Can someone help me with this?

a. The trigonometric ratio sin(Ф/2) = +√(3/10)

b. The trigonometric ratio cos(Ф/2) = +√(7/10)

Trigonometric ratios are the ratios of the sides of a right-angled triangle. They include

where Ф is the angle between the sides

Given that cosФ = 2/5, we use the trigonometric identity

cosФ = 1 - 2sin²(Ф/2)

Making sin(Ф/2) subject of the formula, we have

sin(Ф/2) = ±√(1 - cosФ)/2

So, susbstituting the value of cosФ = 2/5 into the equation, we have

sin(Ф/2) = ±√(1 - cosФ)/2

sin(Ф/2) = ±√(1 - 2/5)/2

sin(Ф/2) = ±√[(5 - 2)/5]/2

sin(Ф/2) = ±√(3/[5 × 2])

sin(Ф/2) = ±√(3/10)

Since Ф is in the first quartile, sin(Ф/2) = +√(3/10)

Given that cosФ = 2/5, we use the trigonometric identity

cosФ = 2coss²(Ф/2) - 1

Making sin(Ф/2) subject of the formula, we have

coss(Ф/2) = ±√(1 + cosФ)/2

So, susbstituting the value of cosФ = 2/5 into the equation, we have

coss(Ф/2) = ±√(1 + cosФ)/2

cos(Ф/2) = ±√(1 + 2/5)/2

cos(Ф/2) = ±√[(5 + 2)/5]/2

cos(Ф/2) = ±√(7/[5 × 2])

cos(Ф/2) = ±√(7/10)

Since Ф is in the first quartile, cos(Ф/2) = +√(7/10)

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The solutions to the system of equations formed by the linear equation 9 · x + 9 · y - 79 = 0 and the quadratic equation x² + 5 · x - y - 4 = 0 are (x₁, y₁) = (5 / 3, 64 / 9) and (x₂, y₂) = (- 23 / 3, 148 / 9).

Herein we find a system of equations formed by a linear equation and a quadratic equation. This system must be resolved by means of algebra properties. First, write the system of equations:

9 · x + 9 · y - 79 = 0

x² + 5 · x - y - 4 = 0

Second, clear the variable y in the first equation:

9 · x + 9 · y - 79 = 0

9 · y = 79 - 9 · x

y = 79 / 9 - x

Third, substitute y on the second equation:

x² + 5 · x - (79 / 9 - x) - 4 = 0

x² + 6 · x - 115 / 9 = 0

Fourth, use the quadratic equation to find the solutions of x:

x₁ = 5 / 3, x₂ = - 23 / 3

Fifth, calculate the solutions of y:

y₁ = 79 / 9 - x₁

y₁ = 64 / 9

y₂ = 79 / 9 - x₂

y₂ = 148 / 9

The solutions are (x₁, y₁) = (5 / 3, 64 / 9) and (x₂, y₂) = (- 23 / 3, 148 / 9).

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Answer:

All beds come in different shapes and sizes but for example a queen sized mattress is 60” x 80”

Step-by-step explanation:

The score that Avery must get on Exam B is given as follows:

470.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.

For exam A, the mean and the standard deviation are given as follows:

[tex]\mu = 350, \sigma = 20[/tex]

She scored 310, hence the z-score of her grade is given as follows:

Z = (310 - 350)/20

Z = -2.

For exam B, the mean and the standard deviation are given as follows:

[tex]\mu = 550, \sigma = 40[/tex]

To do as well as on exam A, she needs a z-score of -2, hence the grade X is obtained as follows:

-2 = (X - 550)/40

X - 550 = -80

X = 470.

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Ansel has to pay an interest of $167.4 per months for the the life of the loan to the Hampton County Bank.

The formula for the monthly installments are-

M = P(r/12)(1 + r)∧12t / (1 + r)∧12t - 1

Put the values;

Principal P =$10,000.

