On a quiz worth 5 points, eight students earned a 5, two students earned a 4, five students earned a 3, six students earned a 2, five students earned a 1, and zero students earned a zero. Find the class average on this quiz.

Express your answer rounded to the tenths place.

Answer:

See attachment

Step-by-step explanation:

The mapping for a dilation with a scale factor k, about the origin is given by:

[tex](x,y) \to \: (kx,ky)[/tex]

From the graph, the coordinates of B are (1,1) and the scale factor is k=4.

We substitute into the rule to get

[tex]B(1,1) \to \: B'(4,4)[/tex]

The image of point B is plotted on the graph in the attachment.

To find the image of point B under a dilation with a scale factor of 4 about the origin (0,0), multiply the coordinates of point B by 4.

To plot the image of point B under a dilation with a scale factor of 4 about the origin (0,0), we need to multiply the coordinates of point B by the scale factor. If point B is represented as (x,y), then the image of B would be (4x, 4y).

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Step-by-step explanation:

Use (a+b)²= a²+2ab+b² formula

We can see that a²=81n² (so a=9n) and b²=100 (so b=10) and 2ab = 2*9n*10=180n.

therefore only √(81n²+180n+100) would be perfect square and this - isn't.

Answer: 70

Step-by-step explanation:

Solve the equation in the innermost parentheses first that means solving 4+1 =5

The next step would be subtracting 9 from five which gives you 4

Next multiply 3 to 4 which gives you 12

Then multiply 5 with 12 which equals 60

Now you have the equation 60+20/4*2

Solve the division and multiplication part of the equation first because of the rule pemdas which shows multiplication comes before addition

First divide 20/4 which gives you 5 then multiply with 2 which gives you ten

After dividing and multiplying you are left with the equation 60+10

The answer is 70

Answer:

Area = [tex]\frac{75}{4} \sqrt{15} sq mm[/tex]

Step-by-step explanation:

Here we are given with all the sides of the triangle , and we are asked to find the area of it. we will use Heron's Formula to find the area. The formula is as under

Area [tex]= \sqrt{s\times (s-a) \times (s-b) \times (s-c)}[/tex]

Where [tex]s= \frac{a+b+c}{2}[/tex]

Where a , b and c are the three sides of the triangle

a=15 , b=10 and c=20

Substituting those values in the two formula one by one we get

[tex]s=\frac{15+10+20}{2}[/tex]

[tex]s=\frac{45}{2}[/tex]

now putting this value of s in main formula we get

Area= [tex]\sqrt{s\times (s-a) \times (s-b) \times (s-c)}[/tex]

Area = [tex]\sqrt{\frac{45}{2} \times (\frac{45}{2}-15) \times (\frac{45}{2}-10) \times (\frac{45}{2}-20)}[/tex]

Area = [tex]\sqrt{\frac{45}{2} \times (\frac{45-30}{2}) \times (\frac{45-20}{2}-) \times (\frac{45-40}{2})}[/tex]

Area = [tex]\sqrt{\frac{45}{2} \times (\frac{15}{2}) \times (\frac{25}{2}) \times (\frac{5}{2})}[/tex]

Area = [tex]\sqrt{\frac{45}{2} \times (\frac{15}{2}) \times (\frac{20}{2}-) \times (\frac{5}{2})}[/tex]

Area = [tex]\frac{1}{4} \sqrt{45 \times 15 \times 25 \times 5}[/tex]

Area = [tex]\frac{1}{4} \sqrt{45 \times 15 \times 25 \times 5}[/tex]

Area = [tex]\frac{1}{4} \sqrt{9 \times 5 \times 5 \times 3 \times 25 \times 5}[/tex]

Area = [tex]\frac{3\times 5 \times 5}{4} \sqrt{3 \times5}[/tex]

Area = [tex]\frac{75}{4} \sqrt{15}[/tex]

The area of a triangle with legs that are 15 mm, 10 mm, and 20 mm is [tex]72.618 mm^{2}[/tex]

For example;

                    =  1/2 x base x height

For example;

In this case we are given, a = 15 mm, b = 10 mm, c = 20 mm

Therefore, we use the Heron's formula;

Area= [tex]s\sqrt{s(s-a)(s-b)(s-c)}[/tex]

 [tex]s =\frac{(a+b+c)}{2}[/tex]

[tex]s= \frac{(15+10+20)}{2} \\s= 22.5[/tex]

Therefore;

Area = [tex]s\sqrt{s(s-a)(s-b)(s-c)}[/tex]

       = [tex]22.5\sqrt{12.5(12.5-15)(22.5-10)(22.5-20)}[/tex]

       =[tex]\sqrt{22.5(7.5)(12.5)(2.5)} \\\sqrt{5273.4375}[/tex]

[tex]= 72.618 mm^{2}[/tex]

Keywords: Area, Area of a triangle, Heron's formula, Sine formula, Scalene triangle.

Level: Middle school

Subject; Mathematics  

Topic: Area

Sub-topic: Area of a triangle

The question revolves around understanding the concepts of fixed costs, marginal costs, and economies of scale in the context of a computer manufacturing company. The company's ability to make substantial profits over a period of four years marks an effective management of these costs and leveraging economies of scale.

The computer company's scenario primarily involves understanding the concept of fixed costs and marginal costs in a business context. The fixed cost noted here is $250, which remains constant irrespective of the number of computers produced. The marginal cost, on the other hand, is variable depending on the volume of production.

For example, the company's marginal cost for producing computers is $700 for the first one, $250 for the second, and so on. The total cost is obtained by adding the fixed cost and the total variable (marginal) costs. Understanding these costs is critically important for the company to make decisions about pricing its products to achieve desired profit margins.

It means that if the company managed to make profits of $80 million after 4 years, they have effectively managed their fixed and variable costs and priced their computers profitably. In this example, by leveraging the economies of scale, that is, an advantage that companies gain when production becomes efficient with the increasing scale of output, the company has managed to reduce the average cost of production and increase profits.

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Answer:  The correct options are

(2) The coefficient is 2.

(3) The constant is 5.

(6) There are two terms.

Step-by-step explanation:  Given that Javier used the expression below to represent his score in a game of mini-golf :

[tex]E=3x+x+5-2x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We are to select the correct statements about the parts of the simplified expression if Javier simplifies the expression.

The simplification of expression (i) is as follows :

[tex]E\\\\=3x+x+5-2x\\\\=(3+1-2)x+5\\\\=2x+5.[/tex]

Therefore, we get

the constant term is 5,

the coefficient of x is 2

and

There are two terms.

Thus, options (2), (3) and (6) are correct.

Answer:

think its 2 3 and 6

Step-by-step explanation:

sorry if im late

Answer: 12

Step-by-step explanation: Multiply the chances of getting a marble, 4, and the chances of spinning the spinner, 3.

4 x 3 = 12

There are 12 outcomes.

Answer:12

Step-by-step explanation:

I did the test

[tex]\bf \textit{Product to Sum Identities} \\\\ sin(\alpha)sin(\beta)=\cfrac{1}{2}[cos(\alpha-\beta)\quad -\quad cos(\alpha+\beta)]\qquad \leftarrow \textit{we'll use this one} \\\\\\ cos(\alpha)cos(\beta)=\cfrac{1}{2}[cos(\alpha-\beta)\quad +\quad cos(\alpha+\beta)] \\\\\\ sin(\alpha)cos(\beta)=\cfrac{1}{2}[sin(\alpha+\beta)\quad +\quad sin(\alpha-\beta)][/tex]

[tex]\bf cos(\alpha)sin(\beta)=\cfrac{1}{2}[sin(\alpha+\beta)\quad -\quad sin(\alpha-\beta)] \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin(5x)sin(3x)\implies \cfrac{cos(5x-3x)-cos(5x+3x)}{2}\implies \cfrac{cos(2x)-cos(8x)}{2}[/tex]

Answer:[tex] \frac{1}{2}\left ( cos\left ( 2x\right )-cos\left ( 8x\right )\right )[/tex]

Step-by-step explanation:

Solution

[tex]Sin\left ( 5x\right )Sin\left ( 3x\right )[/tex]

We know

[tex] 2sin\left ( a\right )sin\left ( b\right )=cos\left ( a-b\right )-cos\left ( a+b\right ) [/tex]

Applying formula

[tex]Sin\left ( 5x\right )Sin\left ( 3x\right )=\frac{1}{2}\left ( cos\left ( 5x-3x\right )-cos\left ( 5x+3x\right )\right )[/tex]

=[tex] \frac{1}{2}\left ( cos\left ( 2x\right )-cos\left ( 8x\right )\right ) [/tex]

Answer:

1

Step-by-step explanation:

Solve the equation for x:

3(x + 5) = -4x + 8

Distribute.

3x + 15 = -4x + 8

Combine like terms.

3x + 15 = -4x + 8

+4x         +4x

7x + 15 = 8

     -15   -15

7x = -7

Divide both sides by 7.

x = -1

The following equation has one solution, x = -1.

Answer:

1 solution,  x = -1.

Step-by-step explanation:

3(x + 5 )= −4x + 8

3x + 15 = -4x + 8

3x + 4x = 8 - 15

7x = -7

x = -1.

Answer:

x = 2.

Step-by-step explanation:

9(x + 1) = 25 + x

9x + 9 = 25 + x

Subtract x from both sides:

9x - x + 9 = 25

Subtract 9 from both sides:

9x - x = 25 - 9

8x = 16

x = 16/8 = 2.

Answer:

x = 2

Step-by-step explanation:

Given

9(x + 1) = 25 + x ← distribute parenthesis on left side

9x + 9 = 25 + x ( subtract x from both sides )

8x + 9 = 25 ( subtract 9 from both sides )

8x = 16 ( divide both sides by 8 )

x = 2

Step-by-step explanation:

let's Recall the properties of a parallelogram

1. the opposite sides of a parallelogram is congruent

AB=CD

8x-7=5x+2

8x-5x=7+2

3x=9

x=3

2. the consecutive angles are supplementary

angle A+angle D=180°

2y+50°+3y+40°=180°

5y+90°=180°

5y=90°

y=18

Answer: 120 cm.

Step-by-step explanation: Each triangle has 3 sides, and each side is 1 cm. Multiply the number of sides for one triangle by the total number of triangles. 3 x 40=120. The perimeter is 120 cm.

Answer:

[tex]\large\boxed{\sqrt{2^2}\cdot\sqrt{2^2}\cdot\sqrt2\cdot\sqrt5\cdot\sqrt7\cdot\sqrt{y^2}\cdot\sqrt{y}}\\\boxed{2\cdot2\cdot y\sqrt{2\cdot5\cdot7\cdot y}}\\\boxed{4y\sqrt{70y}}[/tex]

Step-by-step explanation:

[tex]\begin{array}{c|c}1120&2\\560&2\\280&2\\140&2\\70&2\\35&5\\7&7\\1\end{array}\\\\1,120=2\cdot2\cdot2\cdot2\cdot2\cdot5\cdot7=2^2\cdot2^2\cdot2^2\cdot2\cdot5\cdot7\\\\y^3=y\cdot y\cdot y=y^2\cdot y[/tex]

[tex]\sqrt{1,120y^3}=\sqrt{2^2\cdot2^2\cdot2\cdot5\cdot7\cdot y^2\cdot y}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt{2^2}\cdot\sqrt{2^2}\cdot\sqrt2\cdot\sqrt5\cdot\sqrt7\cdot\sqrt{y^2}\cdot\sqrt{y}\\\\\sqrt{1,120y^3}=\sqrt{2^2}\cdot\sqrt{2^2}\cdot\sqrt{y^2}\cdot\sqrt{2\cdot5\cdot7\cdot y}\qquad\text{use}\ \sqrt{a^2}=a\\\\=2\cdot2\cdot y\cdot\sqrt{2\cdot5\cdot7\cdot y}\\\\\sqrt{1,120y^3}=2\cdot2\cdot y\cdot\sqrt{2\cdot5\cdot7\cdot y}=4y\sqrt{70y}[/tex]

Answer:

5i[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

and [tex]\sqrt{-1}[/tex] = i

Given

[tex]\sqrt{-75}[/tex]

= [tex]\sqrt{25(3)(-1)}[/tex]

= [tex]\sqrt{25}[/tex]  × [tex]\sqrt{3}[/tex] × [tex]\sqrt{-1}[/tex]

= 5 × [tex]\sqrt{3}[/tex] × i

= 5i[tex]\sqrt{3}[/tex]

Answer:

x=-7

Step-by-step explanation:

If a line is parallel to the y-axis, then it is vertical because the y-axis is vertical.

A vertical line is in the form of x=a number.

