The height h (in feet) of a swing above the ground can be modeled by the function h=−8cosθ+10 , where the pivot is 10 feet above the ground, the rope is 8 feet long, and θ is the angle that the rope makes with the vertical. Graph the function. What is the height of the swing when θ is 45º? Round your answer to the nearest tenth. The height is about feet.

The value  0.24 as a fraction is 6/25. .

In mathematics, fractions are defined as part of a whole. A whole can be an object or a group of objects. In real life, if you cut a pie out of the whole pie, that piece becomes part of the pie. Fractions are words of Latin origin. "Fractus" means "broken" in Latin. In ancient times, rest was expressed in words. Later it was introduced in numerical form.

Fractions are also called parts or sections of any quantity. Represented by the symbol '/'. Bachelor/Bachelor For example, 2/4 is the numerator above and the fraction below the denominator. In this article, you will learn the definition of fractions in mathematics, types of fractions, how to convert fractions to decimals, and many solved examples and full explanations

to convert in fraction we will muliply and devide by 100.

0.24*100/100 =6/25

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The geometric mean of two numbers is the square root of their product. Hence, the geometric mean 'a' of 2 and 1/4 is approximately equal to 0.70710678118.

Recall that the geometric mean of two numbers is the square root of their product. This means that we need to multiply the two numbers (2 and 1/4) and then take the square root of the result.

Multiply 2 and 1/4:

2 × 1/4 = 1/2

Take the square root of the result:

a = √(1/2)

Simplify the square root:

a = √(1/2) = √(1)/√(2) = 1/√(2)

Rationalize the denominator by multiplying the top and bottom by √(2):

a = (1/√(2)) × (√(2)/√(2)) = √(2)/2

Approximate the result to a desired level of accuracy, if necessary. In this case, rounding to 11 decimal places gives:

a ≈ 0.70710678118

Therefore, the geometric mean 'a' of 2 and 1/4 is approximately equal to 0.70710678118

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Therefore , the solution of the given problem of parallelograms comes out to be ∠y = 62 degree.

A simple square with two sets of equal intervals is referred to as a parallelogram in Euclidean geometry. The opposite ends of a parallelogram, a special type of quadrilateral, were both straight and equal. There are four distinct parallelogram types, and two of them are exclusive of one another. The four different shapes are rhombuses, equilateral triangles, triangles, and rectangles. A quadrilateral is a parallelogram if it has two pairs of parallel sides.

Here,

Given :

A  parallelogram ABCD and a triangle AED

So,

To find angle y:

∠D + 118 = 180

=> ∠D = 180 -118

=>∠D= 62 Degree

So,

According to alternate interior angle :

∠D= ∠y

=> 62 = ∠y

Thus ,∠y = 62 degree.

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Answer: The function of graph 2 has a higher rate of change than the function of graph 2

Step-by-step explanation:

Answer:

1/10

Step-by-step explanation:

Puppy food portions.

Unish Baskota

Kennedi is feeding her 5 puppies. She has half a bag of dog food left. How much of the bag

will each puppy receive?

If Kennedi has half a bag of dog food left and she has 5 puppies to feed, then each puppy will receive 1/5th of the remaining dog food.

To calculate this, you can divide the remaining dog food (which is half a bag) by the number of puppies (which is 5):

1/2 bag of dog food ÷ 5 puppies = 1/10 bag of dog food per puppy

So each puppy will receive 1/10th of the bag of dog food.

Each puppy would receive 1/10 of food

Answer:

$0.07

Step-by-step explanation:

We know

It cost Nevaeh $5.39 to send 77 text messages.

How much does it cost to send one text?

We take

5.39 / 77 = $0.07 per text

So, it costs $0.07 to send one text.

It costs Nevaeh $0.07 to send one text message.

In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.

To find out how much it costs to send one text message, we can divide the total cost by the number of messages:

Cost per message = total cost/number of messages

In this case, the total cost is $5.39 and the number of messages is 77, so:

Cost per message = $5.39 / 77 = $0.07

Therefore, it costs Nevaeh $0.07 to send one text message.

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The conversion of 77 f to c is equal to 25°C.

To convert temperatures in degrees Fahrenheit to Celsius, deduct 32 and multiply by .5556 ( or 5/9).

