Align the variables in the equations.
2x - 3y = 9
1-6x +9y = -7

The probability that when he enters the restaurant today it will be at least 5 minutes until he is served is  0.2676 and probability that average time until he is served in eight randomly selected visits is 0.0409.

The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean. By calculating the deviation of each data point from the mean, the standard deviation can be calculated as the square root of variance.

Given that mean μ = 4.2 , standard deviation σ = 1.3

1. P(X >= 5) = P((X - μ)/σ >

                    = (5 - 4.2) /1.3

                    = P(Z ≥ 0.6154)

                    = 1 - P(Z < 0.6154)

                    = 1 - 0.7324

                    = 0.2676

The required probability is 0.2676.

2.Given that n = 8 then  [tex]\bar x[/tex] = σ/[tex]\sqrt{(n)[/tex]  = 1.3/√(8) = 0.4596

P(x-bar ≥ 5) = P(([tex]\bar x[/tex] - μ)/σx-bar ≥ (5 - 4.2)/0.4596)

                        = P(Z ≥ 1.7406)

                        = 1 - P(Z < 1.7406)

                        = 1 - 0.9591

                        = 0.0409

The required probability is 0.0409.

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In the given triangle, the value of x = 5.

What is a triangle's definition?

A triangle is a geometrical shape that is defined as a polygon with three sides and three angles. It is a closed figure with three line segments as its sides, and these sides intersect at three points, which are called vertices. When we add all the angles of a triangle then the result will always be 180°.

Now,

As we know the property of a triangle that

sum of all angles of triangle=180°

given angles are (9x-1)°, 74° and 62°

then,

        9x-1+74+62=180°

9x+135=180

9x=45

x=5

Hence,

           the value of x is 5.

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The point that partitions segment AB in a 1:4 ratio is [tex]P = \left(-1, -\frac{2}{5}\right)$[/tex].

To find the point that partitions segment AB in a 1:4 ratio, we can use the section formula.

Let P = (x, y) be the point that partitions segment AB in a 1:4 ratio, where AP:PB = 1:4. Then, we have:

[tex]$\frac{AP}{AB} = \frac{1}{1+4} = \frac{1}{5}$$[/tex]

and

[tex]$\frac{PB}{AB} = \frac{4}{1+4} = \frac{4}{5}$$[/tex]

Using the distance formula, we can find the lengths of AP, PB, and AB:

[tex]AP &= \sqrt{(x+3)^2 + (y-2)^2} \\PB &= \sqrt{(x-7)^2 + (y+10)^2} \\\ AB &= \sqrt{(7+3)^2 + (-10-2)^2} = \sqrt{244}[/tex]

Substituting these into the section formula, we have:

[tex]$\begin{aligned}x &= \frac{4\cdot(-3) + 1\cdot(7)}{1+4} = -1 \ y &= \frac{4\cdot2 + 1\cdot(-10)}{1+4} = -\frac{2}{5}\end{aligned}$$[/tex]

Therefore, the point that partitions segment AB in a 1:4 ratio is [tex]P = \left(-1, -\frac{2}{5}\right)$[/tex].

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Answer:

area=188

Step-by-step explanation:

12×14=168 for the area of the rectangle

2×10=20

20÷2=10 for the area of triangle

168+10+10=188

area=188

The critical value of z for each hypothesis  test is 2.326

In this question, we are asked to use Excel to find the critical value of z for each hypothesis test. We are given a 2 percent level of significance for a two-tailed test. To find the critical value, we can use the NORM.S.INV function in Excel. The syntax for this function is =NORM.S.INV(probability).

We can enter the probability as 1 - (alpha / 2) for a two-tailed test, where alpha is the level of significance. We can then round the result to three decimal places.

To find the critical value for a 2 percent level of significance, two-tailed test, we can follow these steps:

Step 1: Calculate the value of alpha

Alpha = 2% = 0.02

Step 2: Calculate

1 - (alpha / 2)1 - (alpha / 2)

= 1 - (0.02 / 2)

= 0.99

Step 3: Use the NORM.S.INV function in Excel=NORM.S.INV(0.99)

This gives us a critical value of z = 2.326.

