Solve BCD. Round the answers to the nearest hundredth, if necessary.

Answer:

Step-by-step explanation:

The equation for an arithmetic sequence is

[tex]a_n=a_1+d(n-1)[/tex]  where n is the position of the number in the sequence, a1 is the first number in the sequence, and d is the difference between the numbers in the sequence.

Our first number is 2, so a1 = 2; to get from 2 to 5 we add 3, to get from 5 to 8 we add 3. That means that d = 3. Filling in the standard form of the equation:

[tex]a_n=2+3(n-1)[/tex] which simplifies to

[tex]a_n=2+3n-3[/tex] and a bit more to

[tex]a_n=3n-1[/tex] (which should tell you that arithmetic sequences are lines!)

Finding the 13th number simply requires that we replace n with 13 and solve:

[tex]a_{13}=3(13)-1[/tex] so

[tex]a_{13}=38[/tex]

Answer:

38

Step-by-step explanation:

This isn't the most efficient way but it's the best I can do.

2, 5, 8, 11....

The pattern is that we add 3 every time.

2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38,

1 , 2, 3, 4, 5,  6,   7,    8,    9,   10,  11,   12,  13

We can see that 38 is the 13th term of the sequence.

Answer:

[tex]x = 10\\y = 5[/tex]

Step-by-step explanation:

1. Approach

The easiest method to solve this problem is to use the side ratios in a special right triangle. One should start by proving that the triangle is a (30 - 60 - 90) triangle. Since the problem gives on the information that one of the sides has a measure of ([tex]5\sqrt{3}[/tex]), one can use this combination with the ratio of the sides in a special right triangle, to find the unknown side lengths.

2. Prove this triangle is a (30 - 60 - 90) triangle

One is given a right triangle. This means the triangle has a (90) degree or right angle in it. This is indicated by a box around one of the angles. One is given that the other angle in this triangle has an angle measure of (30) degrees. The problem asks for one to find the third angle measure. A property of any triangle is that the sum of angle measures in the triangle is (180) degrees. One can use this to their advantage by stating the following:

[tex](90) + (30) + (unknown) = 180\\[/tex]

Simplify,

[tex](90) + (30) + (unknown) = 180[/tex]

[tex]120 + unknown = 180\\[/tex]

Inverse operations,

[tex]120 + unknown = 180\\[/tex]

[tex]unknown = 60[/tex]

Thus, this triangle is a (30 - 60 - 90) triangle, as its angles have the measures of (30 - 60 - 90).

3. Solve for (y)

The sides ratio in a (30 - 60 - 90) triangle is the following:

[tex]n - n\sqrt{3} - 2n[/tex]

Where (n) is the side opposite the (30) degree angle, ([tex]n\sqrt{3}[/tex]) is the side opposite the (60) degree angle and finally (2n) is the side opposite the (90) degree angle. The side (y) is opposite the (30) degree angle. This means that it is equal to the side opposite the (60) degree angle divided by ([tex]\sqrt{3}[/tex]). Therefore, one can state the following:

[tex]\frac{5\sqrt{3}}{\sqrt{3}}=y\\5=y[/tex]

4. Solve for (x)

Using the same thought process one used to solve for side (y), one can solve for side (x). The side (x) is opposite the (90) degree angle, hence, one can conclude that it is twice the length of the side with the length of (y). Therefore, one can state the following:

[tex]x = 2y\\x = 2(5)\\x = 10[/tex]

Answer:

The Average annual return is:

= 10%.

Step-by-step explanation:

a) Data and Calculations:

Year        Stock Returns

Year 1                 -4%

Year 2             +28%

Year 3              +12%

Year 4              + 4%

Total returns = 40%

Average annual returns = 10% (40%/4)

b) The average annual return is computed as the total returns for the four years divided by 4.  It shows that on the average, the return earned per year from the stock investment is 10%, during the four-year period.  It is the mean of the total returns.

