SAT Scores The national average SAT score (for verbal and math) is 1028. Assume a normal distribution with σ=92. Round intermediate z-value calculations to two decimal places. Part: 0/2 Part 1 of 2 (a) What is the 85 th percentile score? Round the answer to the nearest whole number. The 85 th percentile score is

Answer:

1/4

Step-by-step explanation:

3/4 x 2/4 = 6/24

6/24 simplified is 1/4

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Answer:

6/12 or 1/2

Step-by-step explanation:

Start by multiplying the numerators

3 x 2 = 6

Then multiply the denominators

4 x 3 = 12

Then you get your answer of 6/12

But if you want it simplified then divide both the denominator and numerator by 6 and you will get your final answer of

1/2

Hope this helped

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The critical value for an 80% confidence interval is 1.28.

To find the critical value for constructing an 80% confidence interval for the difference in two proportions, we need to use the z-table.

Step 1: Find the critical value.

Since we want an 80% confidence interval, the remaining area (1 - 0.80 = 0.20) is divided equally into the two tails. Each tail has an area of 0.10. To find the critical value, we look for the z-score that corresponds to an area of 0.10 in the standard normal distribution table.

Using the z-table or a calculator, we find that the z-score for an area of 0.10 (one tail) is approximately 1.28.

Therefore, the critical value for an 80% confidence interval is 1.28.

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The value of slope m = -2 , the value of b = -5/6 and the line equation = y=-2x+(-5/6).

Given table:

x             y

3            5

6            -1

9            -7

12          -13

slope of any two points suppose take (3,5) and (6,-1).

slope m = y2 - y1 / x2 - x1

= -1 - 5 / 6 - 3

= -6/3

m = -2

standard equation is y=mx+b

substitute m value and point(3,5) we get,

5 = (-2)(3)+b

5 = -6b

b = -5/6

substitute m and b value in y=mx+b.

y = (-2)x+(-5/6)

Equation → y=-2x+(-5/6).

Therefore the value of slope m = -2 , the value of b = -5/6 and the line equation = y=-2x+(-5/6).

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Answer:2+6=8 um hope these helped??

Step-by-step explanation:

Answer:

EF and AD

Step-by-step explanation:

EF is 2x as long as AD is

well, the triangle is an equilateral, so all sides are equal, we know that the segment "x" stems out of the vertex and drops perpendicular to the other side, now, the vertex "x" stems from has two equal sides.

what the hell all that means?  well it means that "x" is an altitude and is also  an angle bisector and likewise is also cutting the opposite side into two equal halves, meaning that one side is really 8 + 8 = 16, so then

\(\stackrel{altitude}{height}\textit{ of an equilateral triangle}\\\\ h=\cfrac{s\sqrt{3}}{2} ~~ \begin{cases} s=\stackrel{length~of}{a~side}\\[-0.5em] \hrulefill\\ s=16 \end{cases}\implies h=\cfrac{16\sqrt{3}}{2}\implies h=8\sqrt{3}\)

Answer: 7

Step-by-step explanation:

Answer:

10, 5/4, 6.25, 0.0034, 8.3, 14.32587

Step-by-step explanation:

10 is 10/1

5/4 is 5/4

6.25 is 6 1/4

0.0034 is 34/10000

8.3 is 8 3/10

14.32587 is 1432587/100000

\(\sqrt{13}\) is not rational because 13 is not square.

Answer:

perimeter = 322.5 ft ( to the nearest tenth of a foot)

Step-by-step explanation:

Length the length of the sides of the square be L

Area of a square = L²

∴ 6,500 = L²

L = √(6,500)

L = 80.6226

Next Let us calculate the perimeter

Perimeter of a square = L + L + L + L = 4L

perimeter = 4 × 80.6226

Perimeter = 322.4904 ft

perimeter = 322.5 ft ( to the nearest tenth of a foot)

N:B rounding to the nearest tenth of a foot is same as rounding to 1 decimal place.

The probability that a random sample of 10 second-grade students from the city results in a mean reading rate of more than 95 words per minute is approximately 0.0287.

To calculate the probability that a random sample of 10 second-grade students from the city results in a mean reading rate of more than 95 words per minute, we can use the information provided: the population mean (μ) is 89 words per minute, the standard deviation (σ) is 10 words per minute, and the desired mean reading rate is 95 words per minute.