Therefore, the critical value of z for the hypothesis test with a 2 percent level of significance and a two-tailed test is 2.326.

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Hence, the answer is (4, 3, 1).In conclusion The answer provided above is concise and ng factually correct, and it addresses the question directly.

In order to determine the number of total electron groups, bondiroups, and lone pairs for geometry (a), we need to use the VSEPR theory. According to this theory, the electron groups around a central atom in a molecule will arrange themselves in a way that minimizes their repulsion. The total number of electron groups includes both the bonding and lone pairs of electrons.To determine the number of electron groups for geometry (a), we first need to determine the molecular geometry of the molecule.

From the given name, we can assume that geometry (a) is tetrahedral. In a tetrahedral molecule, there are four electron groups: three bonding groups and one lone pair. Therefore, the number of total electron groups for geometry (a) is four, the number of bonding groups is three, and the number of lone pairs is one.

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The area of the pie is approximately 113.0 square inches.

The ratio of a circle's circumference to its diameter is denoted by the mathematical constant pi . It is roughly equivalent to 3.14159 and is not repetitive or terminal. As pi is an irrational number, it cannot be written as an exact fraction of two integers and its decimal representation never ends. Pi is used to compute the characteristics of circles, spheres, cylinders, and other curved objects in many branches of mathematics and science, including geometry, trigonometry, calculus, physics, and engineering.

The area of the circle is given as:

A = πr²

Here, diameter = 12, thus radius is 6 inches.

Substituting the values:

area = 3.14 x (6)²

area = 113.04 square inches

Hence, the area of the pie is approximately 113.0 square inches.

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The value of the side of the triangles are;

18. 17. 89

19. y = 9. 43, x = 5. 67

Using the Pythagorean theorem stating that the square of the hypotenuse side is equal to the sum of the squares of the other two sides of a triangle.

From the diagram shown, we have;

21² = 11² + x²

find the squares

441 = 121 + x²

collect the like terms

x² = 320

Find the square root

x = 17. 89

To determine the value of y

sin 59 = y/11

y = 11 × 0. 8571

y = 9. 43

To determine the value of x

11² - 9. 43² = x²

x = √32.096

x = 5. 67

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Answer:  ^4√11^5 = 11^(5/4)

Step-by-step explanation: When we apply a radical, we are asking what number, when raised to a certain power, gives us the number under the radical. For example, ^4√16 is asking what number, when raised to the fourth power, gives us 16. The answer is 2, since 2^4 = 16.

So, ^4√11^5 is asking what number, when raised to the fourth power, gives us 11^5. We can simplify this expression using the exponent laws:

^4√11^5 = (11^5)^(1/4) = 11^(5/4)

Therefore, the simplified expression for ^4√11^5 is 11^(5/4). This expression does not have any radicals, making it easier to work with and manipulate.

Hope this helps, and have a great day!

Answer:

Step-by-step explanation:

Standard: 2x^3 - 7x^2 -x-2

Quotient: 2x^3- 7x^2 -x-2

remainder: 0

Answer:

Y = 4x

Step-by-step explanation:

In this equation, x represents the input value, and Y represents the output value. Coefficient 4 illustrates the rate of change or slope of the function, indicating that for every unit increase in x, the value of Y increases by four units. When x is 0, Y is also 0, consistent with the given data. Similarly, when x is 1, 2, and 3, Y is 4, 8, and 12, respectively, matching the provided output values.

Answer:

  13/32

Step-by-step explanation:

You want the area of the shaded portion of the unit square shown.

Points B, C, E are shown as equidistant from point F, so will lie on a circle centered at F. The center of that circle is at the point of coincidence of the perpendicular bisectors of BE, BC, and CE.

