What is the relation between direction cosines of a vector?

Answer:

A. The ratios are both identical (three fifths and three fifths).

Step-by-step explanation:

ratio means fraction

ratio also means division

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sine equals opposite over hypotenuse cosine equals adjacent over hypotenuse tangent equals opposite over adjacent

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sine equals opposite over hypotenuse

sine X equals 3 over 5

cosine equals adjacent over hypotenuse

cosine Y equals adjacent over hypotenuse

cosine Y equals 3 over 5

side thats 3 is adjacent for y but

side thats 3 is also opposite for x

both identical, aka C on their question is right

its the 1st option for flvs

Answer:

x=3 y=1

Step-by-step explanation:

-2/3x+3=2x-5

x=3

y=-2/3(3)+3

y=1

y=2(3)-5

y=1

Answer: Spent $120 originally, profited by $36

Step-by-step explanation:

The total cost Stefan earned from selling the helmet and the bicycle is $139 + $17 = $156.

130% can be rewritten as [tex]\frac{130}{100}[/tex] which is simplified to 1.3.

Set up and this equation to find 130% of this price.

[tex]1.3x = 156\\x = 120[/tex]

Stefan spent $120 on these items.

Subtract this value from the selling price and solve.

[tex]156-120 = 36[/tex]

Stefan made $36 from selling the helmet and bicycle.

Answer:

17 + x + 3 + 17

X is 3

The equation of the line passing through (3, 6) and (6, 0) is 2x + y = 12

An equation shows how two or more numbers and variables are related to each other.

The standard linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept

The line passes through (3, 6) and (6, 0). Hence:

y - 6 = [(0 - 6)/(6 - 3)](x - 3)

y - 6 = -2(x - 3)

y = -2x + 12

2x + y = 12

The equation of the line is 2x + y = 12

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Answer: To find the total cost of the candy including the sales tax, we first need to calculate the amount of tax by multiplying the cost of the candy by the tax rate.

The cost of the candy is 10.00.

The tax rate is 5%, which can be written as 0.05.

The total cost of the candy would be

10 + (10*0.05) = 10+0.5 = 10.50

So the correct answer is $10.50.

Step-by-step explanation:

Jonathan and Oscar will have the same amount of money saved after  2 weeks.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

An equation in math is an equality relationship between two expressions written on both sides of the equal to sign.

For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7. There are different types of equations like linear, quadratic, cubic, etc.

If they have same amount of money then,

f(x) = g(x)

18x+5 = 8x+25

10x = 20

x = 2 weeks

Therefore, Jonathan and Oscar will have the same amount of money saved after  2 weeks.

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Answer:

60 because their a 2 induivedinal in 1 sock.

Step-by-step explanation:

30 x 2 = 60

Answer: 125

Step-by-step explanation:

The first term is 1³. The second term is 2³. The third term is 3³. And the Fourth term is 4³.

So the pattern is n term = n³

plug in 5

= 5³

= 125

The slope is $125 and the slope tells the annual due payment of $125.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Take two points from the graph as (2, 400) and (4, 650)

Then, the slope of line is

slope, m = ( 650- 400) / ( 4- 2)

slope, m = 250 /2

slope , m = 125

Hence, the slope is 125.

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Therefore , the solution of the given problem of circle comes out to be PQ length is 20.5 units.

A moving point on a plane is followed so that its distance from a specific point remains constant to produce the circular form known as a circle. The English term circle derives from the Greek word kirkos, which meaning hoop or ring. Area of circle= πr²

Here,

For each secant, the sum of the lengths from R to the circle's intersection points is the same:

=>RS*RT = RQ*RP

=>40(40 +31) = (44)(PQ +44)

=>40(71)/44 = PQ +44

=>PQ = 2840/44 -44 = 64 6/11 -44 = 20 6/11

=>PQ ≈ 20.5

Therefore , the solution of the given problem of circle comes out to be PQ length is 20.5 units.