1. Calculate the standard error of the mean (SE):

  SE = σ / sqrt(n)

  SE = 10 / sqrt(10)

  SE ≈ 3.1623

2. Convert the desired mean reading rate (95 words per minute) to a z-score:

  z = (x - μ) / SE

  z = (95 - 89) / 3.1623

  z ≈ 1.8974

3. Find the probability using the standard normal distribution table (or calculator):

  P(Z > z) = 1 - P(Z ≤ z)

Using the standard normal distribution table or calculator, we can find the corresponding probability for the z-score of 1.8974:

P(Z > 1.8974) ≈ 0.0287

Therefore, the probability that a random sample of 10 second-grade students from the city results in a mean reading rate of more than 95 words per minute is approximately 0.0287, rounded to four decimal places.

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Complete Question:

The reading speed of second grade students in a large city is approximately​ normal, with a mean of 89 words per minute​ (wpm) and a standard deviation of 10 wpm.

What is the probability that a random sample of 10 second grade students from the city results in a mean reading rate of more than 95 words per​ minute? The probability is 0.0287. ​(Round to four decimal places as​ needed.)

In the point (r, θ), r signifies the distance from O to P, while θ represents the angle counterclockwise from the polar axis to the line segment ¯¯¯¯¯¯¯¯OP.

For the point (r, θ), r is the distance from O to P, and θ is the angle counterclockwise from the polar axis to the line segment ¯¯¯¯¯¯¯¯OP.

In polar coordinates, a point is represented by its distance (r) from the origin (O) and the angle (θ) it forms with the positive x-axis. The distance (r) denotes the length of the line segment connecting the origin to the point P. It indicates how far the point is from the origin. The angle (θ) represents the rotation or angular position of the line segment ¯¯¯¯¯¯¯¯OP from the polar axis (positive x-axis) in a counterclockwise direction. It determines the direction in which the point is located relative to the polar axis.

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Answer: The Jacobian of the transformation is: J = 8v(4w)3u - 8u(4v)3w = 24uvw

Step-by-step explanation:

To determine the Jacobian of the transformation, we first need to get the partial derivatives of x, y, and z with respect to u, v, and w:

∂x/∂u = 8v

∂x/∂v = 8u

∂x/∂w = 0∂y/∂u = 0

∂y/∂v = 4w

∂y/∂w = 4v∂z/∂u = 3w

∂z/∂v = 0

∂z/∂w = 3u

The Jacobian matrix J is then:

| ∂x/∂u ∂x/∂v ∂x/∂w |

| ∂y/∂u ∂y/∂v ∂y/∂w |

| ∂z/∂u ∂z/∂v ∂z/∂w |

Substituting in the partial derivatives we found above, we get:

| 8v 8u 0 |

| 0 4w 4v |

| 3w 0 3u |

So, the Jacobian of the transformation is:J = 8v(4w)3u - 8u(4v)3w = 24uvw

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So here this question is of concept linear equations. As in linear equations we assumes the unknown number as an variable after that an equation would be formed which we would solve and get the answer. Here also we would be doing same.!!

So let us assume the unknown positive integers as a and (a + 1).

★ Product of both integers :-

★ Solving the equation :-

\(: \longrightarrow \: \sf{a \: (a + 1) \: = \: 156} \\ \\ : \longrightarrow \: \sf{a \times (a + 1) \: = \: 156} \\ \\ : \longrightarrow \: \sf{a {}^{2} \: + \: a \: = \: 156} \\ \\ : \longrightarrow \: \sf{a {}^{2} \: + \: a \: - \: 156 = 0} \\ \\: \longrightarrow \: \sf{a {}^{2} \: - \: 12a + 13a\: - \: 156 = 0} \\ \\ : \longrightarrow \: \sf{a(a \: - \: 12) + 13(a\: - \: 12) = 0} \\ \\ : \longrightarrow \: \sf{a(a \: - \: 12) + 13(a\: - \: 12) = 0} \\ \\ : \longrightarrow \: \sf{(a \: - \: 12) (a\: + \: 13) = 0} \\ \\ : \longrightarrow \: \red{\bf{a \: = \: 12 }}\)

Therefore,

★ Second positive integer :-

Look at the attached picture

Hope it will help you

Answer:

a = 4

Step-by-step explanation:

In an equation our aim is to find the value of what we are looking for as well as keeping the equation balanced. For example if we took away 8 only from one side then the equation would change so it's an important rule to keep in mind when solving equations, that you need to keep both sides of the equation the same.

