Mrs. Montoro's class is participating in the Math Olympics. Each week of the quarter, a challenging math question is posted, and the students individually try to correctly answer the question. The results of the Math Olympics are shown in the dot plot below.

Which of the following statements describe the distribution in the dot plot?
(choose all that is correct)

1. The mean is 5 questions answered correctly
2. most students answered between 3 and 6 questions correctly
3. the median is 5 questions answered correctly
4. the median is 4.5 questions answered correctly
5. most students answered between 5 and 7 questions correctly
6. the mean is 4.5 questions answered correctly
7. the students answered between 1 and 9 questions correctly

Answer:

1. There would only be a line that passes through 4 from left to right indicating the y value always being y.

2. For every time x increase by 3 the y value would increase by 1. Ex: (1,1/3),(2,2/3), (3,1)

Step-by-step explanation:

Answer:a squared-b squared

Step-by-step explanation:

Answer:

[tex](a+b)(a-b)=a^{2} -b^{2}[/tex]

Step-by-step explanation:

This is a example of remarkable identities.

We know that the result of multiplication is called product and the values ​​that multiply are called factors.

We call remarkable identities to certain algebraic expressions with binomial products very frequent in the calculation.

For this example, we got a Product of the sum for the difference of two binomials.

[tex](a+b)(a-b)[/tex]

The product of the sum for the difference of two binomials is equal to the square of the first quantity, minus the square of the second.

[tex](a+b)(a-b)=a^{2} -b^{2}[/tex]

Demostration:

[tex](a+b)(a-b)= a^{2} -ab+ab-b^{2}=a^{2} -b^{2}[/tex]

.

im not sure but I think it is b

There are two rational numbers on that list.

B.  √100  =  +10  and  -10

D. √10,000  =  +100  and  -100

Answer: Option D.

Step-by-step explanation:

You need to remember that the circumference of a circle can be calculated with this formula:

[tex]C=2\pi r[/tex]

Where "r" is the radius of the circle and [tex]\pi =3.14[/tex]

In this case the distance 150 feet (From the edge of the track to the center of the circle) is the radius.

Since she walks her horse 4 times around the track, you need to multiply the circumference by 4 to calculate the approximate number of feet that she and her horse will travel:

 [tex]C=4[2(3.14)(150ft)]=3,768ft[/tex]

Let's say the first truck weighs x tons

Then, the weight of 2nd truck = x+2 tons

The weight of 3rd truck = (x + 2) + 2 = x+4 tons

The weight of 4th truck = (x + 4) + 2 = x+6 tons

Total weight of 4 trucks:

x + (x+2) + (x+4) + (x+6) = 32

which can be solved easily to give x = 5

Answer:

[tex]\large\boxed{x=-4}[/tex]

Step-by-step explanation:

[tex]-4x+3=19\qquad\text{subtract 3 from both sides}\\\\-4x+3-3=19-3\\\\-4x=16\qquad\text{divide both sides by (-4)}\\\\\dfrac{-4x}{-4}=\dfrac{16}{-4}\\\\x=-4[/tex]

Step 1: Combine like terms ( 3 and 19) by subtracting 3 to both sides

-4x + (3-3) = 19 -3

-4x = 16

Step 2: Isolate x by dividing -4 to both sides

[tex]\frac{-4x}{-4} =\frac{16}{-4}[/tex]

x = -4

Hope this helped!

Answer:

B, A and C.

Step-by-step explanation:

(7x^2-5x+3)+(2x^2+3x-1) is equivalent to expression B .

(3x^2-4x-4)+(-12x^2+2x+11) is equivalent to expression A .

(4x^2-3x-9)+(5x^2+5x+2) is equivalent to expression C .

You combine like terms to arrive with the answer.

The answer is:

- The first operation match with the polynomial:

B.  [tex]9x^{2} -2x+2[/tex]

- The second operation match with the polynomial:

A. [tex]-9x^{2}-2x+7[/tex]

- The third operation match with the polynomial:

C. [tex]9x^{2} +2x-7[/tex]

In order to solve the given operations, we need to group the like terms.

Remember, like terms are terms that share the same variable and the same exponent.

For example:

[tex]x^{2} +2x^{2} +3x^{3} +2=3x^{2} +3x^{3} +2[/tex]

We only operate with the variables that shares the same exponent.

