In a binomial experiment consisting of five trials, the number of different values that x (the number of successes) can assume is _____

In the formulas for constructing interval estimates based on sample proportions, the expression Pu (l - Pu) has a maximum value of 1/4.Let's discuss interval estimates based on sample proportions first. A proportion is the number of items in one category divided by the total number of items in all categories.

A sample is a smaller version of a population that we use to gather data and infer characteristics about the population. A confidence interval is a range of values that contains the true population parameter with a certain level of confidence. When we want to estimate the proportion of a population that has a certain characteristic, we use a sample proportion to estimate it.

A formula is used to construct a confidence interval around the sample proportion. The formula for constructing interval estimates based on sample proportions is given by: Lower Bound: P - zα/2 * sqrt(PQ/n)Upper Bound: P + zα/2 * sqrt(PQ/n)Where P is the sample proportion, Q is (1 - P), n is the sample size, and zα/2 is the z-score corresponding to the desired level of confidence. The expression Pu (l - Pu) has a maximum value of 1/4.

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The verbal expressions A. half of five more than a number, C. five more than half a number, and D. half of five less than a number represent the given algebraic expression when assigned with a variable. The expressions are 1/2(x + 5), 5 + 1/2x, and 1/2(x - 5).

The verbal expressions that represent the algebraic expressions are A. half of five more than a number, C. five more than half a number, and D. half of five less than a number. To convert these expressions into algebraic form, we need to assign a variable, say x, to the unknown number.

A. Half of five more than a number can be expressed algebraically as 1/2(x + 5). B. Twice a number and five can be written algebraically as 2x + 5. C. Five more than half a number can be expressed algebraically as 5 + 1/2x. D. Half of five less than a number can be written algebraically as 1/2(x - 5).

Therefore, the expressions that represent the given algebraic expression are A. half of five more than a number, C. five more than half a number, and D. half of five less than a number. Expression B represents a different algebraic expression altogether.

To summarize, three of the given verbal expressions represent the given algebraic expression, which can be converted to algebraic form by assigning a variable to the unknown number. These expressions are 1/2(x + 5), 5 + 1/2x, and 1/2(x - 5).

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Answer:

perimeter of inside rectangle: 4x + 2

perimeter of outside rectangle: 14x - 12

Explanation:

perimeter of inside rectangle:

2 ( x + 1 + x )

2 ( 2x + 1)

4x + 2

perimeter of outside rectangle:

2 (  3x - 1 + 4x - 5 )

2 ( 7x - 6 )

14x - 12

Answer:

Perimeter of the smallest rectangle = 4x + 2

Step-by-step explanation:

Perimeter of the smallest rectangle

= 2(x + 1) + 2x

= 2x + 2 + 2x

= 4x + 2

Perimeter of largest rectangle

= 2(3x - 1) + 2(4x - 5)

= 6x - 2 + 8x - 10

= 14x - 12

Perimeter of the largest rectangle MINUS the smallest rectangle (lightest grey shaded area)

= 14x - 12 - (4x + 2)

= 14x - 12 - 4x - 2

= 10x - 14

Answer:

Below

Step-by-step explanation:

Let x and x' be the zeroes of the quadratic polynomial ax^2 +bx + c

● xx'= -c/a

● x + x' = -b/a

The company should not stop the production line, as it is highly unlikely to get exactly 6 baseballs with straight stitching.

To solve this, we need to use the binomial probability distribution to find the probability of getting exactly six out of eight baseballs with straight stitching, given that the proportion of baseballs with straight stitching is 0.938.

The probability of getting exactly k successful outcomes out of n independent trials, where each trial has probability of success p, is given by the formula:

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

where "n choose k" is the binomial coefficient, which is the number of ways to choose k items from a set of n items.

In this case, the number of independent trials is 8, the probability of success is 0.938, and the number of successful outcomes is 6.

so, P(6) = (8 choose 6) * (0.938^6) * (1-0.938)^2

As we can see, this is a very low probability, so the company should not stop the production line, as it is highly unlikely to get exactly 6 baseballs with straight stitching.

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Let an be a sequence, and bn, cn be test sequences and If an = o(bn) and bn = o(cn), then an = o(cn).

