When Xander arranges his pennies into a rectangle with more than one row, he always has some leftover pennies. When he uses two equal rows or three equal rows, he has one leftover penny. When he arranges them into a rectangle with four equal rows, he has three leftover pennies. Remember he has between 10 and 40 pennies total. How many pennies does Xander have?

As a result, AB = 52 and AC = BC = 5 as AC and BC are both the circle's radii since A and B are points of tangency .

A circle is a closed object made up of all points in a plane that are separated from the center by a predetermined distance, known as the radius. The diameter is the distance across the circle that passes through its center, while the circumference is the distance around the circle. The ratio of a circle's circumference to its diameter is always pi (), or roughly 3.14. Pi is also known as the proportionality constant. Circles are significant geometric forms that are used frequently in mathematics, science, and daily life.

given

AC and BC are both the circle's radii since A and B are points of tangency. Hence, AC = BC = 5.

We can apply the Pythagorean theorem to segment AB as follows:

\(AB^2 = 52 + 52 \\AB^2 = AC^2 + BC^2\)

AB² = 50

AB = √50 = 5√2

As a result, AB = 52 and AC = BC = 5 as AC and BC are both the circle's radii since A and B are points of tangency .

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a) The mean of the data-set is of 2 hours.

b) The mean absolute deviation of the data-set means that the measures vary by an average amount of 0.93 hours from the mean.

The dot plot gives a dot to each measure for each time that it appears, hence it says the same thing as a table, in a different format.

The sum of the fifteen observations in this problem is given as follows:

0 x 1 + 1 x 5 + 2 x 3 + 3 x 5 + 4 x 1 = 30.

The mean of the data-set is given as the sum of all the observations divided by the number of values, hence:

30/15 = 2.

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The number of quarts of each constituent she needs to produce 16 quarts of punch is; 12 quarts of fruit juice and 4 quarts of citrus soda.

It follows from the task content that the quantity of each constituent that is required to make 16 quarts of punch are to be determined.

Since it follows that 3 quarts of fruit juice are required to mix with every quart of citrus soda, it follows that the amount of punch made in this scenario is; 4 quarts of punch.

Hence, since there are 4 partitions of 4 quarts punch is 16 quarts punch, the amount of.each constituent needed by proportion are as follows;

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Answer:

Given:

Area of the sector (A) = 104π/9 square inches

Central angle (θ) = 65 degrees

The formula for the area of a sector of a circle is:

A = (θ/360) * π * r^2

We can rearrange this formula to solve for the radius (r):

r^2 = (A * 360) / (θ * π)

Plugging in the given values:

r^2 = (104π/9 * 360) / (65 * π)

r^2 = (104 * 40) / 9

r^2 = 4160 / 9

r^2 ≈ 462.22

Taking the square root of both sides:

r ≈ √462.22

r ≈ 21.49

Therefore, the radius of the circle is approximately 21.49 inches.

Answer: 8 inches

Step-by-step explanation:

For Critters and Co is 7.5,  Little Paws is 8.75 and Wagging rail is 8.5

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

For Critters and Co

(2, 15) and (4, 30)

m=15/2=7.5

Now let us find y intercept

15=15/2(2)+b

b=0

The equation is y=15/2x

For Little Paws

m=52.5-35/6-4

m=17.5/2=8.75

Now let us find y intercept

35=17.5/2(4)+b

35=35+b

b=0

y=17.5/2x is the equation for  Little Paws

For Wagging rail

y=8.5x

Hence, For Critters and Co is 7.5,  Little Paws is 8.75 and Wagging rail is 8.5

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(A) The data provided is modeling a geometric sequence, (B) the recursive formula is T(5) = T(4) * 2., and (C) the explicit formula T(n) = T(1) * r^(n-1).

What is the explicit formula?

The explicit formula for an arithmetic sequence is an = a + (n - 1)d, and any term of the sequence can be computed, without knowing the other terms of the sequence. In general, the explicit formula is the nth term of arithmetic, geometric, or harmonic sequence.

A. The data provided is modeling a geometric sequence.

This is because the common ratio between consecutive terms is a constant value, specifically in this case is the ratio between consecutive terms is multiplied by 2.

B. To find the time Aurora will complete station 5 using a recursive formula,

we can use the formula T(n) = T(n-1) * r,

where T(n) is the time at the nth station, T(n-1) is the time at the (n-1)th station, and r is the common ratio.

