find the mean of the following frequency distribution: score:1,2,3,4,5,6,7. frequently :. 5,9,12,17,14,10,6​

Answer:

\(-\frac{1}{9}\)

Step-by-step explanation:

between (1, 9) and (10, 8), the x moves by 9 and y moves by -1

The slope is equal to: \(\frac{\Delta y}{\Delta x} = \frac{-1}{9} = -\frac{1}{9}\)

Answer:

-1/9

Step-by-step explanation:

plug in the slope formula:

y-y

-----

x-x

=9-8

-------

1-10

=-1/9

Answer:

The answer to this question is:

A = 16,100(1.001)12t; $17,510

Step-by-step explanation:

The model function for compound interest is: \((16000[1.001]^{12t})\)

The balance after 7 years will be $17409.

Let, P = the principle amount

r = the rate of interest, compounded monthly

t = the time period

Therefore, the amount will be

\(= P(1 + \frac{r}{1200})^{12t}\)

Given, the invested amount is $16000.

The rate of interest is 1.2%, compounded monthly.

Total duration of investment is 7 years.

Therefore, the model function of this compound interest is:

= \(= (16000[1 + \frac{1.2}{1200}]^{12t})\\= (16000[1 +0.001]^{12t})\\= (16000[1.001]^{12t})\\\)

The amount will be

\(= (16000[1.001]^{12t})\\= (16000[1.001]^{84})\\= 17409\)

Therefore, after 7 years, the amount will be $17409.

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Step-by-step explanation:

8.3 = 8+ 0.3

= 8 + 3/10

= 8 3/10

The numerical value of x in angle ABD is 9 as angle ABC is divided into two equal halves.

An angle bisector divided an angle into two equal halves.

From the diagram:

Line BD divides angle ABC into two equal halves.

Angle ABD = ( 3x - 7 ) degrees

Angle DBC = 20 degrees

Since angle ABD and DBC are equal haves;

Angle ABD = Angle DBC

Plug in the values:

( 3x - 7 ) = 20

Solve for x:

3x - 7 = 20

Add 7 to both sides:

3x - 7 + 7 = 20 + 7

3x = 27

x = 27/3

x = 9

Therefore, the value of x is 9.

Option A)9 is the correct answer.

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Answer:

26850

Step-by-step explanation:

35,800 × 0.75 is 26,850

The percentage (%), is a mathematical symbol that represents a given amount as a fraction is one hundred equal parts.

Therefore ⇒ 35800 ✖ .75 = 26850  

Answer: The 75 % of 35800 it is 26850.

The vertices of ABCD after 90 degrees clockwise rotation about point C are: A' (0,6), B' (3,7), C' (4,6) and D' (4,3)

The image of the polygon ABCD is not given; however, the question can still be answered because the coordinates are known.

The vertices of polygon ABCD are given as:

A = (4, 6)

B = (5, 3)

C = (4, 2)

D = (1, 2)

The rule of rotation about point C is:

(x,y) = (a + b - y, x + b - a)

Where:

(a, b) = (4, 2) --- the point of rotation.

So, we have:

(x,y) = (4 + 2 - y, x + 4 - 2)

(x,y) = (6 - y, x + 2)

The above means that:

A' = (6 - 6, 4 + 2) = (0,6)

B' = (6 - 3, 5 + 2) = (3,7)

C' = (6 - 2, 4 + 2) = (4,6)

D' = (6 - 2, 1 + 2) = (4,3)

Hence, the image of the rotation and their vertices (i.e. coordinates) are:

A' = (0,6)

B' =  (3,7)

C' = (4,6)

D' =  (4,3)

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Answer:

x = -5

Step-by-step explanation:

X -6= 11 - 11(x + 7)

Distribute

x-6 = 11 -11x -77

Combine like terms

x-6 = -11x -66

Add 11x to each side

x-6+11x = -11x-66+11x

12x-6 = -66

Add 6 to each side

12x -6+6 = -66+6

12x = -60

Divide by 12

12x/12 = -60/12

x = -5

Answer:

12

Step-by-step explanation:

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete but a possibility is that the given parameters are points  on a straight line.

I'll answer base on that assumption.

\(RS = 6y + 2\)

\(ST =2y + 7\)

\(RT =13y -21\)

To solve for y, we have that:

\(RT = RS + ST\)

This gives:

\(13y - 21 = 6y + 2 + 2y + 7\)

Collect Like Terms

\(13y - 6y - 2y = 21 +2+7\)

\(5y = 30\)

Divide both sides by 5

\(y = 6\)

To get the measure of each line. Substitute 6 for y in

\(RS = 6y + 2\)

\(ST =2y + 7\)

\(RT =13y -21\)

\(RS = 6 * 6 + 2 = 36 + 2 = 38\)

\(ST = 2*6 + 7 = 12 +7 = 19\)

\(RT = 13*6 - 21 = 78 - 21 = 57\)

let

width = w

length = 4w + 11

2(length) + 2(width) = perimeter

2(4w + 11) + 2(w) = 162

8w + 22 + 2w = 162

10w + 22 = 162

10w = 140

w = 14 cm (WIDTH)

length = 4w + 11

length = 4(14) + 11

length = 56 + 11

LENGTH = 67 cm

The length is 4(14)+ 11 = 67 cm and width is 14 cm.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values. We frequently observe constant change in specific values in our day-to-day situations.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Perimeter of rectangle = 162 cm

let the width be x .

then, the length is 4x+ 11

Thus, Perimeter of rectangle= 2(l + w)

162 = 2( 4x + 11 + x)

162 = 2( 5x +11)

81 = 5x+ 11

5x= 70

x= 14

Hence, the length is 4(14)+ 11 = 67 cm and width is 14 cm.

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Answer:

X= 5

Step-by-step explanation:

Write in slope-intercept form, y=mx+b.

Hope this helps!

The value of the exponential function when x = 2 is 64

The standard form of exponential equation is expressed as y = ab^x

Given the exponential function expressed as:

f(x) = 2^x

For the value f(6)

f(6) = 2^x

f(6) = 2^6

f(6) = 64

Hence the value of the exponential function when x = 2 is 64

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The slope which shows  the cost per guest is $35 per guest

The given cost for 50 guests is $2150.

The cost for 75 guests is $3025.

It can also be represented as:

(Guest, Cost) =(50, $2150) & (75, $3025)

The slope can now be calculated as

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (50, $2150) & (75, $3025)

Substituting the given values in the equation as follows:

Slope = (3025 - 2150)/(75 - 50)

Slope = 35

Hence, the slope is $35 per guest.

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The largest number of relief supplies that can be put in each box is 75 bottles and 8 cans of food respectively.

The factors of:

1350 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 27, 30, 45, 50, 54, 75, 90, 135, 150, 225, 270, 450, 675 and 1350.

144 = 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.

1350 bottles / 18

= 75 bottles per box

144 cans of food / 18

= 8 cans of food per box

So, there 18 boxes of items, each containing 75 bottles and 8 cans of food respectively.

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Answer:

A. 6x^2-17x+12

Answer:

last one

Step-by-step explanation:

since the only letters that both sets have

Answer:

It is linear. The constant rate of change is 3 cents per hour.

Step-by-step explanation:

15/5 = 3

24/8 = 3

36/12 = 3

72/24 = 3

A pipe whose diameter measures 1 1/4 inches should have less threads per inch than a pipe with a diameter of 11/2 inch. So, the correct answer is (D).

To determine the correct answer, we need to compare the diameters of the two pipes and understand the relationship between pipe diameter and threads per inch.

The number of threads per inch generally decreases as the pipe diameter increases. This means that a larger pipe diameter will have fewer threads per inch compared to a smaller pipe diameter.

Given that the first pipe has a diameter of 1 1/4 inches, we need to find the pipe diameter from the options that is larger than 1 1/4 inches.

The option that meets this requirement is D. 11/2. This represents a pipe diameter of 1 1/2 inches. Therefore, a pipe with a diameter of 1 1/2 inches should have fewer threads per inch than a pipe with a diameter of 1 1/4 inches. Therefore, the correct answer is D. 11/2.

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Therefore, sin θ = 4/5, csc θ = 5/4, and cot θ = -3/4 using trigonometric ratio.

We know that the point (-3, 4) is on the terminal side of the angle θ, and we can use the Pythagorean theorem to find the value of the hypotenuse:

r² = x² + y²

r² = (-3)² + 4²

r² = 9 + 16

r² = 25

r = 5

Now we can find the values of sin θ, csc θ, and cot θ:

sin θ = y/r = 4/5

csc θ = r/y = 5/4

cot θ = x/y = -3/4

Therefore, sin θ = 4/5, csc θ = 5/4, and cot θ = -3/4.

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By fraction method, 55/16 pounds of rice Belle purchased.

In math, what is a fraction?

Part of a whole is a fraction. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction.

                                 Whether it is in the numerator or denominator, a complex fraction contains a fraction. The numerator and denominator of a correct fraction are opposite each other.

  = 2 3/4 * 5/4

   = 5/4 * 2 + 5/4 *  3/4

   = 5/2 + 5/4 * 3/4

  = 5/2 + 15/ 4 * 4

  = 5/2 + 15/16

  common denominator and write the numerators above common denominator   =   5 *8/16 + 15/16

         = 40/16 + 15/16

         = 40 + 15/16

          = 55/16

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Answer:

72%

Step-by-step explanation:

18/25 x 4= 72/100

=72%

Answer:

72%

Step-by-step explanation:

To convert fractions into percentages we could change to decimal and then multiply by 100 but it would be easier to just make the fraction's denominator to 100 by finding an equivalent fraction:

18/25 = 18×4/25×4

72/100

So 72% of students have a pet

Answer:

Option B.  house B; monthly payment of $1,550.89 is the correct answer.

Step-by-step explanation:

In order to calculate the highest payment Pete can afford we have to subtract his expenses from his housing budget.

Given

Total housing budget = $2250

Monthly costs = $215.75

Utilities = $143.50

Taxes = $273

First all expenses can be added together to subtract from the housing budget.

So

\(Monthly\ costs = Insurance\ +\ Utilities\ +\ taxes\\ = \$215.75 + \$143.50 + \$273\\= \$632.25\)

Now the total monthly cost will be subtracted from housing budget.

\(Amount\ for\ monthly\ payment = Housing\ budget - Monthly\ Expenses\\=\$2250\ -\ \$632.25\\=\$1617.75\)

Hence, he saves $1617.75 for monthly payment.

Looking at the options, C and D will be ruled out as both the quantities are greater than 1617.75

Option A and B both are smaller than 1617.75 but as $1,550.89>$1,327.18, Option B is the highest monthly payment Pete can afford.

Hence,

Option B.  house B; monthly payment of $1,550.89 is the correct answer.

A right triangle has legs of 217 and 456. Find the perimeter exactly

Hint: the hypotenuse is a whole number

step 1

Find out the hypotenuse

Applying the Pythagorean Theorem

c^2=217^2+456^2

c^2=255,025

c=505

step 2

Find the perimeter

The perimeter of triangle is equal to

P=a+b+c

substitute the given values

P=217+456+505

P=1,178 units

therefore

Part 2

see the attached image to better understand the problem

we have that

sin(theta)=456/505=0.90 --------> opposite side divided by the hypotenuse

cos(theta)=217/505=0.43-------> adjacent side divided by the hypotenuse

tan(theta)=456/217=2.10 -----> opposite side divided by the adjacent side

Answer:

Step-by-step explanation:

→ let D₁ be the line that represents f :

Slope of D₁ = (-5 - 1)/(2 - 1) = -3

Also D₁ passes through the point (0 , 1)

Then ,

f(x) = -3x + 1

……………………………

→ let D₂ be the line that represents g :

Slope of D₂ = (5 - -1)/(1 - -2) = 6/3 = 2

Also D₂ passes through the point (0 , 3)

Then ,

g(x) = 2x + 3

……………………………

f(x) × g(x) = (-3x + 1)×(2x + 3)

                = -6x² - 9x + 2x + 3

                = -6x² - 7x + 3

Answer:

yes

Step-by-step explanation:

because it has a vertex (-5,6) and y values repeat

Answer:

1031.70833333

Step-by-step explanation:

Answer:

The 3.907 is approximate.

====================================

Explanation:

x = number of hours that elapse

y = f(x) = number of tokens

If we use a graphing tool like a TI84 or GeoGebra, then the approximate solution to -3(2)^(x+1) + 90 = 0 is roughly x = 3.907

At around 3.907 hours is when the number of tokens is y = 0. Therefore, this is the approximate upper limit for the domain. The lower limit is x = 0.

The domain spans from x = 0 to roughly x = 3.907, and we shorten that down to 0 ≤ x ≤ 3.907

------------

Plug in x = 0 to find y = 84. This is the largest value in the range.

The smallest value is y = 0.

The range spans from y = 0 to y = 84, so we get 0 ≤ y ≤ 84

Keep in mind y is the number of tokens. A fractional amount of tokens does not make sense, so we must have y be a whole number 1,2,3,...,83,84.

The x value can be fractional because 3.907 hours for instance is valid.

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Extra info: