At a certain high school, 25 students play only stringed instruments, 15 students play only brass instruments, and 5 students play both. There are also 5 students who play neither stringed nor brass instruments. What is the probability that a randomly selected student plays both a stringed and brass instrument?

Answer:

116

Step-by-step explanation:

10324 divided by 89!!

Answer:

3x and 2x can be combined bc it has ex at the end.

1 and 2x cannot be combined bc 1 doesn't have an x.

1 and -5 can be combined

Answer:

b)

Step-by-step explanation:

As here it's stated that average of first 9 numbers is 23

so,

sum of 9 numbers = 9×23 = 207

Average of first 5 numbers is 20

so,

Sum of first 5 numbers = 5×20 = 100

Sum of remaining numbers = 207-100 = 107

Average of last five numbers = 25

So,

Sum of last five numbers = 5×25 = 125

Fifth Number = Sum of last five numbers- Sum of remaining numbers

                      = 125 - 107 = 18

Answer:

\((3x-7)(4x^{2} -5)\)

Step-by-step explanation:

Add and subtract the second term to the expression and factor by grouping.

The number of downloads of the high quality version that was made was 600.

This is a great system of equations problem

If we call the number of standard version downloads (S)  

The high quality downloads (H).

To find S, we can rearrange the first statement to H = 910 - S,

Then we would substitute (910 - S) wherever you see an H in the second equation so that you have only S's in your equation.

Thus:

2.8(S) + 4.4(910 - S) = 3044

2.8S + 4004 - 4.4S = 3044

-1.6S = -960

s = 600

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A 90° rotation around the origin characterised the transition.

A logical principle that specifies the circumstances in which one assertion can be legitimately inferred from one or more other statements, particularly in codified languages.

(x, y)(x, y) is the formula for a reflection over the x-axis.

Triangle ABC was changed utilizing the (x, y) rule (–y, x). The triangles' vertices are displayed. A (–1, 1) B (1, 1) C (1, 4) (1, 4) A' (–1, –1) (–1, –1) B' (–1, 1) C' (–4, 1) (–4, 1) Which phrase best sums up the change? A 90° rotation around the origin characterised the transition. A 180° rotation of the origin occurred during the transformation.  The transformation was a 270° rotation about the origin. The transformation was a 360° rotation about the origin.

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Answer: A reflection over the y-axis justifies ∆ABC ≅ ∆A'B'C'.

Step-by-step explanation: Took the test, no thanks neeeded :)

Answer:

g[f(x)] = 6x² + 8x - 25

Step-by-step explanation:

g[f(x)] = g(3x² + 4x - 7)

= 2(3x² + 4x - 7) - 11

= 6x² + 8x - 14 - 11

= 6x² + 8x - 25

Given: the three points are plotted on graph.

For the first point it is observed that,

For the x =3/2 the value is y=6/2

For second point ,

For x= 9/2 the y value is y=12/2

For the third point ,

For x= 15/2 the y value is y=18/2

According to obtained information it matched to option J)

Answer: Option J)

There are 853,818,600 ways to award first, second, and third prizes in a contest with 950 contestants, assuming there are no ties.

To determine the number of ways to award first, second, and third prizes in a contest with 950 contestants, we can use the permutation formula:

P(n, r) = n! / (n - r)!

where n is the total number of contestants and r is the number of prizes to be awarded (in this case, 3).

Using this formula, we get:

P(950, 3) = 950! / (950 - 3)!

= 950! / 947!

= 950 × 949 × 948

= 853,818,600

Therefore, there are 853,818,600 ways to award first, second, and third prizes in a contest with 950 contestants, assuming there are no ties.

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Answer:

for 1st depositsx

p=$36000

r=2.6%

t=9years

compound amount =p(1+r/100)^t

=$36000(1+2.6/100)^9=$45355.37

for another deposit.

p=$36000

r=2.6%

t=9years

simple amount

=ptr/100=36000×2.6×9/100=$8424

total amount =$8424+$36000=$44424

the sum of the balances of these accounts at the end of 9 years=$44424+$45355.37=$89,779.37

The three values (60, 62, and 84) are identified as outliers for the age group 40 years to 50 years is D. Only 60 and 84 are identified as outliers

we need to use the same method as for the age group 20 years to 30 years.

The interquartile range (IQR) for the age group 40 years to 50 years is calculated as follows:

Q3 - Q1 = 76 - 70 = 6

To identify outliers, we consider values that are either 1.5 times the IQR greater than the upper quartile (Q3 + 1.5 * IQR) or 1.5 times the IQR less than the lower quartile (Q1 - 1.5 * IQR).

For the age group 40 years to 50 years:

Upper limit = Q3 + 1.5 * IQR = 76 + 1.5 * 6 = 85

Lower limit = Q1 - 1.5 * IQR = 70 - 1.5 * 6 = 61

Now let's compare these limits with the three values:

60 is less than the lower limit (61), so it is considered an outlier.

62 is between the lower and upper limits, so it is not considered an outlier.

84 is greater than the upper limit (85), so it is considered an outlier.

Therefore, the values identified as outliers for the age group 40 years to 50 years are 60 and 84. The value 62 is not considered an outlier.

The correct answer is (D) Only 60 and 84 are identified as outliers.

By applying the same method of identifying outliers based on the 1.5 times IQR rule, we can determine which values fall outside the acceptable range for each age group. Therefore, Option D is correct

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Answer:

-4/5

Step-by-step explanation:

2/5 ÷ -1/2

Copy dot flip

2/5 * -2/1

-4/5

Answer:

[-9,-4]

Step-by-step explanation:

The highest and lowest points this graph gets to on the y axis are -4 and -9 respectively.

This means the range is [-9,-4].

Brackets are used since -9 and -4 are seemingly included.

Answer:

312 cm²

Step-by-step explanation:

The figure is composed of a rectangle and 2 congruent triangles

area of rectangle = 16 × 12 = 192 cm²

area of 2 triangles = 2 × \(\frac{1}{2}\) × 12 × 10 = 12 × 10 = 120 cm²

Area of figure = 192 + 120 = 312 cm²

Answer:

the answer in the simplest form is 1/2 miles and if it's not in its simplest form is 6 /12 .hope it helps.

In summary, the critical points in increasing order are:

x1 = -2

x2 = 0

x3 = 2

To find the critical points of the function f(x) = x^4 - 8x^2, we need to find the values of x where the derivative of f(x) is equal to zero or undefined.

First, let's find the derivative of f(x) with respect to x:

f'(x) = 4x^3 - 16x

To find the critical points, we set the derivative equal to zero and solve for x:

4x^3 - 16x = 0

Factoring out 4x, we have:

4x(x^2 - 4) = 0

Setting each factor equal to zero, we get:

4x = 0 --> x = 0

x^2 - 4 = 0 --> x^2 = 4 --> x = ±2

So, the critical points are:

x1 = -2

x2 = 0

x3 = 2

To determine the nature of these critical points, we can use the second derivative test or examine the behavior of the function around each critical point.

Taking the second derivative of f(x):

f''(x) = 12x^2 - 16

Now we can evaluate the second derivative at each critical point:

f''(-2) = 12(-2)^2 - 16 = 48 - 16 = 32

f''(0) = 12(0)^2 - 16 = -16

f''(2) = 12(2)^2 - 16 = 48 - 16 = 32

Since f''(-2) and f''(2) are both positive, the function has a local minimum at x = -2 and x = 2. Since f''(0) is negative, the function has a local maximum at x = 0.

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Answer:

C

Step-by-step explanation:

- 6 outside of any parenthesis, is down 6, +6, is up 6

- 6 inside any parenthesis is right 6, + 6 is left 6

Answer:

(y+1)(y+5)

Step-by-step explanation:

Answer:

Graph C. Hope this is correct!!!

Step-by-step explanation:

Answer: It should be "B". the vertical axis is the time and the horizontal axis is number of trees.

This is what my teacher sent me.

W+ is closed under scalar multiplication. Since W+ is closed under addition and scalar multiplication, it is a subspace of V. This completes the proof.

(a) Proof that \(W∩W^⊥ = {0}\):
Proof:
Let's suppose for contradiction that there is a non-zero vector, say v, in the intersection of W and its orthogonal complement W+.
Since v is in W+, then it is orthogonal to all the vectors in W. Since v is also in W, then v is orthogonal to itself. Therefore, (v, v) = 0.
Since (v, v) = 0 and v is non-zero, it follows that v is not positive-definite. This is a contradiction since we are working in an inner product space and all vectors are positive-definite. Therefore, the intersection of W and W+ must be {0}. This completes the proof.
(b) Proof that \(W^⊥\) is a subspace of V:
Proof:

Let x and y be vectors in W+. Then (x+y, w) = (x, w) + (y, w)

= 0, since both x and y are in W+.
Therefore, W+ is closed under addition.
Let a be a scalar and x be a vector in W+. Then (ax, w)

= a(x, w)

= 0, since x is in W+.
Therefore, W+ is closed under scalar multiplication.
Since W+ is closed under addition and scalar multiplication, it is a subspace of V. This completes the proof.

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Answer:

Step-by-step explanation:

\(2. \: a. \: \sqrt[3]{ - 1} \)

\( = \sqrt[3]{( - 1 )\times ( - 1 )\times( - 1)} \)

= -1 (Ans)

\(b. \: \sqrt[3]{ - \frac{8}{27} } \)

Since,

\( \sqrt[3]{ - x} = - \sqrt[3]{x} \)

Hence,

\( = - \sqrt[3]{ \frac{8}{27} } \)

\( = - \sqrt[3]{ \frac{2 \times 2 \times 2}{3 \times 3 \times 3} } \)

\( = - \frac{2}{3} (ans)\)

\(3. \: a. \: 10 - 2 \sqrt{9} \)

\( = 10 - 2 \sqrt{3 \times 3} \)

= 10 - 2 × 3

= 10 - 6

= 4 (Ans)

\(b. \: 70 - {( \sqrt[3]{64} )}^{3} \)

\( = 70 - \sqrt[3]{ {64}^{3} } \)

\( = 70 - \sqrt[3]{64 \times 64 \times 64} \)

= 70 - 64

= 6 (Ans)

Answer:

\(50\)

Step-by-step explanation:

Let \(x =\) blank (for convenience)

\(20\%x=10\)

\(0.2x=10\) (change \(20\%\) into its decimal form)

\(x = 10\div 0.2\) (divide \(0.2\) on both sides)

\(x=50\)

∴ Blank = 50

Hope this helps :)

Answer:

B

Step-by-step explanation:

Answer:

B. \(\frac{x^2}{3^2} +\frac{y^3}{2^2} =1\)

Step-by-step explanation:

Answer:

  9/4

Step-by-step explanation:

You want to know the value required to complete the square in the equation 1 = x² -3x.

Your picture shows the required value: (-3/2)² = 9/4.

<95141404393>

Answer:

1) 28m West 2)70km below sea level

The true statements among the given options are written below

bc || ad

ba ≅ cd  

∠cba ≅ ∠bcd

In an isosceles trapezoid, there is one pair of legs of equal length and a pair of parallel lines.

Given that quadrilateral abcd is a isosceles trapezoid.

In the given trapezoid abcd

bc || ad ( pair of parallel sides )

So this is correct.

ba ≅ cd  ( For an isosceles trapezoid legs are equal)

So this is correct

∠cba ≅ ∠bcd (According to  the property of isosceles  trapezoid )

So this is correct.

Hence, bc || ad, ba ≅ cd, ∠cba ≅ ∠bcd are correct

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