Also, we need to remember the distributive property:

[tex](a+b)(c+d)=ac+ad+bc+bd[/tex]

So, we are given the following polynomials:

[tex]A.9x^{2} -2x+7\\\\B. 9x^{2} -2x+2\\\\C. 9x^{2} +2x-7[/tex]

And we need to perform the following operations:

First operation,

[tex](7x^{2}-5x+3)+(2x^{2} +3x-1)=7x^{2} +2x^{2} -5x+3x+3-1\\\\7x^{2} +2x^{2} -5x+3x+3-1=9x^{2} -2x+2[/tex]

So, the first operation match with the polynomial:

B.  [tex]9x^{2} -2x+2[/tex]

Second operation,

[tex](3x^{2}-4x-4)+(-12x^{2}+2x+11)=3x^{2} -12x^{2} -4x+2x-4+11\\\\3x^{2} -12x^{2} -4x+2x-4+11=-9x^{2}-2x+7[/tex]

So, the second operation match with the polynomial:

A. [tex]-9x^{2}-2x+7[/tex]

Third operation,

[tex](4x^{2} -3x-9)+(5x^{2} +5x+2)=4x^{2}+5x^{2} -3x+5x-9+2\\\\4x^{2}+5x^{2} -3x+5x-9+2=9x^{2} +2x-7[/tex]

So, the second operation match with the polynomial:

C. [tex]9x^{2} +2x-7[/tex]

Have a nice day!

From this triangle we know:

THE AREA:

[tex]A=80cm^2[/tex]

THE HEIGHT:

[tex]H=B+12[/tex]

We know that the area, height, and base of a triangle are related according to the following formula:

[tex]A=\frac{BH}{2} \\ \\ Substituting \ H: \\ \\ A=\frac{B(B+12)}{2} \\ \\ Substituting \ A: \\ \\  80=\frac{B(B+12)}{2} \\ \\ 2(80)=B(B+12) \\ \\ 160=B^2+12B \\ \\ B^2+12B-160=0[/tex]

Solving B by quadratic formula:

[tex]B_{12}=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ B_{12}=\frac{-12 \pm \sqrt{12^2-4(1)(-160)}}{2(1)} \\ \\ B_{12}=\frac{-12 \pm \sqrt{12^2-4(1)(-160)}}{2(1)} \\ \\ B_{1}=8 \ and \ B_{2}=-20[/tex]

Since we can’t have a negative value of the base, the correct option is:

[tex]B=8cm[/tex]

We must use the formula:

[tex]h(t)=-5.2t^2+v_{0}t+h_{0}[/tex]

Since James drops the balloon from a height of 45m, then this is the initial height, so [tex]h_{0}=45m[/tex]. Moreover, at the very instant he drops the balloon the initial velocity is zero, so [tex]v_{0}=0[/tex]. When the ballon hit the ground [tex]h(t)=0[/tex]. Therefore:

[tex]0=-5.2t^2+45[/tex]

Solving this equation:

[tex]5.2t^2=45 \\ \\ t^2=\frac{45}{5.2} \\ \\ t^2=8.653 \\ \\ t=\sqrt{8.653} \\ \\ t=2.941s[/tex]

Rounding to the nearest tenth:

[tex]\boxed{t=2.9s}[/tex]

Finally, the water balloon will hit the ground after 2.9 seconds.

We have the equation:

[tex]h(t)=-16t^2+32t+12[/tex]

But we know that this equation follows the form:

[tex]h(t)=-16t^2+v_{0}t+h_{0}[/tex]

According to this:

The height of the platform is [tex]h_{0}=12ft[/tex]

The initial velocity of the ball is [tex]v_{0}=32ft/s[/tex]

Answer:

∠E = ∠F = 41°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Sum the 3 given angles and equate to 180

x + x + 98 = 180 ( subtract 98 from both sides )

2x = 82 ( divide both sides by 2 )

x = 41

Hence

∠E = ∠F = 41°

Substitute:

f(3) = (1/8)(8^(3))

Evaluating the function gives us the answer of 64.

f(3) = 64

A. Getting recommended by a teacher

A getting recommended by a teacher the reason the reason why this is correct is because the teacher is not randomly picking you she already knows who she wants to recommend

Answer:

y = -√(x + 5) + 2.

