if in a game of glass stepping stones. there are 18 tiles of glass. two in each row. one is tempered and will be fine if you jump on it. and the other will break. if 1 player was to play what are his/her chances of getting across?
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Answer:

[tex]\huge\boxed{f(x)=\dfrac{1}{120}x^3-\dfrac{1}{30}x^2-\dfrac{7}{40}x}[/tex]

Step-by-step explanation:

[tex]f(x)=a(x+3)(x-0)(x-7)=ax(x+3)(x-7)\\\\=ax\bigg((x)(x)+(x)(-7)+(3)(x)+(3)(-7)\bigg)\\\\=ax(x^2-7x+3x-21)=ax(x^2-4x-21)\\\\=(ax)(x^2)+(ax)(-4x)+(ax)(-21)\\\\=ax^3-4ax^2-21ax\qquad(*)\\\\f(-8)=-5[/tex]

[tex]\text{substitute}\ x=-8\\\\f(-8)=(a)(-8)^3-(4a)(-8)^2-(21)(-8)a=-512a-(4a)(64)+168a\\\\=-512a-256a+168a=-600a\\\\f(-8)=-5\\\\\text{therefore}\\\\-600a=-5\qquad|\text{divide both sides by (-600)}\\\\a=\dfrac{-5}{-600}\\\\a=\dfrac{1}{120}[/tex]

[tex]\text{Substitute to}\ (*):\\\\f(x)=\dfrac{1}{120}x^3-4\cdot\dfrac{1}{120}x^2-21\cdot\dfrac{1}{120}x=\dfrac{1}{120}x^3-\dfrac{1}{30}x^2-\dfrac{7}{40}x[/tex]

Answer:

159.1

Step-by-step explanation:

The expression would be 10.4+13+8+112+15.7, which equals 159.1 which is the total weight.

Answer:

0.267

Step-by-step explanation:

the answer is 0.267

The table shows the results for spinning the spinner 80 times. The relative frequency for the event​ "spin a 3​" is 0.32.

Relative frequency is the ratio of the considered sub-group's count to the total count. (so its frequency of the considered subgroup relative to the total frequency).

In the problem given,

The table shows the results for spinning the spinner 80 times.

Number of Outcomes of "Spin a 3"=16

Total Number of Trials =50

Therefore,

The relative frequency for the event​ "spin a 3​" = 16/50

                                                                             = 0.32

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The distance between (12,5) and (3,4) approximated to the 1 decimal place is 9.1.

To find the distance between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex], we will use the distance formula:

Distance = [tex]\(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)[/tex]

In this case, [tex]\((x_1, y_1) = (12, 5)\)[/tex] and [tex]\((x_2, y_2) = (3, 4)\)[/tex].

Substituting these values:

Distance = [tex]\(\sqrt{(3 - 12)^2 + (4 - 5)^2}\)[/tex]

Distance = [tex]\(\sqrt{(-9)^2 + (-1)^2}\)[/tex]

Distance = [tex]\(\sqrt{81 + 1}\)[/tex]

Distance = [tex]\(\sqrt{82}\)[/tex]

Now, approximate value of [tex]\(\sqrt{82}\)[/tex] to 1 decimal place:

[tex]\(\sqrt{82} \approx 9.1\)[/tex]

So, the correct response is 9.1.

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Answer:

Step-by-step explanation:

Recall that a proportional relationship is a relationship between two quantities in which the ratio of one quantity to the other quantity is constant. ... When ratios between quantities are not constant, a relationship may be linear but not proportional and the graph does not pass through the origin.

Answer:

Whats the question?

Step-by-step explanation:

Answer:

1,680

Step-by-step explanation

6 slices each 280 calories, 280 x 6 = 1,680

Answer:

40 students earned a B on this paper.

40%×80=32 people who chose action as their fav.

Answer:

12.3

Step-by-step explanation:

i took the quiz

Answer:

Working out 20% of 30

If you are using a calculator, simply enter 20÷100×30 which will give you 6 as the answer.

