit the movies three times a month or more by the total number of students.

Like before, we can multiply this number by 100 to find the percentage:

\((\frac{21+27}{150})*100 \\(\frac{48}{150})*100\\ 32\)

The system of equations as an augmented matrix is \(\left[\begin{array}{ccc|c}1&0&0&100\\0&-5&-7&350\\0&-5&-9&200\end{array}\right]\)

From the question, we have the following parameters that can be used in our computation:

x                  = 100

   -5m  - 7c  = 350

   -5m  - 9c  = 200

The above means that the variables in the system of equations are

x, m and c

So, we have the following representation

x    m     c        

1    0      0        100

0   -5    -7        350

0   -5    -9        200

When represented as an augmented matrix, we have

\(\left[\begin{array}{ccc|c}1&0&0&100\\0&-5&-7&350\\0&-5&-9&200\end{array}\right]\)

Hence, the augmented matrix is \(\left[\begin{array}{ccc|c}1&0&0&100\\0&-5&-7&350\\0&-5&-9&200\end{array}\right]\)

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Let’s solve the equation x^2 - 4x = 5 by factoring:

First, we’ll move all the terms to one side of the equation:

x^2 - 4x - 5 = 0

Now, we’ll factor the left side of the equation. We’re looking for two numbers that multiply to -5 and add to -4. Those numbers are -5 and 1. So we can write:

(x - 5) (x + 1) = 0

Now we’ll use the zero-product property to solve for x. This property states that if the product of two numbers is zero, then at least one of the numbers must be zero. So we have:

x - 5 = 0 or x + 1 = 0

Solving each equation separately, we find that x = 5 or x = -1.

So, the solutions to the equation x^2 - 4x = 5 are x = 5 and x = -1.

Answer:

But it's your work so you shouldn't be the one complaining. You are depending on us.

Btw, the answer is deleted.

Answer:

the answer is lemme cop these 5 points real quick

Answer: Let's assume the rental cost for each movie is M and the rental cost for each video game is G. Then we can set up a system of two equations based on the given information:

3M + 8G = 53 (equation 1)

5M + 2G = 26 (equation 2)

We can use any method to solve this system of equations, but let's use the elimination method by multiplying equation 1 by 2 and subtracting it from equation 2:

10M + 4G = 52 (multiplying equation 1 by 2)

(3M + 8G = 53) (subtracting equation 1 from equation 2)

7M - 4G = -1 (resulting equation)

Now we can solve for one variable in terms of the other. Let's solve for M:

7M - 4G = -1

7M = 4G - 1

M = (4G - 1)/7

We can substitute this expression for M into either equation 1 or equation 2 to solve for G. Let's use equation 2:

5M + 2G = 26

5[(4G - 1)/7] + 2G = 26 (substituting for M)

(20G - 5)/7 + 2G = 26

20G - 5 + 14G = 182 (multiplying both sides by 7 to eliminate the denominator)

34G = 187

G = 187/34

Now we can substitute this value for G into the expression we found for M to get:

M = (4(187/34) - 1)/7 = 3.5

Therefore, the rental cost for each movie is $3.50, and the rental cost for each video game is approximately $5.50 (rounded to the nearest cent).

To check our solution, we can verify that it satisfies both equations:

3(3.5) + 8(5.5) = 53 (first month rental cost)

5(3.5) + 2(5.5) = 26 (second month rental cost)

Both equations are satisfied, so we can be confident in our solution.

Step-by-step explanation:

If the value of sin x = 0.2, then the values for sin(π - x) is 0.2.

Given that,

the value of sin x = 0.2

We have to find the value of sin(π - x).

We know the trigonometric rule that,

sin(π - x) = sin (x)

for any value of x.

So here whatever the value of x, the value of  sin(π - x) is sin (x) itself.

So here sin x = 0.2.

So, by the rule,

sin(π - x) = sin (x) = 0.2

Hence the value is 0.2.

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Answer:

21

Step-by-step explanation:

Answer:

1.67

Step-by-step explanation:

25/15 = 1.67

The mean is estimated by dividing the total of the values by the range of values.

Answer:

There is no mode

Step-by-step explanation:

Mode is the most occurring no. and there's no number which is the most occurring.

Answer:

No mode

Step-by-step explanation:

In a set of numbers, mode is the most repeated number.

1, 4, 24, 14, 98, 37

There are no repeated numbers in this set.

Answer:

C

Step-by-step explanation:

I just did the test rn hopefully I came in time

Answer:

7, 2, -3, -8

Step-by-step explanation:

y = -5x + 2  Substitute in -1 for x

y = -5(-1) + 2

y = 5 + 2

y = 7

y = -5x + 2  Substitute in 0 for x

y = -5(0) + 2

y = 0 + 2

y = 2

y = -5 + 2 substitutes in 1 for x

y = -5(1) + 2

y = -5 + 2

y = -3

y = -5x + 2  Substitute in 2 for x

y = -5(2) + 2

y = -10 + 2

y = -8

Helping in the name of Jesus.