Since the line we are looking for is 7 units to the left of the y-axis, then the line is x=-7.  -7 is 7 units left of 0.

7 units right would have been x=7.

Answer:

Step-by-step explanation:

A line parallel to y-axis is a vertical line.

A vertical line has an equation x = a, where a is any real number.

The line is 7 units to the left of the y-axis. Therefore  the equation of this line is x = -7 (look at the picture).

Answer:

the number 6 is in the tenths place.

Hope this helps!

[tex]\bf \textit{volume of a square pyramid}\\\\ V=\cfrac{1}{3}Bh~~ \begin{cases} B=area~of\\ \qquad its~base\\ h=height\\ \cline{1-1} B=\stackrel{4\times 4}{16}\\ V=37.3 \end{cases}\implies 37.3=\cfrac{1}{3}(16)h\implies 111.9=16h \\\\\\ \cfrac{111.9}{16}=h\implies 6.99375=h[/tex]

Answer:

6.99

Step-by-step explanation:

To find the height use the formula 3*V/b squared

So plug the numbers you have which is the base and volume

3*37.3/4 squared

Now solve:

4 squared = 16

3*37.3 = 111.9

111.9/16 = 6.99375

6.99375 can be rounded down to 6.99

So,

[tex]y>1\wedge y>x[/tex]

1. Graph each inequality separately.

2. Choose a test point to determine which side of the line needs to be shaded.

3. The solution to the system will be the area where the shadings from each inequality overlap one another (purple area)

As for the system of inequalities we say it's unbounded.

Answer:

The amount invested at 5.5% was $36,000 and the amount invested at 9% was $28,000

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]I=P(rt)[/tex]

where

I is the Final Interest Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

Let

x -----> the amount invested at 5.5%

(64,000-x) -----> the amount invested at 9%

in this problem we have

[tex]t=1\ years\\I=\$4,500\\ P=\$64,000\\r1=0.055\\P1=\$x\\P2=\$64,000-\$x\\r2=0.09[/tex]

so

[tex]I=P1(r1t)+P2(r2t)[/tex]

substitute the given values

[tex]4,500=x(0.055*1)+(64,000-x)(0.09*1)[/tex]

[tex]4,500=0.055x+5,760-0.09x[/tex]

[tex]0.09x-0.055x=5760-4,500[/tex]

[tex]0.035x=1,260[/tex]

[tex]x=\$36,000[/tex]

[tex]64,000-x=64,000-36,000=\$28,000[/tex]

therefore

The amount invested at 5.5% was $36,000 and the amount invested at 9% was $28,000

The slope of the line is the change in the Y values over the change in X values.

Using the given points (2,-5) and (-2,3)

The Y values are -5 and 3 and the X values are 2 and -2.

The slope = (3 - (-5)) / -2 - 2) = 8/-4 = -2

The slope is -2

Answer:

  area ≈ 24π

Step-by-step explanation:

We have solved this problem two ways:

__

Drawing

A drawing of the figure (below) can help you find the radius of circle O. It is about 4.89 inches, so the area of circle O is about ...

  area = πr^2 = π(4.89 in)^2 ≈ 23.9π ≈ 24π . . . .square inches

__

Formulas

There is an interesting relationship between the area of the triangle and the radius of the circumscribing circle:

  r = (abc)/(4A) . . . . . where a, b, c are the triangle side lengths, and A is the triangle area

Heron's formula can tell us the area of the triangle from the side lengths:

  A = √(s(s-a)(s-b)(s-c)) . . . . where s = (a+b+c)/2

For the given triangle with side lengths 4, 5, and 8 (inches), the area can be found as ...

  s = (4+5+8)/2 = 8.5

  A = √(8.5·4.5·3.5·0.5) = √66.9375 ≈ 8.1815 . . . square inches

Then the radius of the circle is ...

  r = (4·5·8)/(4·8.1815) = 4.889 . . . inches

The area of the circle is then ...

  Circle O area = πr^2 = π(4.889 in)^2 = 23.9π in^2

__

The closest answer choice is 3.14×22.

Answer:

x=7

y=-1

Step-by-step explanation:

When the two equations are solved together, they form simultaneous equations.

x+y=6

x-y=8

Let us use the elimination method. if we add the two equations, we eliminate y.

