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The probability that at most 2 of the next 10 callers have to wait more than 8 minutes is the sum of the probabilities of 0, 1, or 2 callers having to wait for more than 8 minutes which is 0.810

The probability that at most 2 of the next 10 callers having to wait can be defined using the expression :

P(X ≤ 2) = P(0) + P(1) + P(2)

Using the individual probabilities given by the histogram attached :

P(X ≤ 2) = 0.181 + 0.345 + 0.284

P(X ≤ 2) = 0.810

Therefore, the probability that at most 2 callers have to wait more than 8 minutes is 0.810

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Answer:

Reflection across the A axis

Answer: al

Step-by-step explanation: hope this helps

Answer:

I it is the one on the bottom.

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

The negatives cancel out so -66/-6 comes out to be 66/6 which equals 11.

The required value is the angle theta and the value of the cosine of the angle is 0.9659

Given the expression of sine of an angle expressed as;

\(sin\theta = 0.2588\)

For us to get the cosine of the angle, we need to get the value of theta first as shown:

\(\theta = sin^{-1}0.2588\\\theta = 14.99^0\)

Next is to get the value of cos theta

\(cos \theta = cos 14.99 =0.9659\)

The required value is the angle theta and the value of the cosine of the angle is 0.9659

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\(\\ \rm\longmapsto 4x-2>6x+8\)

\(\\ \rm\longmapsto 4x-6x>8+2\)

\(\\ \rm\longmapsto -2x>10\)

\(\\ \rm\longmapsto -x>5\)

\(\\ \rm\longmapsto x<-5\)

the correct option is a. difference between the groups' averages, large absolute

I am trying to perform an A/B test to see if two samples come from the same underlying distribution. My alternative hypothesis is that the samples do not come from the same underlying distribution. The difference between the groups should be chosen as the test statistic averages  large absolute values of this statistic provide evidence in favor of the alternative hypothesis.

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Answer:

66 inches²

Step-by-step explanation:

Area of 1 triangle = ½ × base × height = ½ × 7 × 4 = 14 in²

Area of 2 triangles = 14 × 2 = 28 in²

Area of outer rectangles = (6 × 2) × 2 = 24 in²

Area of inner rectangle = 2 × 7 = 14 in²

Total surface area = 28+24+14 = 66 in²

Answer:

43

Step-by-step explanation:

Green:  9 - 2(-3) = 9 + 6 = 15

Red:  -2(-3) + 4 = 6 + 4 = 10

Dark blue:  7x + 5 = 19

7x = 19 - 5 = 14

x = 14/7 = 2

Light blue:  6x + 3 = 21

6x = 21 - 3 = 18

x = 18/6 = 3

Red(Lt blue) - Dk blue + Green = 10(3) - 2 + 15 = 43

Answer:

see attached picture, I can't tell what you want for 4

Answer:

Area of whole circle, i.e. 360 degrees = π(8.91)(8.91) = 79.3881 sq. cm

Area of 1 degree = 0.2205225 sq.cm.

Area of 81 degrees = 17.8623225 sq.cm.

The area of the shaded sector is about 16.77 cm2.

We are given that;

The radius=8.91

Now,

Surface area are derived for some standard shapes like circle, triangle, parallelogram, rectangle, trapezoid, etc.

When some shape comes which isn't standard figure, then we find its area by slicing it (virtually, like by drawing lines) in standard shapes. Then we calculate those composing shapes' area and sum them all.

Thus, we have:

\(\text{Area of composite figure} = \sum (\text{Area of composing figures})\)

That ∑ sign shows "sum"

To find the area of the shaded sector, we need to use the formula:

\($A = \frac{\theta}{360} \times \pi r^2$\)

where \(\theta\) is the central angle in degrees, and r is the radius of the circle.

Plugging in the given values, we get:

\($A = \frac{81}{360} \times \pi (8.91)^2A \approx 16.77 \text{ cm}^2$\)

Therefore, by the area answer will be 16.77 cm2.

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The graph of the solutions of the absolute value equation can be seen on the image at the end.

Here we have the absolute value equation:

|2x - 1| = 3

We can "break" that absolute value equation into two simpler ones, we will get:

(2x - 1) = 3

(2x - 1) = -3

Now we can solve these two, we will get for the first one.

2x - 1 = 3

2x = 3 + 1

x = 4/2

x = 2

The other gives.

2x - 1 = -3

2x = -3 + 1

2x = -2

x = -2/2 = -1

The solutions are 2 and -1, then the graph is the one below.

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Answer:

A

Step-by-step explanation:

With function transformation, added/subtracted numbers outside of the x always mean the function is being translated up/down. In this case, since the 2 is being replaced with a 4, the new function is 2 units higher than the previous function.

