If 142 adults are randomly selected, what is the probability that the sample mean would differ from the population mean by more than 1.5 kilograms

Answer: x² - (3/4)x + 9/64 = (x + 3/8)²

Step-by-step explanation:

Concept:

Here, we need to know the idea of completing the square.

Completing the square is a technique for converting a quadratic polynomial of the form ax²+bx+c to the form (x-h)²for some values of h.

If you are still confused, please refer to the attachment below for a graphical explanation.

Solve:

If we expand (x - h)² = x² - 2 · x · h + h²

Given equation:

Since [x² - (3/4)x +___] is the expanded form of (x - h)², then (-3/4)x must be equal to 2 · x · h. Thus, we would be able to find the value of h.

Finally, we plug the final value back to the equation.

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Step-by-step explanation:

Answer:

h(x - 1) = -5x - 2

General Formulas and Concepts:

Pre-Algebra

Algebra I

Terms/Coefficients

Functions

Step-by-step explanation:

Step 1: Define

Identify

h(x) = -5x - 7

Step 2: Find

Answer:

C

Step-by-step explanation:

trust me its easy

Answer:

C: None of the above

Step-by-step explanation:

⠀⠀⠀⠀⠀⠀⠀⠀⠀Stolen from GoogIe :p

The minimum length of wire needed  is approximately 22.5 meters and the maximum length of wire needed is also approximately 22.5 meters.

Let's assume the length of the wire is "L" meters. We need to find the minimum and maximum values of L that satisfy the given conditions.

To find the minimum length of wire needed, we should minimize the combined area of the equilateral triangle and the circle. The minimum occurs when the wire is distributed in a way that maximizes the area of the circle while minimizing the area of the equilateral triangle.

Minimum length (L_min):

Let "x" be the length of the wire used to form the equilateral triangle, and "y" be the length used to form the circle.

The area of an equilateral triangle is given by (√(3)/4) * side², where the side is the length of one of the triangle's equal sides.

The area of a circle is given by π * radius².

Since the perimeter of an equilateral triangle is three times the length of one of its sides, and the circumference of a circle is given by 2 * π * radius, we have:

x + y = L ...(1) (The total wire length remains constant)

x = 3 * side ...(2) (Equilateral triangle perimeter)

y = 2 * π * r ...(3) (Circle circumference)

The area enclosed by the two pieces is given by:

Area = (√(3)/4) * side² + π * r²

We want to minimize this area subject to the constraint x + y = L.

To find the minimum, we can use the method of Lagrange multipliers.

By solving this optimization problem, we find that the minimum value of the combined area is approximately 64 m² when x ≈ 7.5 m and y ≈ 15 m. Thus, the minimum length of wire needed (L_min) is approximately 7.5 + 15 = 22.5 meters.

Maximum length (L_max):

To find the maximum length of wire needed, we should maximize the combined area of the equilateral triangle and the circle. The maximum occurs when the wire is distributed in a way that minimizes the area of the circle while maximizing the area of the equilateral triangle.

By solving this optimization problem, we find that the maximum value of the combined area is approximately 64 m² when x ≈ 15 m and y ≈ 7.5 m. Thus, the maximum length of wire needed (L_max) is approximately 15 + 7.5 = 22.5 meters.

So, the minimum length of wire needed is approximately 22.5 meters, and the maximum length of wire needed is also approximately 22.5 meters.

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Answer:

  b. angle K is acute

Step-by-step explanation:

We're often told not to draw any conclusions from the appearance of a figure in a geometry problem. Here, angle K appears to be somewhat less than 90°, so angle K is acute.

__

Additional comment

This choice of answer is confirmed by the fact that the other two (visible) choices say the same thing. If one of them is correct, so is the other one. Hence they must both be incorrect. (An obtuse angle is more than 90°.)

Answer:

[tex]x=5[/tex]

Step-by-step explanation:

Given [tex]3x+7=22[/tex], our goal is to isolate [tex]x[/tex] such that will have an equation that tell us [tex]x[/tex] is equal to something.

Start by subtracting 7 from both sides:

[tex]3x+7-7=22-7,\\3x=15[/tex]

Divide both sides by 3:

[tex]\frac{3x}{3}=\frac{15}{3},\\x=\frac{15}{3}=\boxed{5}[/tex]

Therefore, the value of [tex]x=5[/tex] makes the equation [tex]3x+7=22[/tex] true.

