first we translate b and place its tail at the tip of a, being careful to draw a copy of b that has the same length and direction. then we draw the vector a b (see the middle figure) starting at the ---select--- point of a and ending at the terminal point of the copy of

A function of an angle is a trigonometric function. They are utilized to connect the triangle's angles and sides' lengths.

A right-angled triangle's angle can be related to side length ratios using trigonometric functions, which are real functions in mathematics. They are extensively employed in all geosciences, including navigation, solid mechanics, celestial mechanics, geodesy, and many more.

A common angle in trigonometry has six different functions. Sine, cosine, tangent, cotangent, secant, and cosecant are their names, respectively, as well as their acronyms.

Given that sin theta = √3/√7

Opposite = √3

Hypotenuse = √7

Get the adjacent

Adj² = (√7)²-(√3)²

simplifying the above equation, we get

Adj² = 7-3

Adj² = 4

Adj = √4

Adj = 2

Cos theta = adj/hyp = 2/√7

csc theta = 1/sin theta = 1/(√3/√7) = √7/√3

sec theta = 1/cos theta = 1/(2/√7) = √7/2

tan theta = opp./adj = √3/2

cot theta = 1/tan theta = 1/(√3/2) = 2/√3

= 2√3/3

The complete question is:

Find the exact value of each of the remaining trigonometric functions of theta. Rationalize denominators when applicable.

sin theta [tex]$=\sqrt{\frac{3}{7}}$[/tex] given that theta is in quadrant I.

cos theta=

csc theta =

sec theta =

tan theta =

cot theta =

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Answer:

The lowest interest rate you would need to earn in order to have 15,000 become 20,000 in 5 years is 6.5%. This is based on the compound interest formula, where you would need to multiply the original amount by the interest rate (15,000 x 0.065 = 975) and add that amount to the original amount to equal your desired total (15,000 + 975 = 20,000).

The perimeter of the equilateral triangle which has sides of length (3x+7) is 9x+21.

A triangle's three sides and angles must be equal for it to be considered an equilateral triangle.

An equilateral triangle is also referred to as an equiangular triangle because it has angles that are each 60 degrees in length. Because its sides and angles are equal, the equilateral triangle is regarded as a regular polygon or triangle.

Depending on how many sides a triangle has, there are three different types. These triangles are equilateral, isosceles, and scalene.

In an equilateral triangles all sides are equal

so,

perimeter = 3x+7 + 3x+7 + 3x+7

perimeter = 9x+21

Thus, perimeter of the equilateral trinagle which has sides of lenght (3x+7) is 9x+21.

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Answer:

a.x (x + 1)

b. 3x (1 - 3x)

c. 7x (x² - 5)

d. 4x² (x + 6).

Therefore , the solution of the given problem of equation comes out to be x value is 8.

The equal letter (=) is used to signify equivalence between the statements in a mathematical formula. Using mathematical equation, which are declarations of reality, it is shown that many mathematical variables are equivalent. For instance, the equal sign in the equation y + 6 = 12 divides the values 12 or b + 6 into two halves. The number of words that each side of a symbol corresponds to can be measured. Typically, a symbol's meaning is at odds with itself.

Here,

Given:

equation : -3(x-9) = x-5

To find the value of x ,

=> -3(x-9) = x-5

=> -3x +27 = x -5

=> 4x = 27 +5

=> 4x = 32

=> x =32/4

=> x= 8

Therefore , the solution of the given problem of equation comes out to be x value is 8.

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By distributive property, the polynomial (3 / 2) · u² · v⁴ - 2 · (1 / 2) · u³ · v⁵ + (1 / 2) · u⁴ · v² is equivalent to polynomial (1 / 2) · u² · v² · (3 · v² - 2 · u · v³ + u²).

In this problem we find a polynomial that must be simplified by means of algebra properties, especially by distributive property.  First, write the entire polynomial:

(3 / 2) · u² · v⁴ - 2 · (1 / 2) · u³ · v⁵ + (1 / 2) · u⁴ · v²

Second, use distributive property to simplify the polynomial thrice:

(1 / 2) · (3 · u² · v⁴ - 2 · u³ · v⁵ + u⁴ · v²)

(1 / 2) · u² · (3 · v⁴ - 2 · u · v³ + u² · v²)

(1 / 2) · u² · v² · (3 · v² - 2 · u · v³ + u²)

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Approximately 99.7 % of the students spent between $ 271 and $ 407  on textbooks in a semester.

Then , according to the Empirical rule , approximately 99.7% of the data lies with in the 2 standard deviations from mean.

Given : The distribution of the amount of money spent by students on textbooks in a semester is approximately normal in shape with

Mean = 339     standard deviation =  34.

