what is 2x multiplied by 7 with the exponent of 4

Answers

Answer 1

The simplified expression of  2x multiplied by 7 with the exponent of 4 is 4,802x.

What is the simplification of the expression?

The expression is simplified by applying the rules of multiplication and exponent rules.

the expression = 2x(7⁴)

simplify 7⁴ as follows = 7 x 7 x 7 x 7 = 2,401

Multiply the resultant solution of 2,401 as follows;

= 2,401 x (2x)

= 4,802x

Thus, the simplified expression of  2x multiplied by 7 with the exponent of 4 is determined by applying basis rules of multiplication.

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Related Questions

Reasoning What is the height of the square​ pyramid? Use pencil and paper. Once you know which length represents the​ hypotenuse, does it matter which length you substitute for a and which length you substitute for​ b? Explain.

Answers

The height of the square pyramid is 35.5 in.

From the given figure we can see that the figure is a pyramid.

The base of the pyramid is a square.

The each side of base square i = 24.8 in.

The slant height is = 37.6 in.

So the right angle formed in between prism has hypotenuse = 37.6 in.

one of the rest two sides = 24.8/2 = 12.4 in.

So another side is the height of the pyramid. Let that side be = x in.

By Pythagoras Theorem we get,

(12.4)² + x² = (37.6)²

153.76 + x² = 1413.76

x² = 1413.76 - 153.76

x² = 1260

x = 35.5 (rounding off to nearest tenth and neglecting the negative value obtained from square root as length cannot be negative.)

Hence the height of the square pyramid is 35.5 in.

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Given that the coefficient of x⁵ in the expansion of (1+kx)⁵ is -672 find the value of k

Answers

The value of k that satisfies the given condition is approximately 0.4041.

In the expansion of (1+kx)⁵, the coefficient of x⁵ is given by the term:

C(5,k) * (kx)⁵ = k⁵ * C(5,k) * x⁵

where C(5,k) is the binomial coefficient or the number of ways to choose 5 items out of k.

So, we have the equation:

k⁵ * C(5,k) = -672

We can use a table of binomial coefficients to find C(5,k) for different values of k, but this can be time-consuming. Alternatively, we can use the fact that C(5,k) = C(5,5-k) and rewrite the equation as:

k⁵ * C(5,5-k) = -672

Expanding C(5,5-k), we get:

k⁵ * C(5,5-k) = k⁵ * C(5,k) = -672

Now, we can use trial and error to solve for k. Using this method, we can find that k = -4 or k ≈ 0.4041. However, since k must be positive (since it appears as a factor in the expansion), the only valid solution is k ≈ 0.4041.

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please I need help in this one​

Answers

Answer: 55

Step-by-step explanation:

The mass of 12 packets of flour and 8 packets of salt is 19 kg. When 7 packets of flour are removed, the mass became 9.9 kg. Find the mass of each packet of salt in kilogram.​

Answers

Answer:

1.235 kg

Step-by-step explanation:

Let's assume that each packet of flour and salt weighs the same.

When we remove 7 packets of flour, we are left with 5 packets of flour and 8 packets of salt. The total number of packets is 13 and their total mass is 9.9 kg.

Therefore, the average mass of each packet is 9.9 kg ÷ 13 = 0.76 kg.

Since we know that 12 packets of flour and 8 packets of salt have a total mass of 19 kg, we can subtract the mass of the 12 packets of flour (12 × 0.76 kg = 9.12 kg) from the total mass to find the mass of the 8 packets of salt:

19 kg - 9.12 kg = 9.88 kg

Finally, we can divide the mass of the 8 packets of salt by the number of packets to find the mass of each packet:

9.88 kg ÷ 8 = 1.235 kg

Therefore, each packet of salt weighs approximately 1.235 kg.

Write the equation of a line parallel to 2y = x – 3 and that passes through point (-4,3) in slope intercept form.

Answers

Answer:

The equation of the line parallel to 2y = x – 3 and passing through point (-4,3) in slope-intercept form is y = (1/2)x + 5.

Step-by-step explanation:

To find the equation of a line that is parallel to 2y = x – 3, we need to determine the slope of the given line.

2y = x - 3 can be written in slope-intercept form y = (1/2)x - 3/2.

The slope of this line is 1/2.

Since we want a line parallel to this line, the slope of the new line will also be 1/2.

Next, we can use the point-slope form of a line to write the equation of the new line.

Point-slope form: y - y1 = m(x - x1)

where (x1, y1) is the given point and m is the slope of the line.

Substituting the values, we get:

y - 3 = (1/2)(x - (-4))

Simplifying, we get:

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

Adding 3 to both sides, we get the final equation in slope-intercept form:

y = (1/2)x + 5

Therefore, the equation of the line parallel to 2y = x – 3 and passing through point (-4,3) in slope-intercept form is y = (1/2)x + 5.

Total score:
of 15 points
(Score for Question 1: of 5 points)
1. The diagram shown is two intersecting lines. The measure of 22 is 29
2
(a) What is the measure of 24? How do you know? Explain your answer in complete sentences.
(b) Suppose the measure of 3 can be represented by (3x - 8)*. What equation can be written to solve for the value of x?
(c) What is the value of x? Show all work.
Answer:
•(Score for Question 2: _ of 5 points)
2. Draw a right triangle with side lengths of 6, 8, and 10 units. For full credit, be sure to include appropriate labels and symbols where necessary. © Stride, Inc. All rights reserved. No reproduction without written consent of Stride, Inc.
Answer:
•Score for Question 3:
_ of 5 points)
3. At a park, a statue has a ring-shaped brick path around it. The outer edge of the brick path is a circle with a radius of 13 m. The inner edge of the brick path is a circle with a radius of 8 m.
Brick path
13 m
8 m
Statue
(a) Write and simplify an expression for the exact area of the brick path. Show all work.
(b) Find the approximate area of the brick path. Use 3.14 to approximate r. Show all work.

Answers

The measure of angle ∠4 is 29°, the equation is 3x = 159 and the value of x is 53

The right angle using the given lengths is attachedThe exact area is 105π square meters and the approximate area is 330 square meters

The two intersecting lines

Given that, we have

∠2 = 29°

(a)

Angles 2 and 4 are vertical angles

So, we have

∠4 = 29°

(b) and (c)

We have

∠3 = (3x - 8)°

Angles 3 and 4 are angles on a straight line

So, we have the equation to be

3x - 8 + 29 = 180

Solving for x, we have

3x = 159

Divide by 3

x = 53

This means that the equation is 3x = 159 and the value of x is 53

The right angle with the given lengths

In this section, we have the following side lengths

Lengths = 6, 8 and 10

This means that

Side lengths = 6 and 8

Hypotenuse = 10

Next, we create the right angle using the given lengths of the legs and the hypotenuse

Calculating the area of the brick path

Here, we have

R = 13

r = 8

The exact area is calculated as

A = π(R² - r²)

So, we have

A = π(13² - 8²)

Evaluate

A = 105π

For the approximate area, we have

A = 105 * 22/7

A = 330

This means that the exact area of the brick path is 105π square meters and the approximate area is 330 square meters

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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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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

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

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))

The pair of polygons is similar. Find the missing side measure

Answers

The missing side measure is equal to: A. 14.

What is scale factor?

In Mathematics and Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):

Scale factor = Dimension of image (new figure)/Dimension of pre-image (original figure)

By substituting the given parameters into the formula for scale factor, we have the following;

Scale factor = Dimension of image/Dimension of pre-image

4/5.6 = 10/x

4x = 56

x = 56/4

x = 14

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

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.

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

what are the coordinates of each point after quadrillateral MNPQ is trans;ated 2units right and 5 units down

Answers

The coordinates of each point after the quadrilateral MNPQ is translated 2 units right and 5 units down are:

M' = (x1 + 2, y1 - 5)

N' = (x2 + 2, y2 - 5)

P' = (x3 + 2, y3 - 5)

Q' = (x4 + 2, y4 - 5)

How to calculate the coordinates?

To calculate the coordinates, we shall assume that the coordinates of the points of the quadrilateral MNPQ are:

M = (x1, y1)

N = (x2, y2)

P = (x3, y3)

Q = (x4, y4)

Next, we translate the quadrilateral 2 units right and 5 units down by adding 2 to the x-coordinate and subtracting 5 from the y-coordinate of each point.

The new coordinates of the points after the translation will be:

M' = (x1 + 2, y1 - 5)

N' = (x2 + 2, y2 - 5)

P' = (x3 + 2, y3 - 5)

Q' = (x4 + 2, y4 - 5)

Therefore, the coordinates of each point after the quadrilateral is translated 2 units right and 5 units down are:

M' = (x1 + 2, y1 - 5)

N' = (x2 + 2, y2 - 5)

P' = (x3 + 2, y3 - 5)

Q' = (x4 + 2, y4 - 5)

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Question completion:

Although part of your question is missing, you might be referring to the below question:

What are the coordinates of each point after quadrilateral MNPQ is translated 2 units right and 5 units down?

Guys can someone help me with these 2 problems please that's the matrix

Answers

The solution of the matrix is [tex]4G + 2F = \begin{bmatrix}32 &-20 &-32& -8 &-40 \\-24& -28 &4 &36 &8 \\16& 24 &12 &28 &20 \\-16&-12 &0 &-40 &-36\end{bmatrix}[/tex]

A matrix is a rectangular array of numbers arranged in rows and columns. The size of a matrix is given by its dimensions, which indicate the number of rows and columns in the matrix. In this question, both matrices G and F have 4 rows and 5 columns, so we say that they are 4x5 matrices.

Scalar multiplication is performed by multiplying each element of a matrix by a scalar, which is simply a number.

Now, to find the value of 4G + 2F, we need to perform scalar multiplication on each matrix and then add the results. We get:

[tex]4G = 4 * \begin{bmatrix}8 &-5 &-8& -2 &-10 \\-6& -7 &1 &9 &2 \\4& 6 &3 &7 &5 \\-4&-3 &0 &-10 & -9\end{bmatrix}\\= \begin{bmatrix}32 &-20 &-32& -8 &-40 \\-24& -28 &4 &36 &8 \\16& 24 &12 &28 &20 \\-16&-12 &0 &-40 & -36\end{bmatrix}[/tex]

[tex]2F = 2 * \begin{bmatrix}1 &8 &-2& -5 &9 \\-9& 10 &6 &-3 &0 \\4& 5 &-4 &3 &7 \\2&-10 &-6 &-1 & -8\end{bmatrix}= \begin{bmatrix}2 &16 &-4& -10 &18 \\-18& 20 &12 &-6 &0\\8& 10 &-8 &6 &14 \\4&-20 &-12 &-2 & -16\end{bmatrix}[/tex]

Now, we can perform matrix addition on 4G and 2F to get:

[tex]4G + 2F = \begin{bmatrix}32 &-20 &-32& -8 &-40 \\-24& -28 &4 &36 &8 \\16& 24 &12 &28 &20 \\-16&-12 &0 &-40 &-36\end{bmatrix}[/tex]

Therefore, the value of 4G + 2F is the 4x5 matrix given above.

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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

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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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"--

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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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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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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what is the interquartile range of this data set? enter answer in box

Answers

Answer:

do it by yourself what you do while teacher is teaching

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

Kyle has three times as much money in his savings account as Hayden Hayden has twice as much money in his savings account as Jeremy combine Kyle Hayden and Jeremy have a total of 612 how much money does Kyle have in his account

Answers

Kyle has $306 in his account so, right answer is Option D.

Let Kyle's money = x

Hayden's money = y

Jeremy's money = z

Given that Kyle has three times as much money in his savings account as  Hayden.

x = 3y   .....Eqn 1

Hayden has twice as much money in his savings account  as Jeremy.

z = 2y  ..... Eqn 2

Now Combined Kyle, Hayden, and Jeremy have a total of  $612.

x+y+z=612   .....Eqn 3

Putting value of x and z from Eqn 1 and 2 in Eqn 3

6y = 612

y = 106

Putting in Eqn 1;

x = 306

Thus, Kyle has $306 in his account.

The right answer is Option D.

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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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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%

3x^6 • 5x^-2 simplified

Answers

Answer:

First, you distribute the 3 into the brackets,

3(x - 2) + 5x

=3(x) + 3(-2) + 5x

=3x - 6 + 5x

Adding the like terms, 3x and 5x, gives you

=8x - 6

Step-by-step explanation:

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).

Learn more about tangent line here:https://brainly.com/question/30162650

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3. Write the following using exponential notation:
(5.
5.5.5.5.5.5.5.5.5) (7.7.7.7.7.7.7.7.7.7.7.7.7.7)

Answers

Answer:

5.5.5.5.5.5.5.5.5 in exponential notation is 5^9

7.7.7.7.7.7.7.7.7.7.7.7.7.7 in exponential notation is 7^13

Therefore, (5.5.5.5.5.5.5.5.5) (7.7.7.7.7.7.7.7.7.7.7.7.7.7) in exponential notation is:

5^9 * 7^13

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
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