4 (2 + a) = 24

→ Expand the brackets

8 + 4a = 24

→ Minus 8 from both sides to isolate 4a

4a = 16

→ Divide both sides by 4 to isolate a and therefore find the value of a

a = 4

→ We can substitute a = 4 back into 4 (2 + a) = 24 to see if we have the correct solution, if we end with the same number on both sides then a =4 is correct.

4 (2 + a) = 24

4 (2 + 4) = 24

4 × 6 = 24

24 = 24

So a = 4 is correct

4 (2

Answer:

It should be \(15*10^{4}\).

Step-by-step explanation:

\(300=3*10^{2}\\500=5*10^{2}\\\\300*500=(3*10^{2})*(5*10^{2})=(3*5)*10^{(2+2)}=15*10^{4}=1.5*10^{5}\)

Answer: 1.5 x 10^5

Step-by-step explanation:

The first step is to re-arrange the factors like this :

5 x 3 x 10^2 x 10^2

Since

5 x 3 = 15

and the index law

10^a x 10^b = 10^a + ^b

gives us

10^2 x 10^2 = 10^2 + ^2 = 10^4

then we can rewrite the product like this :

5 x 3 x 10^2 x 10^2 = 15 x 10^4

Finally, we need to convert this into scientific notation :

15 x 10^4 = 1.5 x 10^5  

So the final answer is

1.5 x 10^5

Answer:

Step-by-step explanation:

Given: d= 12 and h= 14

formula for the volume of a cone:

V= (1/3) · π · r² · h

V= volume

r= radius

h= height

to find the radius of the cone, we will use this formula r = 1/2 · d

r = 1/2 · 12

r = 6

Now that we know the value of the radius we can now plug it in in our formula.

V= (1/3) · π · 6² · 14

V= 1π · 6² · 14 / 3

V= 1π · 2²· 3² · 14 / 3

V= 2² · 14 · 3π

V= 2² · 14 · 3π

V= 2² · 42π

V= 4 · 42π

V= 168π

V=527.79

Hope this helps =D

18 root

2

Step-by-step explanation:

In this question imagine there is no y

It will be 10 root2 +5 root2 +3 root 2 it will be 18 root 2

The solution to given inequality 2(4x + 1) < 3(2x - 3) is x < -11/2

In this question, we have been given an inequality  2(4x + 1) < 3(2x - 3)

We need to solve given inequality.

2(4x + 1) < 3(2x - 3)                          ..............(Given inequality)

8x + 2 < 6x - 9               .............(simplify both sides of the inequality)

8x + 2 - 6x < 6x - 9 - 6x             ............(subtract 6x from both the sides)

2x + 2 < -9

2x + 2 - 2 < -9 - 2                       ............(subtract 2 from each side)

2x < -11

2x/2 < -11/2                               ................(Divide each side by 2)

x < -11/2

Therefore, the solution to given inequality 2(4x + 1) < 3(2x - 3) is x < -11/2

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9514 1404 393

Answer:

  77.3 cm

Step-by-step explanation:

The distance FA is the diagonal of rectangle ABFE. We know the length AB, so we need to find the length BF. That is found using the trig relation ...

  cos(25°) = BC/BF

  BF = BC/cos(25°) ≈ (60 cm)/0.906308 ≈ 66.203 cm

Then the diagonal length FA is found using the Pythagorean theorem:

  FA = √(AB² +BF²)

  FA = √(40² +66.203²) ≈ √5982.79 ≈ 77.349 . . . cm

The diagonal length FA is about 77.3 cm.

The percentage strength of neomycin in the final compounded product is approximately 2.5%.

To determine the percentage strength of neomycin in the final compounded product, we need to calculate the weight of neomycin in the cream and divide it by the total weight of the cream.

