Solve the radical equation.
√3x-2-√11+x= -1

Answers

Answer 1

Answer:

[tex]x = \frac{(1 + \sqrt{11})( \sqrt{3 } - 1) }{2 } [/tex]


Related Questions

I need help with this please

Answers

The matrix formed by performing R2 -> 4R1 + R2 on M is given as follows:

[tex]\left[\begin{array}{ccc}-4&3&1\\-18&9&8\end{array}\right][/tex]

How to do the row operation?

The matrix in the context of this problem is defined as follows:

[tex]\left[\begin{array}{ccc}-4&3&1\\-2&-3&4\end{array}\right][/tex]

The rows are given as follows:

R1: -4, 3 and 1.R2: -2, -3 and 4.

Hence the row 2 of the resulting matrix has the elements given as follows:

Column 1: 4 x -4 - 2 = -18.Column 2: 4 x 3 - 3 = 9.Column 3: 4 x 1 + 4 = 8.

Thus the resulting matrix is:

[tex]\left[\begin{array}{ccc}-4&3&1\\-18&9&8\end{array}\right][/tex]

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Find an equation of the tangent line to the curve x2/3 + y2/3 = 10 (astroid)at the point(−27 ,1)

Answers

The equation of the tangent line to the curve [tex]x^\((2/3) + y^\((2/3)[/tex]= 10 at the point (-27, 1) is  -(1/3)(x + 27).

How to find the equation of the tangent line?

First step is to take the  derivative of both sides of the equation

[tex](2/3 )x ^\((-1/3) + (2/3)y ^\((-1/3)*dy/dx = 0[/tex]

Solve for dy/dx

[tex]dy / dx = -(y ^\(1/3)/x ^(1/3))[/tex]

Substitution

[tex]dy /dx = -(1 ^\((1/3)/(-27) ^ \((1/3)) = -(1/3)[/tex]

Formulate a linear equation

y - y1 = m(x - x1)

Where:

m= slope

(x1, y1)= point (-27, 1):

So,

y - 1 = -(1/3)(x + 27)

Therefore the equation is y - 1 = -(1/3)(x + 27).

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Each of 6 students reported the number of movies they saw in the past year. Here is what they reported. 14, 9, 9, 6, 10, 19 Find the mean number of movies that the students saw. If necessary, round your answer to the nearest tenth.

Answers

The answer is 11.2

The mean is the sum of all numbers divided by how many there is. So 14+9+9+6+10+19 is 67. 67 divided by 6 is 11.1667. But it says round to the nearest tenth which would make it 11.2

Pleas help and I will mark your brainliest. It is simple matrix work!

Answers

The inverse of matrix C is C⁻¹ = [1/9 4/27] [1/27 -5/27].

How to determine inverse of matrix?

To find the inverse of matrix C, use the following formula:

C⁻¹ = 1/det(C) × adj(C)

where det(C) = determinant of matrix C and adj(C) = adjugate of matrix C.

To find the determinant of C, use the following formula for a 2x2 matrix:

|a b|

|c d| = ad - bc

So:

det(C) = |5 1|

|12 -3| = (5)(-3) - (1)(12) = -27

Find the adjugate of C, which is the transpose of the matrix of cofactors of C, which is:

|-3|

| 1| = -(-3) = 3

So the upper left cofactor is 3, which is:

|12|

|-3| = -(12) = -12

So the upper right cofactor is -12, which is:

| 1|

|-3| = -(1) = -1

So the lower left cofactor is -1, which is:

|5|

|1| = 5

So the lower right cofactor is 5. Putting the cofactors into a matrix and transposing it gives the adjugate of C:

adj(C) = [ 3 -12]

[-1 5]

Now find the inverse of C:

C⁻¹ = 1/det(C) × adj(C)

= -1/27 × [ 3 -12]

[-1 5]

= [1/9 4/27]

[1/27 -5/27]

So the inverse of matrix C is:

C⁻¹ = [1/9 4/27]

[1/27 -5/27]

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Hello please I don't understand this exercise..
In an orthonormal frame (o; i; j), we give the points A(3; 1), B(1; 2) and the line (AC) with equation 2x-y-5=0.
1) Determine the equation of the line (AB).
2)a) Show that the direction vectors AB and AB of the lines (AC) and (AB) are orthogonal.
b) Then determine the coordinates of C.