Let an be a sequence, and bn, cn be test sequences. Given that an = o(bn) and bn = o(cn), we can infer the following:

1. an is bounded by some constant times bn as n approaches infinity.
2. bn is bounded by some constant times cn as n approaches infinity.

Since an is bounded by bn and bn is bounded by cn, we can conclude that an must also be bounded by cn, meaning an = o(cn). In other words, an grows no faster than cn as n approaches infinity.

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Answer:

5 less than or equal to x

Step-by-step explanation:

make x subject

Hello! To solve completing by the square, we have to follow some steps:

Now, we have to add the same value in both sides (square):

If we factorize the first part of this expression, we can obtain:

Notice that we obtained the same expression, and now we know the value of the square. So, let's rewrite the first expression and replace the squares by 4:

1)The expression 4x^2-16x+12/x^2-9 is undefined when the denominator, x^2-9, equals zero because division by zero is undefined.

x^2-9 equals zero when x equals 3 or x equals -3. Therefore, the expression is undefined at x = 3 and x = -3. In all other cases, the expression is defined.

2) The given expression is:

(5-2x)/(x+2) + x^2/(x^2-4) - 5

To simplify this expression, we need to first find the LCD (least common denominator) of the two fractions. The denominator of the first fraction is x+2, and the denominator of the second fraction is x^2-4, which can be factored as (x+2)(x-2). So the LCD is (x+2)(x-2). Now we can rewrite the expression with this common denominator:

[(5-2x)(x-2) + x^2(x+2) - 5(x+2)(x-2)] / [(x+2)(x-2)]

Expanding the brackets and simplifying, we get:

(-x^3 - 3x^2 - 3x + 5) / [(x+2)(x-2)]

This expression is undefined when the denominator, (x+2)(x-2), equals zero because division by zero is undefined.

(x+2)(x-2) equals zero when x equals -2 or x equals 2. Therefore, the expression is undefined at x = -2 and x = 2. In all other cases, the expression is defined.

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Answer:

The answer would be 70

Step-by-step explanation:All you have to do is divide 840 by 12 and you get 70 Hope this helps and have a great week:)

Answer:

70

Step-by-step explanation:

This is because 840/12=70

Hope it helps you

PLS RATE AS BRAINLIEST ANSWER

Answer:

E--S

EP--SW

R--D

CE--GS

Step-by-step explanation:

you just match them, out of the 4 letters,  ce were in the middle of the two for parrallelogram RCEP, so we se the two middle letters DGSW, which is GS.

now apply this mechanism to all of the letters side by side.

hope this helps!

We use the Serial Autocorrelation in the classical linear regression model.

In the classical linear regression model the serial autocorrelation is assumed to solve the problem.

Hence, we use the Serial Autocorrelation in the classical linear regression model.

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Answer:

i think its B.............................

The root of the equation sinx = 2x-3 is 0.8401 (approx).

Given equation is sinx = 2x-3

We need to solve this equation using false position method.

False position method is also known as the regula falsi method.

It is an iterative method used to solve nonlinear equations.

The method is based on the intermediate value theorem.

False position method is a modified version of the bisection method.

The following steps are followed to solve the given equation using the false position method:

1. We will take the end points of the interval a and b in such a way that f(a) and f(b) have opposite signs.

Here, f(x) = sinx - 2x + 3.

2. Calculate the value of c using the following formula: c = [(a*f(b)) - (b*f(a))] / (f(b) - f(a))

3. Evaluate the function at point c and find the sign of f(c).

4. If f(c) is positive, then the root lies between a and c. So, we replace b with c. If f(c) is negative, then the root lies between c and b. So, we replace a with c.

5. Repeat the steps 2 to 4 until we obtain the required accuracy.

Let's solve the given equation using the false position method.

We will take a = 0 and b = 1 because f(0) = 3 and f(1) = -0.1585 have opposite signs.

So, the root lies between 0 and 1.

The calculation is shown in the attached image below.

Therefore, the root of the equation sinx = 2x-3 is 0.8401 (approx).