Neomycin (5%) cream: 30g

The neomycin content is 5% of the total cream weight. To find the weight of neomycin in the cream, we multiply the cream weight by the neomycin percentage:

Weight of neomycin = 30g × 0.05 = 1.5g

Now, to calculate the percentage strength of neomycin in the final compounded product, we divide the weight of neomycin by the total weight of the cream and multiply by 100:

Percentage strength of neomycin = (Weight of neomycin / Total weight of cream) × 100

Percentage strength of neomycin = (1.5g / 60g) × 100 ≈ 2.5

Therefore, the percentage strength of neomycin in the final compounded product is approximately 2.5%.

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Answer:

soln;

given equation is 6x + 5 = 2y

or, 6x -2y + 5 = 0

comparing with ax + by + c = 0

a = 6, b = -2, c = 5

By the Pythagoras theorem we know that the if the square of the longest side of the triangle is equal to the sum of the square of other two sides.

The triangle formed by the sides 3.8 cm ,3.7 cm, and 5 cm is​ acute angle triangle.

How to find the type of triangle?

By the Pythagoras theorem we know that the if the square of the longest side of the triangle is equal to the sum of the square of other two sides. Thus,

           \(c^2=a^2+b^2\)

       By this law it is observed that,

         \(c^2<(a^2+b^2)\)

        \(c^2>(a^2+b^2)\)

The sides of the given triangle are  3.8 cm ,3.7 cm, and 5 cm.

Here the longest side is 5 cm. Thus check the type of triangle using above formula. Longest side,

\(c^2=5^2\\c^2=25\)

Other two sides,

\(a^2+b^2=3.8^2+3.7^2\\a^2+b^2=14.44+13.69\\a^2+b^2=28.13\)

Therefore,

\(25<28.13\\\)

Hence the triangle formed by the sides 3.8 cm ,3.7 cm, and 5 cm is​ acute angle triangle.

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\(\measuredangle A\cong \measuredangle E\implies 112=16x\implies \cfrac{112}{16}=x\implies \boxed{7=x} \\\\[-0.35em] ~\dotfill\\\\ \overline{MS}\cong \overline{NR}\implies 41=3x+5y\implies 41=3(7)+5y\implies 41=21+5y \\\\\\ 20=5y\implies \cfrac{20}{5}=y\implies \boxed{4=y}\)

The statement "Linear programming can be used to find the optimal solution for profit, but cannot be used for nonprofit organizations" is False.

Linear programming can be used to find the optimal solution for profit as well as for non-profit organizations. Linear programming is a method of optimization that aids in determining the best outcome in a mathematical model where the model's requirements can be expressed as linear relationships. Linear programming can be used to solve optimization problems that require maximizing or minimizing a linear objective function, subject to a set of linear constraints.

Linear programming can be used in a variety of applications, including finance, engineering, manufacturing, transportation, and resource allocation. Linear programming is concerned with determining the values of decision variables that will maximize or minimize the objective function while meeting all of the constraints. It is used to find the optimal solution that maximizes profits for for-profit organizations or minimizes costs for non-profit organizations.

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Option c) The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B

According to the information given in the question,

A true proportion of 0.325 represents that the two simulations will be conducted for sampling proportions from a population

Simulation A -

Sample size - 100

Trials - 1500

Simulation B -

Sample size - 50

Trials - 2000

Now due to the relation of simulation A and simulation B, they are closely equal-

The total sample size of simulation A= 1500 x 100

= 150000

The total sample size of simulation B = 2000 x 50

= 100000

From the above calculations of simulations A and B, we can see that while comparing the,

Sample Size = Simulation A > Simulation B

Variability = Simulation B < Simulation B

Therefore, option c) The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B is correct.

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In a recent survey, the proportion of adults who indicated mystery as their favorite type of book was 0.325. Two simulations will be conducted for the sampling distribution of a sample proportion from a population with a true proportion of 0.325. Simulation A will consist of 1,500 trials with a sample size of 100. Simulation B will consist of 2,000 trials with a sample size of 50. Which of the following describes the center and variability of simulation A and simulation B?

A) The centers will roughly be equal, and the variabilities will roughly be equal.

B) The centers will roughly be equal, and the variability of simulation A will be greater than the variability of simulation B.

C) The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B.

D) The center of simulation A will be greater than the center of simulation B, and the variability of simulation A will roughly be equal to the variability of simulation B.

E) The center of simulation A will be less than the center of simulation B, and the variability of simulation A will be greater than the variability of simulation B.