Answer:

x = 5

Step-by-step explanation:

Subtract 7 from both sides:  3x + 7- 7 = 22 - 7

Simplify: 3x = 15

Divide both sides by 3

Simplify: x = 5

Hope this helps:)

Answer:

The 90% confidence interval for the population proportion of adults in the U.S. who have donated blood in the past two years is (0.1627, 0.1887).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

A Gallup survey of 2322 adults (at least 18 years old) in the U.S. found that 408 of them have donated blood in the past two years.

This means that [tex]n = 2322, \pi = \frac{408}{2322} = 0.1757[/tex]

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].  

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1757 - 1.645\sqrt{\frac{0.1757*0.8243}{2322}} = 0.1627[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1757 + 1.645\sqrt{\frac{0.1757*0.8243}{2322}} = 0.1887[/tex]

The 90% confidence interval for the population proportion of adults in the U.S. who have donated blood in the past two years is (0.1627, 0.1887).

Answer:

C f(x) = 4(x+1)2-1

Step-by-step explanation:

factor of 4 = 2^2

(x+1)2-1 = 4(x+1) 2-1 = with x

           =   4(+1) 2-1  = without x

           =  (4 - 4) 2 = individual products of -1

           =  (8 - 8 ) = individual products of 2

           =   8 - 8  = 2^2 -2^2

           =  2^2 - 2^2

(x+1)2-1 = 4(x+1)2-1 = with x

            = 2x^2 -2^2

          -x = 2^2 -2^2

            x = -2^2-2^2

            x = 4

which proves f(x) is a factor of 4

Answer:

Step-by-step explanation:

Average rate of change is the same thing as the slope of the line between 2 points. What we have are the x values of each of 2 coordinates. What we don't have are the y values that go with those. But we can find them! Aren't you so happy?

We can find the y value that corresponds to each of those x values by evaluating the function at each x value, one at a time. That means plug in 4 for x and solve for y, and plug in 6 for x and solve for y.

[tex]f(4)=2(4)^3+4[/tex] and doing the math on that gives us

f(4) = 132 and the coordinate is (4, 132).

Doing the same for 6:

[tex]f(6)=2(6)^3+4[/tex] and doing the math on that gives us

f(6) = 436 and the coordinate is (6, 436). Now we can use the slope formula to find the average rate of change (aka slope):

[tex]m=\frac{436-132}{6-4}=\frac{304}{2}=152[/tex] where m represents the slope

9514 1404 393

Answer:

  121/14  or  8 9/14

Step-by-step explanation:

The quotient of 1/8 and 1/4 is ...

  (1/8)/(1/4) = (1/8)(4/1) = 4/8 = 1/2

The product of 2 2/3 and 3 3/7 is ...

  (2 2/3)(3 3/7) = (8/3)(24/7) = (8·24)/(3·7) = 64/7

Subtracting the first result from the second gives ...

  64/7 -1/2 = (128 -7)/14 = 121/14 = 8 9/14

_____

Additional comment

When subtracting fractions with denominators that have no common factors, I find it useful to make use of the formula ...

  [tex]\dfrac{a}{b}-\dfrac{c}{d}=\dfrac{ad-bc}{bd}[/tex]

In this case, that gives us (64·2 -7·1)/(7·2) = (128 -7)/14.

Replace x in the equation with the x value of the point (6) and solve. If it equals the y value (0) it is a solution if it noes not equal (0) it is not a solution.

Y = 6^2 = 36

36 is not 0 so (6,0) is not a solution

Answer:

No, point (6, 0) is not on the equation.

Step-by-step explanation:

To do this question the easiest way, you would use your scientific/graphing calculator and type in your equation. But you can do this with your mind.

Since the equation y = x^2 does not have any number in it (such as m = slope) it does not start anywhere. You will put it in the origin which is (0, 0) from there, you can tell that the equation will not reach (6, 0), but only (1, 1).

Answer:

A

Step-by-step explanation:

ABC triangle is 1/2 the size of DEF triangle. In order to transform ABC to DEF, the scale has to be doubled and the point on the y-axis has to move down to 10

The required value of m for the given triangle is given as m = 12.

In a right-angled triangle, its sides, such as hypotenuse, and perpendicular, and the base is Pythagorean triplets.

Here,
Applying Pythagoras' theorem,
n² = m² - 6² - - - - (1)

m ² + base² = 24²
base² = 24² - m² - - - - (2)

n² + 18² = base²
From equation 1 and 2
m² - 6² + 18² = 24² - m²
2m² = 24² + 6² - 18²
m = 12

Thus, the required value of m for the given triangle is given as m = 12.