Rate of interest r = 6.35%

Time t = 6 years 72 months

M =  10,000(0.0635/12)(1 + 0.0635)∧72 / (1 + 0.0635)∧72 - 1

M = $167.4

Thus, Ansel has to pay an interest of $167.4 per month for the the life of the loan to Hampton County Bank.

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Answer:210 miles

Step-by-step explanation:Gary walking in opposite directions will calculate how long it takes for him to be a given distance apart.

Answer:

The answer would be One solution.

Step-by-step explanation:

y=3x+2;y=2x+2

Step: Solve y=3x+2 for y:

y=3x+2

Step: Substitute 3x+2 for y in y=2x+2:

y=2x+2

3x+2=2x+2

3x+2+−2x=2x+2+−2x(Add -2x to both sides)

x+2=2

x+2+−2=2+−2(Add -2 to both sides)

x=0

Step: Substitute 0 for x in y=3x+2:

y=3x+2

y=(3)(0)+2

y=2(Simplify both sides of the equation)

Answer:

x=0 and y=2

If it was no solution you would not be able to solve. If it was infinite then there would be infinite solutions, but there is not so One Solution is the answer.

Answer:

[tex]\dfrac{1}{3}[/tex]

Step-by-step explanation:

Divide the area of the square by the area of the triangle.

[tex]\dfrac{A_{\textrm{square}}}{A_{\textrm{triangle}}} = \dfrac{3^2}{(9\times 6)\div 2}[/tex]

And simplify.

[tex]= \dfrac{9}{54 \div 2}[/tex]

[tex]= \dfrac{9}{27}[/tex]

[tex]=\dfrac{1}{3}[/tex]

Answer:

0.783

Step-by-step explanation: got it right :)

For the inequality 4x ≤ 28 the solution that makes the inequality true will be x≤7.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

It is given that the inequality is 4x ≤ 28.

Now that the equation has been simplified, we obtain both sides of the inequality equation, divide by 4, and we obtain

x ≤ 7

As a result, x must be less than or equal to 7.

The requirement for x is satisfied by any numbers that are less than or equal to 7.

Thus, for the inequality 4x ≤ 28 the solution that makes the inequality true will be x≤7.

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Answer:

a

Step-by-step explanation:

7

Answer:

-2

Step-by-step explanation:

1. Identify two points with integer (not fraction or decimal) coordinates:

  Ex: (0,5) and (3,-1)

2. subtract the y-coordinates: -1-5 = -6

   and the x- coordinates (IN THE SAME ORDER): 3-0 = 3

3. divide the difference in y (-6) by the difference in x (3): -6/3 = -2

The number of miles travelled by the family in one week is 700 miles

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

Charges per week = $160

Charges per mile = $0.25

Total charges = $335

The above parameters mean that

Total charges = Charges per week + Charges per mile x Number of miles

Substitute the known values in the above equation, so, we have the following representation

160 + 0.25 * Number of miles = 335

This gives

0.25 * Number of miles = 175

Multiply both sides by 4

Number of miles = 700

Hence, the number of miles is 700

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The total distance traveled on the bicycle is 2500m

The total time the bike traveled is 19.4 minutes.

The average speed (in meters/min) of the bicyclist for this trip is 128.9 m/minutes.

Speed is the rate at which an object's location changes in a particular direction. The distance traveled on relation changes to a particular direction. The distance in relation to the time it took to travel the distance is the speed.

The total distance traveled on the bicycle will be:

= 800 + 500 + 1200

= 2500m

The total time the bike traveled will be:

= 1.4 + 16 + 2

= 19.4 minutes

Speed = Distance / Time

= 2500 / 19.4

= 128.9 meters per minute

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Answer: 29

Step-by-step explanation: your welcome

The amount of money after 18 years when the interest is compounded continuously is $15725.

The process of calculating interest and reinvesting it in an account's balance over an infinite number of periods is known as continuous compounding.

Given that Levi invested $8,500 in an account paying an interest rate of 3.4% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest ten dollars?

The compound interest will be calculated as

[tex]P(t) = P_oe^{rt}[/tex]

[tex]P(t) = 8500\times e^{0.034\times 18}[/tex]

P(t) = 8500 x 1.85

P(t) = $15725

Therefore, the amount of money after 18 years when the interest is compounded continuously is $15725.

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Answer:15670

Step-by-step explanation:

Step-by-step explanation:

1). Red

x² = 98² - 44² = 9604 - 1936 = 7668

x =√7668 = 6√213

2) orange

X² = 31²+30² = 1861

x = √1861

The common ratio of given geometric sequence is r = - (1/2)

A geometric sequence is a set of integers that follows a pattern where each term is multiplied by a fixed number called the common ratio, or r, to find the following term.

solution:

a3 = - (3/8)

a8 = 3/256

common ratio = a3 / a8

                        = - (3/8) / 3/256

common ratio = - (1/32)

a8/a3 = (ar^7) / (ar^2)

          = r^5

r^5 = - (1/32)

    r = - (1/2)

Hence the common ratio of given geometric sequence is r = - (1/2)

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Answer:

Step-by-step explanation:

= 604800

The final interval notation is  F ∩ H = [7, 4] &  F ∪ H = [-∞, ∞].

What is the interval notation?

A set of real numbers known as an interval in mathematics contains all real numbers falling inside any two of the set's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 x 1.

We have,

F and H are sets of real numbers defined as follows.

F = { v l v < 4}

H = { v l v ≥ 7}

F is the set of all real numbers that are less than or equal to 4.  H is the set of real numbers greater than 7.

F U H is the union (or combination) of the two sets, so it is the set of all real numbers that are less than equal to 3 or greater than 6:

F ∩ H is the set of real numbers that are in both sets; but since F is less than or equal to 4 and H is greater than 7, there are no numbers that are in both sets.  Hence the answer is the empty set, Ø:

F ∩ H = Ø

F ∩ H = [7, 4]

F ∪ H = [-∞, ∞]

Hence, the final interval notation is  F ∩ H = [7, 4] &  F ∪ H = [-∞, ∞].

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Answer:

The quickest answer is to take the number 72 and divide it by the rate of interest. In this case, it would take approximately 72/6, or 12 years to double.

Step-by-step explanation:

Answer:

The pattern is a repeated triangle and circle.

So, the next shape would be a triangle and a circle.

Step-by-step explanation:

Answer:

distributive property

Answer:

The answer is e

Step-by-step explanation:

Based on the four scenarios of statistical studies given, a study which uses a sample statistic is: D. As part of her senior project, Kaisa asked 84 of her classmates if they voted in the last presidential election, 39 said yes.

In Mathematics and Statistics, a sample statistic can be defined as a small piece of statistical information that is obtained by a researcher or scientist from the sample of a population.

This ultimately implies that, a sample statistic simply refers to any numerical quantity (figure) or data that is generated from the sample of a population by a researcher or scientist.

In this context, we can reasonably infer and logically deduce that 84 of Kaisa's classmates represent the sample of the total population while the 39 classmates who answered yes represent the sample statistic.

In conclusion, the statistical study that was conducted by Kaisa is a study that represent the sample statistic.

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Complete Question:

Four scenarios of statistical studies are given below. Decide which study uses a population parameter.

The average finish time for the Ironman, Kona was 11:32 for the 1883 finishers, with an average swim time of 1:14, an average bike time time of 4:14.

Lakeside Family Dentistry reported that 6 of the 15 patients who came in for a regular cleaning one day had at least one cavity.

Of 351 dog owners who were surveyed, 70 reported owning two dogs.

As part of her senior project, Kaisa asked 84 of her classmates if they voted in the last presidential election, 39 said yes.

Since only the lengths increase by scale factor,  B'C' on the same line as its corresponding side segment BC​ .

What is the Dilation?

