Suppose you have $50 in a savings account and deposit an additional $10 each week.
a) Write a recursive formula to represent the sequence.
b) Write an explicit formula to represent the sequence.
c) How much money do you have in savings after 26
weeks? Show all work.​

Answer: yes it is rational because it’s not within a square root symbol

Step-by-step explanation:

Answer the answer is a

The value of B using Sine law is approximately 41.7 degrees.

To use the sine law to find angle B, we need to have either the length of side b or the sine of angle B. However, we can use the sine law to set up an equation involving sine B and then solve for it.

the sine law states:

a/sin A = b/sin B = c/sin C

where a, b, and c are the lengths of the sides of a triangle, and A, B, and C are the opposite angles.

In this case, we are given a = 28.82 ft, c = 47.74 ft, and we want to find B. We can set up the following equation using the sine law:

a/sin A = c/sin C

Substituting the given values:

28.82/sin A = 47.74/sin C

Now, we need to find sin A and sin C. Since the angles in a triangle add up to 180 degrees, we have:

A + B + C = 180

We know that A and C are the angles opposite to sides a and c, respectively, so we can use the sine ratio to express them in terms of a and c:

sin A = a/cos B

sin C = c/cos B

Substituting these expressions into the equation above, we get:

28.82/(a/cos B) = 47.74/(c/cos B)

Simplifying and solving for cos B, we get:

cos B = (28.82 * c) / (a * 47.74)

Now that we know cos B, we can use the identity sin^2 B + cos^2 B = 1 to find sin B:

sin B = sqrt(1 - cos^2 B)

Substituting the given values, we get:

sin B = sqrt(1 - ((28.82 * 47.74) / (a * c))^2)

Calculating this expression gives:

sin B = 0.667

Therefore, angle B is:

B = sin^-1(0.667) = 41.7 degrees (rounded to one decimal place)

So, angle B is approximately 41.7 degrees.

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_____The given question is incomplete, the complete question is given below:

If c = 47. 74 ft and a = 28. 82 ft, find B using sine law.

For the given congruence triangle:

Congruent triangles are triangles that are precisely the same size and shape. The word congruent has the sign. When the three sides and three angles of one triangle match the same dimensions as the three sides plus three angles of another triangle, two triangles are said to be congruent.

For the given data:

Statement                                  Reasons

U is the midpoint of ST             Given

SV  ≅ TW                                   Given

VU ≅ WU                                  Given

SU = UT                                    U is the midpoint of ST

ΔSUV ≅ ΔTUW                         By Side Side Side (SSS) congruence

∠SVU  ≅  ∠TWU                       BY CPCT

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Answer:

6 and 2/3 feet

Step-by-step explanation:

1 feet=12 inches

x feet=80 inches

80/12=6 and 2/3 feet

At the end of 7 years:

a. The man received approximately GHZ 6425.13 as interest.

b. The total amount received by the man is approximately GHZ 22,294.80.

The interest for the first 4 years at 3% compound interest:

Principal amount (P) = GHZ 14,100.00

Rate of interest (R) = 3% = 0.03

Time period (T) = 4 years

The formula for compound interest:

[tex]A = P (1 + R)^T[/tex]

A = 14,100 x (1 + 0.03)⁴

A = 14,100 x (1.03)⁴

A ≈ GHZ 15,869.67

Interest for the first 4 years = A - P

Interest = 15,869.67 - 14,100

Interest ≈ GHZ 1769.67

The total amount at the end of 7 years at 12% per annum:

(P) = GHZ 15,924.57

(R) = 12% = 0.12

(T) = 3 years (remaining 7 years - initial 4 years)

A = 15,869.67(1 + 0.12)³

A = 15,869.67(1.12)³

A ≈ GHZ 22,294.80

a. Interest for the remaining 3 years = A - P

Interest = 22,294.80 - 15,924.57

Interest ≈ GHZ 6425.13

b. Total amount received at the end of 7 years = Principal amount + Interest for 4 years + Interest for 3 years

Total amount = 14,100 + 1769.67 + 6425.13

Total amount ≈ GHZ 22,294.80

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Answer:

Now: Carolyn 18 yo, Alfred 12 yo

Step-by-step explanation:

Use X represent Alfred's age now, then Carolyn's age is (X+6)

6 years ago, their ages should be current age minus 6. So Alfred's age was (X-6), Carolyn's age was ((X+6)-6).