Answer:

720 I think not sure if im right

Answer: 720 pennies

Step-by-step explanation:

1/2 = 3/6 and 2/3 = 4/6

So the 120 pennies she added was 1/6 of the total size

6 x 120 = 720

The equation of the line is 2x + 5y = 11 hat passes through the points (3,1) and (-2,3)

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

\(\rm m =\dfrac{y_2-y_1}{x_2-x_1}\)

We have two points:

(3,1) and (-2,3)

The equation of the line passing through the points (3,1) and (-2,3)

\(\rm (y - 3) = \dfrac{3-1}{-2-3}(x+2)\)

\(\rm (y - 3) = -\dfrac{2}{5}(x+2)\)

5y - 15 = -2x - 4

2x + 5y = 11

Thus, the equation of the line is 2x + 5y = 11 hat passes through the points (3,1) and (-2,3)

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The area of the figure is equal to 400+32pi \(in^{2}\).

What is a semi-circle?

A semicircle is a half circle created by splitting a circle into two equal parts. It is created when a line pierces the circle's center and touches its two ends.

The given figure consists of a rectangle and a semicircle.

We will individually find the area of the rectangle and the semi-circle and we will at those two to get the area of the given figure.

The length of the sides of the rectangle is 25 inches and 16 inches.

The area of the rectangle is the product of length and width which is equal to 400.

The diameter of the semi-circle is equal to 16 in, so the radius of the semi-circle is equal to 8 in.

The area of the semi-circle is equal to \(\frac{\pi r^{2} }{2} =\frac{\pi 64}{2} =32\pi\).

The total area is equal to 400+32pi \(in^{2}\).

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Answer:

A is the answer

Step-by-step explanation:

did the test hope this helps

Balloon mortgage with balloon payment paid in full, will pay off the mortgage in the shortest time.

A mortgage is a loan that is used to purchase real estate (such as a house) with the property being used as collateral for the loan.

Here, we are given that balloon mortgage is a type of loan that requires a lump sum payment at the end of the loan term (the "balloon payment").

Option A involves paying off the entire mortgage balance at the end of the term, which will result in paying off the mortgage in the shortest amount of time.

A 30-year fixed mortgage and a 7/1 ARM will take 30 years and 7 years plus the adjustment period, to pay off the mortgage.

In a Balloon mortgage with a balloon payment refinanced at a lower rate, the mortgage would still be outstanding after the balloon payment, and the borrower will need to refinance to a new mortgage to continue making payments.

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Therefore, the solution to the given problem is that the upper bound for P(X>15) is 3/25

The variance is the difference between the numbers in a set of data, to put it simply. Each number's variability is a statistical statistic that indicates how far off from the mean and from each other number in the set it is.

Here,

Given : mean = 10

varience = 3

Using chebyshevs inequality we have

P(|X-u| ≥ k)≤ \(\sigma^{2}\)/\(k^{2}\)

hence we can have,

=> P(X>15)  ≤ 3/\(5^{2}\)

=> P(X>15)  ≤ 3/25

Therefore, the solution to the given problem is that the upper bound for P(X>15) is 3/25

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Answer:

10/12?

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

3^x +1 = f(X)

2x-4 = g(x)

find f(2)-g(-1)

we substitute in function f(X) by value (2), and in function g(X) by value (-1)

1. 3^x +1 becomes 3^2+1 =9+1=10

2. 2(-1)-4= -2-4=-6

then f(2)-g(-1)

= 10-(-6) =10+6=16

Answer:

A. t(n) = 20 + 60n

Step-by-step explanation:

$20 is the money Rob had before washing windows.

He earns $60 in each of the first three weekends. So he gains an additional $60 for each weekend.

n = the number of weekends

the total amount of dollars he will have is 20 + 60n

Answer:A. t(n) = 20 + 60n

Step-by-step explanation:

$20 is the money Rob had before washing windows.

He earns $60 in each of the first three weekends. So he gains an additional $60 for each weekend.

n = the number of weekends

the total amount of dollars he will have is 20 + 60n

Answer:

There are 77,899 books in the library

Step-by-step explanation:

1 step

41,362 - 4825 =36,537

2 step

41,362 + 36537 = 77,899

Answer:

11:24am

Step-by-step explanation:

10:45 to the nearest hour is 11am

It takes 15mins to reach the hour. (39-15=24)

Add the remaining 24minutes to the hour and you have your answer.

11:24am