math quarterly
8th grade

Answer:

If you plot points accordingly to the points on the table, Option A. is correct.

Answer:

2.  3.913 kg (3 dp)

3.  light cream

4.  240 CoffeeStops

5.  7 CoffeeStops per square mile

6.  2,861 cups of coffee each day

Step-by-step explanation:

Given:

Question 2

[tex]\begin{aligned}\textsf{1 gallon} & = \sf \dfrac{1}{0.264}\:liters\\\\\implies \textsf{Mass (1 gallon of skim milk)} & = \sf Density \times Volume\\& = \sf 1.033\:kg/l \times \dfrac{1}{0.264}\:l\\& = \sf 3.913\:kg\:(3\:dp)\end{aligned}[/tex]

Therefore, the mass of 1 gallon of skim milk is 3.913 kg (3 dp)

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

Question 3

Given:

[tex]\begin{aligned}\implies \sf Density & = \sf \dfrac{Mass}{Volume}\\\\& = \sf \dfrac{9.108\:kg}{9\:l}\\\\& = \sf 1.012\:kg/l \end{alilgned}[/tex]

Therefore, the container holds light cream.

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

Question 4

Given:

[tex]\begin{aligned}\implies \textsf{Number of Coffeestops} & = \sf \dfrac{population}{density}\\\\& = \sf \dfrac{1,602,000}{100,000/15}\\\\& = \sf \dfrac{1,602,000}{100,000} \times 15\\\\& = \sf 240.3\end{aligned}[/tex]

Therefore, there are 240 CoffeeStops.

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

Question 5

Given

[tex]\begin{aligned}\implies \textsf{CoffeeStops density} & = \sf \dfrac{number\:of\:stores}{land\:area}\\\\& = \sf \dfrac{240}{34}\\\\& \approx \sf 7 \: \textsf{CoffeeStops per square mile}\end{aligned}[/tex]

Therefore, the density of CoffeeStops is 7 per square mile.

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

Question 6

Given:

[tex]\begin{aligned}\implies \textsf{Cups served each week} & = \textsf{number of people} \times \textsf{number of cups per week}\\& = \sf 1,602,000 \times 3\\& = \sf 4,806,000\: \textsf{cups per week}\\\\\implies \textsf{Cups per day} & = \sf \dfrac{\textsf{cups per week}}{\textsf{days in a week}}\\\\& = \sf \dfrac{4,806,000}{7}\\\\& = \sf 686,571\:\textsf{(nearest whole number)}\end{aligned}[/tex]

[tex]\begin{aligned}\implies \textsf{Cups served per day per shop} & = \dfrac{\textsf{cups per day}}{\textsf{number of shops}}\\\\& = \sf \dfrac{686,571}{240}\\\\& = \sf 2,861\: \textsf{(nearest whole number)} \end{aligned}[/tex]

Therefore, each Manhattan CoffeeStop serves approximately 2,861 cups of coffee each day.

Answer:

  66°

Step-by-step explanation:

The angle sum theorem tells you the sum of angles in a triangle is 180°.

__

  79° +x +35° = 180°

  x = 180° -114° . . . . . . . . subtract 114° from both sides

  x = 66° . . . . . simplify

The values of the given trig functions in terms of sinθ and/or cosθ are:

sinθ = tanθ.cosθ

cosθ = sinθ/tanθ

secθ = 1/cosθ

cscθ = 1/sinθ

tanθ = sinθ/cosθ

cotθ = cosθ/sinθ

From the question, we are to determine the values of the given trig functions in terms of sinθ and/or cosθ

NOTE: tanθ = sinθ / cosθ

∴ sinθ = tanθ.cosθ

From above, we can write that

cosθ = sinθ/tanθ

Secant is the inverse of cosine

∴ secθ = 1/cosθ

Cosecant is the inverse of sine

∴ cscθ = 1/sinθ

tanθ = sinθ/cosθ

Cotangent is the inverse of tangent
∴ cotθ = 1/tanθ

But, tanθ = sinθ/cosθ

∴ cotθ = cosθ/sinθ

Hence, the values of the given trig functions in terms of sinθ and/or cosθ are:

sinθ = tanθ.cosθ

cosθ = sinθ/tanθ

secθ = 1/cosθ

cscθ = 1/sinθ

tanθ = sinθ/cosθ

cotθ = cosθ/sinθ

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Answer:3.46

Step-by-step explanation:i dont know the other one

Answer:

144 inches in 12 feet.

Step-by-step explanation:

There are 12 inches in 1 foot.

Find inches when you have 12 ft.