Answer:

x = 12

Step-by-step explanation:

= 6 * (1/6 x)

= (6) * (2)

x = 12

Hope this helps....

Have a good day ahead :)

Answer:

The awnser is D) X=12

Step-by-step explanation:

Sorry if its blurry:<

Answer:

72, 504, 172

Step-by-step explanation:

Let the unknown number be denoted as "x"

The second number = 7x

And the third number = 100 + x

(x) + (7x) + (100 + x) = 748

x + 7x + x + 100 = 748

9x + 100 = 748

9x = 748- 100

9x = 648

x = 648/9

x = 72

The first number = 72

The second number = 7x = 7 × 72 = 504

The third number = 100 + x = 100 + 72 = 172

I'll only look at (37) here, since

• (38) was addressed in 24438105

• (39) was addressed in 24434477

• (40) and (41) were both addressed in 24434541

In both parts, we're considering the line integral

\(\displaystyle \int_C (3x^2-8y^2)\,\mathrm dx + (4y-6xy)\,\mathrm dy\)

and I assume C has a positive orientation in both cases

(a) It looks like the region has the curves y = x and y = x ² as its boundary***, so that the interior of C is the set D given by

\(D = \left\{(x,y) \mid 0\le x\le1 \text{ and }x^2\le y\le x\right\}\)

• Compute the line integral directly by splitting up C into two component curves,

C₁ : x = t and y = t ² with 0 ≤ t ≤ 1

C₂ : x = 1 - t and y = 1 - t with 0 ≤ t ≤ 1

Then

\(\displaystyle \int_C = \int_{C_1} + \int_{C_2} \\\\ = \int_0^1 \left((3t^2-8t^4)+(4t^2-6t^3)(2t))\right)\,\mathrm dt \\+ \int_0^1 \left((-5(1-t)^2)(-1)+(4(1-t)-6(1-t)^2)(-1)\right)\,\mathrm dt \\\\ = \int_0^1 (7-18t+14t^2+8t^3-20t^4)\,\mathrm dt = \boxed{\frac23}\)

*** Obviously this interpretation is incorrect if the solution is supposed to be 3/2, so make the appropriate adjustment when you work this out for yourself.

• Compute the same integral using Green's theorem:

\(\displaystyle \int_C (3x^2-8y^2)\,\mathrm dx + (4y-6xy)\,\mathrm dy = \iint_D \frac{\partial(4y-6xy)}{\partial x} - \frac{\partial(3x^2-8y^2)}{\partial y}\,\mathrm dx\,\mathrm dy \\\\ = \int_0^1\int_{x^2}^x 10y\,\mathrm dy\,\mathrm dx = \boxed{\frac23}\)

(b) C is the boundary of the region

\(D = \left\{(x,y) \mid 0\le x\le 1\text{ and }0\le y\le1-x\right\}\)

• Compute the line integral directly, splitting up C into 3 components,

C₁ : x = t and y = 0 with 0 ≤ t ≤ 1

C₂ : x = 1 - t and y = t with 0 ≤ t ≤ 1

C₃ : x = 0 and y = 1 - t with 0 ≤ t ≤ 1

Then

\(\displaystyle \int_C = \int_{C_1} + \int_{C_2} + \int_{C_3} \\\\ = \int_0^1 3t^2\,\mathrm dt + \int_0^1 (11t^2+4t-3)\,\mathrm dt + \int_0^1(4t-4)\,\mathrm dt \\\\ = \int_0^1 (14t^2+8t-7)\,\mathrm dt = \boxed{\frac53}\)

• Using Green's theorem:

\(\displaystyle \int_C (3x^2-8y^2)\,\mathrm dx + (4y-6xy)\,\mathrm dx = \int_0^1\int_0^{1-x}10y\,\mathrm dy\,\mathrm dx = \boxed{\frac53}\)

The exact solutions of the qudratic equation 3x^2 - 6x + 2 = 0 are:

a. negative 1 plus or minus the square root of 3 divided by

3 (x = (-1 ± √3) / 3) .So, option a is the correct answer.

To find the solutions of the quadratic equation 3x^2 - 6x + 2 = 0, we can use the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 3, b = -6, and c = 2. Substituting these values into the formula, we have:

x = (-(-6) ± √((-6)^2 - 4(3)(2))) / (2(3))

x = (6 ± √(36 - 24)) / 6

x = (6 ± √12) / 6

x = (6 ± 2√3) / 6

x = (3 ± √3) / 3

Therefore, the exact solutions of the equation 3x^2 - 6x + 2 = 0 are:

a. negative 1 plus or minus the square root of 3 divided by 3 (x = (-1 ± √3) / 3)

So, option a is the correct answer.