Step-by-step explanation:

y = -√x

Shifting this 2 units up produces the equation:

y = -√x + 2

Moving it 5 units to the left gives:

y = -√(x + 5) + 2.

The equation of graph of  [tex]y=-\sqrt{x}[/tex] is shifted 2 units up and 5 units left.

[tex]y=-\sqrt{x+5}+2[/tex]

Given :

The graph of  [tex]y=-\sqrt{x}[/tex] is shifted 2 units up and 5 units left.

The parent equation of the graph is [tex]y=-\sqrt{x}[/tex]

The graph is shifted 2 units up

When any graph is shifted up  then we add the units at the end

Graph shifted 'a' units up then f(x) becomes f(x) +a

when a graph is shifted 'a' units left , then we add the units with 'x'

Graph shifted 'a' units left then f(x) becomes f(x+a)

The graph of  [tex]y=-\sqrt{x}[/tex] is shifted 2 units up and 5 units left.

Add 5 units with 'x' and add 2 units at the end

[tex]y=-\sqrt{x+5}+2[/tex]

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Answer:

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

The rate of change of a linear function is the slope m

h(x) = 2x is a linear function with slope m = 2

Hence rate of change is 2

The area of each parallelogram is 240 square inches, and the area of the carpet is 2,160 square inches.

The dimension of the parallelograms is given as:

Base = 12 inches

Height = 20 inches

The area of the parallelograms is calculated as:

Area = Base * Height

So, we have:

Area = 12 * 20

Area = 240 square inches

The area of each parallelogram is calculated as:

Area = 240 square inches

The number of parallelograms is given as:

n = 9

So, the area of the carpet is:

Carpet = 9 * 240 square inches

Evaluate

Carpet = 2160 square inches

Hence, the area of the carpet is 2160 square inches

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Final answer:

To find the total area of Patty's carpet, multiply the area of one parallelogram (base 12 inches, height 20 inches) by the number of parallelograms (9), resulting in a total area of 2160 square inches.

Explanation:

To calculate the area of a parallelogram, the formula is base times height. In the given question, each parallelogram has a base of 12 inches and a height of 20 inches.

So, the area of one parallelogram is:

Area = Base × Height = 12 inches × 20 inches = 240 square inches.

Since Patty's carpet is made up of 9 parallelograms, we multiply the area of one parallelogram by 9 to find the total area of the carpet:

Total area = 240 square inches × 9 = 2160 square inches.

Therefore, the total area of the carpet is 2160 square inches.

Answer:

i) y = 25x + 500

ii) y = 30x + 400

iii) The washing machines would cost the same amount after 20 years of use

iv) Standard machine

Step-by-step explanation:

i)

We are to determine a straight line equation that models the cost of High-Efficiency washing machine over the years;

The first step step is to determine the slope of the line,

( change in y) / ( change in x ) = (550 - 525) / ( 2 - 1) = 25

The equation is slope-intercept form will be;

y = 25x + c

Where y is the cost of the High-Efficiency washing machine and x the number of years. To determine the y-intercept, c, we use any pair of points given in the data table;

when x = 1, y = 525

525 = 25(1) + c

c = 500

Therefore;

y = 25x + 500

ii)

The straight line equation that models the cost of Standard washing machine over the years;

Slope = (460 - 430) / (2 - 1) = 30

The equation is slope-intercept form will be;

y = 30x + c

when x = 1, y = 430

430 = 30(1) + c

c = 400

Therefore;

y = 30x + 400

Where y is the cost of the standard washing machine and x the number of years.

iii)

Given the cost functions for both machines over the number of years, we simply equate the two equations and determine the value of x when both machines would cost the same amount;

We have the cost functions;

y = 25x + 500

y = 30x + 400

Equating the two and solving for x;

25x + 500 = 30x + 400

500 - 400 = 30x - 25x

100 = 5x

x = 20

Therefore, the washing machines would cost the same amount after 20 years of use.

iv)

In order to determine which machine would be the more practical purchase if kept for 9 years we use the cost functions obtained in i) and ii)

The cost function of the High-Efficiency washing machine is;

y = 25x + 500

To determine the cost, we solve for y given x = 9

y = 25(9) + 500

y = 725

The cost function of the Standard washing machine is;

y = 30x + 400

We solve for y given x = 9

y = 30(9) + 400

y = 670

Comparing the two values obtained, the cost for the Standard washing machine is more practical.

