A teacher gives her class a particular examination on mathematics at the end of each year. The results are normally distributed with a mean test score of 60 and a standard deviation of 8. The teacher has told the class that students with a test score in the top 2.5% will win a special prize. Calculate the test score above which 2.5% of all test scores lie. Give your answer to 1 decimal place. Test score

Answer: 311/500 and 62.22%

Step-by-step explanation:

Fraction: 0.622 = 622/1000 = 311/500

Percent: 0.6222 = 62.22 % (Move decimal 2 places down)

The decimal 0.622 in the form of simplest fraction as 311/500 and in percent is 62.2%.

To convert 0.622 to a fraction in simplest form, write it as follows:

0.622 = 622/1000

Now, simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2:

622/1000 = (311 × 2)/(500 × 2)

                 = 311/500

So, 0.622, when expressed as a fraction in simplest form, is 311/500.

To convert 0.622 to a percent, multiply it by 100:

0.622 × 100 = 62.2%

Therefore, 0.622 is equivalent to 311/500 or 62.2%.

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should be 0.10d - 24(m)

Determine 20% of the initial level

20% → 0.2

Write the equation with half-life of 12 hours and initial dose of 25 mg.

Substitute y = 5, and solve for t

Get the natural logarithm of both sides

Rounding the answer to the nearest whole number, the time it takes for the initial dose to be reach 20% of its initial level is 28 hours.

Answer: X<7

Step-by-step explanation:

3x+9<30

-9       -9

3x<21

/3    /3

X<7

Answer:

a1 = 1, a2 = 2Step-by-step explanation:

Answer:

y = 4\(\sqrt{5}\) , ? = 10

Step-by-step explanation:

using Pythagoras' identity on the smallest right triangle

x² = 4² + 2² = 16 + 4 = 20 ( take square root of both sides )

x = \(\sqrt{20}\) = \(\sqrt{4(5)}\) = \(\sqrt{4}\) × \(\sqrt{5}\) = 2\(\sqrt{5}\)

using Pythagoras' identity on the middle right triangle

y² = 8² + 4² = 64 + 16 = 80 ( take square root of both sides )

y = \(\sqrt{80}\) = \(\sqrt{16(5)}\) = \(\sqrt{16}\) × \(\sqrt{5}\) = 4\(\sqrt{5}\)

using Pythagoras' identity on the largest right triangle

?² = x² + y² = (2\(\sqrt{5}\) )² + (4\(\sqrt{5}\) )² = 20 + 80 = 100

Take square root of both sides

? = \(\sqrt{100}\) = 10

Answer:

y=(11-8p)xz

Step-by-step explanation:

xyz+8p=11

xyz=11-8p

y=(11-8p)xz

Answer:

2^4   * 9^4

Step-by-step explanation:

(2*9)^4

We can take the power to each term inside the parentheses

2^4   * 9^4

By answering the presented question, we may conclude that In decimal form, the answer is 0.15, which is close to option A, 0.148. As a result, the answer is A. 0.148.

According to Euclidean geometry, a square is an equilateral quadrilateral having four equal sides and four equal angles. It is often referred to as a rectangle with two nearby sides of equal length. A square is an equilateral quadrilateral because it has four equal sides and four equal angles. Square angles are 90-degree or straight angles. Also, the diagonals of the square are evenly spaced and divide at a 90-degree angle. an adjacent rectangle with two equal sides. a quadrilateral with four equal-length sides and four right angles. A parallelogram with two adjacent, equal sides forming a right angle. A rhombus with straight sides.

To determine the answer, multiply the areas of the shaded squares by the overall area of the figure.

Assuming that both squares are the same size, we may combine the fractions using a common denominator:

2/12 + 2/15 = 5/60 + 4/60 = 9/60 = 3/20

As a result, the entire shaded area is 3/20 of the total area of the diagram.

We can't discover the exact area of the graphic because it's not presented. As a result, we can only represent the answer in fractions or decimals.

In decimal form, the answer is 0.15, which is close to option A, 0.148. As a result, the answer is A. 0.148.

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If the radius is 3 cm, the height of the cylinder is approximately 7.06 cm, which is closest to option B, 7 cm. The correct option is B.

The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height.

We are given that the volume of the cylinder is 637 cm³ and the radius is 3 cm. Substituting these values into the formula, we get:

637 = π(3²)h

Simplifying:

637 = 9πh

h = 637 / (9π)

h ≈ 7.06

Thus, the height of the cylinder is approximately 7.06 cm, which is closest to option B, 7 cm.