Then ,  by

Empirical rule , approximately 99.7 % of the students spent between Mean ± 2 (Standard deviation) on textbooks in a semester.

where , Mean ± 2 (Standard deviation) = 339 ±  2(34)

=(339-2(34) , 339+2(31))

=(271 , 407)

Hence ,  Approximately 99.7% of the students spent between $ 271 and $ 407 on textbooks in a semester.

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Using multiplication operation, the number of ounces of Isabella's spray fixative contained in the economy size is 9¹/₃ ounces.

Multiplication operation is one of the four basic mathematical operations, including addition, division, and subtraction.

The multiplication operation involves the multiplicand multiplied by the multiplier, resulting in a product.

The multiplication operand is depicted using (x), (*), or (of).

The normal spray fixative purchased by Isabella = 6²/₃ = 6.667 ounces

The relative size of the economy can = 1²/₅ of 6²/₃ ounces

The number of ounces in the economy can = 9¹/₃ ounces (1²/₅ x 6²/₃)

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The area of a rectangle is found by multiplying the length by the width. So the area of the original rectangle is (6 m) x (9 m) = 54 m^2.

If we want to find different side lengths that have the same area, we can keep the area constant and manipulate the length and width.

One way to do this is to multiply the original length by a certain factor and multiply the original width by the reciprocal of that factor.

For example, if we multiply the length by 2 and the width by 1/2, the area will remain the same: (6 m) x 2 = 12 m and (9 m) x (1/2) = 4.5 m. The new rectangle's dimensions would be 12 m x 4.5 m.

Another way to find different side lengths that have the same area is to multiply the original length and width by the same factor.

For example, if we multiply both the length and width by 2, the area will remain the same: (6 m) x 2 = 12 m and (9 m) x 2 = 18 m. The new rectangle's dimensions would be 12 m x 18 m.

So, to draw the rectangle with different side lengths that have the same area, you can use any of the above method, and label the side lengths accordingly.

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If 3 inches on the map represents 1.25 miles, we can use that proportion to find how many inches represents 10 miles.

3 inches / 1.25 miles = x inches / 10 miles

We can cross multiply and divide to find x:

x = (3 inches * 10 miles) / 1.25 miles

x = 24 inches

So on the map, 24 inches represent 10 actual miles.

Answer:  .9072 is the awnswer

False is the statement, "Polygon endpoints need not conform to snap points, like the boundaries of a filled-in region."

The surface's perimeter is defined by the edge of a filled-in area. An area is a two-dimensional space that any surface can cover. Typically, the edges of the space serve as the surface's boundary. To create a closed area or surface, the edges or the boundary must link.

Similar to end points, snap points are the ends of a polygon's sides. A closed figure can only be formed when these endpoints are connected. A closed polygon is one that has n sides.

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In repeated sampling from the S distribution, the mean of the values will be close to 4.66, which is the appropriate interpretation of the mean.

The arithmetic mean, also known as the arithmetic average or simply the mean or average, is the sum of a set of numbers divided by the total number of numbers in the set. The collection frequently consists of a set of findings from a survey, experiment, or observational study. The average of a group of values is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.

Here,

The average of the values will be close to 4.66 in repeated sampling from the S distribution, which is the correct interpretation of the mean.

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Answer:

-2

Step-by-step explanation:

The correct order of bond lengths P, Q, and R in the above diagram is P > Q > R. The correct option is A.

The bond length is the distance between the centers of two bound atoms. Consider the fact that a homonuclear diatomic molecule's bonded atoms are separated by half their element's atomic radius (sometimes referred to as the covalent or bonding atomic radius).

Less percentage of s character in a bond means the length of orbitals of the molecule is more, and also the bond length is more.

Therefore, the correct option is A. P > Q > R.

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The question is incomplete. Your most probably complete question is given below:

Which is the correct order of bond lengths P, Q, and R in the above diagram?

P > Q > R

R > Q > P

Q > P > R

Q > R > P

In 1976, 87.76% of the states, including the District of Columbia, voted Republican, which is a relative frequency. This is a relative frequency because it is expressed as a ratio or proportion of the total number of states.

1976: Republican: 43 states, District of Columbia; Democrat: 6 states

2012: Republican: 24 states, District of Columbia; Democrat: 26 states

In 1976, 43/49 (including the District of Columbia) states voted Republican, which is 87.76%. This is a relative frequency.

1. Calculating the total number of states and District of Columbia in 1976: 43 + 6 + 1 = 50.

2. Calculating the percentage of states voting Republican in 1976: 43/50 (including the District of Columbia) = 0.87 or 87.76%.

