given cos alpha=15/17 in Q1, find cos(alpha/2) And sin(alpha/2)​

Answer:5x/(x-1)(x+3)

Step-by-step explanation:Factor -3+2x+x^2 by using the AC method hope this helps. Branliest plz

Answer:

the required equation is:

[tex]x^2 -10 +34[/tex]

Step-by-step explanation:

The equation given is:

[tex]x^2 -()+34[/tex]

Comparing it with standard quadratic equation

[tex]a^2 +bx+c[/tex]

a= 1,

b=?

C= 34

We can find the value of b using Vieta's formulas :

That states that if roots x₁ and x₂ are given then,

x₁ + x₂ = -b/a

We are given roots: 5 ± 3i i.e, x₁= 5 + 3i and x₂= 5 - 3i

solving

5 + 3i + 5 - 3i = -b/1

10 = -b

Since the given equation already gives b as -b so, -b= 10 => b=10

Putting value of b in the missing place the required equation will be:

[tex]x^2 -10 +34[/tex]

To find the missing term in a quadratic equation given complex roots, use the properties of conjugate roots to determine the term.

Since the roots are in the form of a complex number, they are conjugates of each other, which helps in finding the missing term.

Given roots: 5 ± 3i

Using the sum and product of roots formula

Sum: (5 + 3i) + (5 - 3i) = 10. Product: (5 + 3i)*(5 - 3i) = 34

Construct the equation: x2 - (10x) + 34 = 0

Answer:

(A) - Hachi does not earn any money if he does not work

Step-by-step explanation:

If you think about it the graphed point is (0,0), so it is self explanatory that he works 0 hours and OBVIOUSLY he wont earn any money if he doesnt work.

The graph shows the amount of money Hachi earns at his job in relation to the number of hours he works. Hachi does not earn any money if he does not work.

A function is defined as a relation between the set of inputs having exactly one output each.

We can see that the graph linearly increases as the hour he worked and the money he earned will increase.

we know that the graphed point is (0,0),

He earned 10 money per hour of work.

so it is self-explanatory that he works 0 hours and obviously, he won't earn any money if he doesn't work.

Thus, Hachi does not earn any money if he does not work.

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Answer:

5[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Using the sine ratio in the right triangle and the exact value of

sin60° = [tex]\frac{\sqrt{3} }{2}[/tex], then

sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{10}[/tex]

Multiply both sides by 10

10 × sin60° = x

10 ×[tex]\frac{\sqrt{3} }{2}[/tex], hence

x = 5[tex]\sqrt{3}[/tex]

Answer:

P =26%

Step-by-step explanation:

In this problem we have the ages of all new employees hired during the last 10 years of normally distributed.

We know that the mean is [tex]\mu = 35[/tex] years and standard deviation is [tex]\sigma = 10[/tex] years

By definition we know that if we take a sample of size n of a population with normal distribution, then the sample will also have a normal distribution with a mean

[tex]\mu_m = \mu[/tex]

And with standard deviation

[tex]\sigma_m = \frac{\sigma}{\sqrt{n}}[/tex]

Then the average of the sample will be

[tex]\mu_m = 35\ years[/tex]

And the standard deviation of the sample will be

[tex]\sigma_m =\frac{10}{\sqrt{10}} = 3.1622[/tex]

Now we look for the probability that the mean of the sample is greater than or equal to 37.

This is

[tex]P({\displaystyle{\overline {x}}}\geq 37)[/tex]

To find this probability we find the Z-score

[tex]Z = \frac{{\displaystyle{\overline{x}}} -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]Z = \frac{37 -35}{\frac{10}{\sqrt{10}}} = 0.63[/tex]

So

[tex]P({\displaystyle{\overline {x}}}\geq 37) = P(\frac{{\displaystyle{\overline {x}}}-\mu}{\frac{\sigma}{\sqrt{n}}}\geq\frac{37-35}{\frac{10}{\sqrt{10}}}) = P(Z\geq0.63)[/tex]

We know that

[tex]P(Z\geq0.63)=1-P(Z<0.63)[/tex]

Looking in the normal table we have:

[tex]P(Z\geq0.63)=1-0.736\\\\P(Z\geq0.63) = 0.264[/tex]

Finally P = 26%

To find the probability that the sample mean age of 10 employees is at least 37, we can use the Central Limit Theorem and standardize the sample mean. The probability is approximately 2.28%.