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9514 1404 393

Answer:

Step-by-step explanation:

Let x and y represent the weights of the large and small boxes, respectively. Then the two delivery weights give rise to the equations ...

  3x +5y -79 = 0

  12x +2y -199 = 0

Using the "cross multiplication method" of solving these equations, we find ...

  d1 = (3)(2) -(12)(5) = 6 -60 = -54

  d2 = 5(-199) -(2)(-79) = -995 +158 = -837

  d3 = -79(12) -(-199)(3) = -948 +597 = -351

1/d1 = x/d2 = y/d3

x = d2/d1 = -837/-54 = 15.5

y = d3/d1 = -351/-54 = 6.5

The large boxes weigh 15.5 kg; the small boxes weigh 6.5 kg.

_____

Additional comment

My preferred quick and easy way to solve equations like this is using a graphing calculator. In addition to that, an algebraic method is shown.

The "cross-multiplication method" shown here is what I consider to be a simplified version of what you would find in videos. It is a variation of Cramer's rule and the Vedic maths methods of solving pairs of linear equations. I find it useful when "elimination" or "substitution" methods would result in annoying numbers. In such cases, it uses fewer arithmetic operations than would be required by other methods.

Short description: writing the coefficients of the general form equations in 4 columns, where the last column is the same as the first, a "cross multiplication" is computed for each of the three pairs of columns. Those computations are of the form ...

  [tex]\text{column pair: }\begin{array}{cc}a&b\\c&d\end{array}\ \Rightarrow\ d_n=ad-cb[/tex]

The relationship between the differences d₁, d₂, and d₃ and the variable values is shown above.

Answer: 1. When you estimate, it is not an exact measurement. 3ft 8 in gets rounded to 4ft and 12 ft 3 in rounds to 12ft. now find the perimeter. P=2l+2w P= 2*12 +2*4 P=32feet

2. 3ft 8in = 3 8/12 or reduced to 3 2/3  12ft 3in = 12 3/12 or reduced to 12 1/4   The fractional part is referring to a fraction of a foot.

3. The perimeter of the room is P=2l+2w or P=2(12 1/4) + 2(3 2/3) p=24 1/2 + 7 1/3  P= 31 5/6 feet

4. The estimate and the actual are very close. They are 1/6 of a foot apart.

5a. Total baseboard 31 5/6ft - 2 1/4 ft = 29 7/12 feet needed.

5b. Take the total and divide it by 8ft  = 29 7/12 divided by 8= 3.7  You are not buying a fraction of a board so you would need 4 boards.

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Answer:

  (b)  x = 0.25, 0.75, 1.25, 1.75

Step-by-step explanation:

The asymptotes of tan(α) are found at ...

  α = π/2 +nπ

We want to find x such that ...

  2πx = α = π/2 +nπ

Dividing by 2π gives ...

  x = 1/4 +n/2 . . . . . . . for integers n

In the desired range, the values of x are ...

  x = 0.25, 0.75, 1.25, 1.75

Answer:

1. B

2. C

Step-by-step explanation:

Answer:

[tex]5\sqrt{5}[/tex]

Step-by-step explanation:

1. [tex]5^2 + 10^2 = c^2[/tex]

2.[tex]125 = c^2[/tex]

3. [tex]c=5\sqrt{5}[/tex]

Answer:

a , hiro should have divided both sides of the equation by 2

Answer:

30/420 or 1/14

Step-by-step explanation:

3*2*7/5*7*12= 30/420 simplify the you get 1/14

9514 1404 393

Answer:

  48 minutes

Step-by-step explanation:

Since the speed is the same for Stage 2, the time is proportional to the distance.

  t2/(44 mi) = (120 min)/(110 mi)

  t2 = (44/110)(120 min) = 48 min . . . . . . multiply by 44 mi

The time for Stage 2 was 48 minutes.

Answer:

The first year in which Clara will see that Investment B's value will exceed Investment A's value will be year 14.

Step-by-step explanation:

Since Clara made two investments, and Investment A has an initial value of $ 500 and increases by $ 45 every year, while Investment B has an initial value of $ 300 and increases by 10% every year, and Clara checks the value of her investments once to year, at the end of the year, to determine what is the first year in which Clara sees that Investment B's value has exceeded investment A's value, the following calculation must be performed:

500 + (45 x X) = A

300 x 1.1 ^ X = B

A = 500 + 45 x 5 = 500 + 225 = 725

B = 300 x 1.1 ^ 5 = 483.15

A = 500 + 45 x 10 = 950

B = 300 x 1.1 ^ 10 = 778.12

A = 500 + 45 x 15 = 1175

B = 300 x 1.1 ^ 15 = 1253.17

A = 500 + 45 x 14 = 1,130

B = 300 x 1.1 ^ 14 = 1,139.25

Therefore, the first year in which Clara will see that Investment B's value will exceed Investment A's value will be year 14.