3. This is a relative frequency because it is expressed as a ratio or proportion of the total number of states.

In 1976, 87.76% of the states, including the District of Columbia, voted Republican, which is a relative frequency.

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Using the expansion of inequality, The smallest integer , n is 3 .

What in math is an integer?

A full number (not a fraction) that can be positive, negative, or zero is called an integer (pronounced IN-tuh-jer).

                           Integers include things like -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers are examples of non-integer numbers.

we have given in question that , n is an integer such that ,

(x²+y²+z²)²≤n(x⁴+y4⁴+z⁴)

Let us consider, a=x², b=y², and c=z² which are all nonnegative i.e a,b,c >0 , n>3 but we find least value of n

So, the above inequality become,

(a+b+c)² ≤ n (a²+b²+c²) ----(*)

by expanding both side of above equation we get, a² + b²+ c² + 2(ab + bc + ac) ≤n( a²+b²+c²)

2(ab + bc + ac) ≤ (n- 1) (a²+b²+c²)

=> (ab+bc+ac) ≤ (n- 1)/2 (a²+ b²+c²)

=> (xy)²+ (yz)²+(xz)²≤ (n-1)/2(x⁴+y⁴+z⁴)

If we put n=3− ∈ where ∈ >0 and x=y=z then

3 ≤ 2 or 1/2 which is wrong . Hence, the smallest value of n is 3.

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The complete question is -

Find the smallest integer n such that (x2+y2+z2)2≤n(x4+y4+z4)

for all real numbers x,y, and z.

The point on the unit circle that corresponds to the real number t = 7/4 is given as follows:

(-0.1782, 0.9840).

For an angle [tex]\theta[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\theta}, \sin{\theta})[/tex].

With parameter t, the coordinates of the point are given as follows:

(cos(t), sin(t)).

Hence the x-coordinate when t = 7/4 is given as follows:

cos(7/4) = -0.1782.

The y-coordinate when t = 7/4 is given as follows:

sin(7/4) = 0.9840.

Meaning that the coordinates are:

(-0.1782, 0.9840).

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Answer:

Step-by-step explanation:

0.25 L = 250 mL

12 000mL = 12 L

5 L 400mL = 5400mL

[tex] \tt \: 4x + y = 10 ---- eqⁿ[/tex]

[tex] \: [/tex]

-6 is already given ,

[tex] \: [/tex]

so , put the value of y = -6 in the given eqⁿ ~

[tex] \: [/tex]

[tex] \tt \: 4x + y = 10[/tex]

[tex] \: [/tex]

[tex] \tt \: 4x + (-6) = 10[/tex]

[tex] \: [/tex]

[tex] \tt \: 4x = 10 + 6[/tex]

[tex] \: [/tex]

[tex] \tt \: 4x = 16[/tex]

[tex] \: [/tex]

[tex] \tt \:x = \cancel \frac{16}{4} [/tex]

[tex] \: [/tex]

[tex] \underline{\boxed { \red{\tt \large \: x = 4}} { \green✓}}[/tex]

[tex] \: [/tex]

missing value is 4!

hope it helps! :)

Answer:

5/3

Step-by-step explanation:

1 week = 7 days

5 weeks = 5 × 7 days = 35 days

5 weeks to 21 days =

= 35 days to 21 days

= 35/21

= 5/3

Answer:

what to find in this question ?

The range is not likely to vary, which is one of the claims regarding the new salary distribution that is supported.

Therefore,

Given that a small company's salary distribution of 27 employees has a mean of $35,000 and a standard deviation of $2,000,

When a highly unusual value, such as 120000, is taken into account for the 28th employee, we discover that the mean increases.

The new median would be the average of items 14 and 15, as the prior median was the 14th item. Thus, the median may alter.

Because the maximum has been raised up to 120000, the range will undoubtedly vary.

so that we can say

Range changes, median changes, and mean increases.

Thus, we determine that Option B is correct.

The complete question is:

The distribution of 27 salaries at a small company has mean $35,000 and standard deviation $2,000. Suppose the company hires a 28th

28th employee at a salary of $120,000. Which of the following claims about the new salary distribution is supported?

The median is not likely to change. I

The range is not likely to change. II

The mean is likely to increase. III

A) I only

B) III only

C) I and II only

D) I and III only

E) I, II, and III

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The value of x = 19 and the value of z = 70° in the figure given above.

In algebra, the letter "x" is frequently used to denote an unknown value. It is referred to as a "variable" or occasionally a "unknown.

" x is a variable in x + 2 = 7, but we can figure out its value if we try! A variable can be any letter, name, or symbol; it doesn't have to be "x"; examples include "y" and "w." Z-scores are calculated using the formula z = (x-)/, where x represents the raw score, the population mean, and the population standard deviation.