As 6 years ago, Carolyn's age was twice as Alfred's. So

((X+6)-6)=(X-6)×3

X=12 which is Alfred' current age

X+6=18 which is Carolyn' current age

Answer:

  10

Step-by-step explanation:

You want the determinant of the matrix ...

  [tex]\left[\begin{array}{cc}1&-2\\3&4\end{array}\right][/tex]

The determinant of a matrix is a sum of products. Each product is the element of a row or column multiplied by its cofactor.

For a 2×2 matrix, this becomes the difference between the product of diagonal terms and the product of off-diagonal terms:

  (1·4) - (3·(-2))

  = 4 +6

  = 10

__

Additional comment

The cofactor of term a[i, j] is (-1)^(i+j)·det(M[i,j]), where M[i,j] is the minor matrix obtained by removing row i and column j from the original. As you can see, this definition of a determinant is recursive.

The above describes the determinant of a 2×2 matrix. The determinant of a 3×3 matrix resolves to a sum of 6 3-element products. For larger matrices, the computation burden can be reduced by taking advantage of rows or columns containing zeros.

Answer: The last one is a function

Step-by-step explanation:

If A value of x for example 4 produces more than one y value like 1 and 3 it is not a function also graphing it and using the line method helps

Answer:

Calculation:

Frequency table

Other statistical characteristics:

Average (mean): μ=93.9

Absolute deviation: 153.4

Mean deviation: 5.1133333333333

Minimum: 78

Maximum: 104

Variance: 40.956666666667

Standard deviation σ=6.3997395780349

Corrected sample standard deviation s=6.5091447608147

Coefficient of variation cV=0.069319965503884

Signal-to-noise ratio SNR=14.42585830404

Median: 95

Quartile Q1: 89.75

Quartile Q2: 95

Quartile Q3: 99

1st decile: 85.2

2nd decile: 88.2

3rd decile: 91.3

4th decile: 93

5th decile: 95

6th decile: 97

7th decile: 97.7

8th decile: 99

9th decile: 101.9

Interquartile range IQR: 9.25

Quartile Deviation QD: 4.625

Coefficient of Quartile Deviation CQD: 0.049006622516556

Lower fence: 75.875

Upper fence: 112.875

Set of outliers: {} - empty set - no outliers found

Interdecile range IDR: 16.7

Mode: 97 - unimodal

Geometric mean: 93.673540144338

Harmonic mean: 93.43824696186

Sum: 2817

Sum of squares: 1228.7

Sum of absolute values: 2817

Average absolute deviation: 5.1133333333333

Range: 26

Frequency table :

Z-score: {-0.1406, -1.3907, 0.4844, -2.3282, 1.5782, -0.9219, -0.2969, 0.0156, 0.4844, -1.0782, -2.4845, 0.1719, 1.1094, -0.1406, 0.4844, 0.7969, -1.0782, 1.4219, -0.6094, 0.1719, 1.2657, 0.4844, 0.7969, -0.4531, 0.1719, -0.2969, 1.1094, -0.7657, 0.7969, 0.6407}

Count items: 30

Answer:

25.455844, soo around 25

Step-by-step explanation:

A ratio is a couple of numbers that are looked at. Part-to-part, part-to-entire, and entire-to-part correlations are examples of ratios. Units could conceivably be remembered for the ratios.

A two-layered plane framed by the crossing point of an upward line which is known as the y-axis and a horizontal line called the x-axis is known as a coordinate plane. These are a bunch of opposite lines that converge at nothing, which is known as the beginning. The axes partition the coordinate plane into four segments, every one of which is alluded to as a quadrant.

Requested matches are utilized to chart and find focuses on a coordinate plane. The arranged matches are dependably in the (x, y) structure where the primary number is the x-coordinate and the subsequent number is the y-coordinate. The principal coordinate lets you know how far to move along the x-axis, and the subsequent coordinate lets you know how far to go up or down the y-axis.

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Option B :The solution for x in the given circle is x = 5 + 2√6 or x = 5 - 2√6 is near to value 5.

In the given figure, we have two tangents and a secant that intersects the circle at points A and B.

By the tangent-secant theorem, we know that the product of the lengths of the secant segment (AX) and the exterior segment (XB) is equal to the product of the lengths of the entire secant (AB) and the interior segment (CX).

So, we have:

AX * XB = AB * CX

Substituting the given values, we get:

(3 + x) * (7 - x) = 5 * 5

Expanding the left side and simplifying, we get:

[tex]21 - x^2 = 25 - 10x[/tex]

Bringing all the terms to one side and simplifying, we get:

[tex]x^2 - 10x + 4 = 0[/tex]

Using the quadratic formula, we get:

x = (10 ± √([tex]10^2 - 414[/tex])) / (2*1)

x = (10 ± √96) / 2

x = 5 ± 2√6

Therefore, the solutions for x are:

x = 5 + 2√6 or x = 5 - 2√6

So, the answer is (B) 5.

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The relationship between the height of these objects and their shadow length is approximately proportional because increase in height leads to increase in their length.

Direct proportional relationship is defined as the type of relationship whereby an increase in one variable leads to the increase in the other variable.

From the diagram given above, all the objects are of various heights and the length here f their shadow increased with increase in the heights of the objects.

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The probability of spending more than 4 days in recovery is 0.8554

To calculate the probability of spending more than 4 days in recovery, we need to use the standard normal distribution since the patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.6 days and a standard deviation of 1.5 days.

The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.

If X is a normally distributed random variable with mean μ and standard deviation σ, then Z = (X-μ) / σ is a standard normal random variable.

So, P(X > 4) = P(Z > (4-5.6) / 1.5) = P(Z > -1.0667)

Using a standard normal distribution table, we find that P(Z > -1.0667) = 0.8554

Therefore, the probability of spending more than 4 days in recovery is 0.8554, rounded to four decimal places.

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Answer:

I did the first image. I'm sorry but I don't remember fully how to do the other two, and I don't want to give you the wrong answer. GL

Step-by-step explanation:

Okay, for the first image if the perimeter is 48 you can divide that by 3 getting you 16. M=16.

The answer is  option (d)  "The volume of  sphere can be interpreted as  product of  radius cubed and  constant factor."

The volume of a three-dimensional object refers to the amount of space that it occupies. More specifically, it is a measure of the amount of enclosed space within a solid shape, like a cube, sphere, cylinder, or any other three-dimensional object. The formula for calculating volume of  solid depends on its shape. The formula for the volume of a sphere, as mentioned in the previous question, is V=4/3πr³, where r is the radius of the sphere.

Volumes are typically measured in cubic units, like cubic meters, cubic centimeters, or cubic feet.

The statement that is true is: "The volume of sphere can be interpreted as  product of radius cubed and  constant factor."

The formula for the volume of a sphere, V=4/3πr³, shows that the volume is proportional to the cube of the radius. This means that if the radius of a sphere is doubled, the volume will increase by a factor of 2³=8. Similarly, if the radius is tripled, the volume will increase by a factor of 3³=27.

The constant factor in the formula, 4/3π, is a fixed value that applies to all spheres, regardless of their size. It is a constant because it does not depend on the radius of the sphere.

Therefore, we can interpret the formula for the volume of a sphere as the product of the radius cubed and a constant factor.

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If each shirt is the same price, the cost of each one include the following:  B. $20.75.

In Mathematics, a unit price can be defined as the price that is being charged by a seller for the sale of a single unit of product.

In order to determine the unit price for the shirt, we would divide the cost of shirts by the number of shirts based on the following mathematical equation (formula);

Unit price = Cost of shirts/Number of shirts

By substituting the given parameters into the unit price formula, we have the following;

Unit price = $124.50/6

Unit price = $20.75.

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Complete Question:

Luisa will buy 6 shirts for $124.50. If each shirt is the same price, how much does each one cost?

A. $20.07

B. $20.75

C. $27.05

D. $27.50

Toby sold 16 more games than Molly.

A ratio is a comparison of two or more quantities of the same kind. It is often expressed as a fraction or with a colon (:). For example, the ratio of the number of boys to the number of girls in a class of 30 students could be 2:3, which means that for every two boys, there are three girls.

Let's start by finding the total number of parts in the ratio: 5 + 3 + 1 = 9.

Next, we can use the ratio to find out how many parts of the total each person sold:

Katie: 5/9 of 72 games = 40 games

Toby: 3/9 of 72 games = 24 games

Molly: 1/9 of 72 games = 8 games

To find out how many more games Toby sold than Molly, we can subtract Molly's sales from Toby's sales: 24 - 8 = 16.

Therefore, Toby sold 16 more games than Molly.

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Answer:
Toby sold 16 more games than Molly.

Step-by-step explanation:

Let's start by finding the total number of parts in the ratio: 5 + 3 + 1 = 9.

Next, we can use the ratio to find out how many parts of the total each person sold:

Katie: 5/9 of 72 games = 40 games

Toby: 3/9 of 72 games = 24 games

Molly: 1/9 of 72 games = 8 games

Then we subtract Toby's number of games by Molly's. (24-8)

Therefore, Toby sold 16 more games than Molly.

The value of the investment after 3.5 years is approximately $2530.67.

The principal amount refers to the initial amount of money borrowed or invested, excluding any interest or additional fees. For example, if someone takes out a loan for $10,000, the principal amount is $10,000, and this is the amount that must be repaid to the lender, not including any interest that may accrue over time. Similarly, if someone invests $5,000 in a savings account, the principal amount is $5,000, and any interest earned on that amount will be calculated based on the principal amount. The principal amount is an important concept in finance and investing, as it determines the starting point for calculating interest, returns, and other financial transactions.

The formula for compound interest is:

[tex]A= P(1+\frac{r}{n} )^{nt}[/tex]

Where:

A = the final amount

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time (in years)

In this case, we have:

P = 2000

r = 0.04 (4% as a decimal)

n = 12 (compounded monthly, so 12 times per year)

t = 3.5 (3.5 years)

Plugging these values into the formula, we get:

[tex]A= 2000(\frac{1+0.04}{12})^{12*3.5}[/tex]

A = 2000(1.00333333)⁴²

A ≈ 2530.67

Therefore, the value of the investment after 3.5 years is approximately $2530.67.

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Answer:

a. 6x^2

b. 70x^2

c. -360s^2

d. -60x^2

Step-by-step explanation:

Answer:

3 2/3.

Probably the easiest question I've answered all day!

It's 29.75

I divided 85 with 100, which gave me 0.85. Then i calculated the new price(35% of the original one) and i multiplied them.

Hope this helps.

Answer:3,575 lbs, or 45% less

Step-by-step explanation:

Unit for garbage collected: pounds (lbs)

Unit for time: month (mo)

Let's use "t" as the variable for time (in months).

Expression for the amount of garbage collected:

For the initial cleanup: 6,500 lbs

For subsequent cleanups: 45% less garbage collected each month, which means they collect 55% of the previous month's garbage. So, the expression for the amount of garbage collected each month (starting from the second month) would be:

0.55^(t-1) * 6,500 lbs

where "t" represents the number of months after the initial cleanup.

Note that for t=1 (i.e., the first subsequent cleanup), the expression evaluates to 0.55^(1-1) * 6,500 lbs = 6,500 * 1 = 6,500 lbs, which is consistent with the initial cleanup. For t=2, the expression evaluates to 0.55^(2-1) * 6,500 lbs ≈ 3,575 lbs, which is 45% less than the amount collected in the first subsequent cleanup.

The proportion of students who took ACT and scored between 18 and 28, P(18 < X < 28) is 0.607.

The proportion of students who took ACT and scored between 18 and 28, P(18 < X < 28) is given by the formula:

P(18 < X < 28) = P(Z < (28 - 21)/5.5) - P(Z < (18 - 21)/5.5)

We can then calculate the z-scores for the lower and upper bounds of the range as follows:

Z1 = (28 - 21)/5.5 = 1.27Z2 = (18 - 21)/5.5 = -0.55

Using a z-table or calculator, we can find the probabilities associated with these z-scores:

P(Z < 1.27) = 0.898P(Z < -0.55) = 0.291

Therefore,P(18 < X < 28) = P(Z < 1.27) - P(Z < -0.55) = 0.898 - 0.291 = 0.607

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Answer:

41

Step-by-step explanation:

A = LW + (1/2)bh

A = 7 m × 5 m + (1/2)(3 m)(4 m)

A = 35 m² + 6 m²

A = 41 m²

The resultant substraction value of the sum of three hundredths and 256 tenths from 41435 hundredths is equals to the 388.72.

Subtraction is one of the four arithmetic operations along with addition, multiplication and division. Subtraction is an operation representing the removal of an object from a collection. This is indicated by the symbol '-'. For example, there are 5 − 2 books meaning 5 books with 2 taken away, resulting in a total of 3 books. We have sum of three hundredths and 256 tenths. First, 3 hundredths means 3 out of 100, which can be denoted as = 3/100 = 0.03. Similarly, 256 tenth means 256/10 = 25.6. So, the sum of three hundredths and 256 tenths = 25.60 + 0.03 = 25.63 and 41435 hundredths = 414.35. Now, substract 25.63 from 414.35

= 414.35 - 25.63

= 388.72

Hence, required value is 15.805.

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Andrés is 35 years old, Carlos is 31 years old, and Rodolfo is 24 years old based on the sum is given.

Let's assume the age of Andrés is x years.

According to the problem, Carlos' age is (x - 4) years and Rodolfo's age is (x - 11) years.

Now, we know that the sum of their ages is 90, so we write an equation:

x + (x - 4) + (x - 11) = 90

Simplify following equation:

3x - 15 = 90

Adding 15 to both sides, we get:

3x = 105

Dividing by 3, we get:

x = 35

So Andrés' age is 35 years.

Carlos' age is (x - 4) = 31 years.

Rodolfo's age is (x - 11) = 24 years.

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Translation: The sum of the ages of Andrés, Carlos and Rodolfo is 90 years. Andrew's age exceeds Carlos' age by 4 years and Rodolfo's by 11. Determine the ages of all three

The experimental probability of the following spin landing on white is 5/7, or roughly 0.714 based on given events.

The number of times an event occurred divided by the total number of trials done is used to compute the experimental probability of the event. In this instance, there have been 14 trials, and the event is landing on white.

Out of 14 spins, the spinner landed on white 10 times, according to the information provided. the following is the experimental likelihood of landing on white:

Experimental probability is calculated as follows: White landings / total spins

10/14 is the experimental probability.

5/7 is the experimental probability.

Hence, the experimental likelihood that the following spin will land on white is 5/7, or roughly 0.714. It's crucial to keep in mind that this likelihood is just based on the small sample size of 14 spins and might not fully reflect the spinner's long-term chances of landing on white.

The design and balance of the spinner might affect the results, thus if there are any problems with its construction, the spinner may not be an accurate depiction of likelihood. The experimental probability might not be helpful in this situation to forecast future events.

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