4. Simplity \( (x+y)(x+\bar{y})+(\overline{\bar{x} \bar{y})+\bar{x}} \) 5. Simplity \( f(A, B, C, D)=(A B+C+D)(\bar{C}+D)(\bar{C}+D+E) \)

The  standard deviation of the number of errors in students' statistics homework is 0.94

The percentage of students made three error = 13%

The percentage of students made two error = 27%

The percentage of students made one error = 40%

The percentage of students made zero error = 100 - (13+27+40)

= 100 - 80

= 20%

Next we have to find the value of E(x)

E(x) = 0.2(0) + 0.4(1) + 0.27(2) + 0.13(3)

= 0 + 0.4 + 0.54 + 0.39

= 1.33

Next find the value of variance

Variance = 0.2(0-1.33)^2 + 0.4(1-1.33)^2 + 0.27(2-1.33)^2 + 0.13(3-1.33)^2

= 0.35378 + 0.04356 + 0.121202 + 0.362557

= 0.8811

Standard deviation = \(\sqrt{0.8811}\)

= 0.94

Therefore, the standard deviation is 0.94

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Here is the completed two-way frequency table:

                         Comedy     Action     Total

Boys                    37              57              94

Girls                    68               38             106  

Total                   105              95             200

Number of boys that prefer comedy = number of students that prefer comedy - Number of girls that prefer comedy

105 - 68 = 37

Number of boys that prefer action = total numer of boys - Number of boys that prefer comedy

94 - 37 = 57

Total number of students the prefer action = Total number of students - total number of students that prefer comedy

200 - 105 = 95

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The factor are (x^2 - 6)(x + 5).

We have given the polynomial of \(x^3 + 5x^2 - 6x - 30.\)

The grouping method can be used to factor polynomials whenever a common factor exists between the groupings.

\(x^3 + 5x^2 - 6x - 30.\)

factor out the x^2 from first two term and write the remaining term in the bracket

similarly,factor out 6 from the 3rd and 4th term we get

\(x^2(x+5)-6(x+5)\)

by grouping are we get

\((x^2 - 6)(x + 5).\)

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The height of the 10th bounce of the ball will be 0.6 feet.

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.

The nth term of the geometric sequence is given by

\(\sf T_n=ar^{n-1}\)

Where,

According to the given question.

During the first bounce, height of the ball from the ground, a = 4.5 feet

And, the each successive bounce is 73% of the previous bounce's height.

So,

During the second bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 10\)

\(=\dfrac{73}{100}(10)\)

\(\sf = 0.73 \times 10\)

\(\sf = 7.3 \ feet\)

During the third bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 7.3\)

\(=\dfrac{73}{100}(7.3)\)

\(\sf = 5.33 \ feet\)

Like this we will obtain a geometric sequence 7.3, 5.33, 3.11, 2.23,...

And the common ratio of the geometric sequence is 0.73

Therefore,

The sixth term of the geometric sequence is given by

\(\sf T_{10}=10(0.73)^{10-1\)

\(\sf T_{10}=10(0.73)^{9\)

\(\sf T_{10}=10(0.059)\)

\(\sf T_{10}=0.59\thickapprox0.6 \ feet\)

Hence, the height of the 10th bounce of the ball will be 0.6 feet.

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Answer: 7/10

Step-by-step explanation:

multiply 4/5 by 7/8=28/40 or 7/10

Answer:

U' (5, 1 )

Step-by-step explanation:

under a reflection in the x- axis

a point (x, y ) → (x, - y ) , then

U (5, - 1 ) → U' (5, - (- 1) ) → U' (5, 1 )

In the Pythagorean theorem, a²+b²=c² is the formula for finding the missing side length in a right-angled triangle. This formula is useful for determining one of the missing side lengths of a right triangle if you know the other two.

However, the theorem also states that c is the length of the triangle's hypotenuse. So, if you have a right-angled triangle with all three sides provided, you may use the Pythagorean theorem to solve for any of the missing sides. You'll use the hypotenuse length as the c variable when the three sides are given, then solve for the missing side.

To apply the Pythagorean theorem, you must identify the hypotenuse, which is the side opposite the right angle. If you're given three sides, the longest side is always the hypotenuse. As a result, you can always use the Pythagorean theorem to solve for one of the shorter sides by using the hypotenuse length.

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Answer:

A) \(2\sqrt{3}\)

Step-by-step explanation:

Answer:

the anwsers 2squareroot3 aka A

Step-by-step explanation:

just got it right on edge! :)

The maximum number of aphids in the cherry orchard is 1508.