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Answer:

A Yes, because every x-vaule has a single y-vaule

Step-by-step explanation:

None of the points share a point on the x axis meaning none of them are directly vertical of each other they are all seperate from each other.

Answer:

A

Step-by-step explanation:

The measure of angle DCE in this problem is given as follows:

m < DCE = 22.5º.

The triangles in this problem are right triangles, meaning that the trigonometric ratios are used to find the measures.

The three trigonometric ratios are given as follows:

The segment DB is adjacent to angle of 38º, while the hypotenuse is of 12.2 cm, hence the length of segment DB is calculated as follows:

cos(38º) = DB/12.2

DB = 12.2 x cosine of 38 degrees

DB = 9.6 cm.

BE:ED = 3:1, means that segment DE is one-fourth of segment DB, and thus it's length is given as follows:

DE = 1/4 x 9.6

DE = 2.4 cm.

Then for the angle DCE, we have that the opposite side is of 2.4 cm while the adjacent side is of 5.8 cm, hence the tangent is used to find it's measure, as follows:

tan(x) = 2.4/5.8

x = arctan(2.4/5.8)

x = 22.5º

m < DCE = 22.5º.

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Answer:

x = 22.5°

Step-by-step explanation:

Answer:

To find the percentage decrease, we need to find the difference between the original price and the new price, divide that difference by the original price, and then multiply by 100 to express the result as a percentage.

The difference between the original price and the new price is:

990 - 765 = 225

Dividing the difference by the original price gives:

225 ÷ 990 ≈ 0.227

Multiplying by 100 gives:

0.227 x 100 ≈ 22.7

Therefore, the percentage decrease in the monthly price of the contract is approximately 22.7%.

Step-by-step explanation:

Answer:

61..

Step-by-step explanation:

10-11 = +1

21-31=+10

31-50= +19

50-51= + 1

so pattern continues

Answer:

$5,824

Step-by-step explanation:

5,200*.04=208

208*3=624

5,200+624=5,824

Answer:

Step-by-step explanation:

So, here are some examples: 56 is equivalent to 1012 because 5 x 12 = 6 x 10 = 60. 1518 is equivalent to 1012 because 15 x 12 = 18 x 10 = 180. 2024 is equivalent to 1012 because 20 x 12 = 24 x 10 = 240.

We have the following ingredients

0.375 liters of lemon juice

0.35 liters of cranberry juice

1.2 liters of water

We need to perform the decimal addition to find out how much of the special drink can she make

Zee can make 1.925 liters of special drink.

How much more or less than 2 liters will she have?

Now we need to subtract this amount from 2 liters.

Zee will have 0.075 liters less than 2 liters.

How can you estimate the amount of the special drink Zee can make?​

We can estimate by rounding off 0.375 liters of lemon juice to 0.4

We can estimate by rounding off 0.35 liters of cranberry juice to 0.4

So the estimated amount of juice is

0.4 + 0.4 + 1.2 = 2 liters

The length of PQ is 3√5 and its slope is -2

The length of SR is 3√5 and its slope is -2

The length of SP is 5√2 and its slope is -7

The length of RQ is 5√2 and its slope is -1

So PQ ≅ SR and SP ≅ RQ. By the Perpendicular Bisector theorem, adjacent sides are perpendicular. By the selection of  side, ∠PSR, ∠SRQ, ∠RQP and ∠QPS are right angles. So, the quadrilateral is a rectangle.

To find the lengths and slopes of the sides of the quadrilateral PQRS, we apply the distance formula:

D = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)  

and the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

1. Length PQ:

Using the distance formula, the length PQ can be calculated as follows:

PQ = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((3 - 0)² + (-4 - 2)²)

  = √(3² + (-6)²)

  = √(9 + 36)

  = √45

  = 3√5

2. Length SR:

Using the distance formula, the length SR can be calculated as follows:

SR = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((1 - (-2))² + (-5 - 1)²)

  = √((1 + 2)² + (-6)²)

  = √(3² + 36)

  = √(9 + 36)

  = √45

  = 3√5

3. Length SP:

Using the distance formula, the length SP can be calculated as follows:

SP = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((1 - 0)² + (-5 - 2)²)

  = √(1² + (-7)²)

  = √(1 + 49)

  = √50

  = 5√2

4. Length RQ:

Using the distance formula, the length RQ can be calculated as follows:

RQ = \(\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}\)

  = √((-2 - 3)² + (1 - (-4))²)

  = √((-2 - 3)² + (1 + 4)²)

  = √((-5)² + 5²)

  = √(25 + 25)

  = √50

  = 5√2

Now, let's calculate the slopes of the sides:

1. Slope PQ:

The slope of PQ can be calculated using the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (-4 - 2) / (3 - 0)

