Dan spends 1/4 of his wages on rent and 2/3 on food. If he makes £264 per week, how much money does he have left?

The correct proof of the equation is cos3θ =cos(2θ + θ) =  cos²θ - 3cosθsin²θ (Proved)

Given the trigonometry identity below:

cos3∅=cos²∅-3cos∅sin²∅

We are to prove that both sides of the equation are equal.

cos 3θ = cos(2θ + θ)

Using the double angle formula for cosine, we can expand the first term:

cos(2θ + θ) = cos2θ cos θ - sin2θ sinθ

Since cos2θ = cos²θ - sin²θ

cos(2θ + θ) =  cos²θ - sin²θ - 2cosθsinθsinθ

cos(2θ + θ) = cos²θ - sin²θ - 2cosθsin²θ

On simplifying, we can see that;

cos3θ =cos(2θ + θ) =  cos²θ - 3cosθsin²θ (Proved)

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Answer:

Fred and Jon

Ilsa and Hanna

Step-by-step explanation:

Fred has a difference of -5. Jon has a difference of + 5.

Positive and negative 5 are opposite.  

Ilsa had a difference of -3. Hanna had a difference of + 3.

Positive and negative 3 are opposite.

Answer:

\(\dfrac{366}{378}\)

Step-by-step explanation:

The given information is summarized in the table below.

\(\left|\begin{array}{c|cc|c}$Age Bracket&$Respond&$Refuse to respond&$Total\\18-21&70&12&82\\22-29&272&24&296\\--&--&--&--\\$Total&342&36&378\end{array}\right|\)

Probability of getting someone in the 22-29 age bracket = 296/378

Probability of getting someone who agreed to respond = 342/378

Probability of both = 272/378

Therefore:

The probability of getting someone in the 22-29 age bracket or someone who agreed to respond

\(=\dfrac{296}{378} +\dfrac{342}{378} -\dfrac{272}{378} \\\\=\dfrac{366}{378} \\\\=0.9683\)

Answer:

50

Step-by-step explanation:

3/10 of x is 15, which means that 1/10 of x must be 5 because 15/3 = 5.

Now we can multiply 5 x 10, which is 50, so we know that x is equal to fifty

Answer:

=15

Step-by-step explanation:

Furthermore, you can convert "three" to "3" and "tenths" to "10" and then the equation and answer is:

3/10 x 15 = 4.50

Answer:

there are 60 students in math 7

Step-by-step explanation:

3/4 = 75%

75 + 15 = 90

100-90 = 10

10% of students are in math 7.

10% of 600 is 60

60 students are in math 7

hope this helps!

It would take approximately 17.12 years for the amount to reach Birr 56,398.43 with a deposit of Birr 500 at the end of each six-month period, compounded semi-annually at an interest rate of 6%.

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount

P = Principal amount (initial deposit)

r = Annual interest rate (in decimal form)

n = Number of compounding periods per year

t = Number of years

In this case, the principal amount is Birr 500, the annual interest rate is 6% (or 0.06), and the interest is compounded semi-annually, so there are 2 compounding periods per year.

We need to find the number of years (t) it takes for the amount to reach Birr 56,398.43.

Let's substitute the given values into the formula and solve for t:

56,398.43 = 500(1 + 0.06/2)^(2t)

Divide both sides by 500:

112.79686 = (1 + 0.03)^(2t)

Take the natural logarithm of both sides to eliminate the exponent:

ln(112.79686) = ln(1.03)^(2t)

Using the property of logarithms, we can bring down the exponent:

ln(112.79686) = 2t * ln(1.03)

Now, divide both sides by 2 * ln(1.03):

t = ln(112.79686) / (2 * ln(1.03))

Using a calculator, we find t ≈ 17.12.

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Answer:

130 degrees

Step-by-step explanation:

DE+DA=130

The Polynomial x⁵ + x³ - 5 is divided by x - 2, the quotient is x⁴ + 3x³ + 6x² + 12x + 24, and the remainder is 48.

The quotient and remainder when the polynomial x⁵ + x³ - 5 is divided by x - 2, we can use polynomial long division. Here's the step-by-step process:

1. Write the dividend (x⁵ + x³ - 5) and the divisor (x - 2).

   x - 2 | x⁵ + x³ + 0x² + 0x - 5

2. Divide the first term of the dividend (x⁵) by the first term of the divisor (x) to get x⁴. Write x⁴ above the line. x⁴

   x - 2 | x⁵ + x³ + 0x² + 0x - 5

3. Multiply the divisor (x - 2) by the quotient term (x⁴) to get x⁵ - 2x⁴. Write this under the dividend and subtract it.  x⁴

  x - 2 | x⁵ + x³ + 0x² + 0x - 5

 - (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

4. Bring down the next term (-5) from the dividend.

x⁴ + 3x³

x - 2 | x⁵ + x³ + 0x² + 0x - 5

- (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

5. Divide the first term of the new dividend (3x⁴) by the first term of the divisor (x) to get 3x³. Write 3x³ above the line.

