Refraction is the bending that occurs when a wave moves from one medium to another at an angle and
changes speed

True/False?

The missing value of "a" is 2.5.

To find the value of "a", we can use the fact that "m" is the midpoint of segment "fg".

Given that "fm" = 8a + 1 and "fg" = 42, we can set up the equation:

fm = fg / 2

Substituting the given values, we get:

8a + 1 = 42 / 2

Simplifying the right side of the equation, we have:

8a + 1 = 21

To isolate "a", we can subtract 1 from both sides:

8a = 21 - 1
8a = 20

Now, we can solve for "a" by dividing both sides by 8:

a = 20 / 8
a = 2.5

Therefore, the missing value of "a" is 2.5.

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Answer:

Total mean: 4.3

Step-by-step explanation:

(mean for home goals)

Mean: 2.5

(mean for away goals)

Mean: 1.8

it tells us to find the total games played all together..

so:

2.5 + 1.8 = 4.3

Answer:

6

Step-by-step explanation:

The absolute value of a non-negative number is the same number.

Example: The absolute value of 4 is 4.

If a number is negative, its absolute value is the same number, without the negative sign.

Example: The absolute value of -3 is 3.

The value of (double)(5/2) is 2.0. In the expression (double)(5/2), the division operation 5/2 is performed using integer division because both 5 and 2 are integers.

Integer division truncates the decimal part of the result and returns the quotient as an integer. In this case, 5 divided by 2 is equal to 2.

However, by explicitly casting the result to a double (using the (double) operator), we convert the integer value 2 to a double value, which becomes 2.0.

Therefore, the value of (double)(5/2) is 2.0, as the division is performed as an integer division followed by a casting to a double.

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Answer:

Range: {0,3,6}

Step-by-step explanation:

The range is the output, or in this case, the y values

Range: {0,3,6}

Answer:

The range is {0, 3, 6}

Step-by-step explanation:

The range is the set of the second numbers in the ordered airs.

Answer:

80x+65 2.465 3.865

Step-by-step explanation:

x being the number of years so in ten years he will have 80x10=800+65=865

80x5=400+65=465 so 5 is the number of years it would take

and i do not understand number 1 but i put a formula just in case that was it

Answer:

$17.95

Step-by-step explanation:

could be wrong but add the store credit to the amount she had to pay and then divide it by the amount of shirts bought, 4. also some expensive asz shirts.

Hey there! :)

Answer:

x = -5.

Step-by-step explanation:

Solving for x from the equation:

\(\frac{2}{3}x - \frac{1}{2} = \frac{1}{3} +\frac{5}{6}x\)

Begin by creating a common denominator for the terms involving x as well as the constants:

\(\frac{4}{6}x - \frac{3}{6} = \frac{2}{6} +\frac{5}{6}x\)

Now that each term has a common denominator, we can begin solving for x by isolating the variable:

Subtract 5/6x from both sides:

\(\frac{4}{6}x-\frac{5}{6}x - \frac{3}{6} = \frac{2}{6}\)

\(-\frac{1}{6}x - \frac{3}{6} = \frac{2}{6}\)

Add 3/6 to both sides:

\(-\frac{1}{6}x = \frac{5}{6}\)

Divide -1/6 from both sides. (Multiply by the reciprocal, or -6)

\(-\frac{1}{6}x(-6) = \frac{5}{6}(-6)\)

x = -5.

The risk factors should be considered when choosing a form of investment for your money is: interest rate and risk

Investment or investing means that an asset is bought, or that money is put into a bank to get a future interest from it.

While making an investment the investment consider:

So, The risk factors should be considered when choosing a form of investment for your money is: interest rate and risk

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Answer:

Step-by-step explanation:

-i= -i

-i^2= 1

-i^3= -i * 1 = -i

-i^4= 1 * (-1)  = -1

-i^5= -i

-i^6= 1

Answer: -1

Step-by-step explanation:

Answer:

The width of the rectangle is x+2 and the length is x+4

Step-by-step explanation:

Area of a Rectangle

Given a rectangle of width W and length L, the area is calculated by:

A = WL

It's given the area of a rectangle as:

\(A = x^2+6x+8\)

We need to express the area as the product of two factors and assign each factor as the width and the length.

Factoring

\(x^2+6x+8 = (x+2)(x+4)\)

Substituting:

A = (x+2)(x+4)

It means the width of the rectangle is x+2 and the length is x+4

The built rectangle is shown below

Answer:

1338.68 meters

Step-by-step explanation:

Perimeter is all of the lengths of the sides added together.

50.9m + 50.9m + 618.44m + 618.44m = 1338.68m

Answer:

143m

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

55%=.55

52%=.52

.55*.52=.286

.286=.29

29%

Answer:

1 B

2 A

3 A

4 five times

Step-by-step explanation:

6.3×10-11/7×10-5

0.9×10-6

9×10-5

the percent change in the number of cards collected from last month to this month is:

that is equivalent to say:

the percent change in the number of cards collected from last month to this month is 60%

Answer:

2760

Step-by-step explanation:

23 multiply by 120

=2760

The curl of the vector field

curl(F) = -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

The divergence of the vector field

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

To find the curl of the vector field F(x, y, z) = 9ex sin(y), 2ey sin(z), 8ez sin(x), we need to compute the determinant of the curl matrix.