To solve this problem, we need to use the Central Limit Theorem, which states that the sample mean of a large enough sample size will be approximately normally distributed regardless of the shape of the population distribution.

In this case, the mean age of new employees is normally distributed with a mean of 35 and a standard deviation of 10. We want to find the probability that the sample mean age of 10 employees is at least 37.

To find this probability, we first need to standardize the sample mean using the formula z = (x - μ) / (σ / sqrt(n)), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Using this formula, we have z = (37 - 35) / (10 / sqrt(10)) = 2 * sqrt(10).

From a standard normal distribution table, we can find that the probability of getting a z-score less than 2 * sqrt(10) is approximately 1 - 0.0228 = 0.9772. However, we want the probability of getting a sample mean at least 37, so we subtract this probability from 1 to get 1 - 0.9772 ≈ 0.0228.

Therefore, the probability that the sample mean age of 10 employees will be at least 37 is approximately 2.28%.

Answer:

the answer is 11/21 or 0.523809524

hope this helped

Step-by-step explanation:

Answer:

Fraction: 1/250

Decimal: 0.004

Step-by-step explanation:

2/5=0.4 0.4%=0.004 0.004=4/1000=2/500=1/250

Answer:

SSS Congruence Theorem

Step-by-step explanation:

sss congruence theorem. you can get this answer by marking all the givens.

Answer: the difference between the max is 3200.

Step-by-step explanation:

20000-16800= 3200

The difference between the max is 3200.

Subtract the smaller of the two numbers from the larger of the two numbers to find the difference between them. The difference between the two numbers is the sum's product. For instance, you could calculate the difference between 100 and 45 as follows: 100 - 45 = 55.

Given

20,000 - 16,800 = 3200

therefore, The difference between the max is 3200.

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Answer:

The ninth term is -0.75.

Step-by-step explanation:

Let's write the actual formula for this arith. seq.

It will have the general form a(n) = a(1) + (n-1)d, where a(1) is the first term, n is the term counter (1, 2, 3, .... ) and d is the common difference.

Here, a(n) = -2.75 + (n - 1)(0.25)

So the ninth term of this sequence is

a(9) = -2.75 + (9 - 1)(0.25

      = -2.75 + 8(0.25)

      = -2.75 + 2

       = -0.75

The ninth term is -0.75.

Answer:

[tex]a_9=-0.75[/tex]

Step-by-step explanation:

The given sequence has the first term, [tex]a_1=-2.75[/tex] and d=0.25

The general formula for an arithmetic sequence is given by;

[tex]a_n=a_1+d(n-1)[/tex]

Since we want to find [tex]a_9[/tex], it means n=9

We substitute the given values into the formula to obtain;

[tex]a_9=-2.75+0.25(9-1)[/tex]

[tex]a_9=-2.75+0.25(8)=-0.75[/tex]

Hence, the 9th term is

[tex]a_9=-0.75[/tex]

Answer:

To find perimeter, you must add length plus length plus width plus width.

(L+L+W+W)

the length is 5, and the width is 8. since there are 4 sides, we must add 5+5+8+8, and that equals 26.

As we know the formula for finding the perimeter of a rectangle is:

[tex]Perimeter=2(L+B)[/tex]

here, L is the length of the rectangle and B is the breadth of the rectangle.

As the values of the length and breadth are given, we will put in the formula;

[tex]Perimeter=2(8+5)[/tex]

[tex]Perimeter=2(13)[/tex]

[tex]Perimeter=26[/tex]

Hence, the perimeter of the rectangle is 26 units.

Perimeter is the distance around the edge of a shape.

The total length of the boundary of a closed shape is called its perimeter. Hence, the perimeter of that shape is measured as the sum of all the sides. Thus, the perimeter formula is Perimeter(P) = Sum of all the sides.

Any equation expressed in terms of parameters is a parametric equation. The general equation of a straight line in slope-intercept form, y = mx + b, in which m and b are parameters, is an example of a parametric equation.