 x⁴ + 3x³

   x - 2 | x⁵ + x³ + 0x² + 0x - 5

 - (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

6. Multiply the divisor (x - 2) by the new quotient term (3x³) to get 3x⁴ - 6x³. Write this under the new dividend and subtract it.

x⁴ + 3x³

x - 2 | x⁵ + x³ + 0x² + 0x - 5

- (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

- (3x⁴ - 6x³)

6x³ + 0x² + 0x - 5

7. Repeat steps 4-6 until you have subtracted all terms.

x⁴ + 3x³ + 6x² + 12x + 24

x - 2 | x⁵ + x³ + 0x² + 0x - 5

- (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

- (3x⁴ - 6x³)

6x³ + 0x² + 0x - 5

- (6x³ - 12x²)

12x² + 0x + 0

 - (12x² - 24x)

 24x + 0

- (24x - 48)

 48

8. The quotient is x⁴ + 3x³ + 6x² + 12x + 24, and the remainder is 48.

Therefore, when the polynomial x⁵ + x³ - 5 is divided by x - 2, the quotient is x⁴ + 3x³ + 6x² + 12x + 24, and the remainder is 48.

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Answer:

The answer is 21/35 or 3/5

Step-by-step explanation:

35-14=21

Answer:

C) between 3 and 6 hours (5 to 13 cars)

Step-by-step explanation:

**see attached image for question**

To read the graph, find the revelant "number of hours" section.  Look at the dots in that section and write down the approx lowest value and highest value - this is the range.

For example, between 0 and 2 hours, there is only one dot at 2 hours. Reading across to the y-axis, this is at 39 cars.

Looking at the part of the graph between 10 and 12 hours, the lowest dot is at y = 3 and the highest dot is at approx y = 34.  Therefore the number of cars in this time bracket is 3 to 34.

Reading the graph:

8 - 11 hours:  3 - 34 cars

0 - 2 hours:  39 cars

3 - 6 hours:  5 - 13 cars

10 - 12 hours: 3 - 34 cars

Therefore, the answer is C) as it is the only one that concurs with the above graph readings.

Answer:

X = 5

Step-by-step explanation:

Answer:

it's answer is D. 33°

Let the unknown angle be x Then.

x + 100° + 47° = 180° [ being sum of angles of triangle ]

x + 147° = 180°

x = 180° - 147°

x = 33°

Step-by-step explanation:

Answer:

3s=19s=-6

We move all terms to the left:

3s-(19s)=0

We add all the numbers together, and all the variables

-16s=0

s=0/-16

s=0

Answer:

The rate's aren't equivalent.

Step-by-step explanation:

If you find a common number of hours between the two expressions such as 24 hours you will see that the pay isn't the same. $24 for 6 hours of work ($4:1hr) can be turned into $96 for 24 hours of work and $36 hours for 8 hours of work ($4.5:1) turns into $108 for 24 hours of work.

The common ratio is the factor by which each term is multiplied to get the next term, which in this case is 4.

To find the common ratio of a geometric sequence, you can divide any term in the sequence by the previous term.

Looking at the sequence: 1, 1, 1, 2, 8, 32, 128, ...

To get from the 1st term to the 2nd term, we multiply by 1.

To get from the 2nd term to the 3rd term, we multiply by 1.

To get from the 3rd term to the 4th term, we multiply by 2.

To get from the 4th term to the 5th term, we multiply by 4.

To get from the 5th term to the 6th term, we multiply by 4.

The constant ratio between succeeding words is known as the common ratio in a geometric progression (GP). Any phrase in the progression must be divided by the term before it in order to compute it.

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The expression that best reveals the maximum and minimum of the function\(f(x) = x^2 - 8x - 4 is (x - 4)^2 - 20.\) Option A

The vertex form of a quadratic function is given by\(f(x) = a(x - h)^2 + k\) where (h, k) represents the coordinates of the vertex.

In the given quadratic function \(f(x) = x^2 - 8x - 4\), we can rewrite it in the vertex form by completing the square:

\(f(x) = (x - 4)^2 - 16 - 4\\f(x) = (x - 4)^2 - 20\)

From this expression, we can see that the vertex of the quadratic function is at the point (4, -20).

The term\((x - 4)^2\) tells us that the vertex is at x = 4, and the constant term -20 indicates the y-coordinate of the vertex.

The expression that best reveals the maximum and minimum of the function\(f(x) = x^2 - 8x - 4\) is  \((x - 4)^2 - 20.\)

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Answer:

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

Step-by-step explanation:

f(x)=9x^2 --> a=9

f(x)=a(x-h)^2+k -->f(x)=9(x-h)^2+k

vertex= (-3,2) --> h=-3 and k=2--> making it f(x)=9(x+3)^2+2

Answer: is A

Step-by-step explanation:

Third option is correct.The midpoint of WZ of WXYZ with the vertices W(0, 0), X(h, 0), Y(h,b), and Z(0, b) is (0, b/2).

To find the midpoint of segment WZ, we need to average the x-coordinates and the y-coordinates of the endpoints.

The coordinates of point W are (0, 0), and the coordinates of point Z are (0, b).

