Trigonometry: Question 2
In triangle ABC with right angle C, the measure of angle A is 37
degrees, and the length of the hypotenuse is 10. What is the length of
AC?
Select one:
12,5
7.9

Answer:

See explaination

Step-by-step explanation:

Please kindly check attachment for the detailed step by step solution of the given problem.

To find the closest point to y in subspace W, see the projection of y onto W. Solve the appropriate equations to find the scalars for v1 and v2. The sum of these scaled vectors will yield the closest point.

The closest point to y in the subspace W spanned by v1 and v2 can be determined using the projection formulas. First, find a and b such that a*v1 + b*v2 equals the projection of y onto W. To do this, set up the equations a*(v1 . v1) + b*(v1 . v2) = y . v1 and a*(v1 . v2) + b*(v2 . v2) = y . v2. Solve these equations for a and b. The solution will give you the scalars for v1 and v2, respectively. The vector a*v1 + b*v2 will be the closest point in W to y.

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Answer:

(a). Σx= 108, Σx^2 = 4984, Σy^2 = 2,157.

(b). 10.8, 0.1.

(C) and (d) => check explanation.

Step-by-step explanation:

To Calculate for Σx we will have to add all the values for x that is the summation of x-values.

Σx = 11 + 0 + 36 + 22 + 34 + 24 + 25 + -11 + -11 + -22 = 108.

Σx^2 = 11 × 11 + 0 × 0 + 36 × 36 + 22 × 22 + 34 × 34 + 24 ×24 + 25 × 25 + -11 × -11 + -11 × -11 + -22 × -22 = 4984.

Σy^2 = 9× 9 + -3 × -3 + 28 ×28 + 14 × 14 + 23 × 23 + 16 × 16 + 14× 14 + -3 ×-3 + -4 × -4 + -9 × -9= 2,157.

(b). Sample mean for x = 108/10 = 10.8.

Variance for x:

11 - 10.8 = 0.3

0 - 10.8 = -10.8

36 - 10.8 =25.2.

22 - 10.8=11.2.

34 - 10.8 = 23.2

24 -10.8 = 13.2.

25 - 10.8= 14.2

-11 - 10.8 = -21.8.

-11 - 10.8 = - 21.8

-22 -10.8 = -32.8.

Total=0.1

Standard deviation for x = √ s^2 = 0.3162

This can be done for y too

(c). 75% Chebyshev interval around the mean for x values = 10.8 + 2 (0.3162); 10.8 - 2(0.3162).

=> (11.4324, 10.1676).

(d). The coefficient of variation= (0.3162)/10.8 × 100 = 2.92%.

The sample means for annual returns of the Vanguard Total Stock Index (x) and Vanguard Balanced Index (y) have been computed as 10.8 and 8.5 respectively. The inclusion of bonds in a portfolio can lower overall return slightly while also reducing the risk.

The student's task revolves around the subject of statistical analysis, here applied to investment portfolio management. Their goal is to compute the sample mean (average) for two variables - x and y - which each represent annual returns for certain types of portfolios.

Portfolio x represents a 100% stock holding in the Vanguard Total Stock Index, while y represents a 60% stock and 40% bond holding in the Vanguard Balanced Index. Such portfolios carry varying degrees of risk, with all-stock portfolios generally accepted to be more volatile, yet offering higher potential returns than mixed portfolios.

In order to calculate the sample means for x and y, you simply add together all the annual returns for each, then divide by the number of years.

For x: (11 + 0 + 36 + 22 + 34 + 24 + 25 - 11 - 11 - 22)/10 = 10.8 (rounded to the nearest tenth)

For y: (9 - 3 + 28 + 14 + 23 + 16 + 14 - 3 - 4 - 9)/10 = 8.5 (rounded to the nearest tenth)

As seen, stocks did yield a higher average return over the period in consideration, though the range of returns was also much wider. By adding bonds to the portfolio (shown by y), the overall return reduced slightly, but so did the risk (variability) of returns.