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Answer:

10

Step-by-step explanation:

10+x+2=-8+3x

12+x =-8+3x

12+8=3x-x

20=2x

X=20/2

X=10

Answer:

C

Step-by-step explanation:

y = mx + b

meaning that m is the slope and b is the y - intercept

1.) You must find the slope of the line first

    - you can find the slope by using rise over run

    - this answer is m

2.) find where the red line crosses the y - axis

    - this answer is b

3.) just plug your findings into your y = mx + b equation and it will give you your answer.

Answer:

4^3/8+3([ 4 ])-5^2

[ 64 ]/8+3([ 4 ])-5^2

[ 64 ]/8+3([ 4 ])-[ 25 ]

[ 64 ]/8+[ 12 ]-[ 25 ]

[ 8 ]+[ 12 ]-[ 25 ]

[ 20 ]-[ 25 ]

[ -5 ]

Answer:

The final answer is -5.

Step-by-step explanation:

4^3 / 8 + 3 (7-3) - 5^2

4^3 / 8 + 3( 4 ) - 5^2

64 / 8 + 3( 4 ) - 25

64 / 8 + 12 - 25

8 + 12 -25

20 - 25

= -5

So the first part you subtract the numbers in brackets.

Then you reduce the powers as in simplifying them.

From there you multiply 3 and 4.

Then you divide 64 and 8

After that you do the rest just as they are.

HOPE IT HELPED

Answer:

12(2x-1)

Step-by-step explanation:

24x - 12

Factor out a 12 from each term

12*2x -12*1

12(2x-1)

Answer:

\(12(2x - 1)\)

Step-by-step explanation:

\(24x - 12\)

Factor out a 12 from each

\(24x - 12 \\ 12(2x - 1)\)

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

A: 33 (divided by or /) 2.4 = 13.75

B: 13.75

Step-by-step explanation:

He earned 13.75 in one hour.

A). The equation,

x = 33/2.4

B). x = $13.75.

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Given:

Preston earns $33.00 for babysitting his neighbor's children for 2.4 hours.

Let the unit rate be x.

You can use an equation to find out the earnings of Preston per hour.

A). The equation,

x = 33/2.4

B). x = $13.75.

Therefore,  $13.75 per hour is the unit rate.

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Answer:

D)  \(3m + 21\)

Step-by-step explanation:

We know that the average is a value divided by 2: So we can calculate the average in terms of x:

We know that:

\(x = m + 9\)

\(y = 2m + 15\)

\(z = 3m + 18\)

To find the average of x, y, z we can add them then we can divide by 2 to find the average in terms of m:

\(m + 9 + 2m + 15 + 3m + 18 = 6m + 42\)

I have combined like terms and then using that I can divide this by 2:

\(6m + 42 / 2 = 3m + 21\)

Answer:

Hey There!

Let's solve...

First we need to find out the equation of x which is

\(x = \frac{m + 9}{2} \\ \)

Now let's find out the equation of y which is

\(y = \frac{2m + 15}{2} \\ \)

Now let's find out equation of z which is

\(z = \frac{3m + 18}{2} \\ \)

On adding the three equations, we get

\(2x + 2y + 2z = m + 2m + 3m + 9 + 15 + 18\)

Now we get..

\(2(x + y + z) = 6m + 42 \\ \\ x + y + z = 3m + 21\)

Now let's find our the average of x,y snd z which is

\( \frac{x + y + z}{3} \\ which \: is \: \\ \\ \frac{3m + 21}{3} \)

\(now \: factor \: 3m + 21 \: which \\ is \: 3(m + 7)\)

Now simplify..

\( \frac{ \cancel{3}(m + 7)}{ \cancel{3}} \\ \)

So answer is m+7

¬ Vx(Fx → Gx) v 3xFx ⊢ Fx → Gx [1-5, Modus Ponens]

i. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx (5 marks)

Proof:

1. ∃x(Fx & Gx) [Premise]

2. Fx & Gx [∃-Elimination, 1]

3. ∃xFx [∃-Introduction, 2]

4. ∃xGx [∃-Introduction, 2]

5. ∃xFx & ∃xGx [Conjunction Introduction, 3 and 4]

6. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx [1-5, Modus Ponens]

ii. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px (5 marks)

Proof:

1. ¬ 3x(Px v Qx) [Premise]

2. ¬ Px v ¬ Qx [DeMorgan’s Law, 1]

3. Vx ¬ Px [∀-Introduction, 2]

4. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px [1-3, Modus Ponens]

iii. ¬ Vx(Fx → Gx) v 3xFx (10 marks; Hint: To derive this theorem use RA.)