  = -6 / 3

  = -2

2. Slope SR:

The slope of SR can be calculated using the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (-5 - 1) / (1 - (-2))

  = -6 / 3

  = -2

3. Slope SP:

The slope of SP can be calculated using the slope formula:

m =\(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (-5 - 2) / (1 - 0)

  = -7 / 1

  = -7

4. Slope RQ:

The slope of RQ can be calculated using the slope formula:

m = \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

  = (1 - (-4)) / (-2 - 3)

  = 5 / (-5)

  = -1

Therefore, the lengths and slopes of the sides of the quadrilateral PQRS are:

Length PQ: 3√5

Length SR: 3√5

Length SP: 5√2

Length RQ: 5√2

Slope PQ: -2

Slope SR: -2

Slope SP: -7

Slope RQ: -1

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To find the equation of the perpendicular bisector of PQ, we need to first find the midpoint of PQ, and then determine the slope of the line perpendicular to PQ that passes through this midpoint.

The midpoint of PQ is given by the formula:

((x1 + x2) / 2, (y1 + y2) / 2)

where (x1, y1) = (5, -4) and (x2, y2) = (-1, -2)

So, the midpoint of PQ is:

((5 - 1) / 2, (-4 - 2) / 2) = (2, -3)

Now, the slope of the line PQ can be found using the formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) = (5, -4) and (x2, y2) = (-1, -2)

So, the slope of PQ is:

(-2 - (-4)) / (-1 - 5) = 2/3

Since the perpendicular bisector of PQ will have a slope that is the negative reciprocal of the slope of PQ, the slope of the perpendicular bisector is:

-1 / (2/3) = -3/2

Finally, we can use the point-slope form of the equation of a line to find the equation of the perpendicular bisector. We know that the line passes through the point (2, -3), and has a slope of -3/2. So, the equation of the line is:

y - (-3) = (-3/2)(x - 2)

Simplifying this equation, we get:

y + 3 = (-3/2)x + 3

y = (-3/2)x + 0

Hence, the equation of the perpendicular bisector of PQ is y = (-3/2)x.

The original dimensions of the piece of metal were 15 inches by 20 inches.

To solve this problem, we can use the given information to set up an equation. Let's assume that the width of the rectangular piece of metal is x inches. According to the problem, the length of the piece of metal is 5 inches longer than its width, so the length would be (x+5) inches.

When squares with sides 1 inch long are cut from the four corners, the width and length of the resulting box will be reduced by 2 inches each. Therefore, the width of the box will be (x-2) inches and the length will be ((x+5)-2) inches, which simplifies to (x+3) inches.

The height of the box will be 1 inch since the flaps are folded upward.
Now, let's calculate the volume of the box using the formula Volume = length * width * height.

Substituting the values, we have:

234 = (x+3)(x-2)(1)

Simplifying the equation, we get:

234 = x^2 + x - 6

Rearranging the equation, we have:

x^2 + x - 240 = 0

Now, we can solve this quadratic equation either by factoring or by using the quadratic formula. Let's use factoring to find the values of x.

Factoring the equation, we have:
(x+16)(x-15) = 0
Setting each factor equal to zero, we get:
x+16 = 0 or x-15 = 0
Solving for x, we have:
x = -16 or x = 15
Since the width cannot be negative, we take x = 15 as the valid solution.
Therefore, the original dimensions of the piece of metal were 15 inches in width and (15+5) = 20 inches in length.

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\(x = \sqrt{ \frac{y + 7}{2} } + 1\)

1) Just add 1 to both sides.

\(y = 2( {x}^{2} - 2x + 1) - 7\)

1) Square both sides.

\( {x}^{2} - 2x + 1 = \frac{y + 7}{2} \)

2) Multiply both sides by 2.

\(( {x}^{2} - 2x + 1) \times 2 = y + 7\)

3) Regroup terms.

\(2( {x}^{2} - 2x + 1) = y + 7\)

4) Subtract 7 from both sides.

\(2( {x}^{2} - 2x + 1) - 7 = y\)

5) Switch sides.

\(y = 2( {x}^{2} - 2x + 1) - 7\)

Therefor, the answer for Y is y = 2 ( x² - 2x + 1) -7.

a) The parabola opens downwards

b) the x intercept is the value of x at the point where the curve touches the x axis. It is

x = 4

x intercept = 4

It can be written as

(4, 0)

the y intercept is the value of y at the point where the curve touches the y axis. It is y = - 8

y intercept = - 8

It can be written as (0, - 8)

c) The coordinates of the vertex are the values of x and y at the bottom of the curve. They are x = 4, y = 0

Vertex = (4, 0)

d)The axis of symmetry divides the curve into two equal halves. Thus, equation of axis of symmetry is

x = 4