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Answer: 290 beans

Step-by-step explanation:

You multiply 145 by 2 since 145 is half of the beans or do 145 divided by 1/2.

145 * 2 = 290.

145/.5 = 290

Hope this helps!!! :)

Answer:

(5 · x) + (8 · y) + (2 · 1)

Answer:

5x + 2 ( 4y + 1 )

Step-by-step explanation:

i just factorised 8y + 2

The probability that the mean battery life would be greater than 526.4 minutes if in a sample of 81 batteries having a variance of, 2916 and a mean life of 518 minutes is 0.0808.

The ratio of good outcomes to all possible outcomes of an event is known as probability. A lot of successful results for an experimental with 'n' results can be represented by the symbol x.

Given:

The variance = 2916,

The mean life of a battery, m = 518 min,

The total number of samples, n = 81

Calculate the probability of a mean battery life of lower than 526.4 minutes by the following formula,

z = x - m / (σ / √ n)

Here, x is the expected value, σ is the deviation, and z is the probability.

Substitute the values,

z = 526.4 - 518 / (54 / √81)         [σ = √ variance = √2916  = 54]

z = 1.4

Consult the cumulative standard normal table

P (z < 526.4) = 0.9192,

But we know that

P (z > 526.4) = 1 - P (z < 526.4)

P (z > 526.4) = 1 - 0.9192 = 0.0808

Therefore, The probability that the mean battery life would be greater than 526.4 minutes if in a sample of 81 batteries having a variance of, 2916 and a mean life of 518 minutes is 0.0808.

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The number would be 370,000

In the given statement is:
Round to the place value of the underline digit 372,297 underline digit is 7

Now, According to the question:

372,297

Place Value of first 7 = 70000

Place value of second 7 = 7

As 7 is in ten thousand place so after rounding we get,

370,000

Therefore, the number would be370,000

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Answer:

\(8 {x}^{2} - 6x - 5 = x\)

\(8 {x}^{2} - 7x - 5 = 0\)

x = (7 + √((-7)^2 - 4(8)(-5)))/(2×8)

= (7 + √(49 + 160))/16

= (7 + √209)/16

= -.4661, 1.3411 (to 4 decimal places)

F and G are inverse if both of them satisfy the condition h(x)=x. f(g(x))=g(f(x))=x, as we discovered. The argument f(x) and g(x) are inverse functions is thus established.

If f (x) and g (x) are inverse functions, it can be determined using one of two ways. For more information, see the explanation.

Explanation:

Instance 1

Inverse functions of both functions can be found using the first method.

Example.

Inverse of f (x) = x + 7 is what we're looking for.

We attempt to determine x using the equation y = x + 7.

y = x + 7

Inferring that g (x) is the inverse of f (x) from the fact that x = y 7

Finding g (x inverse )'s is now necessary.

g( x ) = x − 7

y = x − 7

x = y + 7

As a result, we discovered that f (x) is the inverse function of g (x).

f and g are equal if g is inverse of f and vice versa.

The second approach entails locating the compound functions f ( g ( x ) ) and g ( f ( x ) ). In this case, f and g are inverse if they are both h (x ) = x.

Example:

f ( g ( x ) =  [ x − 7 ] + 7

G ( x ) placed as x is the expression in brackets.

f ( g ( x ) ) = x − 7  + 7 = x

g (f ( x ) =  [ x + 7 ] − 7

f ( x ) inserted as x is the expression in brackets.

g ( f ( x ) ) = x + 7 − 7 = x

The equation f ( g ( x ) ) = g ( f ( x ) ) = x was what we discovered. The argument f (x) and g (x) are inverse functions is thus established.

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Answer:

1 -1

Step-by-step explanation:

thats what my school taught me if its wrong im sorry:)

Answer: 3/3 or 1

Step-by-step explanation:

So finding slope can be difficult but what you want to do is find the change in y and the change in x. So when I was looking at this you have to find something called the 'pretty point' where the line is perfectly on the corner of the square.

So look at (-2,-1) That is a "pretty point" now count right from there and go to your nect pretty point; (1, -1). Now that you have this information you know that our Run aka change in x is 3! Now do the same thing for our Rise, change in Y. You'll get 3 as well. With this information we know that our slope is 3/3 and you can also say 1.

In conclusion, you can say that the slope rises just as fast as it runs. I hope this is right for you I haven't done it in a while.

Answer: x = -3 or if not solving for x then -2x -6

Step-by-step explanation:

1 - 2x - 7 = 0

-6 - 2x = 0

add 2x on both sides

-6 = 2x

divide 2 on both sides

-6/2 = x

x = -3

The solution to the initial value problem is determined as y = e³ˣ.

The auxiliary equation is determined as follows;

y'' - 7y' + 12y = 0

m² - 7m + 12 = 0

m² - 3m - 4m + 12 = 0

m(m - 3) - 4(m - 3) = 0

m = 3 or 4

\(y = c_1e^{3x} + c_2e^{4x}\\\\y(0) = 1\\\\1 = c_1e^{3\times 0} + c_2e^{4\times 0}\\\\1 = c_1 + c_2 \ --(i)\\\\y' = 3c_1e^{3x} + 4c_2e^{4x}\\\\y'(0) = 3\\\\3 = 3c_1e^{3\times 0} + 4c_2e^{4\times 0}\\\\3 = 3c_1 + 4c_2 \ \ --(ii)\)

solve (i) and (ii)

3 = 3c₁ + 4(1 - c₁)

3 = 3c₁ + 4 - 4c₁

3 = -c₁ + 4

c₁ = 1

c₂ = 0

\(y = e^{3x}\)

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Given that you have a room that has dimensions l and w wherein l is the length of the room while w is the width of the room (shown in a diagram below).

the area of the room can be computed using the equation

Basically, we just multiply the length and the width of the room.

Step-by-step explanation:

As my previous answer got deleted for being wrong (in which it was right), I will answer again.

The answer is 1. Why? Just plug it into the equation. F(1) = 2(1) + 5 = 7.

This is proof that it is right, and that there are some corrupt admins on brainly.

How to get to this solution?

Well notice how we are given what f(a) is. It is 2a + 5. So plug this in for f(a).

If we do so, we get 2a + 5 = 7.

Solving this equation, we get a = 1.

Answer:

I dont know if you still need it but the area of the figure is 51.5 ft2.

The area of the given figure is equivalent to 39.5 square feet.

Area is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write -

V = ∫∫F(x, y) dx dy

Given is to find the area of the given figure as shown in the image.

We can write the area of the given figure as -

A{total} = A{Rectangle} + A{Δ1} + A{Δ2}

A{total} = (8 x 4) + (1/2 x 3 x 3) + (1/2 x 3 x 2)

A{total} = 32 + 4.5 + 3

A{total} = 39.5 square feet

Therefore, the area of the given figure is equivalent to 39.5 square feet.

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Answer:

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

When x = 2, we have:

(2 + 3) * (2 + 3)

5 * 5

25

Answer:

55%

Step-by-step explanation:

55% of the cupcakes were mocha flavored.

Answer:

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

Collinear points are the points on the same line.

There are two lines in the diagram.

The collinear points:

The points that are collinear are  D,G and E  and another set of points which are collinear are L,G and J.

The points which lie on the same straight line are known as collinear points.

Similarly, if three or more number of points are collinear then they form a straight line.

If we observe the figure, the points D,G and E are collinear points as they are on same line.

Similarly the points L, G and H are in the straight line which makes them collinear.

Therefore , the points L,G and J are collinear points.

Hence, the points that are collinear are  D,G and E and another set of points which are collinear are L,G and J

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Answer:

Temperature can change the volume of air.

Step-by-step explanation:

Tire pressure can decrease about 1 PSI for every 10 degrees the temperature drops. The air inside the tire condenses, taking up less space when it's cold. This is temporary because driving will heat up the tire and increase the tire's pressure.

The quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).

A division is a process of splitting a specific amount into equal parts.

We have to find 3x³-2x²+7x+9 divided by x²-3x

3x³-2x²+7x+9 is the dividend and x²-3x is the divisor.

The steps to solve this are given below.

Step 1: Take the first digit of the dividend from the left. Check if this digit is greater than or equal to the divisor.

Step 2: Then divide it by the divisor and write the answer on top as the quotient.

Step 3: Subtract the result from the digit and write the difference below.

Step 4: Bring down the next digit of the dividend (if present).

Step 5: Repeat the same process.

Hence, the quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).

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Answer: The answer is x²+3x

Step-by-step explanation:

hope that helps.

Answer:

5. obtuse

6. acute

7. acute

8. acute

9. acute

10. acute

Step-by-step explanation:

sorry But the 5  might be right/straight  90 degress

Answer:

5. obtuse

6. acute

7. acute

8. acute

9. acute

10. acute

sorry But the 5  might be right/straight  90 degrees

Step-by-step explanation:

sorry But the 5  might be right/straight  90 degrees