Find the volume of each prism and match the volume to the correct prism. The units are understood to be square units, but are not included on the numeric answer.​

The solution of given trigonometric equation, 6sin²θ-13sinθ+7 = 0 is θ = π/2

A trigonometric equation is one that contains a trigonometric function with a variable.

Given is a trigonometric equation,

6sin²θ-13sinθ+7 = 0

Solving for θ

6sin²θ-6sinθ-7sinθ+7 = 0

6sinθ(sinθ-1)-7(sinθ-1) = 0

(6sinθ-7)(sinθ-1) = 0

sinθ = 1

θ = π/2

or,

6sinθ-7 = 0

sinθ = 7/6 [no solution]

Hence, the solution of given trigonometric equation, 6sin²θ-13sinθ+7 = 0 is θ = π/2

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Answer:

The new taxes would be $3300.

Step-by-step explanation:

The assessment value and tax rate determine how much a house will cost in taxes. The amount of taxes would increase if the assessment is raised from $108,000 to $128,000.

To find the new amount of taxes, you need to multiply the increased assessment value by the same tax rate:

$128,000 - $108,000 = $20,000 increase in assessment value

$20,000 * ($2700/$108,000) = $600 increase in taxes

Therefore, the new taxes would be $2700 + $600 = $3300.

Answer:

Brandi needs to receive a score of 46 on the final to have an average score of 80.

Step-by-step explanation:

First, let's understand what is being told to us. We are being asked to find the score Brandi needs on the final, or x. Since the final is worth 2 tests, the final is equal to twice the score she receives, or 2x. Next, we need the average of all the tests, including the final, to be equal to 80. It's important to also note that we will be taking the average of 6 scores. Now, let's use all of our information to write an equation to solve:

( 79 + 80 + 74 + 63 + 92 + 2x ) / 6 = 80.   [Combine like terms]

( 388 + 2x ) / 6 = 80   [Multiply by 6]

388 + 2x = 480   [Subtract 388 from both sides]

2x = 92   [Divide both sides by 2]

x = 46

So, Brandi needs to receive a score of 46 on the final to have an average score of 80.

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Answer:

The width of the rectangle is 9

Step-by-step explanation:

l + l + w + w = perimeter

(x - 8) + (x - 8) + (x) + (x) = 52  

We don't know the length so put it as a variable

x + x + x + x - 8 - 8 = 52         Group together like-terms.

4x - 16 = 52                            Combine like-terms                  

4x = 68                                  Add 16 to both sides

x  =   17                                Divide both sides by 4

We now have the value for the length (x = 17) however we need the value for the width. Just subtract 17 - 8 since the width is 8 in. less than its length.

17 + 17 + 9 + 9 = 52

The value(s) of x that satisfy the given solution is  (5, 7).

Power on both sides: (√4x-5)²-(2x-10)

2 Simplify using exponent power rule (a")=am

x²-4x-5-(2x-10) 2

Expand the expression using (a+b)

2-a2+2ab+

b2: 2-4x-5-(2x) 2-2×2×10+10²

Multiply the monomials: 2-4-5-(2) 2-40

+102 Calculate the power: 2-4-5-(2x) 2-40x+ 100

Simplify using exponent rule with same exponent

(ab)"a"-b" 2-4x-5-22-2-40x+100 Calculate the power: 2-4-5-4x-40+

100

equation: 2-4-5-4x²+40x-100-0 Combine like terms: -3x²+36-105-0

12r+35-0

Rearrange all nonzero terms to the left side of the Reduce the greatest common factor on both sides of the equation: -2+12-35-0 Multiply each term of the equation by -1: 2-

Find two integers: -7-5--12 1-7x (-5)=35

Rewrite the middle term: 2-7x-5x+35-0 Factor the first two terms and the last two terms respectively: (-7) -5(x-7)=0 Apply zero product property that at least one

Extract the common factor: (x-7)(x-5) =0

factor is zero: 2-7-0 or x-5-0 Rearrange unknown terms to the left side of the

equation: -7

Rearrange unknown terms to the left side

equation: =5

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The measure of the central angle associated to the circular arc is equal to 4 / 3 rad.

Herein we find the information of the radius of a circle and the length of its circular arc, whose relationship is shown by the following formula:

s = θ · r

Where:

If we know that r = 6 yd and s = 8 yd, then the measure of the central angle is:

θ = s / r

θ = (8 yd) / (6 yd)

θ = 4 / 3 rad

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Answer:

0.6

Step-by-step explanation:

96/160 = 0.6

Just divide.

The decimal is 0.60, which is 60% of 1.

Answer:

96 of 160 is 60%

102.4 of 160 is 64%

120 of 160 is 75%

128 of 160 is 80%

Hope this helped!

Step-by-step explanation:

The probabilities for this problem are given as follows:

a) Moderate to high, given that it is an aerospace company: p = 4/9 = 0.4444.

b) Moderate to high, given that it is a food retailer: p = 6/11 = 0.5455.

c) As the probabilities are different, the company type is independent of the level of risk of the firm's stock.

A probability is given by the division of the number of desired outcomes by the number of total outcomes.

For item a, the outcomes are given as follows:

Hence the probability is given as follows:

p = 8/18

p = 4/9.

For item b, the outcomes are given as follows:

Hence the probability is given as follows:

p = 30/55

p = 6/11.

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For Given Fraction 5/3, The total number of votes is 7648.

What is a fraction?

In Maths, a fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator. The numerator defines the number of equal parts taken, whereas the denominator defines the total number of equal parts in a whole.

For example, 5/10 is a fraction.

Here, 5 is a numerator and 10 is a denominator.

There are four different types of fractions. They are:

Unit Fraction – In a fraction, the numerator with 1 is called a unit fraction. For example, ½, ¼

Proper Fraction – If a numerator value is less than the denominator value, it is called a proper fraction. Example: 7/9, 8/10

Improper Fraction – If a numerator value is greater than the denominator value, then it is called an improper fraction. Example: 6/5, 11/10

Mixed Fraction – If a fraction consists of a whole number with a proper fraction, it is called a mixed fraction. Example 5 ¾, 10 ½

Now,

As given ratio is 5/3 for Yes votes to no votes

so total votes is 5x+38x

and also given that no votes i.e. 3x=2868

so, x=956

Hence,

            Total votes=8*956=7648

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Answer:

269

Step-by-step explanation:

big × square root 05 is Justin Beiber

Answer:

301/8200

Step-by-step explanation:

82 x (X) = 301/100

82x/1 = 301/100

now we cross multiply.

8200x = 301

x = 301/8200

it may be wrong, sorry if it is :(

The quotient is 3x²+5x+5.

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.

The given expressions are 3x³-x²-5x-10 and x-2.

Here, (3x³-x²-5x-10)/(x-2)

x-2|3x³-x²-5x-10|3x²+5x+5

  (-)3x³-6x²

____________

          5x²-5x-10

       (-)5x²-10x

   ____________

               5x-10

            (-)5x-10

      ____________

                   0

Therefore, the quotient is 3x²+5x+5.

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Answer:

23.

Step-by-step explanation:

1) if 'G is the midpoint of DF and H is the midpoint of EF', then 0.5*DE=GH, and

2) it is possible to write: 0.5(18+4x)=3x+2, where x=7.

3) if x=7, then GH=3*7+2=23.

Answer:

44/87

Step-by-step explanation:

There are 87 fair managers.  44 of them have a college degree.  Being that he is a fair manager, the chance of him having a college degree is 44 out of 87, otherwise written as 44/87.

The value of expression y ' (-1) is, 24.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ y = (4x² - 5)³

Now, We can differentiate with respect t x as;

⇒ y (x) = (4x² - 5)³

⇒ y' (x) = 3(4x² - 5)² × (4×2x - 0)

⇒ y' (x) = 3 (4x² - 5)² × 8x

⇒ y' (x) = 24x (4x² - 5)²

Substitute x = 1, we get;

⇒ y ' (1) = 24 × 1 (4 × 1² - 5)²

⇒ y' (1) = 24 (- 1)²

⇒ y' (1) = 24

Thus, The value of expression y ' (-1) = 24

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The solution of the initial value problem xy' + y = 8e is equal to

log (x ) =  - log ( 8e - y ) .

Solution of the initial value problem is:

xy' + y = 8e

⇒ x (dy /dx ) + y = 8e

⇒ x (dy/dx ) = 8e -y

⇒  dx / x  = ( 1 / (8e -y ) ) dy

Integrate both the sides we get,

⇒ log (x ) =  - log ( 8e - y ) + c  ____(1)

Now , we have y ( 1 ) = -1 + 8e

Substitute the value  y ( 1 ) = -1 + 8e in (1) we get,

⇒ log ( 1 ) = - log ( 8e - ( -1 + 8e )) + c               ( value of log (1) = 0 )

⇒ 0 = - log ( 8e + 1 - 8e ) + c

⇒ 0 = log ( 1 ) + c

⇒ c = 0

Now substitute c =0 in (1) we get,

log (x ) =  - log ( 8e - y )

Therefore, the explicit solution of the initial value problem is equal to

log (x ) =  - log ( 8e - y ) .

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The amount of taxes collected is proportional to the population, so if the population increased by 3 million - 2 million = 1 million, the amount of taxes collected should increase by the same factor.

So, in 2017, 4 billion * (3 million / 2 million) = 6 billion dollars in taxes were collected.

Answer:

Since the amount of taxes collected is proportional to the population of the city, we can write the relationship between the amount of taxes and the population as:

T = kP

where T is the amount of taxes, P is the population, and k is the constant of proportionality.

From the information given, we can find the value of k:

4 billion = k * 2 million

k = 4 billion / 2 million = 2

So, for the population of 3 million in 2017, the amount of taxes collected would be:

T = k * P = 2 * 3 million = 6 billion

So, in 2017 the city collected 6 billion dollars in taxes.

With the help of given pie chart, He is Under for some categories and over for other categories.

What is a pie chart?

The “pie chart” is also known as a “circle chart”, dividing the circular statistical graphic into sectors or sections to illustrate the numerical problems. Each sector denotes a proportionate part of the whole. A pie chart requires a list of categorical variables and numerical variables. To find out the composition of something, Pie-chart works the best at that time. In most cases, pie charts replace other graphs like the bar graph, line plots, histograms, etc.

The total value of the pie is always 100%.

Now,

Categories   Spend value    Spending guidelines    Over/Under(O/U)

Rent              $2200               $1830                            O-$370

Student

Loan             $350                $305                              O-$45

Food             $750                $1220                            U-$470

Car payment $150       Together in transportation

and Car            +

insurance      $75                 $671                               U-$446                                            

Savings         $50                 $610                               U-$560

I would suggest Jonathan to save more and spend less on rent and more on food for better health.

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Answer:

The table can't be completed as I can't see the table.

However, I can give you the values:

4 Oranges for every 1 Cup of Orange Juice

4, 1

8, 2

12, 3

16, 4

20, 5

Step-by-step explanation:

$2.4 is the discount used to purchase a pair of sunglasses

percentage, a relative value indicating hundredth parts of any quantity.

Given that Alexandra bought a pair of sunglasses online for $24.

She used a coupon code to get a 20% discount.

The website also applied a 10% processing fee to the price after the discount.

20%-10%=10%

Now 10% of price is 24

10/100×24=x

2.4=x

24+2.4=26.4 is the actual price.

Hence, $2.4 is the discount used to purchase a pair of sunglasses

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Answer:

I think so.

Step-by-step explanation:

Answer:

x = ±√13 - 8

Step-by-step explanation:

Move the constant term to the right side of the equation.

x² + 16x + 51 = 0

x² + 16x = -51

We complete the square by taking half of the coefficient, squaring it, and adding it to both sides of the equation. The formula is (b/2)².

x² + 16x = -51

here the formula would be (16/2)² = 64

x² + 16x + 64 = -51 + 64

Now just simplify by factoring the left side and adding up the right side.

(x + 8)² = 13

You have to isolate x to find what it equals. Here start by taking the square root of both sides

x + 8 = √13

Subtract 8 to both sides

x = ±√13 - 8

The answers are k = 12√2 and [tex]\theta=\frac{\pi }{2}+2\pi n[/tex]

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Given are questions related to trigonometric functions:

a) k cos² (π/6) - k sin² (π/6) = 6√2

Finding k,

k cos² (π/6) - k sin² (π/6) = 6√2

Taking k common,

k [cos² (π/6) - sin² (π/6)] = 6√2

Since, cos²x-sin²x = cos2x

Therefore,

k[cos2(π/6)] = 6√2

k[cos(π/3)] = 6√2

Since, cos(π/3) = cos 60° = 1/2

Therefore,

k[1/2] = 6√2

k = 6√2 × 2

k = 12√2

b) sinx / cscx+cotx

[tex]\frac{sinx}{cscx+cotx}= \frac{sinx}{\frac{1}{sinx}+\frac{cosx}{sinx}}= \frac{sinx}{\frac{1+cosx}{sinx}}= \frac{sin^2x}{1+cosx}= \frac{1-cos^2x}{1+cosx}= \frac{(1+cosx)(1-cosx)}{1+cosx}\\\\= 1-cosx[/tex]

Hence, proved.

c) sinθ = 2cos²θ + 1

Solving for θ

[tex]\sin \left(\theta\right)-2\cos ^2\left(\theta\right)-1=0[/tex]

[tex]-3+\sin \left(\theta\right)+2\sin ^2\left(\theta\right)=0[/tex]

[tex]\sin \left(\theta\right)=1,\:\sin \left(\theta\right)=-\frac{3}{2}[/tex]

[tex]\sin \left(\theta\right)=1 : \theta=\frac{\pi }{2}+2\pi n\\\sin \left(\theta\right) = -\frac{3}{2} : no solution\\\theta=\frac{\pi }{2}+2\pi n[/tex]

Where n is any integer,

Hence, the answers are k = 12√2 and [tex]\theta=\frac{\pi }{2}+2\pi n[/tex]

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Answer:

2y-3

Step-by-step explanation:

GCF of 32 and 48=16

(32y-48)/16=2y-3

The length of the statue on the drawing is 6.33 inches.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

1 inch = 3 feet

The length of the statue = 19 feet

Now,

3 feet = 1 inch

Multiply 19/3 on both sides.

19 feet = 6.33 inch

Thus,

The statue on the drawing is 6.33 inches.

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The amount of rainfall in Nashville than in Miami would be 0.67.

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

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the rainfall in Albany is 0.33. The amount of rainfall in Miami is calculated as:-

Rainfall = 1 - 0.33

Rainfall = 0.67

Hence, the amount of rainfall in Nashville than in Miami would be 0.67.

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Answer:

118°

Step-by-step explanation:

Answer:

a) The equation to solve this problem would be:

10 + 3.75h = 41.88

b) To solve for h, we first need to subtract 10 from both sides:

3.75h = 31.88

Then, divide both sides by 3.75:

h = 8.50 (rounded to the nearest tenth)

So Amanda rented the bike for 8.5 hours.

Step-by-step explanation:

Answer:  a) To solve the problem, we can use the equation:

Cost = 10 + 3.75h

Where h is the number of hours Amanda rented the bike.

b) We know that the cost is about $41.88, so we can plug that in for the cost and solve for h:

41.88 = 10 + 3.75h

31.88 = 3.75h

h = 31.88/3.75

h = 8.5 hours

So Amanda rented the bike for 8.5 hours. (rounding to the nearest tenth)

Step-by-step explanation:

The equation of the linear function represented by the table below in slope intercept form is f(x) = 4x - 1.

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

General equation of a linear function in slope intercept form is,

y = f(x) = mx + c

Here c is the y intercept and m is the slope.

y intercept is the point on the line when x coordinate equals zero.

Given four points on the line (-1, -5), (1, 3), (3, 11) and (5, 19).

Consider two points (1, 3) and (3, 11).

Slope, m = (11 - 3) / (3 - 1) = 8 / 2 = 4

So the equation is y = 4x + c.

Substitute (1, 3) in the above equation.

3 = (4 × 1) + c

c = 3 - 4

c = -1

So the equation is y = 4x - 1.

Hence the given function can be represented as f(x) = 4x - 1.

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The function representing number of fish each 't' year

n ( t ) = (600t + 500) / ( 0.5t + 1) best defines option A. The number of fish get larger every year , but does not exceed the number 1200.

Let 'n' represents the number of fish.

't' represents the year.

The function representing the number of fish in 't' years is :

n ( t ) = (600t + 500) / ( 0.5t + 1)

Number of cans poured in the lake by farmer is equal to 5

Number of fish in each can = 100

Let t = 1

n(1) = 600(1) + 500 / 1.5

     = 733.33

t= 2

n(2) =  600(2) + 500 / 2

       =850

n(3) = 600(3) + 500 / 2.5

      = 920

Therefore, the function n ( t ) = (600t + 500) / ( 0.5t + 1) best describes the option A. The number of fish get larger every year , but the number does not exceed  1200.

The above question is incomplete, the complete question is:

The wildlife game commission poured 5 cans of fish (each can contained approximately 100 fish) into a farmer's lake. the function n defined by

n ( t ) = (600t + 500) / ( 0.5t + 1) represents the approximate number of fish in the lake as a function of time (in years).Which one of the following best describes how the number of fish in the lake changes over time?

A. The number of fish gets larger each year, but does not exceed 1200.

B. The number of fish gets smaller every year but does not get smaller then 1200.

C. The number of fish gets larger each year, but does not exceed 600.

D. The number of fish gets larger each year, but does not exceed 500.

E. The number of fish gets smaller every year, but does not get smaller than 500.

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