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There are three types of asymptotes solved in the following way:

1. Horizontal asymptotes is y = k  for x→∞ and x→ -∞ , when degree of denominator > degree of numerator.

2. Vertical asymptote is x = k for y→∞ and y→ -∞ , when degree of denominator < degree of numerator.

3. Slant asymptotes is y = mx + c.

Therefore, the three types of asymptotes solved in the following way:

1. Horizontal asymptotes is y = k  for x→∞ and x→ -∞ , when degree of denominator > degree of numerator.

2. Vertical asymptote is x = k for y→∞ and y→ -∞ , when degree of denominator < degree of numerator.

3. Slant asymptotes is y = mx + c.

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Real value numbers are both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5) and irrational numbers such as √3, π(22/7), etc are all real numbers.

The real number that consist of different types of numbers for example prime numbers, odd numbers, even numbers, rational numbers, whole numbers, etc. These numbers can be expressed in the form of figures.Any number that we can think except complex numbers is a real number.

Real numbers encompass three classifications of numbers.Whole numbers, rational numbers, and irrational numbers are all real numbers.Even counting and natural number are all real numbers.

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The value of p is 12.322

In mathematics, the logarithmic function is an inverse function to exponentiation. The logarithmic function is defined as: For x > 0 , a > 0, and a ≠1, y= logₐ x if and only if x = a^y Then the function is given by f(x) = logₐ x The base of the logarithm is a. This can be read it as log base a of x.

Given here p=-log(2.1×10¹²)

                  p= - ( log(2.1) +12 log10)

                  p= -(0.322+12)

                  p=12.322

Hence, the value of p is 12.322

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The margin of error is $148.89. The upper limit is $2215 and lower limit is $1914.

In statistics, confidence is another word for probability. If you create a confidence interval, for instance, with a 95% level of confidence, you can be sure that 95 out of 100 times, the estimate will fall between the upper and lower values indicated by the confidence interval.

First we need to name some of the variables we are given:

n = 38 the sample size

x = 6.88 the sample mean

= 1.86 the population standard deviation

We need to find a 90% confidence interval for the mean price per 100 lbs of watermelon:

= 1-.90 = .10

/2 = .05

z(/2) = -1.64

-z(/2) = 1.64

This can give us a probability expression:

P(-1.645 < z < 1.645) = .90

The margin of error is calculated with the formula: E = z(/2)(/√n)

E = 1.645(1.86/√38) = $.4963(300) = $148.89  

Then to calculate the upper and lower limit we add and subtract E from x:

lower limit = 6.88 - .4963 = $7.38(300) = $2214

upper limit = 6.88 + .4963 = $6.38(300) = $1914

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Answer:

Step-by-step explanation:

Converting 0.632 to a fraction, Step-by-Step

Step 1:

The first step to converting 0.632 to a fraction is to re-write 0.632 in the form p/q where p and q are both positive integers. To start with, 0.632 can be written as simply 0.632/1 to technically be written as a fraction.

Step 2:

Next, we will count the number of fractional digits after the decimal point in 0.632, which in this case is 3. For however many digits after the decimal point there are, we will multiply the numerator and denominator of 0.632/1 each by 10 to the power of that many digits. For instance, for 0.45, there are 2 fractional digits so we would multiply by 100; or for 0.324, since there are 3 fractional digits, we would multiply by 1000. So, in this case, we will multiply the numerator and denominator of 0.632/1 each by 1000:

\frac{0.632 × 1000}{1 × 1000} = \frac{632}{1000}

1×1000

0.632×1000

​

=

1000

632

​

Step 3:

Now the last step is to simplify the fraction (if possible) by finding similar factors and cancelling them out, which leads to the following answer:

\frac{632}{1000} = \frac{79}{125}

1000

632

​

=

125

79

​

The comparison operator "≥" in logic means that the number is either greater than or equal to a number , the greater than equal to symbol is used to describe the relationship between two terms .

What is a Comparison Operator ?

The Comparison operator in logic is used to compare logic statements ,such as [tex]a > b[/tex] or [tex]a < b[/tex] , by using a , b as variables, the operator compares their values, returns true and false.

The Comparison Operator "≥" , in logic is read as " greater than equal to" , For Example : if the statement is [tex]a \geq b[/tex] , then if the variable is greater than or equal to b , then the operator will return TRUE and if not then it will return FALSE .

The given question is incomplete , the complete question is

What does the comparison  operator "≥"(greater than equal to) mean in logic ?