1) y=25x+500

2) y=30x+400

3) 20

4) standard machine

Answer: The answer is 100.

Step-by-step explanation: 40 divided by 2 = 20

x=20

20x5=100

Answer: answer is 140 on gradpoint.com

Answer:

See below.

Step-by-step explanation:

x^2 + 2x = 19

(x + 1)^2 - 1 = 19

(x + 1)^2 = 20.

Answer:

(x+1)2+2x=19

Step-by-step explanation:

i just did it on a p e x

Graphing the linear equation -2x - 3y = -7: Identify three points satisfying the equation, such as (0, 3), (1, 1), and (2, 1). Plotting these points on the graph, connect them to depict the line representing the equation on the Cartesian plane.

To graph the linear equation -2x - 3y = -7, we can first rearrange it to solve for y:

-2x - 3y = -7

-3y = 2x - 7

[tex]\[ y = \frac{2}{3}x + \frac{7}{3} \][/tex]

Now, we can select three points to plot on the graph. For simplicity, let's choose some integer values for x to find corresponding y values:

1. When x = 0: [tex]\(y = \frac{7}{3}\)[/tex], giving the point [tex](0, \(\frac{7}{3}\))[/tex].

2. When x = 3: y = 3, giving the point (3, 3).

3. When x = -3: y = -1, giving the point (-3, -1).

Now, plot these three points on the graph and connect them to visualize the line represented by the equation.

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Answer:

1  3/4 miles in 1/4 hour.

Step-by-step explanation:

Write and solve an equation of ratios:

 x           (1/4) hr

--------- = ------------

14 mi       2 hr

Cross multiplying, we get 2x = (1/4)(14), or

                                              x = (1/4)(7), or x = 7/4

Steve can jog 7/4 miles in 1/4 hour.  That's 1  3/4 miles in 1/4 hour.

Answer:

Step-by-step explanation:

ANSWER

Infinitely many solutions.

EXPLANATION

The given system t;

8x + 9y = –5

–8x – 9y = 5

We use the elimination method:

Let us add the two equations to obtain:

-8x+8x+9y-9y=-5+5

This simplifies to:

0=0

This implies that, the system has infinitely many solutions because the two lines coincide.

Let me know if you can see this photo

Answer:

There are  8 boys in the chorus and 16 girls in the chorus

The graph in the attached figure

Step-by-step explanation:

Let

x----> the number of boys

y----> the number of girls

we know that

[tex]y=2x[/tex] -----> equation A

[tex]x=y-8[/tex] ----> equation B

Solve the system of equations by graphing

Remember that the solution of the system of equations is the intersection point both graphs

The solution is the point (8,16)

see the attached figure

therefore

There are  8 boys in the chorus

There are  16 girls in the chorus

Answer:

B

Step-by-step explanation:

A(rectangle) = 14 * 21 = 294

A(triangle) = ((21 - 12) * 16) / 2 = 72

A(figure) = 294 + 72 = 366

Answer:

B 366 cm²

Step-by-step explanation:

Multiply 21 by 14 to find area of the rectangle

21 × 14 = 294

Subtract 12 from 21

21 - 12 = 9

Multiply 9 by 16

144

Divide 144 by 2 to get area of triangle

144 ÷ 2 = 72

Add 72 with 294 to get final answer

72 + 294 = 366

Answer: B 366 cm²

Answer:

A. 7 units

Step-by-step explanation:

Answer:

The correct option is A. The length of chord ST in P is 7 units.

Step-by-step explanation:

Given information: QR=7, distance between center and QR is 3.2 units and the distance between center and ST is 3.2 units.

If two chords are equidistant from the center of the circle, then the length of both chords are same.

From the given figure it is clear that the two chords QR and ST are equidistant from the center of the circle,so the length of both chords are same.

[tex]QR=ST[/tex]

[tex]7=ST[/tex]

The length of chord ST in P is 7 units. Therefore the correct option is A.

Answer: (5x^2 + 2)(3x - 1)

I'll break it down:

You start off with 15x^3 - 5x^2 + 6x - 2

You first group the first two terms together, and then the last two pairs together: (15x^3 - 5x^2) (6x - 2)

Then you simplify (just factor out as much as you can): 5x^2(3x - 1) 2(3x - 1)

Then you take the terms that you get from doing that.