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Answer: (0.15,0.37)

Step-by-step explanation:

did the quiz

The range of possible values that best describes the estimate for the population parameter is [0.16, 0.38]. Therefore, the correct answer is option D.

Given that, a sample proportion is 0.26.

In statistics, the sample proportion is an estimate for the population parameter. When given a sample proportion, the range of possible values that best describes the estimate for the population parameter is typically the 95% confidence interval for the sample proportion. The 95% confidence interval states that if the same sampling procedure is repeated on many samples, then 95% of the confidence intervals constructed this way will contain the true population parameter.

The 95% confidence interval for a sample proportion is given by [p-1.96√(pq/n), p+ 1.96√(pq/n)], where p is the sample proportion, q is the complement of the sample proportion (q = 1 − p), and n is the sample size.

In this case, the sample proportion given is 0.26, and so p = 0.26, q = 0.74, and the sample size can be assumed to be large (n ≥ 30). Substituting these values into the 95% confidence interval equation yields the range of possible values that best describes the estimate for the population parameter: [0.16, 0.38].

Therefore, the correct answer is option D.

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"Your question is incomplete, probably the complete question/missing part is:"

If a sample proportion is 0.26 which of the following is most likely the range of possible values that best describes an estimate for the population parameter?

A. (0.14, 0.36)

B. (0.17, 0.39)

C. (0.15, 0.37)

D. (0.16, 0.38)

Step-by-step explanation:

dude i have no idea sorry

The Calculating area and perimeter worksheet from works.com

#4

Area: [tex]360 yd^2[/tex]

Perimeter: 30 yd

#5

Area: [tex]45 yd^2[/tex]

Perimeter: 22 yd

#6

Area: 87 yd^2

Perimeter: 30 yd

#7

Area: 72 ft^2

Perimeter: 24 ft

#8

Area: 150 ft^2

Perimeter: 30 ft

#9

Area: 2128 ft^2

Perimeter: 70 ft.

Area is the amount of space that a two-dimensional shape takes up. It is measured in square units, such as square feet (ft^2), square yards (yd^2), or square meters (m^2).

To calculate the area of a rectangle, multiply the length by the width.

Area of a rectangle = length * width

To calculate the area of a square, multiply the side length by itself.

Area of a square = side length * side length

To calculate the area of a triangle, multiply the base by the height and divide by 2.

Area of a triangle = base * height / 2

Perimeter is the total length of all the sides of a two-dimensional shape. It is measured in linear units, such as feet (ft), yards (yd), or meters (m).

To calculate the perimeter of a shape, add up the lengths of all the sides.

Perimeter of a shape = sum of the lengths of all the sides

Example:

To calculate the area and perimeter of the rectangle in question #4, we would use the following formulas:

Area = length * width = 5 yd * 72 yd = 360 yd^2

Perimeter = sum of the lengths of all the sides = 5 yd + 72 yd + 5 yd + 72 yd = 30 yd

Answers to the remaining questions:

#5:

Area = 45 yd^2

Perimeter = 22 yd

#6:

Area = 87 yd^2

Perimeter = 30 yd

#7:

Area = 72 ft^2

Perimeter = 24 ft

#8:

Area = 150 ft^2

Perimeter = 30 ft

#9:

Area = 2128 ft^2

Perimeter = 70 ft.

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Answer:

fghjk²;.

Step-by-step explanation:

Final answer:

To find the product of 3840 and 5 using an area model, we can draw a rectangle with a length of 3840 units and a width of 5 units. Then, we divide the rectangle into smaller squares or rectangles of equal size. The product of 3840 and 5 is 19,200.

Explanation:

To find the product of 3840 and 5 using an area model, we can draw a rectangle with a length of 3840 units and a width of 5 units. Then, we divide the rectangle into smaller squares or rectangles of equal size. For example, we can divide the rectangle into 384 squares of length 10 and width 5, or into 192 squares of length 20 and width 10. After that, we count the total number of squares to find the product. In this case, the product of 3840 and 5 is 19,200.