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Answer:11.5

Step-by-step explanation:

distance=6 2/5 + 2 3/4 + 2 1/3

d=(5x6+2)/5 + (4x2+3)/4 + (3x2+1)/3

d=32/5 + 11/4 + 7/3

d=(12x32+15x11+20x7) ➗ 60

d=(384+165+140) ➗ 60

d=689 ➗ 60

d=11.5

The total distance  did she run is 11.5 miles.

It is required to find the total distance.

The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.

Given:

Melissa ran 6 2/5 miles north ,2 3/4 west and 2 1/3 south.

According to given question we have,

Total distance=6 2/5 + 2 3/4 + 2 1/3

d=(5x6+2)/5 + (4x2+3)/4 + (3x2+1)/3

d=32/5 + 11/4 + 7/3

d=(12x32+15x11+20x7) /60

d=(384+165+140) / 60

d=689 / 60

d=11.5 miles.

Therefore, the total distance  did she run is 11.5 miles.

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Answer:

x=8,3

Step-by-step explanation:

Move  

24  to the left side of the equation by adding it to both sides.

x 2−11x+24=0

Factor x2−1 1x+ 24

using the AC method.

(x−8)(x−3)=0

If any individual factor on the left side of the equation is equal to  

0 , the entire expression will be equal to 0

x−8=0   x−3=0

Set the first factor equal to  

0  and solve.

x =8

Set the next factor equal to  0  and solve.

x  = 3

The final solution is all the values that make  

( x− 8)(x−3)=0 true.

x =8,3

Solving:

Move constants to the left

[tex]x^2-11x=24\\[/tex]

write as a difference

[tex]x^2-11x+24=0[/tex]

factor

[tex]x^2-3x-8x-+24=0[/tex]

factor again

[tex]x(x-3)-8(x-3)=0[/tex]

separate

[tex](x-3)(x-8)=0[/tex]

solve all possible equations.

[tex]x-3=0\\x-8=0[/tex]

therefore, our answers are:

[tex]x=3,x=8[/tex]

Answer:

(See explanation for further details)

Step-by-step explanation:

A. [tex]x^{3} + 3\cdot x^{2} - 2\cdot x + 7[/tex] : V. Four terms.

B. [tex]3\cdot a \cdot b^{6}[/tex] : I . 9th Degree Monomial (Instead, 7th Degree Monomial)

C. [tex]3\cdot x^{4} - 9 \cdot x^{3} + 5\cdot x^{8}[/tex] : VII - Equivalent to [tex]5\cdot x^{8} + 3\cdot x^{4} - 9 \cdot x^{3}[/tex]

D. [tex]7\cdot a^{3}\cdot b^{2} + 18\cdot a \cdot b^{2}\cdot c - 9\cdot a^{3}[/tex] : III - 7th degree polynomial.

E. [tex]2\cdot x^{5} - 9\cdot x^{3} + 8\cdot x[/tex] : VI - 5th degree polynomial.

F. [tex]4\cdot x^{8} - 7\cdot x^{2} + 9[/tex] : IV - Leading coefficient of 4.

G. [tex]x^{2} - 7[/tex] : II - Constant term of -7.

Final answer:

Davide's age is determined by first calculating the total age of the four individuals and then subtracting the total age of the remaining three. With the given averages, Davide is found to be 10 years old.

Explanation:

The question asks us to find the age of Davide given that the average age of Aldo, Bruno, Carlo, and Davide is 16 years, but without Davide, the average age of the remaining three is 18 years.

First, we calculate the total age of all four by multiplying the average age by the number of people: 16 years × 4 = 64 years.

Next, we calculate the total age of Aldo, Bruno, and Carlo by multiplying the new average age by three: 18 years × 3 = 54 years.

Now, we can determine Davide's age by subtracting the total age of the three from the total age of all four: 64 years - 54 years = 10 years.

Therefore, Davide is 10 years old.

To calculate the surface area, the formula is the sum of the areas of all faces in a shape.

Back Prism:

1 base: 8 by 8.

4 lateral faces: 8 by 2.

One shared base: 64 – 32 = 32 square units.

Front Prism:

1 base: 8 by 4.

2 lateral faces: 8 by 2.

2 lateral faces: 2 by 4.

Therefore, one shared base: an area covered by another prism.