To find the x-coordinate of the midpoint, we average the x-coordinates of W and Z:

(x-coordinate of W + x-coordinate of Z) / 2 = (0 + 0) / 2 = 0 / 2 = 0

To find the y-coordinate of the midpoint, we average the y-coordinates of W and Z:

(y-coordinate of W + y-coordinate of Z) / 2 = (0 + b) / 2 = b / 2

Therefore, the midpoint of segment WZ is (0, b/2).

So, the correct answer is (0, b/2).

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Answer:

FH = 35.64

Step-by-step explanation:

(∠A = 360 so the other angle is 40)

By law of cosines,

FH² = AH² + FA² - 2(AH)(FA) * cos(A)

= 30² + 25² - 2(30)(25) * cos(80)

= 900 + 625 - 1500 * 0.17

= 1525 - 255

FH²  = 1270

FH = √1270

FH = 35.64

Answer:

1.5

Step-by-step explanation:

Christina makes 4 bracelets in one day, and the graph shows she makes 2.5 necklaces in one day (y = 2.5x). 4 - 2.5 = 1.5

P(A∪B)=P(A)+P(B)−P(A∩B)= 1.2, and P(A∩B) = 0.9 with the help of probability.

The likelihοοd οf an event οccurring is defined by prοbability.

In real life, there are many times when we need tο predict what will happen.

The οutcοme οf events may οr may nοt be knοwn tο us.

I say that if this happens, the event may οr may nοt οccur.

In general, prοbability has many great uses in games, prοbability-based ecοnοmics, and in this burgeοning field οf artificial intelligence.

A prοbability fοrmula can be used tο determine the prοbability οf οccurrence by simply dividing the favοrable number οf pοssibilities by the tοtal number οf pοssible οutcοmes.

According to our question-

P(A∪B)+P(A∩B)=P(A)+P(B)

P(A)+P(B)=0.65+0.15=0.8

1.2

Then P(A∩B) = 0.75 × 1.2

P(A∩B) = 0.75 × 1.2

P(A∩B) = 0.9

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Answer:

For A), put a dot at -2, 7, -5, and 1 on the number line.

For B=), put a dot at 9, -4, 3, and -8.

Step-by-step explanation:

After answering the presented question, we can conclude that probability Therefore, the probability of 30 or more seconds between vehicle arrivals is approximately 0.0498.

Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% because there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many fields, including statistics, economics, science, and engineering.

Sketch of exponential probability distribution with mean of 12 seconds:

   |                            

   |                            

   |              .            

   |             . .            

   |             . .            

   |             . .            

   |             . . .          

   |             . . .          

   |             . . .          

   |             . . .          

   |             . . .          

   |             . . . .        

   |             . . . .        

   |             . . . .        

   |             . . . . .      

   |             . . . . .      

   |_____________. . . . . . .

        0       12             X

The X-axis represents the time between vehicle arrivals, and the Y-axis represents the probability density. The peak of the distribution is at 12 seconds, which is the mean.

b. Probability of the arrival time between vehicles being 12 seconds or less:

Since the mean of the exponential distribution is 12 seconds, we can use the cumulative distribution function (CDF) to find the probability of the arrival time being 12 seconds or less:

\(P(X < = 12) = 1 - e^(-12/12) = 1 - e^(-1) ≈ 0.6321\)

Therefore, the probability of the arrival time between vehicles being 12 seconds or less is approximately 0.6321.

c. Probability of the arrival time between vehicles being 6 seconds or less:

\(P(X < = 6) = 1 - e^(-6/12) = 1 - e^(-0.5) ≈ 0.3935\)

Therefore, the probability of the arrival time between vehicles being 6 seconds or less is approximately 0.3935.

d. Probability of 30 or more seconds between vehicle arrivals:

\(P(X > = 30) = e^(-30/12) ≈ 0.0498\)

Therefore, the probability of 30 or more seconds between vehicle arrivals is approximately 0.0498.

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Answer:

To calculate 2 3/4 of 500 grams, follow these steps:

1. Convert the mixed number to an improper fraction:

2 3/4 = (2 x 4 + 3)/4 = 11/4

2. Multiply the improper fraction by 500:

11/4 x 500 = (11 x 500)/4 = 2,750/4

3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2

Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.

Step-by-step explanation:

Answer:

It's a circle

Step-by-step explanation:

Based on the angle-angle similarity theorem (AA), the similar triangles in the image given can be named as: ΔBAC ~ ΔEDF.

When two triangles have the same shape but have different sizes, it means the triangles have corresponding pairs of congruent angles and corresponding pairs of sides that are proportional to each other. The triangles are said to be similar.

The image given show two set of triangles that have two corresponding pairs of congruent angles, based on the angle-angle similarity theorem, it means that they are similar to each other.

Therefore, the similar triangles are:

ΔBAC ~ ΔEDF.

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Answer:

the answer is 0.79 rounded to the nearest hundreth

Step-by-step explanation:

Answer:

41 adults and 82 kids

Step-by-step explanation:

divide 123 by 3 two parts are kids one part is adults.