Answer:

10

Step-by-step explanation:

The altitude of a graph is displayed as the square root of the two parts of the hypotenuse multiplied together. Over here, the two values are 5 and 15. That means the altitude of the graph is the square root of 5 times 15, which means the altitude of the bigger triangle is equal to the square root of 75. Now, we can use the Pythagorean theorem on the smallest triangle to figure out the value of x. We have:

[tex]5^2+(\sqrt{75})^2=x^2[/tex]

5 squared is 25 and the square root of 75 squared is 75.

[tex]25+75=x^2[/tex]

Combining like terms:

[tex]100=x^2[/tex]

Taking the square root of both sides:

[tex]10=x[/tex]

The value of x is 10.

Answer:

the answer is the number 6

Answer:

1.774 standard deviations

Step-by-step explanation:

From the data, the minimum value is x = 13 and the maximum value is x' = 18. The mean X = 15.75 and the standard deviation, σ = 1.55.

The difference between the mean and the minimum value is the deviation from the mean. So, X - x = 15.75 - 13 = 2.75. To find the number of standard deviations this is, we divide it by the standard deviation, σ = 1.55.

So, 2.75/1.55 = 1.774.

So, the number of standard deviations to contain the value 13 is 1.774σ

Also, the difference between the maximum value and the mean is the deviation from the mean. So, x' - X = 18 - 15.75 = 2.25. To find the number of standard deviations this is, we divide it by the standard deviation, σ = 1.55.

So, 2.25/1.55 = 1.452.

So, the number of standard deviations to contain the value 18 is 1.452σ

Since 1.774σ > 1.452σ and 1.774σ would contain both the values of 13 and 18, the number of standard deviations from the mean required to contain the values is  1.774 standard deviations.

Answer:

2x^2 + 9x - 4

18x^2 - 3x - 10

Step-by-step explanation:

use foil method

Image of figure ABCD is missing and so i have attached it.

Answer:

D_new = (-1, - 12)

Step-by-step explanation:

From the figure attached, the current coordinates of D are; (-5, -2)

Now, we are told the figure undergoes a translation of (x,y) (x+6,y-10)

Thus, this means we add 6 to the x value and subtract 10 from the y-value.

Thus, new coordinate of D is;

> (-5 + 6, -2 - 10)

> (-1, - 12)

Answer:

1, -12

Step-by-step explanation:

D = -5, -2

|

-5 + 6 = 1

|

-10 and -2 is -12

1, -12

did it on edge, got it right.

Answer:

Hi!

Step-by-step explanation:

-5 (x-3) + 3(4 - x) + 2x

Let's distribute the -5 within its parentheses.

A negative multiplied by a negative number has a positive result.

Let's distribute the 3 within its parentheses.

-5x+15+12-3x+2x

Combine like terms...

-5x-3x+2x=-6x

15+12=27

-6x+27

Both numbers are divisible by 3...

3(-2x+9)

or -3...

-3(2x-9)

Answer:

65 degrees because tangent chord angles are half the size of the arc

Answer:

Step-by-step explanation:

xy-3x-5y+15

x(y-3)-5(y-3)

(y-3)(x-5)

Answer:

130.81

Step-by-step explanation:

Given that :

Mean, μ = 100

Standard deviation, σ = 15

To obtain the upper 2% of scores :

We find the Zscore (value) of the upper 2% from the normal probability distribution table ;

Zscore corresponding to the area in the left of (1 - 0.02) = 2.054

Using this with the Zscore formula :

Zscore = (x - μ) / σ

2.054 = (x - 100) / 15

2.054 * 15 = x - 100

30.81 = x - 100

30.81 + 100 = x

x = 130.81

Answer:

-4m/s²

Step-by-step explanation:

Given Equation of velocity :-

Differenciation of first order will give acclⁿ :-

At t = 0 ,

Answer: First Choice. 3 ( x - 5 )

Step-by-step explanation:

Concept:

When we are doing factoring, we should try to find any Greatest Common Factor (GCF) of all constants in the given expression.

The Greatest Common factor is the largest value of the values you have, that multiplied by the whole number is able to "step onto both".

Solve:

Factors of 3: 1, 3

Factors of 15: 1, 3, 5, 15

As we can see from the list above, 3 appears in both lists of factors and is the greatest for 3. Therefore, [3] is the GCF of 3 and 15

Divide 3 for both numbers to find the remaining.

Check whether or not the remaining can be divisible

Put the factored out 3 and remaining together

Hope this helps!! :)

Please let me know if you have any questions

Answer:

x=19.86

Step-by-step explanation:

use cosine,

cos 19°=x/21

x=cos 19° * 21

x=19.86

Answer:

C. 4(x + y)

Step-by-step explanation:

Use the distributive property.

4(x + y) = 4x + 4y

Answer:

C. 4(x + y)

Step-by-step explanation:

If you multiply this answer out (4 times x and 4 times y) it is the equivalent to 4x + 4y.

Answer:

m = negative StartFraction 10 over 4 EndFraction

m = negative five-halves

Step-by-step explanation:

Given equation :

Which equations are equivalent to Three-fourths + m = negative StartFraction 7 over 4 EndFraction

3/4 + m = - 7/4

Subtracting 3/4 from both sides

3/4 + m - 3/4 = - 7/4 - 3/4

m = - 10/4

m = - 5/2

Answer:

Point C

Step-by-step explanation:

We want to reflect across the x axis

That means the y coordinate changes sign

Z = ( 5 1/2 , 3)

Z' = ( 5 1/2 , -3)

That is point C

Answer:

hope this might help you

Answer:

65

Step-by-step explanation:

because

Answer:

1st coin:  the probability for it to be a nickel is 6/29.

the 2nd coin, the probability for it to be a dime is 8/28.

total probability is 6/29 * 8/28 = 14/203.

Answer:

B

Step-by-step explanation:

If you plug in x=1, then you get that f(1)=5, meaning that (1, 5) is a point on the graph.

Since graph B has the only line that passes through (1, 5), it must be the answer.

Answer:

assuming that it is  [tex](1/3)^{6}[/tex] that would be

  [tex]\frac{1}{729}[/tex]

Step-by-step explanation:

Answer:

rs 90

Step-by-step explanation:

10% discount means that you multiply the initial amount by 1-0.1. Therefore, since 0.9 x 100 is 90, you will pay rs 90

Answer: Rs 90

Explanation:

Marked Price - Rs 100

Discount = 10%

= 10/100×100

= Rs 10

Therefore after discount (100-10) = 90

The customer will pay Rs 90

Answered by Gauthmath must click thanks and mark brainliest

Answer:

Step-by-step explanation:

change in x (horizontal) = 4 - 1 = 3

Change in y (vertical)  = 9 - 3 = 6

Slope = change in x / change in y

slope = 3 / 6 = 1/2

Answer:

it should be the third option

Step-by-step explanation:

I hope this help

Answer:

40

Step-by-step explanation:

here

3200/80

1600/40

800/20

400/10

40

Answer:

Step-by-step explanation:

-(--4,5)= -(4,5)= -4,5

Answer:

A.

–2; –250; –156,250

Step-by-step explanation:

A(1) = -2 x 5(1) - 1 = -11

A(4) = -2 x 5(4) -1 = -41

A(8) = -2 x 5(8) -1 = -81

...............................................................................................................................................

an=a1(r)^(n-1)

a1=first term

r=common ratio

n=which term

so

an=-2(5)^(n-1)

first term is -2

4th term is subsitue 4 for n

a4=-2(5)^(4-1)

a4=-2(5)^3

a4=-2(125)

a4=-250

4th term is -250

--------------------------

8th term

a8=-2(5)^(8-1)

a8=-2(5)^7

a8=-2(78125)

a8=-156250

8th term is -156250

...............................................................................................................................................

A(1)=2*5^1-1=2*5^0=2*1=2

a(4)=2*5^4-1=2*5^3=2*125=250  

a(8)=2*5^8-1=2*5^7=2*78,125=156,250

...............................................................................................................................................

2, 250, 156, 250