Total surface area: 240 square units.

A surface area is the outer part of the uppermost layer of something. This is known in maths as the amount of space covering the outside of a three-dimensional shape.

Hence, we can see that to calculate, the formula is the sum of the areas of all faces in a shape which sums up to 240 square units.

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Answer:

3.5, three-and-a-half, 7/2

Answer:

D

Step-by-step explanation:

There is more than one way to solve this; the easiest way is to plug in some numbers for x. We can see the roots are (3,0) and (7,0) and the lowest point is (5,0). So when we plug in 3 or 7, we should get zero.

B: (3-3)(3-7)=0

D: 3(3-3)(3-7)=0

So we have two possible solutions, So to check, let's find a point where we can easily find the y value.

When x is equal to 4,5, or 6, there is an integer value for y. so let's plugin 5:

(5-3)(5-7)=-4

We can see when x is five, y has to be -12, so that is not the answer, thus d is the final answer.

Answer:

The painting area is approximately 28980 years old.

Step-by-step explanation:

The model for the amount of carbon-14 after t years is given by:

[tex]A(t) = A(0)e^{-0.000121t}[/tex]

In which A(0) is the original amount.

The paint contained 3% of the original carbon-14.

This means that [tex]A(t) = 0.03A(0)[/tex]. This means that we have to find t.

[tex]A(t) = A(0)e^{-0.000121t}[/tex]

[tex]0.03A(0) = A(0)e^{-0.000121t}[/tex]

[tex]e^{-0.000121t} = 0.03[/tex]

[tex]\ln{e^{-0.000121t}} = \ln{0.03}[/tex]

[tex]-0.000121t = \ln{0.03}[/tex]

[tex]t = -\frac{\ln{0.03}}{0.000121}[/tex]

[tex]t = 28980[/tex]

The painting area is approximately 28980 years old.

Answer:

a) 256 m^2

Step-by-step explanation:

Area of a Trapezoid = (a+b)/2×h

*where a and b are the "top" and "bottom" lengths and h is the height

So: (13+19)/2×16= 32/2×16= 16×16 = 256 m^2

Answer:

i=-12

Step-by-step explanation:

1.) Add 10 to -82 to get the equation 6i=-72

2.) Divide -72 by 6 to get the answer i=-12

The question is missing informations. The complete question is:

Find the (a) mean, (b) median, (c) mode, and (d) midrange for the given sample data. An experiment was conducted to determine whether a deficiency of carbon dioxide in the soil affects the phenotype of peas. Listed bellow are the phenotype codes where 1 = smooth-yellow, 2 = smooth-green, 3 = wrinkled-yellow and 4 = wrinkled-green. Do these results make sense?

4 3 3 1 3 4 1 1 1 4 2 3 1 1

(a) The mean phenotype code is _____

(b) The median phenotype code is _____

(c) Select the correct choice bellow and fill in any answer boxes within your choice

(A) The mode phenotype code is ___

(B) There is no mode

(d) The midrange of the phenotype code is ___

Do the measures of center make sense?

A. Only the mode makes sense since the data is nominal.

B. All the measures of center make sense since the data is numerical

C. Only the mean, median and midrange make sense since the data is nominal

D. Only the mean, median and midrange make sense since the data is numerical.

Answer: (a) mean = 2.285

(b) median = 2.5

(c) A) The mode phenotype code is 1

(d) midrange = 2.5 and A. Only the mode makes sense since the data is nominal.

Step-by-step explanation: Mean and Median are the average value of a data set, however, median is the value in the middle of the set while mean is the average value a data set must be if all the values were the same.

(a) To calculate mean:

mean = [tex]\frac{4+3+3+1+3+4+1+1+1+4+2+3+1+1}{14}[/tex]

mean = 2.285

(b) To find median: The set has an even number of elements (14), so, in this case, to determine the middle term:

median = [tex]\frac{7th + 8th}{2}[/tex]

median = [tex]\frac{2+3}{2}[/tex]

median = 2.5

(c) Mode is the value which has the highest frequency. For this data set, mode = 1, since the number 1 appears 6 times.