Temperatures, across the world, are measured either in Fahrenheit( the US temperature scale) or Celsius( the metric scale), two of the most popular and extensively used scales.

Temperature Conversion- Degrees Fahrenheit into Degrees Celsius.

To convert a temperature from Fahrenheit (°F) to Celsius (°C),  we can use the formula:

°C = (°F - 32) x 5/9

By applying this formula, we can convert 77 °F to Celsius as follows

°C = (77 - 32) x 5/9

°C = 45 x 5/9

°C = 25

Therefore, 77°F is equal to 25°C.

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Answer:

11 /16

Step-by-step explanation:

There are 4 possible answers for the first question and 5 possible answers for the second question, so there are a total of 4 x 5 = 20 possible outcomes.

A set of potential outcomes from a random experiment is known as a sample space. The sample space is identified by the letter "S." Events are the subset of possible experiment results.The results in a sample area could vary depending on the experiment. Discrete or finite sample spaces are those that have a finite number of outcomes.

The sample space showing all possible outcomes of the two questions is the Cartesian product of the two sets of answer choices, which is:

{(A, A), "(A, B), "(A, C), "(A, D), "(A, E), "(C, A), "(C, B), "(C, C), "(C, D), "(C, E")," "(D, A), "(D, B), "(D, C), "(D, D), "(D, E)}.

There are 4 possible answers for the first question and 5 possible answers for the second question, so there are a total of 4 x 5 = 20 possible outcomes. Each outcome is a pair of answers, where the first element of the pair is the answer to the first question and the second element of the pair is the answer to the second question.

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The temperature in Fahrenheit that is equal to 17 degree Celsius is  62.6 Fahrenheit .

The Celsius (°C) and Fahrenheit (°F) are two common temperature scales which are used to measure the temperature. Celsius is based on the metric system, and is widely used in most countries. Fahrenheit, on the other hand, is used mostly in the United States and a few other countries.

We use the the formula "°F = (°C × 1.8) + 32" , to convert the temperature from degree Celsius to degree Fahrenheit ;  

In this case  , we have to convert 17 Celsius to Fahrenheit,

So , we can write the formula as : °F = (°C × 1.8) + 32

⇒ °F = (17 × 1.8) + 32 ;

⇒ °F = 30.6 + 32 ;

⇒ °F = 62.6  .

Therefore, 17 Celsius is equal to 62.6 Fahrenheit .

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Answer:

no solution

Step-by-step explanation:

7 | y + 6 | + 3 < - 18 ( subtract 3 from both sides )

7 | y + 6 |  < - 21 ( divide both sides by 7 )

| y + 6 | > - 3

the absolute value function cannot be negative

thus the equation has no solution

Answer:

1=24.5

Step-by-step explanation:

2*2=98

4=98

2= 49

which means

1 is 24.5

The measurement of the LM will be 42.0

The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC² = AB² + AC² in the triangle ABC signifies this. Base AB, height AC, and hypotenuse BC are all used in this equation. The longest side of a right-angled triangle is its hypotenuse, it should be emphasized.

Here given in the question that one side of the wall 5 feet

So as it is a rectangular bedroom it can be split into 2 right-angled triangles.

So the hypotenuse of the triangle is 13 feet

Now using the Pythagoras theorem we can find out the length of the other wall

b² = h² -p²

given KM = 52, NL = 33

So the triangle MLN

LM = √(33²+26²) = 42.0

Hence The measurement of the LM will be 42.0

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The number of  used games consoles is 9 and the number of new game consoles is 5

Here we use the Linear equation method to solve the problem. Since we don't know the number games, represent them with variables x and y.

Now for two linear equations according to the conditions as given in the problem. Solve the equations for the values of both x and y by using the substitution method.

Here we have

An electronics store sells used game consoles for $79.00 and new ones for $149.00

Let 'x' and 'y' be the number of used and new game consoles respectively

Cost of 'x' used games consoles = 79x

Cost of 'y' new game consoles = 149y

Given total profit =$ 1456    

=> 79x + 149y = 1456 ----- (1)

The total number of game consoles = 14

=> x + y = 14

=> x = 14 - y ---- (2)

Substitute (2) in (1)

=> 79(14 - y)  + 149y = 1456

=> 1104 - 79y + 149y = 1456

=> 70y = 350

=> y = 5

From (2) => x = 14 - 5 = 9

Therefore,

The number of  used games consoles is 9 and the number of new game consoles is 5

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Therefore, the equations that represent circles with a diameter of 12 units and a center on the y-axis are: x² + (y - 3)²=36 and x² + (y + 8)²=36.

