Matthew's dad is 5 times as old as him. If the differences of their ages is 28, how old is matthew?

The value of trignometric function sin(2x) is 2√24/25, cos(2x) is -23/25 and tan(2x) is  -10/9

Using the given information, we can determine that sin(x) = -√24/5 and cos(x) = √1-24/25 = √1/25 = 1/5.

To find sin(2x), we can use the double angle formula: sin(2x) = 2sin(x)cos(x) = 2(-√24/5)(1/5) = -2√24/25.

To find cos(2x), we can use the double angle formula: cos(2x) = cos²(x) - sin²(x) = (1/25) - 24/25 = -23/25.

To find tan(2x), we can use the identity: tan(2x) = (2tan(x))/(1-tan²(x)) = (2(-1/5))/(1-1/25) = -10/9.

In summary, sin(2x) = -2√24/25, cos(2x) = -23/25, and tan(2x) = -10/9. These calculations were made using the double angle formula and the identity for tan(2x).

To know more about double angle formula click on below link:

https://brainly.com/question/30402422#

#SPJ11

9514 1404 393

Answer:

  3. 8; 29; 11; 12

  4. B. 11, 5, 13

  5. D. sides are 1; hypotenuse is √2

Step-by-step explanation:

3. Each of these can be figured from the Pythagorean theorem. The right-most blank is presumed to be the hypotenuse, so for all but the second blank the missing number is the root of the difference of the squares. Interestingly, you can compute this in your head by using the factoring of the difference of squares:

  a = √(c^2 -b^2) . . . . . . where c is the hypotenuse

  a = √((c +b)(c -b)) . . . . difference of squares is factored

For the first, this is b = √((10+6)(10 -6)) = √(16·4) = 4·2 = 8

For the third, this is a = √((61+60)(61-60)) = √121 = 11

For the fourth, this is b = √((13+5)(13-5)) = √(18·8) = √(9·2·2·4) = 3·2·2 = 12

For the second blank, we can do it the usual way:

  c = √(20² +21²) = √(400 +441) = √841 = 29

The blanks are filled with 8, 29, 11, 12.

Note: You may notice that (6, 8, 10) is double the triple (3, 4, 5). The triple (5, 12, 13) comes into play in the next problem.

__

4. The first few Pythagorean triples are (3, 4, 5), (5, 12, 13), (7, 24, 25). It can be useful to remember these.

By comparing these to the first three choices, you can see that choice B lists three numbers that cannot be a right triangle. (If the shortest and longest sides are 5 and 13, then the other side must be 12 if it is a right triangle.)

__

5. Darnell's finding that 1² +1² = (√2)² means that a triangle with sides in the ratio 1 : 1 : √2 is a right triangle. This description matches choice D.

Note: It can be useful to remember that sides 1 : 1 : √2 make an isosceles right triangle. It means the diagonal of a square is √2 times the side length, for example.

Answer: 0.0188

Step-by-step explanation:

Using the Central Limit Theorem, it is found that the standard deviation of the sampling  distribution of p is 0.0144.

In this problem:

Then, the standard deviation is:

\(s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.7(0.3)}{1012}} = 0.0144\)

The standard deviation of the sampling  distribution of p is 0.0144.

To learn more about the Central Limit Theorem, you can take a look at https://brainly.com/question/16695444

Answer:

m= -5x+6y all over k

Step-by-step explanation:

first, move over 5x to get -5x+6y. then divide it by k and thats your answer.

Answer:

m=6y/k - 5x/k

Step-by-step explanation:

Isolate the variable by dividing each side by factors that dont contain the variable

Answer:

k = -5

Step-by-step explanation:

Answer: $26.24

Step-by-step explanation:

Same method

I hope it helps you

Answer:

\(y = 0 \: .x = \frac{2}{3} y\)

Step-by-step explanation:

\( \frac{2 {x}^{2} - 5 }{3xy - 2 {y}^{2} } \)

\(3xy - 2 {y}^{2} = 0\)

\(y \times (3x - 2y) = 0\)

\(y = 0 = 3x - 2y = 0\)

\(y = 0 = 3x = 2y\)

\(y = 0\)

\(x = \frac{2}{3} y\)

\(y = 0. \: x = \frac{2}{3} y\)

P = -2x^2 + 8x + 2

for maximum P, dP/dx = 0

dP/dx = -4x + 8 = 0

4x = 8

x = 2

The company should produce 2,000 units per week to earn maximum profit.