Step-by-step explanation:

Answer:

Step-by-step explanation:

what is 20% of 30? how would you calculate it?

30 : 100 * 20 = 6

or

30 * 0.20 = 6

Answer:

3/2 is the slope and (0,5) is the y-intercept

Step-by-step explanation:

We need slope-intercept form for this question, so we simplify the equation into:

-2y=-10-3x which is just

y=5+3/2x =

y=3/2x+5

When we compare this to y=mx+b, we see that 3/2 is the slope and (0,5) is the y-intercept.

Answer: The slope is [tex]\frac{3}{2}[/tex] and the y-intercept is 5.

Step-by-step explanation:

The equation is 3x - 2y = -10

We need to turn 3x - 2y = -10 into slope intercept form.

y = mx + b → slope-intercept form

3x - 2y = -10

-3x           -3x

-2y = -3x - 10

Divide the whole equation by -2

y = [tex]\frac{3}{2}[/tex]x + 5

The slope of the equation is [tex]\frac{3}{2}[/tex] and the y-intercept is -2.

There are 123 Asians, 25 Africans, 21 Europeans and 8 Americans in the village.

To determine the number of Asians, Africans, Europeans, and Americans in the village, the following calculation must be performed:

Therefore, there are 123 Asians, 25 Africans, 21 Europeans and 8 Americans in the village.

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Answer:

y = 0.45 × x

y = 0.45 × 12

y = 5.4

Step-by-step explanation:

The chair costs $5 and 40 cents

1.00065528... Is the correct answer.

ABC=50

DCE=65

DEF= I think 115

I hope that helps I would appreciate brainliest if possible :)

[tex]b = 2 - \dfrac 1a\\\\\implies ab = 2a -1\\\\\implies 2a -ab = 1\\\\\implies a(2-b) =1\\\\\implies a = \dfrac 1{2-b}[/tex]

Answer:

it should be 2/12 and 9/11

Step-by-step explanation:

Answer: 6

Step-by-step explanation: Solution: Perimeter of the triangle is the sum of the lengths of its sides. Thus, perimeter = 10 cm. 6.

The definition of the set E gives you a natural choice for the limits in the integral:

[tex]\displaystyle \iiint_E y \, dV = \int_0^6 \int_0^x \int_{x-y}^{x+y} y \, dz \, dy \, dx[/tex]

Computing the integral, we get

[tex]\displaystyle \iiint_E y \, dV = \int_0^6 \int_0^x y ((x+y)-(x-y)) \, dy \, dx = 2 \int_0^6 \int_0^x y^2 \, dy \, dx[/tex]

[tex]\displaystyle \iiint_E y \, dV = 2 \int_0^6 \frac13 (x^3 - 0^3) \, dx = \frac23 \int_0^6 x^3 \, dx[/tex]

[tex]\displaystyle \iiint_E y \, dV = \frac23 \cdot \frac14 (6^4 - 0^4) = \boxed{216}[/tex]

The evaluation of the triple integral ∭E y dV, where E = {(x, y, z) | 0 ≤ x ≤ 3, 0 ≤ y ≤ x, x − y ≤ z ≤ x + y} is 216

Triple integral integrates the integrand over three dimensions.

Given that:

E = {(x, y, z) | 0 ≤ x ≤ 3, 0 ≤ y ≤ x, x − y ≤ z ≤ x + y}

Evaluating the integral:

[tex]I = \int \int \int _E y \: dV[/tex]