To find the First Term:

5x^2(3x - 1) 2(3x - 1)

(5x^2 + 2)

To find the Second Term:

5x^2(3x - 1) 2(3x - 1)

(3x - 1)

So your terms are (5x^2 + 2) and (3x -1)

Final Answer: (5x^2 + 2)(3x - 1)

The resulting expression will be (5x² + 2)(3x - 1). The correct answer is option A.

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

The grouping of the given expression will be done as:-

You start off with 15x³ - 5x²+ 6x - 2

You first group the first two terms together, and then the last two pairs together: (15x³ - 5x²) (6x - 2)

Then you simplify (just factor out as much as you can): 5x²(3x - 1) 2(3x - 1)

Then you take the terms that you get from doing that.

To find the First Term:

5x² (3x - 1) 2(3x - 1)

(5x² + 2)

To find the Second Term:

5x²(3x - 1) 2(3x - 1)

(3x - 1)

So your terms are (5x² + 2) and (3x -1)

Therefore the resulting expression will be (5x² + 2)(3x - 1)

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Answer:

a building

Step-by-step explanation:

Your exams? Probably at home, unless it’s AZmerit or CAmerit.

First make a triangle by connecting the center point of the circle to one of the end points of the chord.

This will make a right triangle. The new formed line is the radius of the circle and will be the hypotenuse of the right triangle too.

Since one of the legs of the right triangle is half the chord, divide the chord in to two.

9.6 / 2 = 4.8

Now we can calculate for the hypotenuse.

Pythagorean theorem states that  a²+b² = c²

So

√2.4² + 4.8² = c

√5.76 + 23.04 = c

√28.8 = c

5.4 = c

C is the hypotenuse and the hypotenuse is known as the radius of the circle.

So the radius is 5.4

The value of x can be any number between 1.5 to 4.5. Some translations imply that 'x' is being used in scientific notation or being adjusted by standard deviations in statistical calculations. Furthermore, finding 'x' in equations could result in more than one solution.

The question is about finding the value of x, which is a mathematical variable. Without a proper equation or context, it is not possible to determine the specific value of x. However, some details were given, stating '1.5 ≤ x ≤ 4.5', meaning that the value of x can be any number between 1.5 and 4.5. Additionally, the concept of scientific notation or exponential notation appears in the data provided ('x x 10¹'). This can help express very large or small numbers in a simplified form. For instance, if 'x' is 8.4 and '10¹' indicates we have 14 placeholder zeros, the actual measurement value would be 8.4 followed by 14 digits (840,000,000,000,000).

Furthermore, the question has hints of statistics, shown when 'x' is increased and decreased by standard deviations, which are instructions to calculate different characteristic values from certain distributions (e.g., '(x + 1s)').

Remember that solving equations may result in more than one solution, pointing out the characteristic of quadratic equations that give two solutions. And finally, dividing and multiplying by powers of 10 simply means shifting decimal points right or left respectively, according to the number of zeros in the power of ten.

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Answer:

23.79

Step-by-step explanation:

since 1 is less than 4 it turns into zero

[tex]\bf \textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}~~ \begin{cases} r=&radius\\ \theta =&angle~in\\ &degrees\\ \cline{1-2} r=16\\ \theta =80 \end{cases}\implies s=\cfrac{(80)\pi (16)}{180}\implies s=\cfrac{64\pi }{9} \\\\\\ s\approx 22.34\implies \stackrel{\textit{rounded up}}{s=22}[/tex]

Final answer:

The length of the arc intercepted by a central angle of 80 degrees in a circle with a radius of 16 inches is approximately 22 inches to the nearest inch.

Explanation:

To find the arc length of a circle that is intercepted by a central angle of 80 degrees, we first need to know the formula for the circumference of a circle, which is 2πr.

In a full circle, which is 360 degrees, the arc length is equal to the circumference. However, because we are only dealing with an 80-degree angle, we need to find the fraction of the circumference that corresponds to this angle. The formula to calculate the arc length (As) for any given angle (Θ) in degrees is:

As = (2πr * Θ) / 360

Given a radius (r) of 16 inches, and a central angle of 80 degrees, the arc length is:

As = (2π * 16 * 80) / 360 ≈ (100.53 inches * 80) / 360 ≈ 8033.6 / 360 ≈ 22.3 inches

Therefore, to the nearest inch, the length of the arc is 22 inches.