Answer:

[tex]sin(t) =\frac{\sqrt{7}}{4}[/tex]

Step-by-step explanation:

By definition we know that

[tex]sec(t) = \frac{1}{cos(t)}[/tex]

and

[tex]cos ^ 2(t) = 1-sin ^ 2(t)[/tex]

As [tex]sec(t) = -\frac{4}{3}[/tex]

Then

[tex]sec(t) = -\frac{4}{3}\\\\\frac{1}{cos(t)} =-\frac{4}{3}\\\\cos(t) = -\frac{3}{4}[/tex]

Now square both sides of the equation:

[tex]cos^2(t) = (-\frac{3}{4})^2[/tex]

[tex]cos^2(t) = \frac{9}{16}\\\\[/tex]

[tex]1-sin^2(t) =\frac{9}{16}\\\\sin^2(t) =1-\frac{9}{16}\\\\sin^2(t) =\frac{7}{16}\\\\sin(t) =\±\sqrt{\frac{7}{16}}[/tex]

In the second quadrant sin (t) is positive. Then we take the positive root

[tex]sin(t) =\sqrt{\frac{7}{16}}[/tex]

[tex]sin(t) =\frac{\sqrt{7}}{4}[/tex]

The value of sin(t) = √7/4 because sine is positive in Quadrant II.

First, recall that sec(t) is the reciprocal of cos(t):

sec(t) = 1/cos(t)

Given: sec(t) = -4/3, so:

cos(t) = -3/4

Since angle t lies in Quadrant II, cosine is negative, and sine is positive. Use the Pythagorean identity:

sin²(t) + cos²(t) = 1

Substitute cos(t):

sin²(t) + (-3/4)² = 1

sin²(t) + 9/16 = 1

Solve for sin²(t):

sin²(t) = 1 - 9/16

sin²(t) = 16/16 - 9/16

sin²(t) = 7/16

Take the square root of both sides:

sin(t) = √(7/16) = √7/4

Since we are in Quadrant II, sine is positive:

sin(t) = √7/4

Answer:

h = 47.70 ft

The antenna is 47.70 ft tall.

Step-by-step explanation:

The height of the antenna is approximately 47.4ft when calculated using the Pythagorean theorem: √((50ft)^2 - (15ft)^2).

The question is asking for the height of the antenna. We can solve this problem by using the Pythagorean theorem, which states that in a right triangle the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Here, the hypotenuse is the length of the cable (50 ft), one side is the distance from the base of the antenna to the anchor point (15 ft) and the other side (which we are trying to find), is the height of the antenna.

According to the Pythagorean theorem, the height of the antenna can be calculated as follows: Height = √(Hypotenuse^2 - Base^2), which translates into Height = √((50ft)^2 - (15ft)^2). When you calculate that you get the height of the antenna as approximately 47.4 feet, rounded to the nearest tenth.

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Final answer:

After descending 7 feet, ascending 22 feet, and descending 9 feet, the individual is 6 feet above the ground level.

Explanation:

The question involves a sequence of movements by an individual on a ladder at a construction site. To solve this, let's track each movement relative to the initial position at ground level.

Therefore, the individual is 6 feet above the ground after these movements.

Answer:

Choice C

Step-by-step explanation:

(f+g)(x) is a composite function which is obtained by adding the two given functions f(x) and g(x)

(f+g)(x) = f(x) + g(x)

            = [tex]3^{x} +10x+4x-2[/tex]

            = [tex]3^{x} +14x-2[/tex]

I think they are complementary angles but i am not sure

Answer:

They form a linear pair.

Step-by-step explanation:

Because both are not 180 so that marks out the last checkbox and the second. Plus, they both don't add up to 90 so it checks off the first.

Answer

Their combined score is 331 points

Explanation

Determine each person's score

Collin score: 139

Brian: 139 + 53 = 192

Add the scores together

139 + 192 = 331

Colin scored 139 points and Brian scored 53 points more than Colin, which is 192 points. Adding Colin's and Brian's scores gives a combined score of 331 points.

In the game of darts, Colin and Brian scored different points. We know that Colin scored 139 points. As per the information given, Brian scored 53 points more than Colin. So, to find out how many points Brian scored, we can add 53 to Colin's score of 139, which gives us 192 points for Brian.

To find out the combined score of Colin and Brian, we simply add Colin's score to Brian's score. So, 139 (Colin's score) plus 192 (Brian's score) equals 331.