Maximum profit = -2(2)^2 + 8(2) + 2 = -8 + 16 + 2 = 10

Therefore, the maximum weekly profit is $1,000.

Answer:

we need the linear graph ._.

Step-by-step explanation:

Answer:

I believe thats 8 to the power of 7

Step-by-step explanation:

Answer:

i clicked your link adn it looks like 8^7 or 8 to the 7th power which would be 2,097,152

Step-by-step explanation:

The age that represents the 48th percentile is 53.

To find the age that represents the 48th percentile given the data below, we first need to arrange the data in ascending order.43, 45, 48, 50, 52, 52, 52, 53, 58, 58, 61, 62, 67, 67Next, we need to determine how many values are in the data set. In this case, there are 14 values. We need to find the rank of the 48th percentile, which is equal to 0.48 * 14 = 6.72, which we can round up to 7 since we can't have a fraction of a rank.The age that represents the 48th percentile is the 7th value in the ordered data set, which is 53. Therefore, the age that represents the 48th percentile is 53.

Learn more about percentile :

https://brainly.com/question/16797504

#SPJ11

Answer:

245

Step-by-step explanation:

70% =.07

350 × .07 =245

Answer:

2.876073e+128

Step-by-step explanation:

your welcome

Answer:

2.876073e+128

Step-by-step explanation:

8747464647396497346585764868738763897645487248737563847538763487Times 32878937498374398487937498743749873928742398787429837429374328947 = 2.876073e+128

Answer:

Step-by-step explanation:

.

Answer:

see below

Step-by-step explanation:

a) They could be congruent because having the same angles doesn't necessarily mean that they are congruent.

b) These triangles are  congruent by ASA because using the sum of angles in a triangle they have the same angles and one congruent side.

Answer:

a) F

b) C

Step-by-step explanation:

Brainliest please?

For a) it only tells you all the angles, which makes them similar triangles, but none of the sides are given, so it cannot be determined whether they are congruent.

For b) it is not to scale and using a little subtraction, you can quickly use the fact that there are 180 degrees in a triangle, you can determine that the 2 triangles have the same angles, with the side with 9.2 cm between 58 and 68 degree vertices on both triangles, making the 2 triangles congruent by ASA.

QED

The mean is approximately 5.47, the median is 5, and the mode is 5 for the given data set of yogurt pretzels.

The given data set represents the number of yogurt pretzels in various bags. The numbers in the data set are: 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 7, 7, 8.To summarize the data set, we can calculate the measures of central tendency, such as the mean, median, and mode:

Mean: The mean is calculated by summing up all the values and dividing by the total count. In this case, the sum is 82, and there are 15 values. So, the mean is 82/15 ≈ 5.47.

Median: The median is the middle value when the data set is arranged in ascending or descending order. In this case, the median is 5, as it lies in the middle when the values are sorted.

Mode: The mode is the value that appears most frequently. In this data set, the mode is 5, as it occurs six times, more than any other number.

For more such questions on mean

https://brainly.com/question/1136789

#SPJ8

The algorithm is correct and can be proven using the loop invariant theorem. The loop invariant for this algorithm is that at the start of each iteration of the loop, the value of j is a divisor of m.

To prove the correctness of the algorithm using the loop invariant theorem, we need to establish three properties: initialization, maintenance, and termination.

Initialization: Before the loop starts, j is initialized to 0. At this point, the loop invariant holds because 0 is a divisor of any positive integer m.