Without loss of generality, we can let line EF lie on the x-axis such that E is at the origin. Chord EB of the circle has a rise of 1/2 for a run of 1, so a slope of 1/2. Its midpoint is (1, 1/2)/2 = (1/2, 1/4). The perpendicular line through this point will have slope -2, so its equation can be written ...

  y -1/4 = -2(x -1/2)

  y = -2x +5/4

Then the x-intercept (point F) will have coordinates (0, 5/8):

  0 = -2x +5/4 . . . . . y=0 on the x-axis

  2x = 5/4

  x = 5/8

Trapezoid EFCD will have upper base 5/8, lower base 1, and height 1/2. Its area is ...

  A = 1/2(b1 +b2)h

  A = (1/2)(5/8 +1)(1/2) = (1/4)(13/8) = 13/32

The shaded area is 13/32.

__

Additional comment

The point-slope equation of a line through (h, k) with slope m is ...

  y -k = m(x -h)

The best interpretation of the interval is: We are 95% confident that the mean time for response is between 2.8 minutes and 12.3 minutes. Option D is correct

A confidence interval is a measure of how accurately an estimate (such as the sample average) corresponds to the actual population parameter. It is a range of values that the researcher believes is very likely to include the actual value of the population parameter.

Here, a 95 percent confidence interval for the mean time, in minutes, for a volunteer fire company to respond to emergency incidents is determined to be (2.8. 12.3). Thus, we can say that we are 95% confident that the mean time for response is between 2.8 minutes and 12.3 minutes. Therefore, option D is correct.

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Around 0.13% or 0.0013 of children find relief for less than four hours.

The percentage of children who experience relief for less than four hours if the relief time follows a lognormal distribution is determined as follows:

Step 1: Define the parameters of the problem. Assume that relief times are normally distributed with a mean of μ = 5.5 hours and a standard deviation of σ = 0.5 hours. We want to find the percentage of children who experience relief for less than four hours.

Step 2: Convert the normal distribution to the standard normal distribution using the formula: z = (x - μ) / σwhere x is the relief time in hours.

Step 3: Find the z-score corresponding to the value of x = 4:z = (4 - 5.5) / 0.5 = -3

Step 4: Use a standard normal distribution table to find the percentage of the area under the curve to the left of z = -3. This is equivalent to the percentage of children who experience relief for less than four hours.

Using the standard normal distribution table or calculator, we get that the percentage of children who experience relief for less than four hours is approximately 0.13% or 0.0013.


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The given series diverges to negative infinity as the terms cancel out, leaving only two terms at the beginning and end of the series.

To determine the convergence of the given series, we can use the telescoping series method.

Let's write out a few terms of the series to see if we can spot a pattern:

n=1: 1/2 - 3/4 = -1/4

n=2: 2/3 - 4/5 = -2/15

n=3: 3/4 - 5/6 = -1/8

n=4: 4/5 - 6/7 = -2/35

...

We can see that the terms of the series cancel out, leaving only two terms at the beginning and end of the series. Therefore, we can write the series as:

∑ (n/n+1 - n+2/n+3) = 1/2 - (n+2)/(n+3)

As n approaches infinity, the second term approaches 1, so the series diverges to negative infinity.

Therefore, the given series diverges.

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_____The given question is incomplete, the complete question is given below:

Which of the series in exercises 17–56 converge, and which diverge? use any method, and give reasons for your answers

(∑ ∞ to n = 1) = (n/n+1 - n+2/n+3)

Answer:

1+2=90° .so complementary angle

The surface area of the playhouse is 564 square feet.

Frank is building a playhouse for his daughter.

The playhouse is a composite figure with a floor and no windows.

The playhouse is a rectangular prism and a triangular prism.

The formula for the surface area of a rectangular prism is 2lw + 2lh + 2wh,

where l is the length,

w is the width,

and h is the height.

Therefore, the surface area of the rectangular prism portion of the playhouse can be calculated by substituting the given values into the formula.

Surface area of the rectangular prism = 2lw + 2lh + 2wh

For the rectangular prism, l = 10 feet, w = 8 feet, and h = 6 feet.

Substituting the values in the formula.

Surface area of the rectangular prism

= 2lw + 2lh + 2wh

= 2 (10 feet × 8 feet) + 2 (10 feet × 6 feet) + 2 (8 feet × 6 feet)

= 160 feet2 + 120 feet2 + 96 feet2= 376 feet2

The surface area of the rectangular prism of the playhouse is 376 square feet.