Therefore, the combined score of Colin and Brian is 331 points.

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ANSWER

B(r,0)

or

B(0,s)

EXPLANATION

In rectangle ABCD, the coordinates of A are (0, 0) and of C are (r, s).

When we name the triangle in a clockwise direction.

Then B must bear the y-coordinate of A and bear the x-coordinate of C.

This gives us (r,0)

When we name the triangle in an anticlockwise direction.

Then B must bear the x-coordinate of A and bear the y-coordinate of C.

This gives us (0,s)

Answer:

What is the probability of getting a vowel (a success) for the spinner shown?

✔ 1/3

Suppose you spin the spinner 5 times.

✔ P(3 successes) means “the probability of getting a vowel on exactly 3 of the spins.”

Step-by-step explanation:

edg 2020

Using the binomial distribution, it is found that:

For each spin, there are only two possible outcomes, either it is a vowel, or it is not. The result of a spin is independent of any other spin, hence the binomial distribution is used to solve this question.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem:

The probability of 3 successes is given by:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 3) = C_{5,3}.(0.3333)^{3}.(0.6667)^{2} = 0.1646[/tex]

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Answer:

10

Step-by-step explanation:

Answer is...

23.55

See attached photo

[tex]\text{Hey there!}[/tex]

[tex]\text{The answer is: (3g + 2)(g + 2)}[/tex]

[tex]\text{To make sure it comes back to the original problem}\bf{(3g^2+8g+4)}[/tex] [tex]\text{You would have to distribute the answer}[/tex]

[tex]\text{3g(g)=}3g^2\\ \text{3g(2)=6g}\\ \text{2(g)=2g}\\ \text{2(2)=4}[/tex]

[tex]\text{After distributing combine your like terms:}[/tex]

[tex]\text{In this particular answer we have: 1 term with TWO LIKE TERMS}[/tex]

[tex]\text{6g+2g=8g(That's how we got the 8g in the original equation)}[/tex]

[tex]\text{The}\bf{\ 3g^2}\text{ stays the same because there's nothing to go with it}[/tex]

[tex]\text{The 4 also stays the same because nothing goes with it as well}[/tex]

[tex]\boxed{\boxed{\text{Answer:(3x + 2 (x + 2)})}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

x ≤ - 4

Step-by-step explanation:

Given

3 - x ≥ 2x + 15 ( add x to both sides )

3 ≥ 3x + 15 ( subtract 15 from both sides )

- 12 ≥ 3x ( divide both sides by 3 )

- 4 ≥ x, hence

x ≤ - 4

3 - x is greater than equal to 2 X + 15

3 is greater than equal to 3X + 15

- 12 is greater than equal to 3 x

- 4 is greater than equal to x

hence x b - 4 - 4 is greater than x

She is 4 years an d3 months old

Answer:

111 months

Step-by-step explanation:

First, look at how many whole years old Emma is. Emma is 9 whole years old. 1 year consists of 12 months. So, multiply 9 [years] by 12 [months] to get 108. The number 108 is how many months are in 9 years. However, Emma is 9 months and 1/4 years old.

To find out how many months 1/4 of a year is, multiply 1/4 [year] by 12 [months] . 12 is the same as 12/1, so multiply the numerators and denominators of 1/4 and 12/1

1 x 12 = 12

4 x 1 = 4

12/4 = 3

Therefore, 1/4 year is 3 months. Now, add 108 months and 3 months to get 111 months. Therefore, Emma is 111 months old.

I hope this helps! :)

Answer:

Second option

Step-by-step explanation:

Option 1:

1. Original cost: 90% * 1000 = $900

2. Interest: A = P(1 + rt), A = amount, P = original amount, r = rate, t = years

Plug in: A = 900(1 + 0.05*3)

Multiply + add: A = 900(1.15)

Multiply: A = $1035

Option 2: $1000

So, paying full price upfront will save more money if all goes to plan.

Answer:

$39.91

Step-by-step explanation:

6*5.55=33.30

33.30*1.07=35.63

35.63*1.12=39.91

Don't know how to delete the incorrect answer that my sister put but I can edit it, so this is what I'm editing it to.