Mode = 1

(d) Midrange is the average of the smallest and largest on the set.

midrange = [tex]\frac{1+4}{2}[/tex]

midrange = 2.5

Nominal variable is a type of variable used to name, categorize or label attributes that are being measured. Mode is the most common used measure of central tendency and with it, it is possible to determine if the set is unimodal (one mode) or multimodal (two or more modes). In conclusion, mode makes sense because data is nominal.

The mean, median, and midrange of the given phenotype codes are all 2.5.

1. Mean

The mean is the average of the data set. We sum all the phenotype codes and divide by the number of observations.

2. Median

The median is the middle value of an ordered data set. For an even number of observations, it's the average of the two middle values.

3. Mode

The mode is the value that occurs most frequently. Here, each code appears only once, so there is no mode.

4. Midrange

The midrange is the average of the highest and lowest values in the data set.

Since each code represents a distinct phenotype, the measures provide a way to summarize the data set but don't hold biological significance independently. They mainly help to understand the distribution of phenotype observations numerically.

Answer:

In order for the statement to be true, the value of x has to be 19.

Step-by-step explanation:

3(x - 3) - 16 = 2(x - 8) + 10

3x - 9 - 16 = 2x - 16 + 10

3x - 25 = 2x - 6

x - 25 = - 6

x = 19

Answer:

b) 19

Step-by-step explanation:

Let's solve the problem,

→ 3(x - 3) - 16 = 2(x - 8) + 10

→ 3x - 9 - 16 = 2x - 16 + 10

→ 3x - 25 = 2x - 6

→ 3x - 2x = -6 + 25

→ [ x = 19 ]

Hence, option (b) is correct.

Answer:

The weight of pears is 3.08 kg

Step-by-step explanation:

A farmer sells 7.7 kilograms of apples and pears.

3/5 of this weight is apples.

This means that the weight of apples is:

3/5 of 7.7

=> [tex]\frac{3}{5} * 7.7 = 4.62kg[/tex]

The weight of apples is 4.62 kg.

The weight of pears will therefore be:

[tex]7.7 - 4.62 = 3.08 kg[/tex]

The weight of pears is 3.08 kg.

Answer: People will pay about $5 for a ticket if 50 are sold.

Step-by-step explanation:

What we can deduce from this graph is the more expensive the tickets are, the less tickets are sold.

So far, the greatest number of tickets sold are 40 with a price of around $10.

Now, if people were to sell 50 tickets, following with the graph, it

would mean that the price would have to be less than 10.

Only one of the options is less than 10, and that is 5, so therefore, the answer is 5.

Answer:

∠AGB and ∠EGD are vertical angles.

∠DGC and ∠CGB are supplementary angles.

m∠EGD = 30

m∠AGF = 50

m∠EGF = 100

Step-by-step explanation:

Answer:

veryical

Step-by-step explanation:

Answer:

-2097152

Step-by-step explanation:

(-8)(-8)(-8)(-8)(-8)(-8)(-8) =

-2097152

Answer: -2097152

Step-by-step explanation:

(-8)(-8)(-8)(-8)(-8)(-8)(-8)=

(-8)^7

=-2097152

Answer:

1 1/2 cups

Step-by-step explanation:

2/4 = 1/2

(1/2) cups * 3 =  1.5 cups

Answer:

1 1/2 or 3/2 cups of flour

Step-by-step explanation:

2/4 + 2/4 + 2/4= 6/4

to simplify:

divide 6/4 by 2/2 to get 3/2

3/2 =1 1/2

Answer:

For this case we are trying to proof if the mean number of sick days this year is different from the mean number of sick days last year (10.6 days). And that would represent the alternative hypothesis. And the complement would represent the null hypothesis.

Then the system of hypothesis are:

Null hypothesis: [tex]\mu =10.6[/tex]

Alternative hypothesis: [tex]\mu \neq 10.6[/tex]

And the best option would be:

H0:μ=10.6Ha:μ≠10.6 B

Step-by-step explanation:

For this case we are trying to proof if the mean number of sick days this year is different from the mean number of sick days last year (10.6 days). And that would represent the alternative hypothesis. And the complement would represent the null hypothesis.