[tex]\frac{12feet}{1} *\frac{12 inches}{1 foot} = 144 inches[/tex]

Feet cancel out leaving inches.

There are 144 inches in 12 feet.

Answer:

C. 103,748

Step-by-step explanation:

The one in the first number is worth 10,000

The one in the Second number is worth 100,000

Answer:

She is wrong.

Step-by-step explanation:

The mean score is

7 + 8 + 3 + 0 + 2= 20

We then divide it by the number which is 5

20/5= 4.

Therefore, Maria is wrong.

This is because she divided by 4 instead of 5, as she didn't include the rational number 0.

Answer:

Freshmen to sophomores - (17:19)

Sophomores to freshmen - (19:17)

Step-by-step explanation:

I hope this helps! Have a lovely day!! :)

The vslue of the angle based on the information given will be 142°.

From the information given, it can be deduced that the shape has four sides. The total angles will be:

= (n - 2) × 180

= (4 - 2) × 180°

= 360°

The value of the last angle will be:

= 360° - (49° + 63° + 106°)

= 360° - 218°

= 142°

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Answer:

50

Step-by-step explanation:

Add all of the values together, which will equal 600, and then divide this number by how many numbers are here, which is 12.

600 / 12 = 50.

Answer:

B

Step-by-step explanation:

If you are allowed to use a graphing calculator, this can solve a lot of time. Graphing y = (x - 705)(x - 795) + 800(x - 750)(x - 835) gets us a parabola with x-intercepts of 749.97 and 834.924.

These roots are real and distinct, or choice B.

If you aren't allowed to use a graphing calculator, you can expand and combine like terms to get 801x^2 − 1269500x + 501560475. Looking at the discriminant, we see that (−1269500)^2 - 4*801*501560475 = 4630488100 is greater than 0 and not a perfect square, so it is real and distinct, or choice B.

I hope that helps!

Answer: 1/3x + 2/3

Step-by-step explanation:

f(x)= 3x - 2 =>

y= 3x - 2 =>

x= 3y - 2 =>

3y - 2= x =>

3y= x + 2 =>

y= 1/3x + 2/3 =>

f-1(x)=1/3x + 2/3

Answer:

x = 6

x = 0

Step-by-step explanation:

identify the coefficients

[tex]9x^2-54x=0\\a=9\\b=-54\\c=0[/tex]

coefficient a = 1

[tex]9x^2-54x=0\\9/9x^2-54x/9=0/9\\x^2-6x=0\\\rightarrow a=1\\\rightarrow b=-6\\\rightarrow c=0[/tex]

complete the square

[tex]b=-6\\(\frac{b}{2})^2=(\frac{-6}{2})^2\\(\frac{x}{y})^2=\frac{x^2}{y^2}\\=(\frac{-6}{2})^2=\frac{-6^2}{2^2}\\\frac{-6^2}{2^2}=\frac{36}{4}\\36 \div 4=9\\\\\downarrow\\\\x^2-6x=0\\x^2-6x+9=0+9\\x^2-6x+9=9\\\frac{b}{2}\\\frac{b}{2}=\frac{-6}{2}\\\frac{b}{2}=\frac{\left(-3\cdot 2\right)}{\left(1\cdot 2\right)}\\\frac{b}{2}=-3\\x^2-6x+9=9\\(x-3)^2=9\\[/tex]

solve for x

[tex](x-3)^2=9\\\sqrt{(x-3)^2}=\sqrt{9}\\x-3=+-\sqrt{9}\\x-3+3=3+-\sqrt{9}\\x=3+-\sqrt{9}\\x=3+-3\\x_1=6\\x_2=0[/tex]

≡ In the end, you have 2 values for x, because you can either subtract 3 by 3 or add 3 by 3 to get six or zero.

Answer:

This equation has 2 solutions.

1. [tex]x=\frac{-15+\sqrt{89}}{8}[/tex]

2. [tex]x=-\frac{15+\sqrt{89}}{8}[/tex]

Answer:

D

Step-by-step explanation:

because 3/10 is 0.3

Hope this helps!

The type of data that contains results from other people that are of similar age and gender is known as normative data.

Normative data is a type of data that is observed that contains information about the characteristics of a population of interest. For example, normative data about students in a class would contain information such as age, gender, height.