What is population growth?

Population growth is the term used to describe the relative increase in population over a period of time. The growth rate is defined as growth per unit of time.

Given, N(t) = 1500-3t*ln(0.1t)-t

For maximum/minimum,  \(\frac{dN}{dt} =0\)

or, -3*ln(0.1t) - \(\frac{3t}{0.1t} *0.1\) - 1 = 0

or, -3*ln(0.1t) = 4

or, ln(0.1t) = -4/3

or, t = 2.64

Then, \(\frac{d^{2} N}{dt^{2} } = \frac{-3*0.1}{0.1t} = \frac{-3}{t}\) at t = 2.64

= -1.1381 < 0

Hence, it is maximum.

For the maximum number of Aphids put t = 2.64, we get

N = 1508

Hence, the maximum number of aphids in the cherry orchard is 1508.

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Answer:

B. -11

Step-by-step explanation:

ascending order means least to greatest.

-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7,...

3, -1, \(\sqrt{5}\), 13, -11

-11 is the least number because it is the greatest negative number

The given path [(√y, y) ∈ R² | y ∈ R] is 0. To find the limit of the function f(x, y) = (x^2y) / (x^2 + y^2) at the point (0, 0) along the given path,

we substitute the path's coordinates into the function and evaluate the limit as (x, y) approaches (0, 0) along that path.

The given path is [(√y, y) ∈ R² | y ∈ R].

Substituting these coordinates into the function:

f(√y, y) = (√y)^2 * y / (√y)^2 + y^2

         = y^1.5 / y + y^2

         = y^1.5 / (y(1 + y))

         = y^0.5 / (1 + y)

Now, let's evaluate the limit as y approaches 0:

lim(y->0) (y^0.5 / (1 + y))

We can apply direct substitution to find the limit:

lim(y->0) (0^0.5 / (1 + 0))

        = 0 / 1

        = 0

Therefore, the limit of the function f(x, y) = (x^2y) / (x^2 + y^2) at the point (0, 0) along the given path [(√y, y) ∈ R² | y ∈ R] is 0.

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Answer: $14.60/guest

Step-by-step explanation:

$6,124/240 = $14.60/guest

Answer:

x = 44/7

Step-by-step explanation:

7x+3 = 47

Subtract 3 from each side

7x+3-3 = 47-3

7x = 44

Divide by 7

7x/7 = 44/7

x = 44/7

Answer:

Option (4)

Step-by-step explanation:

If we draw a graph against x(Number of months) and y(Number of stamps),

We will get a straight line.

Let the equation of straight line be,

y = mx + b

Here, m = Stamps purchased per month

b = Jasmine was given stamps initially

From the table attached,

m = \(\frac{70-65}{2-1}\) = 5 stamps per month

Therefore, equation of the line will be,

y = 5x + b

Since, a point (1, 65) lies on this line,

65 = 5(1) + b

b = 60

That means she was given 60 stamps initially.

Option (4) will be the answer.

Answer:

218 (not positive its correct)

Step-by-step explanation:

Answer:

i think it's c

Step-by-step explanation:

sorry if I'm wrong

Answer:

c

Step-by-step explanation:

i took the test on e2020

The theoretical probability of this event is 0.2222.

What is probability?

Probability is simply how likely something event is to happen. It is computed by dividing the number of possible outcomes by the total number of possible outcomes.

For balls,

Total balls = 3

Favourable outcome (2 or 3) = 2

So, P(drawing a ball with number 2 or 3) = 2 / 3

For cards,

Total cards =  = 58 + 57 + 66+ 57 + 59 + 64 + 61 + 64 + 64 =  550

Cards with drawing Q = 180

P(drawing a card with letter Q) = 180 / 350 = 1 / 3 (approx)

The theoretical probability of this event = P(drawing a ball with number 2 or 3) * P(drawing a card with letter Q)

= 2/3*1/3 = 2/9 = 0.2222

The theoretical probability of this event is 0.2222.

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Answer:

1 miles

Step-by-step explanation:

5 min =  0.5 miles

so 10 min = 1 miles

Answer: Z = 65

Step-by-step explanation:

An inscribed angle is equal to 1/2 the circumference of the part of the circle across from it. Since we are given angle 50, we know the part of the circle’s circumference across from it equals 100. We also know a whole circle’s circumference is equal to 360. Let’s take 360-100 and see the remaining parts of the circumference is equal to 260. Since the two parts left of the circumference are labeled as x, we know they are equal. So, 260/2 = 130.