2x=14

x=7

Let us substitute for the value of x obtained above.

x-y=8

7-y=8

y=7-8

y=-1

For a standard normal distribution, the standard deviation is always equals 1

Z score is used to determine by how many standard deviations the raw score is above or below the mean.

It is given by:

z = (raw score - mean) / standard deviation

For a standard normal distribution, the standard deviation is always equals 1

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Answer:

4.2 meters.

Step-by-step explanation:

Area = 1/2 * base * height.

6.72 = 1/2 * 3.2 * h

h = 6.72 / 1.6

= 4.2 m.

Answer:

4.2 meters

Step-by-step explanation:

The height of a triangle with an area of 6.72 square meters and a base of 3.2 meters is 4.2 meters.

6.72 = 1/2 * 3.2 * h

[tex]\bf 60z+50-97z=-37z+49\implies 50~~\begin{matrix} -37z \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~=~~\begin{matrix} -37z \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~+49\implies \stackrel{\textit{the what?!}}{50=49}[/tex]

well, clearly 50 ≠ 49.

but, whenever we get a result of this kind, is just a way to say no solutions.

you can look at it this way, is a system of equations, the equations are

y = -37z + 50

y = -37z + 49

now, notice, since both equations are in slope-intercept form, both equations have the same slope of -37, however, the y-intercept differs, meaning both equations are parallel and never touch each other.

since a solution for them is where they intercept and they never do, no solutions.

The given equation will have no solution.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given is an equation,  60z+50-97z=-37z+49

On solving, we get,

0 = -1

Which is not possible.

Hence, There is no solution.  

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Answer with step-by-step explanation:

We are given that at one farmer’s market, bananas cost $0.80 per pound while at another market, bananas are sold in 5 pound bags for $4.50 per bag.

We are to explain how to find the better buy.

For the first market, the rate of bananas is given per pound but for the other market, the rate is given for a 5 pound bag so we will find the rate of bananas per pound to compare the rates of both markets.

One pound of bananas at 2nd market = 4.50/5 = $0.9

Therefore, getting bananas from the first market at $0.80 per pound is a better buy.

Answer: A

Step-by-step explanation:on My quiz I got it right

Answer:

The correct answer options are,

A: 0

B: There is one real root with a multiplicity of 2.

Step-by-step explanation:

Discriminant of a quadratic equation ax² + bx + c = 0 is given by,

b² - 4ac

It is given a quadratic equation 9x² + 24x + 16 = 0

To find the discriminant

Here a = 9, b = 24 and c = 16

Discriminant = b² - 4ac

 = 24² - (4 * 9 * 16)

 = 576 - 576

 = 0

The correct options are

A: 0

B: There is one real root with a multiplicity of 2.

The discriminant of the quadratic equation 9x^2+24x+16=0 is 0, which means there is one real root with a multiplicity of 2.

Let's examine the quadratic equation 9x^2+24x+16=0 to find the discriminant and interpret its meaning for the roots of the equation.

A: The discriminant of a quadratic equation in the form ax^2+bx+c=0 is given by the formula b^2-4ac. Substituting the coefficients from our equation (where a=9, b=24, and c=16) into this formula gives us the discriminant:

discriminant = b^2 - 4ac = 24^2 - 4(9)(16) = 576 - 576 = 0.

B: The discriminant tells us about the nature of the roots of the quadratic equation. Since the discriminant is zero, this implies that there is one real root with a multiplicity of 2. Therefore, the quadratic equation has a perfect square factor and the graph of the equation touches the x-axis at one point, indicating that both roots are the same.

Answer: 84 inches, 7 feet tall.

Step-by-step explanation:

4 x 21 = 84 inches

84/12 = 7 feet ( there are 12 inches in 1 foot)

Answer:

2

Step-by-step explanation:

To find the slope of a line given two points [tex](x_1,y_1) \text{ and } (x_2,y_2)[/tex] you could use the formula: [tex]\frac{y_2-y_1}{x_2-x_1} \text{ or even } \frac{y_1-y_2}{x_1-x_2}[/tex].

However, what I'm fixing to do is equivalent to that except I think easier to remember.

You line up the points vertically and subtract, then put 2nd difference over 1st difference.

Like this:

 ( 3  ,   4)

- ( 5  ,   8)

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

-2        -4

So the slope is -4/-2=4/2=2.

The slope is 2.