In mathematics, an equation is a statement that asserts the equality of two expressions. It consists of two expressions separated by an equals sign (=). The expression on the left side of the equals sign is called the left-hand side (LHS), and the expression on the right side of the equals sign is called the right-hand side (RHS). Solving an equation means finding the value of the variable that makes the equation true. I

Here,

A circle with diameter 12 units and center on the y-axis has its center at (0, c), where c is a constant. The radius of the circle is half the diameter, which is 6 units.

The equation of a circle with center (0, c) and radius r is given by:

x² + (y - c)² = r²

Substituting r = 6 and simplifying, we get:

x² + (y - c)² = 36

The only two equations among the options given that match this form are:

x² + (y - 3)² = 36 (center at (0,3))

x² + (y + 8)² = 36 (center at (0,-8))

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Answer:

[tex]x=-5,5[/tex]

Step-by-step explanation:

[tex]y=x^2-25\\0=x^2-25\\0=(x+5)(x-5)\\x=-5,5[/tex]

Answer:

Both have 4 points, and sides.  

Squares have 4 even sides

Rectangles have 2 short sides and 2 long sides.

If y*=y1/2(y2+1) then -3(16* - 9*) = -10.5y1(y2 + 1), called polynomial.

A polynomial is an expression that consists of variables, numbers, and operations (like addition, subtraction, multiplication, and division). It is similar to a mathematical equation, but instead of an equals sign, it uses coefficients and variables in a power form. The power of a polynomial is determined by the highest power of the variables in the expression.

For example, if the polynomial is x2 + 5x + 2, then the power is 2. Polynomials are used in many areas of mathematics, such as calculus, algebra, and number theory.

If y*= y1/2(y2+1) then -3(16* - 9*)

= -3(16(y1/2(y2 + 1)) - 9(y1/2(y2 + 1)))

= -3(8y1(y2 + 1) - 4.5y1(y2 + 1))

= -3(3.5y1(y2 + 1))

= -10.5y1(y2 + 1)

In this problem, 16* is equal to 16(y1/2(y2 + 1)) and 9* is equal to 9(y1/2(y2 + 1)). When -3 is multiplied to 16* - 9*, the result is -3 times the difference of 16* and 9*. The expression then simplifies to -10.5y1(y2 + 1).

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160 children between the ages of 5 and 15 comprise the cases.

Age and sex child cheated are the variables and types.

What impact do age, sex, being an only child, and whether or not kids received instructions have on the frequency of cheating in games?

a) What are the cases?

The cases are: the 160 children between the ages of 5 to 15.

b) What are the variables and their types?

The variables and types are: age (discrete numerical), sex (regular categorical), whether they were an only child or not (regular categorical), the result of the coin flip (regular categorical), whether the children were given instructions or not (regular categorical), and whether the child cheated (regular categorical).

c) What is the main research question?

The main research question is: What is the effect of age, sex, only child status, and whether or not children were given instructions on the rate of cheating in a game?

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the equation of the line will be 5y = 7x -7. Option c is correct.

A linear equation is an algebraic equation of the form y = mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given, a linear equation that passes through the points (5,0) and (0, -7)

The slope-intercept form of the equation of a line

y=mx+b,

where m is the slope

b is the y-intercept

since, slope = (y - y')/(x -x')

In our case,

slope = (-7 -0)/(0-5)

slope = 7/5

b = -7

thus,

the equation of the line will be:

y = 7/5x -7

multiply by 5 on both sides

5y = 7x -7

Therefore, the equation of the line will be 5y = 7x -7.

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Viola has covered a horizontal distance of 199.7 meters when driving 200 meters up a hill that makes an angle of 3 degrees with the horizontal.