Answers

The equation of the line AB,with slope of -1/2 is  y = (-1/2)x + 7/2. We then use the dot product to show that the direction vectors of the lines AB and AC are orthogonal, and the coordinates of point C is (6,7).

In an orthonormal frame (o; i; j), the points A and B are given as A(3;1) and B(1;2), and the line (AC) is given by the equation 2x-y-5=0.

To determine the equation of line (AB), we need to find the slope (or gradient) of the line passing through A and B. We can find this by using the formula

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

where (x1, y1) and (x2, y2) are the coordinates of two points on the line. Substituting the values of A and B, we get

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

Now that we have the slope, we can use the point-slope form of a line to find the equation of line (AB). Let (x,y) be any point on the line, then we have

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

Simplifying, we get

y = (-1/2)x + 7/2

So the equation of line (AB) is y = (-1/2)x + 7/2.

To show that the direction vectors AB and AC of the lines (AB) and (AC) are orthogonal, we need to find the direction vectors of these lines and show that their dot product is zero. The direction vector of a line is just the vector that "points" in the direction of the line. To find it, we can take any two points on the line and subtract their coordinates to get a vector.

For line (AC), we can take A and C as two points on the line. Since we don't know the coordinates of C yet, we can solve the equation of line (AC) for x to get

x = (y + 5) / 2

Now substituting x by the above expression in the coordinates of point A we get

C((y + 5)/2, y)

Thus, the direction vector of line (AC) is

AC = C - A = ((y + 5)/2 - 3, y - 1) = (y/2 - 7/2, y - 1)

Similarly, we can take A and B as two points on the line (AB) to get the direction vector of line (AB):

AB = B - A = (1-3, 2-1) = (-2, 1)

Now, the dot product of AB and AC is

AB · AC = (-2)(y/2 - 7/2) + (1)(y - 1) = -y + 7

We can see that the dot product is zero when y=7. Hence, direction vectors AB and AC are orthogonal at point C(3,7).

To determine the coordinates of C, we substitute y=7 in the equation of line (AC) we obtained earlier

2x - y - 5 = 0

2x - 7 - 5 = 0

2x = 12

x = 6

Therefore, C has coordinates (6,7).

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Which statement correctly describes confidence level? A confidence level is the probability that a simple event will occur. A confidence level is a value that is added and subtracted from a given value to give an interval where something will likely happen. A confidence level is the probability that something will fall outside of a confidence interval. A confidence level is the probability that something will fall within a confidence interval.

Answers

The statement which correct describe "confidence-interval" is (d) confidence level is considered as probability that something will fall within "confidence-interval".

A "Confidence-Interval" is a statistical term used to describe the amount of uncertainty associated with a sample estimate. It refers to the percentage of all possible samples that can be expected to include the true population parameter being estimated.

For example, if a study reports a 95% confidence level, it means that 95% of all possible samples would contain the true population parameter. This can be considered as the probability that the estimate falls within a certain range or interval, called the confidence interval.

Therefore, option (d) is the correct statement.

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The given question is incomplete, the complete question is

Which statement correctly describes confidence level?

(a) A confidence level is the probability that a simple event will occur.

(b) A confidence level is a value that is added and subtracted from a given value to give an interval where something will likely happen.

(c) A confidence level is the probability that something will fall outside of a confidence interval.

(d) A confidence level is the probability that something will fall within a confidence interval.

Answer:

A confidence level is the probability that something will fall within a confidence interval.

Step-by-step explanation:

Plato/Edmentum

Make x the subject of m= n+ 1 + x/p​

Answers

Answer:

Step-by-step explanation:

m = n + 1 + x/p

First, we can start by subtracting (n+1) from both sides:

m - (n+1) = x/p

Then, we can multiply both sides by p to isolate x:

p(m - (n+1)) = x

So the final answer is:

x = p(m - (n+1))

1. Convert the following Mayan numbers to decimal (base 10).
b)
||:
:|| || ()

Answers

The given Mayan number which is: :|| :|| in decimal (base 10) is 42.

How to solve

The Mayan number system is a base-20 system that uses three symbols: a dot (.), a horizontal bar (|), and a shell-like symbol (:). The symbol for zero is a shell-like symbol (:).

In order to obtain the decimal equivalent (base 10) of a Mayan numeral, it is imperative to comprehend the positional significance of each constituent symbol.