Maintenance: Assuming the loop invariant holds at the start of an iteration, we need to show that it holds after the iteration. In this algorithm, j is incremented by 1 in each iteration. Since j starts as a divisor of m, adding 1 to j does not change its divisibility property. Therefore, the loop invariant is maintained.

Termination: The loop terminates when j becomes greater than m. At this point, the loop invariant still holds because j is not a divisor of m. Thus, the loop invariant is maintained throughout the entire execution of the algorithm.

Since the initialization, maintenance, and termination properties hold, we can conclude that the algorithm is correct. The loop invariant, in this case, is that at the start of each iteration, the value of j is a divisor of m.

Learn more about algorithm here:

https://brainly.com/question/21172316

#SPJ11

Check the picture below.

well, according to the line vertical test, if a vertical line anywhere on the graph hits the graph only once, then yeap, it's a function.

Answer:

y = 2x + 6

Step-by-step explanation:

slope-intercept form => y = mx + b

substitute two of the (x, y) into the equations: y = mx + b  to solve for m and b

=> 0 = -3m + b, 6 = 0m + b

6 = 0m + b => b = 6

substitute b = 6 into 0 = -3m + b to solve for m:

=> 0 = -3m + 6 => -3m = -6 => m = 2

plug in b = 6 and m = 2 into the equation y = mx + b:

=> y = 2x + 6

......the correct answer is 0

Answer:

$1265

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × width

here length = 40 and  A = 2800 , then

2800 = 40 × width ( divide both sides by 40 )

70 = width

the perimeter (P) is calculated as

P = 2(length + width) = 2(40 + 70) = 2 × 110 = 220 ft

cost = 220 × $5.75 = $1265

Answer:

$1265

Step-by-step explanation:

area = length × width

area = 2800

length = 40

2800 / 40 = 70

So, the width of the lot is 70ft , and the length is 40

when building a fence, it would surround the entire property's perimeter (which is the length of the outside edges/sides of the shape added together)

so, it would need to cover 70 + 40 + 70 + 40

(the perimeter = 70 + 40 + 70 + 40)

= 220

so, if each foot costs 5.75, we can multiply 220 × 5.75 to find the cost:

220 × 5.75 = 1265

So, this will cost him $1265

hope this helps! have a lovely day :)

Answer: They divided the numbers into the smallest numbers they could (prime factors) and then made matches between them.

Step-by-step explanation:

Prime factors are the numbers that can't be divided. For instance, 10 can be divided into 2 x 5, but 2 and five can't be divided except by one, so 2 and 5 are prime factors.

What they did for 24 was basically divide it by two until they couldn't anymore. So, 24 divided by 2 was 12. You can write down 2 as a prime factor and then see how much more you can divide the 12 left over. Let's say 12 divided by 4 is 3. We can't divide 3 any further, so we can write it down as a prime factor with 2. Then 4 divided by 2 is 2. So, we can write down two more 2s with our other numbers.

Now we can write out all the prime factors we found: 2 x 2 x 2 x 3

When we do the same thing with 36 we get 36/12 = 3, 12/4 = 3, 4/2 = 2.

so, we have 2 x 2 x 2 x 3

and also 2 x 2 x 3 x 3

Now we can look at the two rows of numbers and find matching pairs.

We have two pairs of 2s and one pair of 3s. That means that 2, 2, and 3 are the common factors.

Even though there are two extra prime factors, we can't count those because they aren't in a pair. Also, you only say one number for each pair of prime factors. That's why it says 2, 2, and 3 instead of 2, 2, 2, 2, 3, 3.

Good luck:)

Answer:

3.5/100*8=.28

Step-by-step explanation:

The probability that a tarot hand has a void is 1.1%, a tarot hand has a void if it does not contain any cards of a particular suit. There are 4 suits in a tarot deck, so there are 4 ways for a hand to have a void.

The probability that a hand has a void in a particular suit is the probability that none of the 18 cards in the hand are of that suit. There are 14 cards of each suit in a tarot deck, so the probability that a particular card is not of a particular suit is 1 - 14/78 = 1 - 2/7 = 5/7.