[tex]I = \mathlarger{\int_0^6 (\int_0^x (\int_{x-y}^{x+y} y\: dz)dy)dx}\\\\I = \int_0^6 (\int_0^x [yz]_{z=(x-y)}^{z=(x+y)}dy)dx\\\\I = \int_0^6 (\int_0^x y( (x+y) - (x-y)) \: dy)dx\\\\ I = \int_0^6 (\int_0^x y(2y) \: dy)dx\\\\I =2 \int_0^6 \left [\dfrac{y^3}{3}\right ]_{y=0}^{y=x} dx\\\\I = 2 \int_0^6 (x^3/3) dx\\\\I = \dfrac{2}{3} \left[\dfrac{x^4}{4} \right]_{x=0}^{x=6} = \dfrac{2}{3} \times \dfrac{6^4}{4} =216[/tex]

Thus, the evaluation of the triple integral ∭E y dV, where E = {(x, y, z) | 0 ≤ x ≤ 3, 0 ≤ y ≤ x, x − y ≤ z ≤ x + y} is 216

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Answer:

Step-by-step explanation:

-3y<-14

divide both sides by -3

y<4.67

i’m not exactly sure what the question is asking or what you’re trying to find, but this is what i could figure out.

Answer:

y>14/3

I'll provide the step by step solution too.

=3y÷(-3)>-14÷(-3)

y>-14÷(-3)

y>14÷3

turn it into a fraction

y>14/3

hence your given answer above

Answer:

9)    a = ¾, vertex: (-4, 2),  Equation: y = ¾|x + 4| + 2

10)  a = ¼, vertex: (0, -3),  Equation: y = ¼|x - 0| - 3

11)   a = -4,  vertex: (3,  1),   Equation: y = -4|x - 3| + 1

12)  a = 1,    vertex: (-2, -2),  Equation: y = |x + 2| - 2

Step-by-step explanation:

I could only work on questions 9, 10, 11, 12 in accordance with Brainly's rules. Nevertheless, the techniques demonstrated in this post applies to all of the given problems in your worksheet.

The given set of graphs are examples of absolute value functions. The general form of absolute value functions is: y = a|x – h| + k, where:

|a|  = determines the vertical stretch or compression factor (wideness or narrowness of the graph).

(h, k) = vertex of the function

x = h represents the axis of symmetry.

Solve for a:

In order to solve for the value of a, choose another point on the graph, (0, 5) and substitute into the general form (equation):

y = a|x – h| + k

5 = a| 0 - (-4)| + 2

5 = a| 0 + 4 | + 2

5 = a|4| + 2

5 = 4a + 2

Subtract 2 from both sides:

5 - 2 = 4a + 2 - 2

3 = 4a

Divide both sides by 4 to solve for a:

[tex]\LARGE\mathsf{\frac{3}{4}\:=\:\frac{4a}{4}}[/tex]

a = ¾

Therefore, given the value of a = ¾, and the vertex, (-4, 2), then the equation of the absolute value function is:

Equation:  y = ¾|x + 4| + 2

Solve for a:

In order to solve for the value of a, choose another point on the graph, (4, -2) and substitute into the general form (equation):

y = a|x – h| + k

-2 = a|4 - 0| -3

-2 = a|4| - 3

-2 = 4a - 3

Add 3 to both sides:

-2 + 3 = 4a - 3 + 3

1 = 4a  

Divide both sides by 4 to solve for a:

[tex]\LARGE\mathsf{\frac{1}{4}\:=\:\frac{4a}{4}}[/tex]

a = ¼

Therefore, given the value of a = ¼, and the vertex, (0, -3), then the equation of the absolute value function is:

Equation:  y = ¼|x - 0| - 3

Solve for a:

In order to solve for the value of a, choose another point on the graph, (4, -3) and substitute into the general form (equation):

y = a|x – h| + k

-3 = a|4 - 3| + 1

-3 = a|1| + 1

-3 = a + 1

Subtract 1 from both sides to isolate a:

-3 - 1 = a + 1 - 1

a = -4

Therefore, given the value of a = -4, and the vertex, (3, 1), then the equation of the absolute value function is:

Equation:  y = -4|x - 3| + 1

Solve for a:

In order to solve for the value of a, choose another point on the graph, (-4, 0) and substitute into the general form (equation):

y = a|x – h| + k

0 = a|-4 - (-2)| - 2

0 = a|-4 + 2| - 2

0 = a|-2| - 2

0 = 2a - 2

Add 2 to both sides:

0 + 2  = 2a - 2 + 2

2 = 2a

Divide both sides by 2 to solve for a:

[tex]\LARGE\mathsf{\frac{2}{2}\:=\:\frac{2a}{2}}[/tex]

a = 1

Therefore, given the value of a = -1, and the vertex, (-2, -2), then the equation of the absolute value function is:

Equation:  y = |x + 2| - 2

Step-by-step explanation:

RV = QV but also = PV = 26

because RVQ and RVP are both isoceles triangles.

TR = QR/2 = 24/2 = 12

because T is the middle point of RQ.

Step-by-step explanation:

First, you need to calculate how much they will earn per hour by multiplying their raise per hour by there hours and adding it to their earnings divided by the hours worked. Then, whoever's is the highest will be the answer.

Hanna will earn more per hour after the raise, with an hourly rate of $10.75 compared to Dien's hourly rate of $10.60.

A division is a process of splitting a specific amount into equal parts.

To find the new earnings per hour for Hanna and Dien

Divide their total earnings after the raise by the total number of hours they worked after the raise.

The raise per hour is already given, so we can simply add it to their old hourly rate.

For Hanna, her new hourly rate would be:

(New earnings) / (Hours worked) = (78 + 8) / 8

= 86 / 8

= $10.75

This means that Hanna will earn $10.75 per hour after the raise.

For Dien, his new hourly rate would be:

(New earnings) / (Hours worked) = (60.60 + 3) / 6

= 63.60 / 6

= $10.60

This means that Dien will earn $10.60 per hour after the raise.

Therefore,  Hanna will earn more per hour after the raise, with an hourly rate of $10.75 compared to Dien's hourly rate of $10.60.

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Answer:

rude customers and complaints

Answer:

Ignorant managers.

Step-by-step explanation:

Ignore them

Find somewhere else to move.

Answer:

[tex]y < 3x - 4[/tex]

Step-by-step explanation:

We can tell right away, that the line has a positive slope, since it goes upwards and to the right. To find the slope exactly, we will use rise/run. We will count the units from the first given point until we reach the next point.

So we can tell that the slope is 3/1 or just 3.

Also, since the line crosses the y-axis at -4, this will be the y-intercept.

Next, since the line is dotted, we know that the inequality sign will either be the "greater than" sign, or the "lesser than" sign. In this case, since the shaded area is below the line, we will use the "lesser than" sign.

So all together, we have y < 3x - 4.

Hope this helps you :)

Answer:

3.544 < 3.55 < 3.554

Step-by-step explanation:

Answer:

3.554 3.55 3.544

Step-by-step explanation:

i hope this answer helps you <3

Answer:

y=(7/4)x + 12, y=(-4/7)x -46/7

Step-by-step explanation:

first for the perpendicular line: we know the slope is the opposite reciprocal of -4/7, so m= 7/4. now we have y= 7/4 x +b. b is the y-intercept. to find b plug in the point (-8,-2). -2=(7/4)(-8) + b = -14+b so b=12. so the slope of the perpendicular line is y=(7/4)x + 12

parallel:

since the line is parallel the slope is -4/7. so we have y=(-4/7)x + b. next plug in the point (-8, -2) to find b: -2 = (-4/7)(-8) + b = 32/7 + b. so b= -46/7

Answer:

D: Both the slopes and the y-intercepts are the same.

Answer:

its the same

Step-by-step explanation:

the slope is -2 and the y-intercept is (0,3)

Answer:

x = 1

Step-by-step explanation:

2(3x - 7) + 18 = 10 ( subtract 18 from both sides )

2(3x - 7) = - 8 ( divide both sides by 2 )

3x - 7 = - 4 ( add 7 to both sides )

3x = 3 ( divide both sides by 3 )

x = 1