The numerical system employed here assigns a weight to each digit that corresponds to a certain power of 20. Specifically, the weight associated with the least significant digit is 20 raised to the exponent of 0, while the weight of the digit to its immediate left is 20 raised to the exponent of 1, and so forth.

The Mayan number given, : :|| :||, can be broken down as follows:

The leftmost position has no symbol, which represents a value of 0.

The second position from the left has two shell-like symbols (:), which represent a value of 2x20¹ = 40.

The third position from the left has two horizontal bars (||), which represent a value of 2x20⁰ = 2.

The given Mayan number in decimal (base 10) is 40 + 2 = 42.

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What is the domain indicated on the graph for each portion of the piecewise function?
f(x) = StartLayout enlarged left-brace 1st Row 1st column negative 2, 2nd column Domain 1st piece 2nd row 1st column 2 x + 1, 2nd column Domain 2nd piece Third row 1st column negative one-half x, 2nd column Domain 3rd piece EndLayout

Answers

The domain of the 1st piece is -10 < x < 0, for 2nd piece is 0 < x < 4, and for 3rd piece is 4 < x < 8.

What is a function?

A function is a particular kind of relationship where there is a set domain and range, and every input value in the domain is associated with a single output value in the range.

We have a piecewise function shown in the picture:

From the graph:

f(x) = -2, Domain: -10 < x < 0

f(x) = 2x + 1, Domain: 0 < x < 4

f(x) = (-1/2)x, Domaim: 4 < x < 8

Thus, the domain of the 1st piece is -10 < x < 0, for 2nd piece is 0 < x < 4, and for 3rd piece is 4 < x < 8.

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I really need help I will give you points

A.
x = 60; m∠ROS = 28°
B.
x = 62; m∠ROS = 31°
C.
x = 28; m∠ROS = 60°
D.
x = 31; m∠ROS = 62°

Answers

Answer:

D.

x = 31; m∠ROS = 62°

Step-by-step explanation:

we know that a right angle is always 90 degrees, so we subtract 90° by ∠QOR:

[tex]90 - 28 = 62[/tex]

Then we insert the 62 with the (2x)

[tex]62 = 2x[/tex]

we divide both sides by 2 and we get:

[tex]31 = x[/tex]


so the answer is D

x is equal to 31 and we can multiply 31 by 2 and we can get 62°

please I need help in this one​

Answers

Answer: 55

Step-by-step explanation:

Find the length of the missing side

Answers

Answer:

24

Step-by-step explanation:

10^2+x^2=26^2

x^2=26^2-10^2

x^2=576

x=[tex]\sqrt{576}[/tex]=24

Solve for measure of angle a.
a
96°
140°
a = [?]°
If 2 secant lines intersect outside a circle: Enter
2-b

Answers

The measure of angle a is solved to be 22 degrees

How to find angle a

When two secant lines intersect outside a circle the formula for the vertex angle at a is

To find the vertex angle at point A where two secant lines intersect outside a circle, you can use the following formula:

angle A = 1/2 * (measure of arc 1 - measure of arc 2)

let arc 1 = 140 degrees

arc 2  = 96 degrees

plugging in the values

angle A = 1/2 * (140 - 96)

angle A = 1/2 * 44

angle A = 22 degrees

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What does |23| mean?

Answers

The vertical lines on each side of the number are used to mean the absolute value of the number. If the number is negative, make it positive. If the number is positive, leave it alone.

|23| = 23
|-23| = 23

A triangle has side lengths of (6.2x - 9.4y) centimeters, (6.2x - 2.5z)
centimeters, and (8.3z + 1.4y) centimeters. Which expression represents the
perimeter, in centimeters, of the triangle?
O-3.2xy +3.7xz +9.7yz
O 12.4x8y + 5.8z
O-10.5yz +20.7xz
O-1.1z + 12.4x - 1.1y
Submit Answer

Answers

The perimeter of the given triangle is 12.4x-8.0y+5.8z. Therefore, option C is the correct answer.

Given that, triangle has sides of lengths of (6.2x-9.4y) centimeters, (6.2x-2.5z) centimeters and (8.3z+1.4y) centimeters.

We know that, perimeter of triangle is sum of all the sides.

Now, perimeter = 6.2x-9.4y+6.2x-2.5z+8.3z+1.4y

= (6.2x+6.2x)+(-9.4y+1.4y)+(-2.5z+8.3z)

= 12.4x-8.0y+5.8z

Therefore, option C is the correct answer.

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help pleaseeeeeeee

here is the picture is about Row Ops

Answers

The result of adding -4 (row 1) to row 3 is determined as (0  - 9   2)|12.

What is the result of the row multiplication?

The resultant of the row multiplication in the Matrice is calculated by applying the following method;

row 1 in the given matrices = [1  2  1] | -5

To multiply row by -4, we will multiply each entity by 4 as shown below;

= -4(1 2  1) | -5

= (-4  -8  - 4) |20

To add the result to 3;

(-4  -8  - 4)|20 + (4  - 1   6) | -8

= (0  - 9   2)|12

Thus, the result of the row multiplication is determined by multiplying each entry in row 1, by - 4.

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Solve for x. Round to the nearest tenth, if necessary.

Answers

Answer:

x = 16.2

Step-by-step explanation:

Using trig functions:

cos theta = adjacent side/ hypotenuse

cos 72 = 5/x

Solving for x

x = 5 /cos 72

x=16.18033

Rounding to the nearest tenth

x = 16.2

Answer: x = 16.2 units

Step-by-step explanation:

     We are given an angle (72°), the adjacent side (5), and the hypotenuse (x). We will use the cosine function to solve.

cos(θ) = [tex]\frac{adjacent}{hypotenuse }[/tex]

cos(72°) = [tex]\frac{5}{x }[/tex]

xcos(72°) = 5

x = [tex]\frac{5}{cos(72\°)}[/tex]

x = 16.1803398 ≈ 16.2

14 15. A composite figure is created from a cylinder and a cone like in the image below. Use the informative given in the image to find the volume of the composite figure. Select the closest estimate for the volume of the figure. 15 7 feet h​

Answers

The volume of the composite figure made of a cone and cylinder is derived to be equal to 3388 cubic feet.

How to evaluate for the volume of the composite figure

We shall calculate for the volumes of the cone and the cylinder, the sum of each volume will give the volume of the composite figure

The cone have;

radius = 7 ft

height = 34ft - 16ft = 18ft

Volume of the cone = 1/3 × 22/7 × 7ft × 7ft × 18ft

Volume of the cone = (22 × 7 × 6) ft³

Volume of the cone = 924 ft³

The cylinder have;

radius = 7 ft

height = 16 ft

Volume of the cylinder = 22/7 × 7ft × 7ft × 16ft

Volume of the cylinder = (22 × 7 × 16) ft³

Volume of the cylinder = 2464 ft³

Volume of the composite figure = 924 ft³ + 2464 ft³

Volume of the composite figure = 3388 ft³

Therefore, the volume of the composite figure made of a cone and cylinder is derived to be equal to 3388 cubic feet.

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Solve for x. Round to the nearest tenth, if necessary.

50 points

Answers

Answer: 8.7

Step-by-step explanation:

Given:

hypotenuse = 9

Angle x =75

opposite of angle = x

Solution:

From SOH CAH TOA, use SOH

sin x = [tex]\frac{opposite}{hypotenuse}[/tex]                  > substitute

sin 75  = [tex]\frac{x}{9}[/tex]                           > multiply both sides by 9

9*sin 75 =x

x=8.7

‼️‼️WILL MARK BRAINLIEST IF HELPFUL‼️‼️

Answers

The area of the composite figure is equal to 75.5 square meters

How to calculate for the area of the figure

The composite figure can be observed to be made up of a big rectangle, a smaller rectangle, a triangle and a smaller triangle. We calculate for the area of the four shapes and sum the results to get the total area of the composite figure as follows:

area of the big rectangle = 6 m × 4 m = 24 m²

area of the smaller rectangle = 7 m × 2 m = 14 m²

area of the big triangle = 1/2 × 10 m × 6 m = 30 m²

area of the smaller triangle = 1/2 × 5 m × 3 m = 7.5 m²

total area of the composite figure = 24 m² + 14 m² + 30 m² + 7.5 m²

total area of the composite figure = 75.5 m²

Therefore, the area of the composite figure is equal to 75.5 square meters

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Question 6(Multiple Choice Worth 5 points)
(Reflections MC)

Triangle NMO has vertices at N(−5, 2), M(−2, 1), and O(−3 , 3). Determine the vertices of image N′M′O′ if the preimage is reflected over y = −2.

N′(−3, 2), M′(0, 1), O′(−5, 3)
N′(−5, 0), M′(−2, −1), O′(−3, 1)
N′(−5, 1), M′(−2, 0), O′(−3, 2)
N′(−5, −6), M′(−2, −5), O′(−3, −7)



Please Fast only have 10 minutes.

Answers

The image coordinates of NMO after the translation is option d: N′(−5, −6), M′(−2, −5), and O′(−3, −7).

What is the  image coordinates?

To get the image coordinates of the preimage translated -2 units to the left, we simply subtract -2  from the y-coordinates of each vertex:

N' = (Nx - (-2), Ny) = (−5 , 2- (-2)) = (−5, 4)

M' = (Mx - (-2), My) = (−2 , 1 - (-2)) = (−2, 3)

O' = (Ox - (-2), Oy) = (−3 , 3- (-2)) = (−3, 5)

Therefore, based on the above, the image coordinates of NMO after the translation are N′(−5, 4), M′(-2,3 ), O′(−3, 5)

So the reflected vertices are:

The distance from N to the line y = -2 is 4, and -6 - (-2) = -4, so one need to move down 4 units to have  a y-coordinate of -6.

The distance from M to the line y = -2 is 3, and -5 - (-2) = -3, so  one need to move down 3 units to have a y-coordinate of -5.

The distance from O to the line y = -2 is 5, and -7 - (-2) = -5, so  one need to move down 5 units to have  a y-coordinate of -7.

So it will be: N′ (−5, −6), M′(−2, −5), O′(−3, −7)

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Answer:

D) N′(−5, −6), M′(−2, −5), O′(−3, −7)

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

Given triangle MNO with vertices:

N = (-5, 2), M = (-2, 1) and O = (-3, 3)

It is reflected in line y = - 2.

This reflection doesn't affect the x-coordinates of the vertices and the y-coordinates change.

Since y = - 2 is the line of symmetry,  it also represents midpoints of the segments formed by corresponding endpoints of image and preimage.

Using midpoint equation, find the y-coordinates.

Point N'(2 + y)/2 = - 2 ⇒ 2 + y = - 4 ⇒ y = - 6Point M'(1 + y)/2 = - 2 ⇒ 1 + y = - 4 ⇒ y = - 5Point O'(3 + y)/2 = - 2 ⇒ 3 + y = - 4 ⇒ y = - 7

So the coordinates of the image are:

N′(−5, −6), M′(−2, −5), O′(−3, −7)

This is matching the option D.

See attached for visual representation of the problem.

find area of the triangle help please

Answers

The calculated area of the triangle is 7.5 square inches

Finding the area of the triangle

From the question, we have the following parameters that can be used in our computation:

The triangle with the following dimensions

base = 6 inches

height = 2.5 inches

Using the above as a guide, we have the following:

Area = 1/2 * base * height

Substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * 6 * 2.5

Evaluate

Area = 7.5

Hence, the area of the triangle is 7.5 square inches

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answer: 7.5

because: 1/2 base * height

Kyle submits a design for the contest, but his explanation was misplaced. How can figure A be mapped onto figure B? Can any other transformation be used to map figure A onto figure B

Answers

Answer:

A

Step-by-step explanation:

ita a bc i know its I did this before

Function g is a transformation of f(x) = 2x. Compare the graphs of the functions. Select all that apply.
g(x)
(Table)
0 1 2 3 4
1/2 1 2 4 8

A.They have the same y-intercept.
B.They have the same asymptote.
c. They have the same range.
D.They have the same domain.

Answers

The functions have the following characteristics:

A. They have the same y-intercept.

D. They have the same domain.

How to compare the graphs of the functions

When a function f(x) is transformed by multiplying its input by a constant "a", it results in a new function g(x) = f(ax). In this case, f(x) = 2x, so when we multiply x by a constant "a", we get g(x) = f(ax) = 2ax.

Therefore, the functions f(x) = 2x and g(x) = 2ax have the same y-intercept (0,0) and the same domain (-∞, +∞).

The range of g(x) is determined by the value of "a", which is different from the range of f(x), so option C is not correct. Asymptotes are not relevant for linear functions, so option B is not correct.

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When Sarah opens a map of her neighborhood on her cell phone, she notices that the park near her house is 0.5 cm wide. She zooms in until it is 3 times as large. If the park is 15 m wide, what is the scale of her zoomed-in map?

A 10cm=1 m
B 1cm= 10 m
C 1cm= 30 m
D 3cm= 10m

Answers

The scale of Sarah's zoomed-in map is 1cm = 1000 cm or 1cm = 10 m. So the answer is (B) 1cm = 10 m.

To find the scale of Sarah's zoomed-in map, we can use the ratio of the width of the park on the map to its actual width.

Let's first convert the width of the park from meters to centimeters, since the width of the park on the map is given in centimeters.

15 m = 1500 cm

Next, we can set up a proportion:

0.5 cm / x = 1500 cm / (3x)

where x is the scale of the zoomed-in map.

Simplifying the proportion, we get:

0.5(3x) = 1500

1.5x = 1500

x = 1000

Therefore, the answer is (B) 1cm = 10 m.

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Examine the steps below. Between which two lines was a mistake made?

A.
between line 1 and line 2
B.
between line 2 and line 3
C.
between line 3 and line 4
D.
between line 4 and line 5

Answers

Answer:

A and D

Step-by-step explanation:

A- when multiplying -5 and -3 it should be positive 15.

D- when dividing 3 they just outta nowhere forgot about the negative, it should've been -5

Please help fast. Thanks! (:

Answers

The value of variable y from the system of vertical angles is equal to 125.

How to find the values of a variable associated with system of vertical angles

In this problem we need to determine by algebra properties the value of a variable y from a system of two pairs of vertical angles. The system is represented by the following expression:

x + 20 = 3 · x - 50

2 · x = 70

x = 35

Then, by definition of supplementary angles:

(x + 20) + y = 180

55 + y = 180

y = 125

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To answer the question, "How do students in the United States pay for their higher education?", a questionnaire was sent out to collect 100 responses from one higher education institution per state.

Answers

The given scenario is Biased, since those who chose to respond may be systematically different than those who chose not to respond. So, the correct answer is C).

The sampling method is biased, since those who chose to respond may be systematically different than those who chose not to respond. This is known as non-response bias, where the opinions and characteristics of those who choose not to respond to the survey may differ from those who choose to respond.

Additionally, only one higher education institution per state was selected, which may not be representative of all institutions within the state. Therefore, the sample may not accurately reflect the population of students in the United States who pay for their higher education. So, the correct option is C).

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--The given question is incomplete, the complete question is given

" To answer the question, "How do students in the United States pay for their higher education?", a questionnaire was sent out to collect 100 responses from one higher education institution per state.

Is the sampling method biased or unbiased and why?

Unbiased, since a random sample was selected

Unbiased, since a large sample was selected

Biased, since those who chose to respond may be systematically different than those who chose not to respond

Biased, since all higher education institutions are represented

Unbiased, since a questionnaire was used

Biased, since every state will be represented in the sample"--

someone pls help i really need help with this

Answers

Answer:

50° F

Step-by-step explanation:

35 - -15= 50

Check
-15 + 50 = 35

And 35 - 50 = -15

A pharmaceutical company receives large shipments of ibuprofen tablets and uses an acceptance sampling plan. This plan randomly selects and tests 29 tablets, then accepts the whole batch if there is at most one that doesn't meet the required specifications. What is the probability that this whole shipment will be accepted if a particular shipment of thousands of ibuprofen tablets actually has a 15% rate of defects?

Answers

Answer:

Step-by-step explanation:

This problem can be solved using the binomial distribution, which gives the probability of obtaining a certain number of successes in a fixed number of independent trials.

Let p be the probability that a single ibuprofen tablet has a defect, which is given as 15% or 0.15. Then, the probability that a single ibuprofen tablet does not have a defect is 1 - p = 0.85.

The acceptance sampling plan requires that at most one tablet does not meet the required specifications out of 29 tablets. This means that the shipment will be accepted if there are 0 or 1 defective tablets in the sample of 29.

The probability of getting exactly k defective tablets in a sample of n tablets is given by the binomial probability formula:

P(k) = (n choose k) * p^k * (1 - p)^(n - k)

where (n choose k) = n! / (k! * (n - k)!) is the number of ways to choose k defective tablets out of n, and ! denotes the factorial function.

To find the probability that the whole shipment will be accepted, we need to find the probability that there are 0 or 1 defective tablets in the sample of 29:

P(0 or 1 defects) = P(0 defects) + P(1 defect)

= (29 choose 0) * 0.15^0 * 0.85^29 + (29 choose 1) * 0.15^1 * 0.85^28

≈ 0.1098

Therefore, the probability that the whole shipment will be accepted is approximately 0.1098 or 10.98%

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