X=130. Notice that X is directly across from inscribed angle Z. This means Z = 1/2 X.

Z= 130/2

Z= 65

The three numbers are 62, 74, and 63.

Let's assume the first number is x.

The second number exceeds the first by 12 units, so it is x + 12.

The third number is one less than double the first, so it is 2x - 1.

According to the given information, the sum of the three numbers is 199. We can express this as an equation:

x + (x + 12) + (2x - 1) = 199.

Simplifying the equation, we combine like terms and solve for x:

4x + 11 = 199.

4x = 188.

x = 47.

Therefore, the first number is 47.

The second number is 47 + 12 = 59.

The third number is 2 * 47 - 1 = 93 - 1 = 92.

Hence, the three numbers are 47, 59, and 92.

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Answer: By the 8th week.

Step-by-step explanation:

Let the time that matteo and luca have the same amount of money be represented by x.

The information given in the question can be formed into an equation as:

400 - 10x = 200 + 15x

Collect like terms

400 - 200 = 15x + 10x

200 = 25x

x = 200/25

x = 8

Matteo and Luca will have the same amount of money by the 8th week.

Answer:

y

=

m

x

+

b

to find the equation.

y

=

−

2

x

+

8

Step-by-step explanation:

The appropriate actions when carrying out the order to remove a client's indwelling urinary catheter would be e. All of the above.

For any process involving bodily fluids, gloves should be worn to preserve good hygiene and stop the transmission of infection. Using the right antiseptic solution to clean the catheter insertion site lowers the chance of infection during catheter removal.

To check for any changes or anomalies and monitor the client's urinary function, it is required to empty the bladder and measure the urine flow. For accurate and complete medical records, the removal of the catheter must be properly documented. It guarantees appropriate communication and care continuity among healthcare professionals.
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The complete question is:

The nurse has received an order to remove a client's indwelling urinary catheter. which actions are appropriate when carrying out this order? select all that apply.

a. Wearing gloves

b. Cleaning the catheter insertion site

c. Emptying and measuring the urine output

d. Documenting the catheter removal

e. All of the above.

Let S be the subspace of P3 consisting of all polynomials p(x) such that p(0) = 0 and let T be the subspace of all polynomials q(x) such that q(1) = 0.

a) The two vectors are linearly independent and span S which means {x, \(x^{2}\)} forms a basis for S.

b) The two vectors are linearly independent and span T which means \({(x -1),(x - 1)^2}\)forms a basis for T.

c) The vector is linearly independent and spans S∩T which means {x(x−1)} forms a basis for S ∩ T.

We have the information from the question:

Let S be the subspace of \(P_3\) consisting of all polynomials p(x).

We have:

p(0) = 0 and let T be the subspace of all polynomials q(x) such that q(1) = 0.

a) S is all polynomials of the form p(x) = \(ax^2 + bx\) where a, b are

real numbers.

p(0) = \(a(0)^2 + b(0)\) = 0 for all a, b.

I propose that {x, \(x^{2}\)} forms a basis for S.

We must show that:

The vectors x and \(x^{2}\) are linearly independent and span S.

To show they are linearly independent we must show that:

\(\alpha _1(x^2) + \alpha _2(x) = 0(x^2) + 0(x)\)

Only has the solution :

\(\alpha _1=\alpha _2=0\)

Upon grouping the terms we find:

\(\alpha _1=0\\\\\alpha _2=0\)

Thus the two vectors are clearly linearly independent.

Now to show that the two vectors span S we must show that any element

in S which I will represent by p(x) = ax^2 + bx can be written as:

\(\alpha _1(x^2) + \alpha _2(x) = ax^2 + bx\)

where, \(\alpha _1,\alpha _2\) are scalar  vectors.

Upon grouping the terms we find that:

\(\alpha _1=a\\\\\alpha _2=b\)

With this solution we have:

\(\alpha _1(x^2) + \alpha _2(x) = ax^2 + bx\)

which means the two vectors span S.

Thus, the two vectors are linearly independent and span S which means {x, \(x^{2}\)} forms a basis for S.

b)T is all polynomials of the form :

\(q(x) = a(x - 1)(bx + c) =abx^2 + acx - abx - ca = ab(x^2) + (ac - ab)x - ac\)where a, b, c are real numbers.

This is because q(1) = a(1 − 1)(b + c) = 0 for all a, b, c.

Let s = ab and t = ac.