In this case T(5) = T(4) * 2

and T(4) = 24 (from the data provided)

Therefore, T(5) = 24 * 2 = 48 minutes

C. To find the time Aurora will complete the 9th station using an explicit formula,

we can use the formula T(n) = T(1) * r^(n-1)

In this case, T(9) = T(1) * 2^(9-1)

and T(1) = 3 (from the data provided)

Therefore, T(9) = 3 * 2^8 = 3 * 256 = 768 minutes

The explicit formula assumes that the first term of the sequence is T(1) and the common ratio of the consecutive term is r.

Hence, (A) The data provided is modeling a geometric sequence, (B) the recursive formula is T(5) = T(4) * 2., and (C) the explicit formula T(n) = T(1) * r^(n-1).

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Answer:

I think it's the first one... but I'm not pretty sure.

Answer:

C

Step-by-step explanation:

edge 2020

Answer:

$90

Step-by-step explanation:

i dont have an explanation but teah sorry

The fraction of the area of the tray occupied by the blondies is 1/9.

To find the fraction of the area of the tray occupied by blondies, we need to determine the area occupied by the blondies and compare it to the total area of the tray.

Let's calculate the area of each individual blondie:

The blondies are squares with 3-inch sides, so the area of each blondie is 3 inches × 3 inches = 9 square inches.

Now, let's calculate the area occupied by the blondies in each row:

Since there are 4 rows of blondies and each row contains 4 blondies, the total number of blondies is 4 rows × 4 blondies per row = 16 blondies.

So, the total area occupied by the blondies is 16 blondies × 9 square inches per blondie = 144 square inches.

Next, let's determine the area occupied by the brownies:

The brownies are squares with 6-inch sides, so the area of each brownie is 6 inches × 6 inches = 36 square inches.

Since there are also 4 rows of brownies and each row contains 4 brownies, the total number of brownies is 4 rows × 4 brownies per row = 16 brownies.

Therefore, the total area occupied by the brownies is 16 brownies × 36 square inches per brownie = 576 square inches.

Now, let's calculate the total area of the tray:

Given that the tray is completely full and has an area of 648 square inches, we can subtract the area occupied by the brownies from the total area to find the remaining area occupied by the blondies:

Total area of the tray - Area occupied by the brownies = Area occupied by the blondies

648 square inches - 576 square inches = 72 square inches.

So, the fraction of the area of the tray occupied by the blondies is:

Area occupied by the blondies / Total area of the tray = 72 square inches / 648 square inches.

To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 72 in this case:

72 square inches / 648 square inches = 1/9.

Therefore, the blondies' percentage of the tray's surface area is 1/9.

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Answer:

legs

Step-by-step explanation:

Answer:

The Legs of a right triangle are the two sides of a right triangle that intersect to form the right angle

Step-by-step explanation:

Two legs plus a hypotenuse make up a right triangle. The hypotenuse is the longest side of the right triangle and the side opposite the right angle, and the two legs meet at a 90° angle. Right triangles come in a variety of shapes, including 45°-45° right triangles and 30°-60° right triangles.

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Answer:

Step-by-step explanation:

The area to be resurfaced is the area of the

whole circle including garden and lanes minus  

the area of the garden.

Area of a circle is (pi)r2

radius of garden is (1/2)diameter = 8 m

Garden area:  (pi)82 = 64(pi) m2

Diameter of garden plus traffic lanes is

16 + 2(6) because we add 6 m to both sides

of the diameter of the garden.

Full diameter = 16+12 = 28 m

Full radius = 28/2 = 14 m

Full area:  (pi)142 = 196(pi) m2

Area to be resurfaced:

196(pi) - 64(pi) = 132(pi) m2  ≅ 415 m2

The statement translated to an algebra equation will give the value of the unknown number w = 11/5

Algebra is the branch of mathematics that helps to represent problems or values in the form of mathematical expressions using letters to represent unknown values.

Let us represent the unknown number with the letter w so that the statement can be written as the equation:

5w - 8 = 3

add 8 to both sides

5w - 8 + 8 = 3 + 8

5w = 11

divide through by 5

5w/5 = 11/5

w = 11/5

Therefore, the statement translated to an algebra equation will give the value of the unknown number w = 11/5

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Sara should expect a paycheck of $91.80 from her first full of work.

In the question, we are given that Sara just started her first job as an assistant at an after-school child care center. She works 12 hours a week and makes $9 per hour. She has been told that 15% of her paycheck will be deducted for federal, state, and local taxes.