The z-score is simply the raw score less the population mean, divided by the population standard deviation, as the calculation demonstrates. A raw score's position relative to its distance from the mean is described by the z-score.

Using The property Vertically opposite angles are equal

110° = 9x - 61

⇒ 9x = 110 +61

⇒ 9x = 171

⇒ x = 171/9

⇒ x = 19

As all angles equal 360°

110° + 110° + 2z = 360°

⇒ 2z = 360° - (110° + 110°)

⇒ 2z = 140

⇒ z = 140/2

⇒ z = 140/2

⇒ z = 70°

Thus, The value of x = 19 and the value of z = 70° in the figure given above.

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The results from Ralph's survey are not statistically different from the national results.

Population Parameter: The percentage of teens who seldom or never argue with their parents in Ralph's large high school.

Null Hypothesis (H0): The percentage of teens who seldom or never argue with their parents in Ralph's large high school is equal to the nationwide percentage of 28%.

Alternative Hypothesis (H1): The percentage of teens who seldom or never argue with their parents in Ralph's large high school is not equal to the nationwide percentage of 28%.

H0: p = 0.28

H1: p ≠ 0.28

To calculate whether or not the results from Ralph's survey are significantly different from the national result, a one-sample z-test can be used. The z-score is calculated using the following formula: z = (x-µ)/(σ/√n). In this example, x is the sample proportion of teens who seldom or never argue with their parents (Ralph's survey), µ is the population proportion (the nationwide poll results of 28%), σ is the population standard deviation, and n is the sample size (175).

If the z-score is outside of the critical region, then it can be said that the results from Ralph's survey are statistically different from the national results. If the z-score is within the critical region, then it can be said that the results from Ralph's survey are not statistically different from the national results.

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Answer:

$24.50

Step-by-step explanation:

hourly rate on Sunday is 1.75 times his normal hourly rate, that is

1.75 × $14 = $24.50

hourly rate on a Sunday is $24.50

The weighted average total return for the mutual funds covered by Morningstar is 9.20%, calculated by taking the sum of the products of the total return and the number of funds for each of the four categories.

a. The weighted average total return for the mutual funds covered by Morningstar is 9.20%.

This is calculated by taking the sum of the products of the total return and the number of funds for each of the four categories:

(4.65 * 9191) + (18.15 * 2621) + (11.36 * 1419) + (6.75 * 2900) / (9191 + 2621 + 1419 + 2900) = 9.20%

b. Yes, there is a difficulty associated with using the number of funds as the weights in computing the weighted average total return for Morningstar. This is because the number of mutual funds in each category can fluctuate over time, and thus, the weights used to calculate the average total return may not accurately reflect the true performance of the mutual funds.

An alternative to using the number of funds as weights would be to use the dollar amount invested in each type of mutual fund as the weight. This would give a more accurate representation of the performance of the mutual funds.

c. The expected return on the portfolio is 9.63%.

This is calculated by taking the sum of the products of the total return and the amount invested in each of the four categories:

(4.65 * 2000) + (18.15 * 4000) + (11.36 * 3000) + (6.75 * 1000) / (2000 + 4000 + 3000 + 1000) = 9.63%

The weighted average total return for the mutual funds covered by Morningstar is 9.20%, calculated by taking the sum of the products of the total return and the number of funds for each of the four categories. However, using the number of funds as weights may not accurately reflect the true performance of the mutual funds, and an alternative would be to use the dollar amount invested in each type of mutual fund as the weight. The expected return on the portfolio is 9.63%, calculated by taking the sum of the products of the total return and the amount invested in each of the four categories.

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Answer: C(n)=24n+5 =24

(A)=A/6 =0

Step-by-step explanation:

The total capacity of Harold's computer hard drive is 750 GB.

Total free space on Harold's computer hard drive = 131.25 GB

Percentage of free space on Harold's computer hard drive = 17.5%

Let

Total capacity of the hard drive = x

17.5% of x = 131.25

17.5/100 × x = 131.25

0.175 × x = 131.25

0.175x = 131.25

divide both sides by 0.175

x = 131.25 / 0.175

x = 750 GB

Hence, Harold's computer hard drive has a total capacity of 750 GB

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The solved for x round to the nearest tenth is x≈ 14.

What is meant by round ?

Remember Sine of an angle is = opposite side /hypotenuse

So let the hypotenuse be  x :

sin(54°) = opposite side / x

sin(54°) = 12 / x

To solve for x, divide sin(54°) by 12:

x = 12 / sin(54°)

x≈14

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