Sofia reads 8 books over summer break. Her brother reads 3 fewer books than she reads. How many books do Sofia and her brother read in all? They read books in all. ​

The solution of the sequence aₙ = −6aₙ₋₁− 5aₙ₋₂ for n ≥ 3 with the initial conditions is a₂ = -316

From the question, we have the following sequence that can be used in our computation:

aₙ = −6aₙ₋₁− 5aₙ₋₂ for n ≥ 3

Also, we have the initial conditions of the sequence to be

aₙ = 28 and a₁ =−76

The above parameters imply that we set the value of the variable n to 2 in the equation aₙ = −6aₙ₋₁− 5aₙ₋₂

So, we have the following representation

a₂ = −6a₂₋₁− 5a₂₋₂

Evaluate the difference in the above equation

So, we have the following representation

a₂ = −6a₁− 5aₙ

Substitute the known values in the above equation, so, we have the following representation

a₂ = −6 * 76− 5 * -28

Evaluate the expression

a₂ = -316

Hence, the solution is a₂ = -316

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A. The area of the triangle is 108 mm².

B. The area of parallelogram is 286√2 in²

A. Area of a triangle (A) = 1/2 * Base (b) * Height (h)

We have:

b = 18 mm

h = 12 mm

Thus:

A = 1/2 * 18 * 12

A = 108 mm²

B. The area of parallelogram is given by:

A = b * h

where b is the base and h is the height

We have:

b = 26 in

Using trig.:

sin 45 = h/22

h = 22 * sin 45

h = 11√2 in

Thus,

A = 26 * 11√2

A = 286√2 in²

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Answer:4

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Each pound is equal to 3 of the 1/3 pound patties

multiply 3 by 4 and you get 12.

Answer:

The answer for this promblem is 11

Step-by-step explanation:

Because 11 plus 6 is 17 which is not less than 14.

Answer: The answer is 11

Step-by-step explanation: The answer is 11 because the question clearly states which is NOT in the solution set of x + 6 < 14

Answer:

Area = 4x^2 + 12x + 9

Perimeter = 8x + 12

Step-by-step explanation:

Answer:

h>-21

Step-by-step explanation:

So, you solve it like an equation, so you do -7 divided by -1/3

which is

and since you divided it by a negative, you switch the sign.

Answer:

  angle 1 = 108°

Step-by-step explanation:

You want the measure of angle 1, given the measure of angle 4 is 72° in the diagram.

Angles 1 and 4 are a linear pair, so are supplementary:

  angle 1 + angle 4 = 180°

  angle 1 + 72° = 180°

  angle 1 = 108° . . . . . . . subtract 72°

Answer:

a. 8

Step-by-step explanation:

1+1 = 2

1+2 = 3

2+3 = 5

3+5 = 8

Answer:

16.1 cm (nearest tenth)

Step-by-step explanation:

Pythagoras’ Theorem

\(a^2+b^2=c^2\)

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Given:

Substitute the given values into the formula and solve for c:

\(\implies 16^2+2^2=c^2\)

\(\implies 256+4=c^2\)

\(\implies c^2=260\)

\(\implies c=\sqrt{260}\)

\(\implies c=2\sqrt{65}\)

\(\implies c=16.1 \sf \: cm\:(nearest\:tenth)\)

16.1 is rounded to the nearest tenth

Answer:

1/26

Step-by-step explanation:

'or' in the question means add

theres only 1 card that is 10 of spades

and

theres only 1 card that is four of diamonds

1/52 + 1/52 = 2/52 = 1/26

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Answer:

Exponents are important in math because they allow us to abbreviate something that would otherwise be really tedious to write. If we want to express in mathematics the product of x multiplied by itself 7 times, without exponents we'd only be able to write that as xxxxxxx, x multiplied by itself 7 times in a row.

Step-by-step explanation:

Answer:

x=−3.207703,−1.142291,2.183328

Step-by-step explanation:

x−6x3−13x2+34x+48=0

−6x3−13x2+35x+48=0

1. Use cubic formula.

x=−3.207703,−1.142291,2.183328

The length of side CB to one decimal place is 89.3.

To find the length of side CB in the given triangle, we can use the sine rule. The sine rule states that in a triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

In this case, we have the angle C as 53° and the side opposite to it, side CB, as the unknown. Let's denote the length of side CB as x.

According to the sine rule:

sin(C) / x = sin(A) / AB

We know that angle A is 37° and AB is 120 units. Plugging in the values:

sin(53°) / x = sin(37°) / 120

To find x, we can rearrange the equation:

x = (120 * sin(53°)) / sin(37°)

Calculating this expression gives us:

x ≈ 89.32

Rounding this value to one decimal place, the length of side CB is approximately 89.3.

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Answer:

1   1/5

Step-by-step explanation:

yw

The set (A U B) n (A U C) is {2, 5, 7, 10}. A.

To find the set (A U B) n (A U C), we first need to calculate the union of sets A and B, and then calculate the union of that result with set C. Finally, we find the intersection of these two sets.

Set A U B:

The union of sets A and B, denoted as A U B, is the combination of all elements from both sets without any repetitions.

A contains the elements 2, 5, 7, and 10, while B contains the elements 1, 2, and 3.

A U B consists of the elements {1, 2, 3, 5, 7, 10}.

Set (A U B) U C:

Next, we calculate the union of the set (A U B) with set C, denoted as (A U B) U C. A U B contains the elements {1, 2, 3, 5, 7, 10} and C contains the elements {1, 2, 3, 4, 5}.

Taking the union of these two sets results in {1, 2, 3, 4, 5, 7, 10}.

Finding the intersection:

Finally, we find the intersection of (A U B) U C with A U C. A U C consists of the elements {2, 5, 7, 10}.

The intersection of these two sets is the combination of common elements.

The common elements are {2, 5, 7, 10}.

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The initial investment of the function is 20 dollars.

The rate growth in percentage is 4%.

The investment after 10 years is 29.6 dollars.

The function \(y=20(1.04)^{t}\) represents the value y of a saving account after t years.

Therefore, the initial investment of the function is 20 dollars.

The rate growth in percentage can be calculated as follows;

rate growth in percent = 0.04 × 100

rate growth in percent = 4 %

Let's find the value of the investment after 10 years.

Therefore,

\(y=20(1.04)^{t}\)

t = 10

\(y=20(1.04)^{10}\)

\(y=20(1.48024428492)\)

y = 29.6048856984

Therefore, the investment after 10 years is as follows:

y = 29.6 dollars

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The total distance covered by Jeremy is 1320 m

What is a line segment ?

A line segment in geometry is bounded by two separate points on a line. Another way to describe a line segment is as a piece of the line that joins two points. A line segment has two fixed or distinct endpoints while a line has no endpoints and can stretch in both directions indefinitely.

For sapling 1 = No distance is covered.

For sapling 2, distance covered = 10 m

Return distance=10 m

For sapling 3, distance covered =20 m

Return distance=20 m and so on

Thus the distances covered for saplings can be represented as : 0,2(10), 2(20),...i.e. 0,20, 40,...

Therefore total distance covered by Jeremy for planting 12 saplings and coming back to original position = S 12

Total distance covered = 122 [2(0) + (12 − 1) 20 ]

Total distance covered = 6 (11)(20) = 1320 m

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Complete question:

There are 12 saplings to be planted in a straight line at an interval of 10 m between

two consecutive saplings. Jeremy can carry only one sapling at a time and he has to

come back to the original point to take the next sapling. He plants 12 saplings in this

manner, planting the first sapling at the original point. After planting all the saplings,

he comes back at the original point,

In the process, what is the total distance that Jeremy covers?

​

Answer:

The difference between the first and second friends' total earnings is $154.

BRAINLIEST, PLEASE!

Step-by-step explanation:

32 x $17 = $544

26 x $15 = $390

$544 - $390 = $154

Answer:  NONE

Step-by-step explanation:

Consider that m is the degree of the numerator and n is the degree of the denominator.

The rules for horizontal asymptote (H.A.) are as follows:

If m > n   then no H.A. (use long division to find the slant asymptote)

If m = n   then H.A. is y = leading coefficient of numerator/leading coefficient of denominator

If m < n   then H.A. is y = 0

Given: g(x) = 5x⁵/(x³ - 2x + 1)

--> m = 5, n = 3

Since m > n then there is no H.A.

Another way to write the compound inequality is 2 ≤ y+3 < 6. The 1st option is the answer

An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g 2x > 4

Given: y + 3 ≥ 2 and y + 3 < 6

To write these in another way, change the inequality sign of one of the inequalities by rearranging. That is:

y + 3 ≥ 2 can be rewritten as 2 ≤ y+3. Thus, we have:

2 ≤ y+3 and y + 3 < 6

Combine the two:

2 ≤ y+3 < 6

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Answer:

The value of \(\frac{14}{8} + \frac{15}{12}\)  = 3

Step-by-step explanation:

Explanation

Given       \(\frac{14}{8} + \frac{15}{12}\)

L.C.M     8 , 12   is  24

       \(\frac{14}{8} + \frac{15}{12} = \frac{14 X 3 + 15 X 2}{24}\)

                  = \(\frac{42 +30}{24} = \frac{72}{24} = 3\)

Final answer:-

The value of \(\frac{14}{8} + \frac{15}{12}\)  = 3

Answer:

50 feet

Step-by-step explanation:

Set up a 3-dimensional coordinate system (see the attached image).

This setup shows an axis that runs North-South (South is negative, North is positive), an axis that runs East-West (East is positive, West is negative), and an axis that runs Up-Down (Up is positive, Down is negative).

The two points in question are then:

First person's location (12, -20, -12), and the second person's location is (-20, 10, 12).

The distance between two points  \(\left( x_1,\,y_1,\,z_1\right)\)  and  \(\left( x_2,\,y_2,\,z_2\right)\) is

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2\)

\(d=\sqrt{(-20-12)^2+(10-(-20))^2+(12-(-12))^2}\\\\d=\sqrt{(-32)^2+30^2+24^2}\\\\d=\sqrt{2500}\\\\d=50\)

Answer:

3

Step-by-step explanation:

Given the data :

2, 3, 7, 8, 9, 13

2 5

3 4

7 0

8 1

9 2

13 6

The mean, = Σx / n ; n = sample size

Mean = 42 / 6 = 7

The mean absolute deviation = Σ|x - mean| / n

The mean absolute deviation is Hence,

(5 + 4 + 0 + 1 + 2 + 6) / 6

Mean absolute deviation = 18 / 6

Mean absolute deviation = 3

We can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the left foot is longer than the right foot.

A statistical test is required to determine whether the length of the left foot is greater than the length of the right foot. The null hypothesis states that there is no difference in average length between the left and right feet. The alternative hypothesis is that the left foot's average length is greater than the right foot's average length.

This hypothesis is one-tailed, as we are only interested in whether the left foot is longer than the right foot. We are not considering the possibility that the right foot could be longer than the left foot.

A t-test can be used to determine whether the difference in average length between the left and right feet is statistically significant. We can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the left foot is longer than the right foot if the p-value of the t-test is less than the chosen significance level (e.g., 0.05).

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By using probability, it can be calculated that-

Probability that the next chew Gianna removes from the bag will be cherry chew = 42.86%

What is probability?

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probability of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

Here, number of times an experiment is performed = 49

A pineapple chew was selected 25 times.

A cherry chew was selected 21 times.

A lime chew was selected 3 times.

Probability that the next chew Gianna removes from the bag will be cherry chew = \(\frac{21}{49} = \frac{3}{7}\)

         = \(\frac{3}{7} \times 100\)

         = 42.86%

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Answer:

Step-by-step explanation:

We can factor out 2 to give us 2(2mn+n)

Answer:

the even number is two

Step-by-step explanation:

the box with the question mark has the two while the one without a question mark is one which is an odd number. when 2 multiplies 1, it gives 2

Answer:

(a) 1/6. One out of six sides will give you the desired result.

(b) 3/6. 3 out of 6 sides will give you the desired result.

(c) 2/3. 4 out of 6 sides will give you the desired result.