The probability that a hand has a void in all 4 suits is then (5/7)^18. This is because the events that a card is not of a particular suit are independent, so we can multiply the probabilities to get the joint probability.

The probability that a tarot hand has a void is then 4 * (5/7)^18 = 0.0110838..., which is about 1.1%.

Here is the Python code that I used to calculate the probability:

Python

import math

def probability_of_void():

 """

 Calculates the probability that a tarot hand has a void.

 """

 return 4 * (5 / 7)**18

print(probability_of_void())

This code prints the probability of a tarot hand having a void, which is about 1.1%.

To know more about probability click here

brainly.com/question/15124899

#SPJ11

Answer:

6.7%

$$\frac{\dbinom41\dbinom{64}{18} - \dbinom42\dbinom{50}{18} + \dbinom43\dbinom{36}{18} - \dbinom44\dbinom{22}{18}}{\dbinom{78}{18}}.$$

Answer:

The angle measures of trapezoid PQRS are equal to the corresponding angle measures of trapezoid P'Q'R'S'.

Step-by-step explanation:

Answer:

1. Yes  2. Yes   3. No   4. No    5. Yes.   6. No.     7. No.     8. yes.      9. Yes.     10. No.       11. Yes.     12. Yes.    

Step-by-step explanation:

You would assume that in this figure, the number of colored sections with which are not colored with respect to a " touching " colored section, would be half of the total colored sections. However that is not the case, the sections are not alternating as they still meet at a common point. After all, it notes no two touching sections, not adjacent sections. Their is no equation to calculate this requirement with respect to the total number of sections.

Let's say that we take one triangle as the starting. This triangle will be the start of a chain of other triangles that have no two touching sections, specifically 7 triangles. If a square were to be this starting shape, there are 5 shapes that have no touching sections, 3 being a square, the other two triangles. This is presumably a lower value as a square occupies two times as much space, but it also depends on the positioning. Therefore, the least number of colored sections you can color in the sections meeting the given requirement, is 5 sections for this first figure.

Respectively the solution for this second figure is 5 sections as well.

The values for numbers #21 through #26 are as follows:

#21: 2.33% or 0.0233. #22: $56.4842. #23: 1.85% or 0.0185. #24: $56.4148. #25: 3.64% or 0.0364. #26: $57.4397

#21: 2.33% (arithmetic mean as a fraction: 0.0233)

#22: $56.4842 (result of the calculation)

#23: 1.85% (geometric mean as a fraction: 0.0185)

#24: $56.4148 (result of the calculation)

#25: 3.64% (continuous mean as a fraction: 0.0364)

#26: $57.4397 (result of the calculation)

To fill out numbers #21 through #26, we need to calculate the values for each term using the given information and convert the percentages to fractions.

#21: The arithmetic mean is given as a percentage. Convert it to a fraction by dividing by 100. Therefore, #21 = 2.33% = 0.0233.

#22: Multiply the starting price ($53.07) by the compound factor (1 + arithmetic mean)^3. Substitute the value of #21 into the calculation. Therefore, #22 = $53.07 x (1 + 0.0233)^3 = $56.4842.

#23: The geometric mean is given as a percentage. Convert it to a fraction by dividing by 100. Therefore, #23 = 1.85% = 0.0185.

#24: Multiply the starting price ($53.07) by the compound factor (1 + geometric mean)^3. Substitute the value of #23 into the calculation. Therefore, #24 = $53.07 x (1 + 0.0185)^3 = $56.4148.

#25: The continuous mean is given as a percentage. Convert it to a fraction by dividing by 100. Therefore, #25 = 3.64% = 0.0364.

#26: Multiply the starting price ($53.07) by the continuous factor e^(continuous mean x 3). Substitute the value of #25 into the calculation. Therefore, #26 = $53.07 x e^(0.0364 x 3) = $57.4397.

Hence, the values for numbers #21 through #26 are as calculated above.

To learn more about fraction, click here: brainly.com/question/28372533

#SPJ11