We are asked for the amount that Sara should expect her paycheck of, from her first full week of work.

The time for which Sara works weekly = 12 hours.

The per hour earning of Sara = $9.

Thus, the total earnings after working for 12 hours at the rate of $9 per hour is 12*$9 = $108.

Now, the deduction is given to be 15%.

Thus, the total deduction = 15% of $108 = $16.20.

The amount on the paycheck = The total earnings less the deduction,

or, the amount on the paycheck = $108 - $16.20 = $91.80.

Thus, Sara should expect a paycheck of $91.80 from her first full of work.

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Answer:

Therefore, 1 + 2cos a can be expressed as the product of 2 and (cos a/2 + 1).

1 + 2cos a = 2(cos a/2 + 1)

Step-by-step explanation:

We can use the trigonometric identity:

cos 2a = 1 - 2 sin^2 a

to rewrite 1 + 2cos a as:

1 + 2cos a = 1 + 2(1 - sin^2 a/2)

= 1 + 2 - 2(sin^2 a/2)

= 3 - 2(sin^2 a/2)

Now, using another trigonometric identity:

sin a = 2 sin(a/2) cos(a/2)

we can rewrite sin^2 a/2 as:

sin^2 a/2 = (1 - cos a)/2

Substituting this into the expression for 1 + 2cos a, we get:

1 + 2cos a = 3 - 2((1 - cos a)/2)

= 3 - (1 - cos a)

= 2 + cos a

Therefore, 1 + 2cos a can be expressed as the product of 2 and (cos a/2 + 1).

1 + 2cos a = 2(cos a/2 + 1)

Answer:

m ∠DGA  =  78°

Step-by-step explanation:

∠CGB and ∠DGA are vertically opposite angles formed at the intersection of the two rays AB and CD

Such angles are equal to each other

Therefore
m ∠DGA  = m ∠CGB  = 78°

Answer:

You can replace "a number" with a variable to represent an unknown value.

You can replace "sum" with an addition sign.

You can replace "one-third" with 1/3.

Step-by-step explanation:

"the sum" means to add.

Let "a number" = x:

The sum of a number and one-third = x + 1/3.

You can replace "a number" with a variable to represent an unknown value.

You can replace "sum" with an addition sign.

You can replace "one-third" with 1/3.

The measure of the side MN is 19.1.

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

The different trigonometric identities are expressed as:

From the information given, we have that:

Using the tangent identity:

\(\text{tan} \ \theta = \dfrac{\text{opposite}}{\text{adjacent}}\)

Substitute the values

\(\text{tan}(60) =\dfrac{\text{MN}}{11}\)

Cross multiply the values, we have:

\(\text{MN} = \sf 1.73(11)\)

\(\text{MN} = 19. 05 \thickapprox\bold{\underline{19.1 \ ft}}\)

Hence, the measure of the side MN is 19.1.

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On solving the provided question, we can say that Therefore, you would need multiply  approximately 27.84 pounds of food each day for your horse.

One of the four mathematical operations, along with arithmetic, subtraction, and division, is multiplication. Mathematically, adding subgroups of identical size repeatedly is referred to as multiplication. The multiplication formula is multiplicand multiplier yields product. To be more precise, multiplicand: Initial number (factor). Number two as a divider (factor). The outcome is known as the result after dividing the multiplicand as well as the multiplier. Adding numbers involves making several additions. as in 5 x 4 Equals 5 x 5 x 5 x 5 = 20. 5 times by 4 is what I did. This is why the process of multiplying is sometimes called "doubling."

First, we need to convert the weight of the horse from kilograms to pounds, so:

678 kg x 2.20462 lbs/kg = 1495.69 lbs

Next, we need to calculate how many Mcal the horse needs per day:

0.0333 Mcal/kg x 678 kg = 22.58 Mcal/day

Then, we can convert the Mcal to kcal:

22.58 Mcal/day x 1000 kcal/Mcal = 22,580 kcal/day

Finally, we can divide the total daily kcal needed by the kcal per pound of food to find the total pounds of food needed:

22,580 kcal/day ÷ 810 kcal/lb = 27.84 lbs/day

Therefore, you would need approximately 27.84 pounds of food each day for your horse.

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The total number of whole number between -4 and 6 are 7 that are 0,1,2,3,4,5,6.