Answer:

see explanation

Step-by-step explanation:

(a)

Using the recursive rule and a₁ = 4 , then

a₂ = 2([tex]\frac{1}{3}[/tex] + a₁ ) = 2([tex]\frac{1}{3}[/tex] + 4) = 2 × 4 [tex]\frac{1}{3}[/tex] = 2 × [tex]\frac{13}{3}[/tex] = [tex]\frac{26}{3}[/tex]

a₃ = 2([tex]\frac{1}{3}[/tex] + a₂) = 2([tex]\frac{1}{3}[/tex] + [tex]\frac{26}{3}[/tex] ) = 2 × [tex]\frac{27}{3}[/tex] = 2 × 9 = 18

a₄ = 2([tex]\frac{1}{3}[/tex] + a₃) = 2([tex]\frac{1}{3}[/tex] + 18) = 2 × 18 [tex]\frac{1}{3}[/tex] = 2 × [tex]\frac{55}{3}[/tex] = [tex]\frac{110}{3}[/tex]

a₅ = 2([tex]\frac{1}{3}[/tex] + a₄) = 2([tex]\frac{1}{3}[/tex] + [tex]\frac{110}{3}[/tex]) = 2 × [tex]\frac{111}{3}[/tex] = 2 × 37 = 74

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

(b)

Using the recursive rule and a₁ = 6 , then

a₂ = [tex]\frac{2}{a_{1} }[/tex] = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]

a₃ = [tex]\frac{3}{a_{2} }[/tex] = [tex]\frac{3}{\frac{1}{3} }[/tex] = 9

a₄ = [tex]\frac{4}{a_{3} }[/tex] = [tex]\frac{4}{9}[/tex]

a₅ = [tex]\frac{5}{a_{4} }[/tex] = [tex]\frac{5}{\frac{4}{9} }[/tex] = 5 × [tex]\frac{9}{4}[/tex] = [tex]\frac{45}{4}[/tex]

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

(c)

The sequence has a common ratio

r = [tex]\frac{\frac{2}{3} }{\frac{1}{6} }[/tex] = [tex]\frac{\frac{8}{3} }{\frac{2}{3} }[/tex] = 4

Multiply the previous terms by 4 , then

a₄ = 4 × [tex]\frac{8}{3}[/tex] = [tex]\frac{32}{3}[/tex]

a₅ = 4 × [tex]\frac{32}{3}[/tex] = [tex]\frac{128}{3}[/tex]

Answer:

0.08x + 0.15y

Step-by-step explanation:

multiply the amount of pints with the given percent of fat

Answer:

Hence total fat in mixture is 8x+15y100 pints

Answer:

The answer is "Sample size is important when the population is not normally distributed ".

Step-by-step explanation:

The theorem for the central limit indicates that perhaps the sample distribution of means by the sample is close to the confidence interval independent of the underlying population demographics when large samples are derived from every population, with [tex]mean = \mu[/tex] and confidence interval [tex](S.D) = \sigma[/tex]. The bigger the sample, the stronger the approach (typically [tex]n \geq 30[/tex]). The sample is therefore significant unless the population is not typically spread.

Answer:

Step-by-step explanation:

Which expression is equivalent to One-fourth minus three-fourths x?

Answer:

C: 112 feet

Step-by-step explanation:

Answer:

Between 19.3 and 55.9 animals.

Step-by-step explanation:

Chebyshev Theorem

The Chebyshev Theorem can also be applied to non-normal distribution. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].

In this question:

Mean of 37.6, standard deviation of 6.1.

Between what two numbers of animals does Chebyshev's Theorem guarantees that we will find at least 89% of the days?

Within 3 standard deviations of the mean, so:

37.6 - 3*6.1 = 19.3

37.6 + 3*6.1 = 55.9

Between 19.3 and 55.9 animals.

Step-by-step explanation:

swap the variables:

y=6x−4 becomes x=6y−4.

Now, solve the equation x=6y−4 for y.

y=x+46 is the inverse function

f^-1(62)

substitude x=62

y=x+46

y= 62+46

y=108

f^-1(62)=108

brainliest please~