Now we have that T is all polynomials of the form

\(q(x) = sx^2 + (t - s)x - t\)

\({(x - 1),(x - 1)^2}\)forms a basis for S.

In order to confirm this we must show that the vectors x − 1 and \((x - 1)^2\)are linearly independent and span S.

To show they are linearly independent we must show that:

\(\alpha _1((x -1)^2) + \alpha _2(x - 1) = 0(x - 1)(0(x) + 0)\)

only has the solution α1 = α2 = 0

Upon grouping the terms we find:

\(\alpha _1=0\\\\\alpha _2=0\)

Thus the two vectors are clearly linearly independent.

Now to show that the two vectors span T we must show that any element

in T which I will represent by \(q(x) = sx^2 + (t - s)x - t\) can be written as:

\(\alpha _1((x - 1)^2) + \alpha _2(x - 1) = sx^2 + (t - s)x - t\)

Where, \(\alpha _1,\alpha _2\) are scalars.

Upon grouping the terms we find that:

\(\alpha _1=s\\\\\alpha _2=s+t\)

With this solution we have:

\(sx^2 + (t - s)x - t = sx^2 + (t - s)x - t\)

which means the two vectors span T

Thus, the two vectors are linearly independent and span T which means \({(x -1),(x - 1)^2}\)forms a basis for T.

c)  S∩T is all polynomials of the form \(c(x) = a(x-1)(bx) = abx^2-abx\)

where a, b are real numbers.

This is because \(c(0) = a(0 - 1)^2\)

(b(0)) = 0 and

c(1) =\(a(1 - 1)^2\)

(b(1)) = 0 for all a, b.

Let ab = t

This means S∩T is all polynomials of the form \(c(x) = tx^2-tx = tx(x-1).\)

I propose that {x(x − 1)} forms a basis for S ∩ T.

Now, we must show that the vector x(x − 1) is linearly independent and spans S ∩ T.

To show it is linearly independent we must show that:

\(\alpha _1\)(x(x − 1)) = 0(x(x − 1))

only has the solution \(\alpha _1\) = 0.

Upon grouping the terms we find:

\(\alpha _1\) = 0

Thus the two vectors are clearly linearly independent.

Now to show that the vector spans S ∩ T we must show that any element

in S ∩ T which I will represent by c(x) = tx(x − 1) can be written as:

\(\alpha _1\)(x(x − 1)) = tx(x − 1).

where \(\alpha _1\) is a scalar.

Upon grouping the terms we find that:

\(\alpha _1\) = t

With this solution we have:

tx(x − 1) = tx(x − 1)

which means the vector spans S ∩ T.

Thus, the vector is linearly independent and spans S∩T which means {x(x−1)} forms a basis for S ∩ T.

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If Lola uses only ³/₄ gallons of fruit juice, proportionately, she will need the following quantities of the other ingredients:

Proportion is the ratio or relative relationship of one value against another.

Proportion is used to show the quantity of a number contained in another.

Proportions are depicted using fractions, decimals, or percentages.

Available Ingredients for a Punch Recipe:

Bottles of ginger ale = 2 liters

Gallons of fruit juice = 1 gallon

Gallons of sherbet = ¹/₂ gallons

The proportion of fruit juice used = ³/₄ gallons

The proportion of ginger ale to be used = 1¹/₂ liters (2 x ³/₄)

The proportion of sherbet to be used = ³/₈ gallons (¹/₂ x ³/₄)

Thus, in proportion, Lola will use 1¹/₂ liters of ginger ale and ³/₈ gallons of sherbet if she cuts the recipe by using ³/₄ gallons of fruit juice.

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If the temperature is -5 degrees in one city and it is four degrees less in another city, the temperature in the other city would be -9 degrees.

This is because subtracting four from -5 results in a decrease of four units, giving us -9 degrees.

In the given scenario, the temperature in the other city is four degrees less than the temperature in the first city. When we subtract four from the original temperature of -5 degrees, we obtain -9 degrees.

Thus, the temperature in the other city is -9 degrees, indicating that it is colder by four degrees compared to the first city.

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For the following inequalities, if it is known that the function g is decreasing on its domain. g(5-x^2)≤g(3x-5) the solution is mathematically given as

1 ≤ x < 6

Generally, the equation for the inequalities is mathematically given as

g(5-x^2)≤g(3x-5)

therefore,

x^2<5x+6

-1< x <6

In conclusion, the solution to the inequalities are

1 ≤ x < 6

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