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Answer:

17%

Step-by-step explanation:

Firstly, we can establish that the tip is a percentage of the bill, excluding tips. This means that the $75.29 would be 100%, thus to find the percentage of tip received, we would take
$12.80/$75.29 × 100 = 17%

Therefore , the solution of the given problem of expression comes out to be 794.0481.

combinations of numbers, symbols, and operations (such + and) that show how much something is worth. Examples: • 2 + 3 is the formula.

• 3 x/2 variable  is another formula.There is no equals sign in the expression. A mathematical expression is a sentence made up of variables, numbers, or both. There is never an equal symbol in an expression. These expressions are examples. An equation is a mathematical statement proving the equality of two expressions.

Here,

Given : 5 + [tex](5.3)^{4}[/tex]

=> 5 + (5.3)*(5.3)*(5.3)*(5.3)

=> 789.0481 + 5

=> 794.0481

Therefore , the solution of the given problem of expression comes out to be 794.0481.

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Answer: length of EF is 18 units.

Step-by-step explanation:

similar triangles (as displayed in the photo) have the same angle measures, but can have different side lengths. however, these side lengths are proportional to each other, meaning that with similar triangles, there will ALWAYS be a number you can multiply the first triangle by to get its similar triangle.

you can find this number by dividing one side length of whichever triangle is bigger with its corresponding side on the other triangle (for example, sides DF and AC correspond, so you'd divide whichever value's bigger by the smaller one. in this case you'd divide 21 by 14.) this gives you 1.5, which tells you that triangle DEF is 1.5 times larger than triangle ABC. so to get EF, just multiply BC (which is 12) by 1.5. this gives you 18. so, EF equals 18. hope this helped :3

FG stands for Function Generator, which is a device that produces electrical signals with a function of frequencies and amplitudes. It is commonly used in scientific laboratories to generate signals for testing and research purposes.

A function generator is an electrical device used to generate electrical signals with a range of frequencies and amplitudes. It is commonly used in scientific laboratories to generate test signals for testing and research purposes. Function generators typically consist of an oscillator, amplifier, and waveform selector. The oscillator generates a signal of a given frequency and amplitude, while the amplifier adjusts the output voltage. The waveform selector allows the user to choose from a variety of waveforms, such as sine, square, triangle, and sawtooth. Function generators can be used to simulate various types of electrical signals, such as AC and DC signals, as well as a variety of noise signals. They are also used to test various types of electronic components, such as transistors and capacitors, and to conduct research in fields such as telecommunications and signal processing. The acronym FG stands for Function Generator.

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0.167 or 0.17 rounded to the nearest hundredth.

How do you round off decimal to the nearest hundredth?

When rounding to the nearest hundredth, you want to look at the third decimal place, the one to the right of the hundredth place. If the value in the third decimal place is less than 5, you truncate everything to the right of the hundredth place, leaving the number unchanged.

If the value in the third decimal place is greater than or equal to 5, you add one to the number in the hundredth place.

The total area of the rectangle is 15*5 = 75 square feet.

The area of the triangle inside the rectangle is (1/2)25 = 12.5 square feet.

The shaded region is the area of the triangle, so the probability that a randomly chosen point lies inside the shaded region is

12.5/75 = 0.167 or 0.17 rounded to the nearest hundredth.

Hence, 0.167 or 0.17 is rounded to the nearest hundredth.

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Answer:

m = 2

Step-by-step explanation:

Slope = rise / run or (y2 - y1) / ( x2 - x1)

Let's pick 2 points (0,0) (1,2)

We see the y increase by 2 and the x increase by 1, so the slope is

m = 2

The values of x and y, given the angles in the diagram, can be found to be :

The angles given above are called vertical angles and they are such that the two corresponding angles are equal to each other.

This means that ( 8 x + 7 ) ° is equal to ( 9 x - 4 )° and 5 y° is equal to  ( 7y - 34 )°.

The value of x is :

8 x + 7 = 9 x - 4

9x - 8x = 7 + 4

x = 11

The value of y is :

5 y = 7y - 34

7y - 5y = 34

2 y = 34

y = 34 / 2

y = 17

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[tex]2x = 25-3x[/tex]

Simplify:

[tex]2x=-3x+25[/tex]

Add 3x to both sides:

[tex]2x+3x=-3x+25+3x[/tex]

[tex]5x=25[/tex]

Divide both sides by 5:

[tex]\dfrac{5x}{5} =\dfrac{25}{5}[/tex]

[tex]\fbox{x = 5}[/tex]