Then the system of hypothesis are:

Null hypothesis: [tex]\mu =10.6[/tex]

Alternative hypothesis: [tex]\mu \neq 10.6[/tex]

And the best option would be:

H0:μ=10.6Ha:μ≠10.6 B

And the data from the sample is:

[tex]\bar X = 12.9[/tex] represent the sample mean

[tex]n =40[/tex] the sample size

Answer: 8 senior tickets, 12 normal tickets.

Step-by-step explanation:

You can find the answer to this by creating two equations: one for the amount of tickets sold and the other for how much money was collected.

I will represent the variables as A for normal tickets and C for senior tickets.

[tex]A + C = 20\\12A + 6C = 192[/tex]

To solve this, you can solve for one of the variables. I will solve for A in the first equation:

[tex]A = 20-C\\12A + 6C = 192[/tex]

Then, you can substitute the new value of A in the second equation:

[tex]12(20-C) + 6C = 192\\240-12C+6C=192\\240-6C=192\\-6C=-48\\C=8[/tex]

Knowing that there were 8 senior tickets sold and 20 tickets sold total, we know that there were 12 normal tickets sold.

Answer:63.6 units

Step-by-step explanation:

Theta=90°

Radius =9

area of sector=(theta)/360 x π x r x r

area of sector=90/360 x 3.14 x 9 x 9

area of sector=(90x3.14x9x9)➗360

area of sector=22890.6 ➗ 360

area of sector=63.535

area of sector=63.6 approximately

Answer:

It's 63.62

Step-by-step explanation:

Answer:

The weight of a box is 10 kg.

Step-by-step explanation:

Weight of each book is 2 kg

So, the weight of 3 books is 6 kg.

Weight of a container is 4 kg

3 books and one container is in a box. We need to find the weight of the box.

It is equal to the sum of weights of 3 books and one container. So,

Total weight = 6 kg + 4 kg

W = 10 kg

So, the weight of a box is 10 kg.

Answer: 45

Explanation: Remember that dividing by a fraction is the same thing as multiplying by the reciprocal of that fraction or that fraction flipped.

Also, think of the 15 in this problem as 15/1.

So we can rewrite 15/1 ÷ 1/3 as 15/1 · 3/1.

Multiplying across the numerators and the denominators,

we find that our answer is 45/1 or just 45.

15 divided by 1/3 is equal to 45.

To divide 15 by 1/3, we can interpret it as finding how many groups of 1/3 can be made from 15.

To begin, we can convert the division of 15 by 1/3 into a multiplication problem by taking the reciprocal of 1/3, which is 3/1 or simply 3.

So, we have:

15 ÷ (1/3) = 15 x 3

Multiplying 15 by 3, we get:

15 x 3 = 45

Therefore, 15 divided by 1/3 is equal to 45.

In other words, 15 can be divided into 45 equal parts of size 1/3. Each of these parts represents the quotient when dividing 15 by 1/3.

When we multiply 1/3 by 45, we get 15. This confirms that 15 divided by 1/3 is indeed equal to 45.

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Answer: 21

Step-by-step explanation: If you lost the numbers in order from creates to least, and cross the least and the greatest the number in the middle or median is 21

Answer:

All of them

Step-by-step explanation:

Answer:

A,B,C,D,E,F

Step-by-step explanation:

to sum it up all of them !

Answer:

if its length then its cm

if its area then its cm²

if its volume then its cm³

Step-by-step explanation:

Answer: 3/5

Step-by-step explanation: The fourth quadratic in the list is the square of a binomial:

25x^2 - 30x + 9 = (5x - 3)^2

Therefore, the repeated root of this quadratic is the solution to 5x - 3=0, which is 3/5

First we have to figure out how much 3 bags cost using the total cost of $8.25

That means. we would do 8.25/3 and 8.25 divide by 3 equals 2.75.

Now we know that each bag costs approximately $2.75

All we have to do now is multiply 2.75 by 4 to get the cost for the total of 4  bags.

4 times 2.75 is exactly 11 dollars, if might change if theres tax.

But, the answer would be 4 bags costs $11.

Answer:

6

Step-by-step explanation: