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The value of x, y, and z are 15/2,  (15√3)/2, and  (15√3)/2 after applying the trigonometric ratios.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

To find the value of x:

In right-angle triangle x-z-15:

sin30 = x/15

x = 15sin30 = 15/2

To find the value of y:

sin60 = y/x = y/(15/2)

sin60 = 2y/15

√3/2 = 2y/15

y = (15√3)/2

To find the value of z:

cos30 = z/15

√3/2 = z/15

z = (15√3)/2

Thus, the value of x, y, and z are 15/2,  (15√3)/2, and  (15√3)/2 after applying the trigonometric ratios.

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The real-life problem will be:- The total number of chocolates is 24 and there are 3 boxes what will be the number of chocolates filled in each box. The number of chocolates in each box will be 8.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The given expression is:-

[tex]24\times \dfrac{1}{3}[/tex] = 8

The real-life problem will be given the as:-The total number of chocolates is 24 and there are 3 boxes what will be the number of chocolates filled in each box. The number of chocolates in each box will be 8.

Hence the number of chocolates in each box will be 8.

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Answer:

1 1/2

Step-by-step explanation:

Convert both fractions into decimals

⇒ 3/4 (0.75) and 1/2 (0.50)

Divide the decimals:

⇒0.75 ÷ 0.50

Find the quotient

⇒ 1.5

Convert the quotient to a fraction

⇒ 1 1/2

Terms:

Operations with fractions

The rate of change of the function over the interval [ 4, 8 ] will be 6.

The rate of change function represents the rate at which one quantity changes in relation to another. Simply put, the rate of change is the difference between the amount of change in one item and the comparable amount of change in another.

Given function:-

The formula for calculating the rate of change will be given as:-

[tex]ROC = \dfrac{F(x_2)-F(x_1)}{x_2-x_1}[/tex]

We have x₁ = 4 and x₂ = 8 given in the question

F(x₂) =  x²₂ - 6x₂ + 10 = (8)² - ( 6 x 8 ) + 10 =

F(x₂) = 64 - 48 + 10

F(x₂) = 26

F(x₁) =  x²₁ - 6x₁ + 10 = (4)² - ( 6 x 4 ) + 10 =

F(x₁) = 16 - 24 + 10

F(x₁) = 2

[tex]ROC = \dfrac{F(x_2)-F(x_1)}{x_2-x_1}[/tex]

[tex]ROC = \dfrac{26 -2}{8-4}=\dfrac{24}{4}=6[/tex]

Therefore the rate of change of the function over the interval [ 4, 8 ] will be 6.

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The cost of the item whose price $ 55 is $ 50.

The cost price is the price paid by an individual to buy an item or any other commodity. Or this can also be taken as the total amount of money spent by the manufacturer to assemble a product or deliver a service.

Here, Price equation in terms of cost

       P = C + C/10

      P =  (10C+C)/10

      P = 11C/10

      C = 10P /11

For P = $ 55, the cost will be

      C = 10 X 55 / 11

      C = 10 X 5

      C = $ 50

Thus, the cost of the item whose price $ 55 is $ 50.

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The standard deviation is a better measure of spread for movies than it is for basketball games.

A box plot is a graphical rendition of statistical data based on the minimum, first quartile, median, third quartile, and maximum.

As, Movies is more centric to mean and not skewed on a particular side whereas basketball games is not centric to mean but is skewed right then left.

Now, Standard deviation just measures the deviation or spread with respect to mean of collected data.

So, In the movies the data is more collected. Thus standard deviation is best suited for movie data.

Now, interquartile range. IQR relies on if the data is skewed.

So, in the basketball data the standard deviation will not give the information.

Hence, the  standard deviation is a better measure of spread for movies than it is for basketball games.

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A die is tossed twice and a number of dots facing up in each toss are counted and noted in the order of occurrence.

a) The sample space is given as:

Sample Space (S)= {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5),(2,6),(3,1),(3,2),(3,3)(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1)(5,2)(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),c),(6,6)}.

A sample space is a collection of a set of possible outcomes of a random experiment. The sample space is represented using the symbol S.

b) the set corresponding to the event number of dots in the first toss is not less than the number of dots in the second toss.

{(6,6),(6,5)(6,3)(6,2)(6,1)(6,4),(5,1)(5,2)(5,3),(5,4),(5,5),(4,1),(4,2),(4,3),(4,4),(3,1),(3,2), (2,1), (2,2),(1,1)}

c) find the set b corresponding to the event number of dots in the first toss is 6.

{(6,1),(6,2),(6,3),(6,4),c),(6,6)}.

e) a does not imply b or does b imply a.

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The expression are; [tex](h - g) (x) = 3x^{3} -x^{2}[/tex], [tex](h + g) (x) = 3x^{3} +x^{2}[/tex] , [tex](h.g) (-1) = -3[/tex].

The function is a type of relation, or rule, that maps one input to specific single output.

Given function;

g(x) = [tex]x^{2}[/tex]

h(x) = [tex]3x^{3}[/tex]

The expression;

[tex](h - g) (x) = 3x^{3} -x^{2}[/tex]

[tex](h + g) (x) = 3x^{3} +x^{2}[/tex]

[tex](h.g) (-1) = x^{2} .3x^{3} \\\\(h.g) (-1) = 3x^5\\\\(h.g) (-1) = 3(-1)^5\\\\(h.g) (-1) = -3[/tex]

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Answer: Options 1 and 2

Step-by-step explanation:

To model exponential decay, the base of the exponential has to be less than 1.

Model exponential decay equation are

y = 0.34(0.98)^x

y = 8 (0.28)^x

Model exponential decay equation

Option C and D have the base value greater than 1. So it can't be model exponential decay equation.

Hence, the model exponential decay equation are

y = 0.34(0.98)^x

y = 8 (0.28)^x

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Answer: [tex]AB=4.7, BC=8.8, \angle C=28^{\circ}[/tex]

Step-by-step explanation:

As angles in a triangle add to 180 degrees,

[tex]\angle C=180^{\circ}-90^{\circ}-62^{\circ}=\boxed{28^{\circ}}[/tex]

We know that:

[tex]\sin 62^{\circ}=\frac{BC}{10}\\\\BC=10\sin 62^{\circ} \approx \boxed{8.8}[/tex]

Similarly,

[tex]\cos 62^{\circ}=\frac{AB}{10}\\\\AB=10\cos 62^{\circ} \approx \boxed{4.7}[/tex]

The length of the diagonal of the square is 22.05 units

A square have all its sides equal to each other.

Therefore, using Pythagoras theorem,

c² = a² + b²

c² = (9√3)² + (9√3)²

c² = 81 × 3 + 81 × 3

c² = 243 + 243

c² = 486

square root both sides

c = √486

c = 22.045407685

c = 22.05 units

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1200 pounds of protein supplement and 600 pounds of standard protein is used.

Let a be the protein supplement and b be the standard protein.

Given that protein supplement and standard protein make 1800 pounds of high grade protein.

i.e., a+b = 1800 ------- (1)

45% a + 15% b = 35% 1800

0.45a + 0.15b = 1800 (3.5)

By (1), a = 1800 - b

Substituting, we get

0.45 (1800-b) + 0.15b = 630

810 - 0.45 b + 0.15b = 630

- 0.3 b = - 180

b = -180/-0.3

b = 600

Substituting b = 600 in (1),

we get

a = 1200.

Hence, 1200 pounds of protein supplement and 600 pounds of standard protein is used.

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Answer: -1

Step-by-step explanation:

[tex]f(-1)=(-1)^2 - (-1)-1=1\\\\f(1)=1^{2}-1-1=-1\\\\\therefore \frac{f(-1)-f(1)}{-1-1}=\frac{1-(-1)}{-1-1}=\frac{2}{-2}=\boxed{-1}[/tex]

Answer:

y=5x

Step-by-step explanation:

A product means multiplication, and you need to multiply x by 5 in order to make the product have a factor of 5.

The expanded expressions are shown below:

Perfect square trinomials are polynomials of grade 2 with the form (a + b)² = a² + 2 · a · b + b². In this case, we have to expand six perfect square trinomials:

a) (x + 1)² = x² + 2 · x + 1

b) (x - 3)² = x² - 6 · x + 9

c) (x + 4)² = x² + 8 · x + 16

d) (x - 1/2)² = x² - x + 1/4

e) 3 · (x - 5)² = 3 · (x² - 10 · x + 25) = 3 · x² - 30 · x + 75

f) (1/2) · (x - 2)² = (1/2) · (x² - 4 · x + 4) = (1/2) · x² - 2 · x + 2

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Answer:

7s²7p⁴

Step-by-step explanation:

Livermorium is located in the seventh period and sixteenth column of the periodic table. The noble gas configuration for livermorium is [Rn]7s²5f¹⁴6d¹⁰7p⁴. The valence electrons are the ones in the orbitals with the highest quantum number (coefficient). Remember, there can be up to 8 valence electrons at one time. Therefore, the valence electron configuration is 7s²7p⁴.

Let's check

Electronic configuration

Valence electrons

Using proportions, considering the relation between the height and the shadow, it is found that the cell phone tower is 50 feet.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

When the shadow is of 8 feet, the height is of 10 feet. What is the height when the shadow is of 40 feet? The rule of three is:

8 feet - 10 feet

40 feet - h feet

Applying cross multiplication:

8h = 10 x 40

Simplifying by 8:

h = 10 x 5 = 50 feet.

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Using a calculator, the equation of the trend line that can be generated by using the data from years 1 and 5 is:

y = 6.75x + 81.25.

To find the equation, we need to insert the points (x,y) in the calculator.

In this problem, the points, in the format (x,y), are given as follows:

(1,88), (2,95), (3,100), (4,108), (5,115).

Hence, using a calculator, the regression line is:

y = 6.75x + 81.25.

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Answer:

.wfhytrsssssssssd

Step-by-step explanation:

dddddddddddddddddd

Answer:

x-intercept: (1,0)

y-intercept: (0,1)

Step-by-step explanation:

Given: Find the x and y intercepts of 2x + 2y = 2

To solve for a x - intercept we have to substitue 0 in for y and solve for [tex]x[/tex]

Lets do it:

2x + 2(0) = 2

2x + 0 = 2

2x = 2

x = 1

Therefore, this means that when y = 0, x = 1 or (1,0)

To solve for a y - intercept we have to substitue 0 in for x and solve for [tex]y[/tex]

Lets do it:

2(0) + 2y = 2

0 + 2y = 2

2y = 2

y = 1

Therefore, this means that when x = 0, y = 1 or (0,1)

Answer:

(5a - 8) + (2a² + 2a − 1) = 2a² + 7a - 9 - correct.

Step-by-step explanation:

(5a - 8) + (2a² + 2a − 1) = 2a² + 7a - 9 - correct;

(6² +6b-4) (3b +6²) = 26² +36-4 - incorrect (correct is: 18b²+...36²);

(9c-4c²) - (2c² + c) = -6c² + 10c - incorrect (correct is: -6c² + 8c).

Square perimeter =4x cm.

The complete length that a square's edge encompasses is referred to as its perimeter. Any enclosed geometric shape's perimeter may be computed by measuring the space around it.

By calculating the total of all the sides of a square, the perimeter may be determined. The perimeter of a square will be stated as,

The perimeter of square = s + s + s + s

⇒Perimeter of square = 4s, where "s" is the side length of the square.

This is because all edges of a square are equal and each edge measures "s" units.

Mathematically, the formula for calculating a square's perimeter is: Square perimeter, (P) = 4 Side

⇒P= 4x cm

It is concluded that the solution is 4x cm.

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Smaller angle = 50
Larger angle = 130

Let smaller angle be x degree

=> larger angle= [tex]3x - 20[/tex]

Since these angles are supplementary , So

[tex]= > x + 3x - 20 = 180\\= > 4x = 200\\= > x = 50\\= > 3x - 20\\ = > 150 - 20 = 130[/tex]

So smaller angle would be 50 deg & larger angle would be  130 deg.

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Answer:

26.2 feet

Step-by-step explanation:

tan(50°) = h/22

h = 22 × tan(50°) = 26.2 feet

Answer:

Answer:

x = 12

Step-by-step explanation:

m∠S + m∠T = 180

8x + 7x = 180

15x = 180

x = 12

does this help?

135inches2

Step-by-step explanation:

by multiplying both length and width you can get the sum

The average rate of change for the height of the plant measured in centimeters per day between day 0 and day 20 is 1.32 cm per day.

The average height is the ratio of change in height of the plant and the time taken taken for that change.

Given is the height of a plant in centimeters is modeled as a function of time, in days.

For day 0, the height is 18cm and the height for day 20 is 42 cm, then the average height change is

height per day = 42 - 18/ 20 -0

height per day  = 1.2 cm/day

Thus, the average height of plant is  1.2 cm/day.

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Answer:

D. x^6 - x + √6

Step-by-step explanation:

Last option:

⇒  x^6 - x + √6

Cannot be simplified further and has three terms.

Therefore is a trinomial.

The algebraic expression that is a trinomial is 2x³-x².

An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

A trinomial is a polynomial that has three terms.

In the given options, the only expression that has three terms is "2x³-x²". It has the terms 2x³, -x², and 0x (which is often omitted).

The other options have different numbers of terms or they have terms with fractional or radical exponents, which do not fit the definition of a trinomial.

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