The formula for the surface area of a triangular prism is 2lw + lh + ph,

where l is the length, w is the width, h is the height, and p is the slant height.

Therefore, the surface area of the triangular prism portion of the playhouse can be calculated by substituting the given values into the formula.

Surface area of the triangular prism = 2lw + lh + ph

For the triangular prism, l = 8 feet, w = 5 feet, h = 6 feet, and p = 10 feet.

Substituting the values in the formula.

Surface area of the triangular prism = 2lw + lh + ph= 2 (8 feet × 5 feet) + (8 feet × 6 feet) + (10 feet × 6 feet)= 80 feet2 + 48 feet2 + 60 feet2= 188 feet2

The surface area of the triangular prism of the playhouse is 188 square feet.

The total surface area of the playhouse can be found by adding the surface area of the rectangular prism and the surface area of the triangular prism.

Surface area of the playhouse = surface area of rectangular prism + surface area of triangular prism.

= 376 square feet + 188 square feet

= 564 square feet.

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The value of x using similar triangles theorem is = 13/3.

Triangles that resemble one another but may not be exactly the same size are said to be comparable triangles.

When two objects have the same shape but different sizes, they can be said to be comparable.

This indicates that comparable shapes superimpose one another when amplified or de-magnified.

The term "Similarity" refers to this characteristic of like shapes.

Now in the given figure,

the proportion of the triangles' side is same.

So, 12/4 = 13/x

x = 13/3

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Area of the solid composite shape with triangle and rectangle is =832cm².

The area of a composite shape can be determined by adding or subtracting its component pieces.

Hence, we can use two formulas:

Area of Composite Shape + Area of Composite Shape + Area of Basic Shape A (additive)

Basic Shape Area A, Basic Shape Area B, and Composite Shape Area (subtractive)

In the figure,

Dimensions of the triangle are height, h = 16cm and base, b = 12cm.

Area = 1/2 ×b ×h

= 1/2 × 16× 12

=96cm²

There are two triangles, so the total area = 96+ 96 = 192cm².

Now area of the rectangle = length × width

= 20 × 32

= 640cm².

Total area of the solid= 192 + 640 = 832cm².

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Answer:Hence, Nathan rode 2 miles

Step-by-step explanation:ask if you need any questions

Answer: multiplied by 5 or squared

Step-by-step explanation:

If the number 5 goes in and 25 is the result, the rule could be multiplying by 5 or squaring the number that goes in (input).

5 x 5 = 25

5^2 = 25.

The area of the given parallelogram is A- 33(1/2) ft² using the base and height of the parallelogram. the correct answer is (c).

A quadrilateral with two sets of analogous edges is appertained to as a parallelogram. In a parallelogram, the opposing edges are of equal length, and the opposing angles are of equal size. also, the internal angles that are supplementary to the transversal on the same side. 360 ° is the sum of all internal angles. A parallelepiped is a three- dimensional shape with parallelogram- shaped sides. The base( one of the analogous lines) and height( the distance from top to bottom) of the parallelogram determine its area. A parallelogram's border is determined by the lengths of its four edges. The characteristics of a parallelogram are participated by the shapes of a square and cell. What's area? The size of a section on a face is determined by its area. face area refers to the area of an open face or the border of a three- dimensional object, whereas the area of an area area plane region or area  area plane area refers to the area of a shape or planar lamella.

The area of a parallelogram is given by

[tex]base*height.base=8(1/3)ft[/tex]

height=4ft

[tex]Area=b*h =(25/3)*4 =100/3 = 33[/tex]

[tex][base]\frac{1}{3}[(hieght)] ft^{2}[/tex]

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Therefore, approximately 68.26% of people are expected to score higher than 2.5 but lower than 3.5.

Based on the information provided, the mean (X) is 3.00 and the standard deviation (SD) is 0.50. To find the percentage of people expected to score higher than 2.5 but lower than 3.5, we will use the standard normal distribution (z-score) table.

First, we need to calculate the z-scores for both 2.5 and 3.5:
z1 =[tex] (2.5 - 3.00) / 0.50 = -1.0[/tex]
z2 = [tex](3.5 - 3.00) / 0.50 = 1.0[/tex]

Now, we can use the standard normal distribution table to find the probability of the z-scores. For z1 = -1.0, the probability is 0.1587 (15.87%). For z2 = 1.0, the probability is 0.8413 (84.13%).

To find the percentage of people expected to score between 2.5 and 3.5, subtract the probability of z1 from the probability of z2:

Percentage = [tex](0.8413 - 0.1587) x 100 = 68.26%[/tex]

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The correct answer to the question, "Which of the following is equivalent to the probability of getting less than 50% democrats in a random sample of size 100?" is: B. P( z < 50 — 55/ √55(45)/100).

To find the probability, we first calculate the z-score using the formula:

z = (x - μ) / σ

where x is the value (50%), μ is the mean (55%), and σ is the standard deviation.

The standard deviation can be calculated as:

σ = √(np(1-p))

where n is the sample size (100) and p is the proportion of democrats (0.55).

Now, plug in the values into the z-score formula:

z = (50 - 55) / √(100 * 0.55 * 0.45)

The probability is then found as P(z < z-score), which is represented by the option B.

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Answer: the team amassed 88i points total, by shooting t two-point baskets and u 1-point free throws.

t+u = 53

total is:  2t + u = 88.

Step-by-step explanation:

hope i makes sense

Mr. Kha Lipat should invest $5,000 today in order to receive $400.00 in interest one year from now at an 8% interest rate.

To calculate how much money Mr. Kha Lipat should invest today to receive $400.00 one year from now at an 8% interest rate, we can use the formula for calculating simple interest though compound intrest:

I = P * r * t

where I is the interest earned, P is the principal (the initial amount invested), r is the interest rate (as a decimal), and t is the time period (in years).

We know that Mr. Kha Lipat wants to earn $400.00 in interest, the interest rate is 8% or 0.08 (as a decimal), and the time period is 1 year. We can plug these values into the formula and solve for P:

I = P * r * t

400 = P * 0.08 * 1

400 = 0.08P

P = 400 / 0.08

P = 5000

Therefore, Mr. Kha Lipat should invest $5,000 today in order to receive $400.00 in interest one year from now at an 8% interest rate.

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(a) To find P(0 < Z < 2.74), you'll want to look up the z-score for 2.74 in a standard normal table or use a calculator with a built-in normal distribution function. The probability is the area under the curve between 0 and 2.74.

(b) To find P(0 < Z < 1), you'll look up the z-score for 1 in a standard normal table or use a calculator. The probability is the area under the curve between 0 and 1.

(c) To find P(-2.40 < Z < 0), you'll look up the z-score for -2.40 in a standard normal table or use a calculator. The probability is the area under the curve between -2.40 and 0.

(d) To find P(-2.40 < Z < 2.40), you can first calculate the probability for P(-2.40 < Z < 0) and P(0 < Z < 2.40), and then sum the two probabilities.

(e) To find P(Z > 1.63), look up the z-score for 1.63 in a standard normal table or use a calculator. The probability is the area under the curve to the right of 1.63.

(f) To find P(Z < -1.74), look up the z-score for -1.74 in a standard normal table or use a calculator. The probability is the area under the curve to the left of -1.74.

(g) To find P(-1.4 < Z < 2.00), first look up the z-scores for -1.4 and 2.00 in a standard normal table or use a calculator. Subtract the smaller probability from the larger probability to find the area under the curve between these two values.

(h) To find P(1.63 < Z < 2.50), first look up the z-scores for 1.63 and 2.50 in a standard normal table or use a calculator. Subtract the smaller probability from the larger probability to find the area under the curve between these two values.

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Answer:

≈283,39 mm^2

Step-by-step explanation:

The diameter is 19 mm, so the radius is half diameter (9,5 mm)

[tex]a = \pi \times {r}^{2} = 3.14 \times {9.5}^{2} = 3.14 \times 90.25 ≈ 283.39[/tex]