(a) Curl of F:

The curl of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the following formula:

curl(F) = (∂R/∂y - ∂Q/∂z)i + (∂P/∂z - ∂R/∂x)j + (∂Q/∂x - ∂P/∂y)k

In this case, we have:

P(x, y, z) = 9ex sin(y)

Q(x, y, z) = 2ey sin(z)

R(x, y, z) = 8ez sin(x)

Taking the partial derivatives, we get:

∂P/∂y = 9ex cos(y)

∂Q/∂z = 2ey cos(z)

∂R/∂x = 8ez cos(x)

∂R/∂y = 0 (no y-dependence in R)

∂Q/∂x = 0 (no x-dependence in Q)

∂P/∂z = 0 (no z-dependence in P)

Substituting these values into the curl formula, we have:

curl(F) = (0 - 2ey cos(z))i + (8ez cos(x) - 0)j + (0 - 9ex cos(y))k

= -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

Therefore, the curl of the vector field F is given by:

curl(F) = -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

(b) Divergence of F:

The divergence of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the following formula:

div(F) = ∂P/∂x + ∂Q/∂y + ∂R/∂z

In this case, we have:

∂P/∂x = 9e^x sin(y)

∂Q/∂y = 2e^y sin(z)

∂R/∂z = 8e^z

Substituting these values into the divergence formula, we have:

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

Therefore, the divergence of the vector field F is given by:

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

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Answer:

(2,3) ; (-2.11)

Step-by-step explanation:

Answer:

(2, 3); (-2, 11)

Step-by-step explanation:

f(x) = x² - 2x + 3

f(x) = -2x + 7

f(x) = f(x)

x² - 2x + 3 = -2x + 7

x² = 4

x = ±2

x = 2

f(2) = -2(2) + 7 = -4 + 7 = 3

x = -2

f(-2) = -2(-2) + 7 = 4 + 7 = 11

Answer: (2, 3); (-2, 11)

The number line that shows the number of miles where A is less expensive has a solution of x > 60

From the question, we have the following parameters that can be used in our computation:

Option    Daily Cost ($) Cost per mile ($)

   A               25                   0.15  

   B                10                    0.40

So, the cost functions are

A = 25 + 0.15x

B = 10 + 0.4x

Where x is the number of miles

When A is less expensive, we have

25 + 0.15x < 10 + 0.4x

Evaluate the like terms

15 < 0.25x

So, we have

0.25x > 15

Divide

x > 15/0.25

Evaluate

x > 60

Hence, the number line is (a)

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Answer:

270°

Step-by-step explanation:

req angle= 360-90=270°

A composite number is one that is greater than one and contains more than 2 factors.

For the given statement;

9 is divisible by 3 can be written as;

9/3  = 3 ; as 3 is the prime number, the statement is regarded as prime statement.

For, 9 is odd.

As, 9 is not a prime but a composite number, the statement is considered as the compound statement.

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Answer:

Triangle ABC is similar to triangle A prime B prime C prime., because Triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 2. and then rotating it about the origin by 180 degrees

Step-by-step explanation:

Step 1: Dilation by a scale factor of 1/2.

A point (x, y) is sent to (1/2 x, 1/2 y).

A(2, 2) ---> (1, 1)

B(2, 10) ---> (1, 5)

C(8, 12) ---> (4, 6)

Step 2: Rotate about the origin 180 degrees

A point (x, y) is sent to (-x, -y).

(1, 6) --->  A'(-1, -1)

(1, 5) --->  B'(-1, -5)

(4, 6) ---> C'(-4, -6)

Answer:

No

Step-by-step explanation:

The sum of the squares of the lengths of the two shorter sides is \(10^2+12^2=244\).

The square of the length of the largest side is \(14^2=196\).

Because these two values are not equal, the side lengths do not satisfy the Pythagorean theorem. Therefore, the triangle is not a right triangle.

Answer:

The vertex form of 8-2x=3(y+1)^2 is: y= -1/6x^2 + 4x - 8.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

70.74

Step-by-step explanation:

2 -----  15.72

9  ------  ?

x = 9 * 15.72 / 2

= 70.74

The probability that a pupil uses neither pool nor gym is 11/70

Probability is the likelihood that an event will happen. This can range from an event being impossible to some likelihood to being absolutely certain. In math terms, probability is on a scale from 0 to 1. Zero means the event is impossible, like rolling a seven on a die that only has digits from 1 to 6.

Number of pupil that can use pool and gym = 28

Number of people that can use pool = 48

Number of people that can use gym = 39

Number of people that can use pool only = 48 - 28 which is 20

Number of people that can use gym only = 39 - 28 = 11

Total number of persons that can use either pool, gym or both = 20 + 11 + 28 which is 59

Number of people that cannot use either or both of the facilities = 70 - 59 which is 11.

Probability = required outcome / possible outcome

Required outcome = 11

possible outcome = 70

Probability = 11/70

In conclusion, the probability that a pupil uses neither swimming pool nor gym is 11/70

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