Math definition of dilation Resizing an object is accomplished through a change called dilation. The objects can be enlarged or shrunk via dilation. A shape identical to the source image is created by this transformation. The size of the form does, however, differ.

The following are the properties of dilation of the triangle:

1)measures of the angles will not change

2)The sides  of the image of the triangle are multiplied  by the scale factor 2.

So,

A'B'=2AB

B'C'=2BC

A'C'=2AC

Since only the lengths  increase by scale factor,  B'C' on the same line as its corresponding side segment BC​ .

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The circumference of a circle with one-third the curvature of a circle of radius 1 is 18.85 units

What is circumference ?

The perimeter of a circle is known as its circumference. It is the length of the circle's whole perimeter. The diameter of a circle and the constant are multiplied to get the circumference of the circle. This measurement of a circle's circumference is necessary for someone to cross a circular park or for a circle-shaped table to have a border. The units of the circumference are the same as the units of length and it is a linear value.

If a circle has a radius of 1,

the curvature is inversely proportional to this

So, the curvature= 1

A circle with a curvature of 1/3 :

radius=3

Thus, the circumference of the circle  =  2 *π * radius

                                                               =  2*π * 3

                                                               =  6π

                                                               ≈ 18.85 units

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Answer:

17.3

Step-by-step explanation:

The value of the variable x in the equation xˣ²⁻²ˣ⁺¹ = 2x + 1 is  1 + √2

An equation is a mathematical statement that shows that two mathematical expressions are equal.

An equation combines two expressions connected by an equal sign. These two expressions on either side of the equals sign are called the “left-hand side” and “right-hand side” of the equation. We generally assume the right-hand side of an equation is zero.

Basically, an equation is a statement that equate or says two expressions are equal to one another.

The problem given may be assumed as an exponential equation

xˣ²⁻²ˣ⁺¹ = 2x + 1

Solving for x by isolating the variable;

x = 1 + √2

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Answer:

  x = 1 ±√2

Step-by-step explanation:

You want to solve the exponential equation ...

  x^(x² -2x +1) = 2x +1

without using a calculator.

There are no algebraic methods for solving such an equation.

We can solve quadratic equations, so we can guess that the exponent of x is 2:

  x² -2x +1 = 2

  x² -2x -1 = 0

Using 2 as an exponent, the given equation becomes ...

  x² = 2x +1 . . . . . . . exponent on the left is 2

  x² -2x -1 = 0

That is, the exponent being 2 is consistent with the requirements on x.

The solution to the quadratic can be found using the quadratic formula:

  x² -2x -1 = 0

  x = (-(-2) ±√((-2)² -4(1)(-1))/(2(1)) = (2±2√2)/2

  x = 1±√2

Either of these values will make the exponent of x be 2, so both are solutions to the equation. The negative solution is not found by the graphing calculator (attached).

Answer: d = -8

Step-by-step explanation: look at the attached link

(a) The probability that the first person selected is a pledge is; 10/35

(b) The probability that the first person selected is not a pledge is; 25/35

(c) The probability that the second person selected is a pledge if the first person selected was also a pledge is; 9/34

We are given;

Total number of members in the Sorority = 35

Number of full members = 25

Number of members that are pledges = 10

Formula for probability is;

Probability = Number of Favorable Outcomes / Total Number of Outcomes.

1) Probability that the first person selected is a pledge = number of pledges/total number of members = 10/35

2) Probability that the first person selected is not a pledge = 1 - (Probability that the first person selected is a pledge)

= 1 - 10/35 = 25/35

3)  If the first person selected was also a pledge, then for the second pledge, one pledge is out, so we have 9 pledges in 34 people.

P = number of pledges / total = 9/34

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Complete question is;

A sorority has 35 members, 25 of whom are full members and 10 are pledges. Two persons are selected at random from the membership list of the sorority. Find the requested probabilities. (Enter the probabilities as fractions.)

(a) The first person selected is a pledge.

(b) The first person selected is not a pledge.

(c) The second person selected is a pledge if the first person selected was also a pledge.