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Answer:

[tex]3 < x < 5[/tex]

Step-by-step explanation:

Given inequality:

[tex]|2x - 8| < 2[/tex]

[tex]\textsf{Apply absolute rule}: \quad \textsf{If }|u| < a\:\textsf{ when } \: a > 0,\: \textsf{then }-a < u < a[/tex]

[tex]\implies u=2x-8\: \textsf{ and }\:a=2[/tex]

[tex]\implies -2 < 2x-8 < 2[/tex]

Therefore:

[tex]\implies -2 < 2x-8[/tex]

[tex]\implies 6 < 2x[/tex]

[tex]\implies 3 < x[/tex]

And:

[tex]\implies 2x-8 < 2[/tex]

[tex]\implies 2x < 10[/tex]

[tex]\implies x < 5[/tex]

Merge the overlapping intervals:  [tex]3 < x < 5[/tex]

Proof

Graph:  [tex]y=|2x-8|[/tex]

Add a line at  [tex]y=2[/tex]

The interval that satisfies  [tex]|2x - 8| < 2[/tex]  is the area under the points of intersection (shaded area on the attached graph).

The values of x when [tex]y=|2x-8|[/tex] is less than 2 is more than x = 3 and less than x = 5.

So

Case-1

Case-2

So solution is

If Monique continues getting coffee at this rate then the money that she will have spent on coffee by the end of the year is $163.44.

An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.

If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:

a, a + d, a +  2d, ... , a + (n+1)d, ...

Its nth term is

Tₙ = a + (n-1)d

(for all positive integer values of n)

Given Monique goes out for coffee once per week. she has already spent $40.86 this year on her coffees and each one is $4.54. Therefore, the sequence can be written as,

4.54, 9.08, 13.62, 18.16, 22.7, 27.24, .........

Therefore,

Since 9 weeks (40.86/4.54 = 9) are already over, and there are 27 more weeks, therefore, the spending till 36 weeks will be,

a₃₆ = 4.54 + (36-1)4.54

a₃₆ = 163.44

Hence, if Monique continues getting coffee at this rate then the money that she will have spent on coffee by the end of the year is $163.44.

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Answer:

He read 10% of the book, so 90% remains to be read.  That 90% consists of 45 pages, so

45=0.90n

n= 45/0.90

n=50

There are 50 pages total in the book

Step-by-step explanation:

Answer:

  A

Step-by-step explanation:

The rate of change for the table is found using the slope formula. The rate of change for the linear function is the coefficient of x.

__

The slope formula tells us the rate of change is ...

  m = (y2 -y1)/(x2 -x1)

  m = (-9 -(-10))/(-1 -(-4)) = 1/3

The coefficient of x in the equations of the offered answer choices are 1/4 and 6.

The relations between the various slopes are ...

  1/4 < 1/3 < 6

That is, the equation with a slope of 1/4 has a rate of change less than that of the function represented by the table:

  y = 1/4x +4 because ... table of values is 1/3

Given the value of p and b in the equation ((  p-2b ) / 2 ), the value of m is 20.

Given that;

First, we substitute the value of p and b into the equation.

m = ( p-2b ) / 2

m = ( 57.4 - 2(8.7) ) / 2

m = ( 57.4 - 17.4 ) / 2

m = 40 / 2

m = 20

Given the value of p and b in the equation ((  p-2b ) / 2 ), the value of m is 20.

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Answer:

x+2

Step-by-step explanation:

x^2+x-7 = x+2

Answer:

The answer is 1/4!!

<3 love

Answer:

I believe it's c because Greg downloaded 5 song which is 6.45 total then bought certain song at sale price Wich ended at 9.42

Answer:

Step-by-step explanation:

The number of bottles of water and cheese sticks will be the same when both numbers are equal to the least common multiple (LCM) of 6 and 10, the numbers in each kind of package.

__

The LCM can be found by factoring out the greatest common divisor of each of the numbers:

  6 = 2 × 3

  10 = 2 × 5

The LCM is the product of the unique numbers here: 2 × 3 × 5 = 30.

The number of packages of bottles of water will be 30/6 = 5 packages.

The number of packages of cheese sticks will be 30/10 = 3 packages.

_____

Additional comment

You may notice that the number of packages of each kind is the unique factor in the other number.

Answer:

-2

Step-by-step explanation:

For a straight-line graph, pick two points on the graph.

The gradient of the line = (change in y-coordinate)/(change in x-coordinate)

             (x, y)

Point 1: (2, 0)

Point 2: (3, 2)

Gradient = (change in y)/(change in x)

= (2 - 0) / (3 - 2)

= 2 / 1

= 2

Note: gradient is basically slope where slope = rise / run

Answer:

help has arrived its -2

Step-by-step explanation:

Answer:

2900

Step-by-step explanation:

2,870 rounded up to the nearest hundred is 2900.Pls mark me as brainliest.