Proof:

1. ¬ Vx(Fx → Gx) v 3xFx [Premise]

2. (¬ Vx(Fx → Gx) v 3xFx) → (¬ Vx(Fx → Gx) v Fx) [Implication Introduction]

3. ¬ Vx(Fx → Gx) v Fx [Resolution, 1, 2]

4. (¬ Vx(Fx → Gx) v Fx) → (Fx → Gx) [Implication Introduction]

5. Fx → Gx [Resolution, 3, 4]

6. ¬ Vx(Fx → Gx) v 3xFx ⊢ Fx → Gx [1-5, Modus Ponens]

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The probability of the random item chosen that it is less than 16.4 inches long is 2.7%

Probability means ?

The likelihood of an event happening is calculated using the probability formula. To review, probability is the probability that an event will occur. What is the likelihood that a specific event will occur when a random experiment is considered? is one of the first queries that pops into our heads. A prediction's chance is expressed as a probability. If we suppose that, for example, x represents the probability that an event will occur, then (1-x) is the probability that the event will not occur.

Variance of sample mean =1.3^2/1= 1.69

S D of sample mean =1.69^(1/2)= 1.3

Z score for length of 16.4 is( 16.4-15.4)/1.3= 0.7692307

The p value for -1.67 in standard normal table is 0.04746

The required probability =0.02764

Only 2.7% of the time will the sample mean be shorter than 16.4 inches.

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It is known that all the gold ever mined is about 10 000 000 000 ounces (10 billion ounces). And, we need to find the length of one wall to fit it into a cubic shaped room.

Firstly, let's determine the volume of the gold. Since, we know that the gold would fill a cubic shaped room, thus its volume will be equal to the volume of the room. Therefore, the volume of the gold will be given by:

Volume of gold = Volume of the cubic room

                          = l³  (where l is the length of one wall)

Next, let's calculate the volume of 1 ounce of gold using the density of gold.

Density of gold is given as: 19.3 grams/cubic cm≈ 0.697 lb/ cubic in 1 ounce

                                                                                = 1/16 lb

Therefore, volume of 1 ounce of gold = 1/0.697

                                                              ≈ 1.43 cubic inches

Now, let's convert cubic inches to cubic feet.

1 foot = 12 inches

1 cubic foot = 12 x 12 x 12 cubic inches

                   = 1728 cubic inches

Therefore,1 cubic inch = (1/1728) cubic feet

Hence, the volume of 1 ounce of gold in cubic feet will be:

1.43 cubic inches = (1.43/1728) cubic feet

                             = 0.000827 cubic feet

Finally, substituting this value in the expression of the volume of the gold, we get:

l³ = Volume of the gold

Volume of the gold = 10 billion x 0.000827 cubic feet

                                = 8,270,000 cubic feet

So, the length of one wall to fit all the gold ever mined in a cubic shaped room would be:

l³ = 8,270,000 cubic feet

l = cube root (8,270,000)

  ≈ 200.5 feet (rounded to one decimal place)

To solve the given problem, we need to determine the length of one wall of a cubic shaped room to fit all the gold ever mined. We start with calculating the volume of the gold, which will be equal to the volume of the cubic room. We know that the volume of a cubic room is given by the cube of the length of one wall. So, we need to find the cube root of the volume of the gold. To calculate the volume of the gold, we need to first determine the volume of 1 ounce of gold using its density, and then multiply it by the total number of ounces of gold ever mined. We know that density of gold is approximately 19.3 grams/cubic cm. Thus, we can convert this density to pounds per cubic inch since we know that 1 cubic inch is equal to 0.0005787 cubic centimeters. 1 ounce is equal to 1/16 pound. We then convert cubic inches to cubic feet and get the value of the volume of 1 ounce of gold in cubic feet. Substituting the values of the volume of 1 ounce of gold and the total ounces of gold ever mined in the expression of the volume of the gold, we get the volume of the gold. Finally, we calculate the cube root of the volume of the gold to obtain the length of one wall of the cubic room.

Therefore, the length of one wall to fit all the gold ever mined in a cubic shaped room would be approximately 200.5 feet.

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The roots of the quadratic equation 0 = 2x² + 12x-14 is (C) x=-7 and x=1.

Any equation in algebra that can be written in the standard form where x stands for an unknown value and a, b, and c stand for known values is said to be a quadratic equation.

In general, it is assumed that a > 0; equations with a = 0 are regarded as degenerate since they become linear or even simpler.

So, the roots of 0 = 2x² + 12x-14 are:

2x² + 12x-14  = 0

2x² + 14x - 2x -14

2x(x + 7) - 2(x + 7)

(2x - 2) (x + 7)

Now, use the zero product property as follows:

2x - 2 = 0

2x = 2

x = 2/2

x = 1

And

x + 7 = 0

x = -7

Therefore, the roots of the quadratic equation 0 = 2x² + 12x-14 is (C) x = -7 and x = 1.

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Correct question:

What are the roots of the quadratic equation 0 = 2x² + 12x-14?

a. 1,6, -7

b. 2,12,-14

c. -7,1

d. -1,7

The chance of the event B is 0.4 when using the probability for the two independent two event formula.

In the given question, if a and b are independent events with p(a) = 0.65 and p(a ∩ b) = 0.26, then we have to find the value of p(b).

Events classified as independent do not depend on other events for their occurrence.

Event A's likelihood of happening is P(A)=0.65.

The likelihood of the two events A and B intersecting is P(A∩B)=0.26.

Given that the likelihood of the two independent events is:

P(A∩B) = P(A)⋅P(B)

Then the probability of the event B will be,

P(B) = P(A)/P(A∩B)

P(B) = 0.65/0.26

P(B) =0.4

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Answer:

i think x=36

Step-by-step explanation:

3x + 2x = 5x = 180

x = 180÷5 =36

Check the picture below.

Answer:

(6, -3) aka x = 6 and y = -3

Step-by-step explanation:

since you are given y = -2x + 9, you should start by substituting the expression -2x + 9 for y in the equation 2x + 3y = 3.

here's your equation after plugging in the expression that's equal to y:

2x + 3(-2x + 9) = 3

distribute 3 to -2x

2x + 3(-2x + 9) = 3 ⇒ 3 · -2x = -6x

...and to 9.

2x + 3(-2x + 9) = 3 ⇒ 3 · 9 = 27

now you're left with 2x - 6x + 27 = 3.

combine like terms.

2x - 6x + 27 = 3 ⇒ -4x + 27 = 3

subtract 27 from both sides of the equation. since +27 and -27 cancel each other out, you're left with subtracting 27 from 3, which gives you -24.

now your equation is -4x = -24.

divide both sides of the equation by -4.

-24/-4 = 6

...therefore x = 6.

since you have your x value now, you can plug that into the equation for y in order to solve for y.

y = -2x + 9 ⇒ y = -2(6) + 9

multiply -2 and 6.

y = -2(6) + 9 ⇒ y = -12 + 9

add -12 and 9.

y = -12 + 9 ⇒ y = -3

...and now you've solved for y, which is -3.

therefore, your solution is (6, -3), aka x = 6 and y = -3.

hope this helps! have a nice day <3

Answer:

The first differences are 5, 9, 13, 17, and so the second differences are all 4.

Halving 4 gives 2, so the first term of the sequence is 2n^2.

Subtracting 2n^2 from the sequences gives 1,0,-1-2,-3 which has the nth term -n+2.

Therefore, the formula for this sequence is 2n^2 -n +2.

Answer:

2n^2 - n +2

Step-by-step explanation:

3,8,17,30,47

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

this is the final form I got after playing for a while:

.....

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

tested in excel and works:

1 2 3 4 5 6 7 8 9 10

3 8 17 30 47 68 93 122 155 192