Viola drives 200 meters up a hill that makes an angle of 3 degrees with the horizontal. To find the horizontal distance she covered, we can use the cosine formula:

Cos(θ) = adjacent/hypotenuse

In this case, the adjacent side is the horizontal distance we are trying to find, the hypotenuse is the distance she drove (200 meters), and the angle is 3 degrees. Plugging in these values, we get:

Cos(3º) = adjacent/200

Rearranging the equation to solve for the adjacent side, we get:

adjacent = 200*cos(3)

Using a calculator, we find that cos(3) is approximately 0.9986. Multiplying this by 200 gives us:

adjacent = 199.72

Therefore, the horizontal distance that Viola covered is approximately 199.72 meters.

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Answer:

42 m

Step-by-step explanation:

Equilateral triangle means that all sides are the same thus if the perimeter is 12 m

12m/3 = 4m for each side

The length of the boom will then how many triangles make the length which looks to be about 10.5

So 10.5 x 4 = 42 m

Answer:

F  = (9/5)C  + 32 is a function because every Celsius temperature is associated with only one Fahrenheit temperature.

hope this helps!!

Answer:

The probability that the first two chocolates Bob eats will have almonds is 5/51 or 9.8% (nearest tenth).

Step-by-step explanation:

Given that Bob has a box of chocolates containing 6 chocolate covered almonds, 4 chocolate covered peanuts, and 8 plain chocolates, the total number of chocolates in the box is:

[tex]\implies \sf Total=6 + 4 + 8 = 18[/tex]

[tex]\boxed{\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}}[/tex]

Therefore, the probability that the first chocolate Bob eats will have almonds is:

[tex]\implies \sf P(first\;almond)=\dfrac{6}{18}[/tex]

As Bob has eaten one almond chocolate there are now 5 chocolate covered almonds left and a total of 17 chocolates.  Therefore, the probability that the next chocolate Bob eats will have almonds is:

[tex]\implies \sf P(second\;almond)=\dfrac{5}{17}[/tex]

To find the total probability for two or more events, multiply the probabilities.  Therefore, the probability that the first two chocolates Bob eats will have almonds is:

[tex]\begin{aligned}\implies \sf P(first\;almond)\;and\;P(second\;almond) & =\dfrac{6}{18} \times \dfrac{5}{17}\\\\ &=\dfrac{30}{306}\\\\&=\dfrac{5}{51}\\\\&=0.0980392...\\\\&=9.80392...\%\end{aligned}[/tex]

Therefore, the probability that the first two chocolates Bob eats will have almonds is 5/51 or 9.8% (nearest tenth).

The table of values for the function f(x)=1/2 are shown as follow:

What is function?

A function is an expression or relationship that involves one or more variables. It has several inputs and outputs. Each input has a single output. The function describes how the inputs relate to the output.

The function f(x) = 1/2 is a horizontal line that crosses the y-axis at the point (0, 1/2). Since the value of f(x) is constant for all values of x, the table of values for this function will have the same output value of 1/2 for every input value of x.

The table of values for the function f(x)=1/2 are shown as follow:

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In the given question, the rocket will hit the ground in 7 seconds. The width of the rectangle is 3 cm. Kirk makes the wall in 5.5 hours. The student needs 97 marks.

The relation between the height and the time of the toy rocket has been given in the question as,

h = -4.9t²+33.6t + 4.9

where,

h= height of the rocket after getting launched

t= time after which the rocket has been launched

So, if we have to calculate how much time the rocket takes to reach the ground,

we have to take h=0 (at ground).

So, the equation becomes

0 = -4.9t²+33.6t + 4.9

Now, the roots of this equation will give the time at which the rocket will hit the ground.

So, after calculating we get

t = -0.1428 sec

or

t = 7 sec

since negative time is not possible,

the time at which the rocket will hit the ground is 7 seconds.

The length of the rectangle is = 5b-7 cm

Hence, the area is = b(5b-7) = 24

Hence, the width comes out to be = 3 cm

Kirk would be able to make the wall in 5.5 hours. This is because Jeff can make it one hour earlier than him i.e., K-1 hours. So, we get -

= (K-1) + K = 10

= 2K = 11

= K = 5.5 hours

The student already has 87 + 85 + 91 = 263 marks. He needs at least -

= (263 + x) / 4 = 90

= 97 marks

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The slope of UN is solved to be

The slope of UN is solved using the points denoting U and N and the points are

U (4, -2) and N (1, 2)

Formula for slope is

= change in y direction  / change in x direction

= (-2 - 2) / (4 - 1)

= -4 / 3

The slope of UN is -1 1/3

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