Whole numbers are the complete set of natural numbers plus '0'. Examples include: 0, 11, 25, 36, 999, 1200, and so on. Learn more about numbers by clicking here.

Integers supplement this set of numbers because they include negatives, but otherwise follow the same rules. As a result, all whole numbers are integers (because they are all positive integers), but not all integers are whole numbers (because some are negative).

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Answer: it depends; if exam day, no

Step-by-step explanation:

Answer:

14: 16 is the ratio of girls to boys

And the ratio 14:30 is the ratio of girls to the total of students

Step-by-step explanation:

Answer:

$60

Step-by-step explanation:

40 text messages × .25 each = $10. Plus the $50 per month is $60.

Answer:

it should be $60 a month

Answer:

We can use the formula for compound interest to find the future value (FV) of Natalie's investment:

FV = P * (1 + r/n)^(n*t)

Where:

P is the principal amount (the initial investment), which is $2,000 in this case

r is the annual interest rate as a decimal, which is 11% or 0.11

n is the number of times the interest is compounded per year, which is 12 since interest is compounded monthly

t is the number of years, which is 20

Substituting the values into the formula, we get:

FV =

2

,

000

∗

(

1

+

0.11

/

12

)

(

12

∗

20

)

�

�

=

2,000 * (1.00917)^240

FV = $18,255.74

Therefore, after 20 years of compounded monthly interest at a rate of 11%, Natalie's investment of 2,000 will be worth approximately 18,256.

Answer:

$17,870

Step-by-step explanation:

You must use the formula for compound interest.

A = P(1 + r/n)^nt

I suggest you look it up at some point so that you can do these more easily in the future!

Answer:

First, if we look at these angles, we can see that they are vertical.

Vertical angles are congruent(meaning they measure the same degrees).

So let's set up an equation where -2x - 6 is equal to 40°, because they are vertical angles.

-2x - 6 = 40°

Solve for x!

Get rid of constants by performing the inverse operation of subtraction which is addition(because 6 is negative).

Make sure to apply this to both sides!!

(Add 6 to both sides)

+6           +6

-2x = 46

Now, we isolate x by getting of x's co-efficient.

To do that, we also perform the inverse operations.

The inverse operation of multiplication is division (since -2 is being multiplied by x).

(Divide -2 from both sides)

÷ -2 ÷ -2

x = -23

Therefore, x measures -23°.

Answer:

x = -23

Step-by-step explanation:

Vertical Angle Theorem

A pair of opposite angles formed by intersecting lines.

Vertical angles are congruent.

⇒ -2x - 6 = 40

Add 6 to both sides:

⇒ -2x = 46

Divide both sides by -2

⇒ x = -23

Answer:

x>_-1

Step-by-step explanation:

x is such that x is greater or equal to -1

Answer: 9/4

Step-by-step explanation:

Reciprocal means flip the fraction

The reciprocal of 4/9  is  9/4

Answer: the rciprocal is 9/4

Step-by-step explanation:

The value of common ration r is 4.

Given that,

a₁ = 9

a₅ = 2304

We know that,

A geometric sequence  is a sequence in which each term (except from the first term) is multiplied by a fixed amount to obtain the following term.

The following term in the geometric sequence must be obtained by multiplying it by a set term (referred to as the common ratio), and the previous term in the sequence can be obtained by dividing it by the same common ratio.

Since we know that nth term of GP is,

\(a_{n}\) = a₁ \(r^{n-1}\)

Therefore,

a₅ = a₁ \(r^{4}\)  = 2304

⇒  9 x \(r^{4}\)  = 2304

⇒        \(r^{4}\)  = 256

⇒           r = 4

Hence, r = 4

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M = 270,000 * (0.5833% * (1 + 0.5833%)^240) / ((1 + 0.5833%)^240 - 1).  Calculating this equation will give us the monthly mortgage payment for Abigail and Curtis Siebert.

Abigail and Curtis Siebert have a $270,000 mortgage at an interest rate of 7% for a term of 20 years.

To calculate the monthly mortgage payment, we can use the formula for an amortizing mortgage:

M = P * (r * (1 + r)^n) / ((1 + r)^n - 1),

where M is the monthly mortgage payment, P is the principal amount (loan amount), r is the monthly interest rate, and n is the total number of monthly payments.

First, we need to convert the annual interest rate to a monthly interest rate. Since there are 12 months in a year, the monthly interest rate is 7% divided by 12, which is approximately 0.5833%.

The total number of monthly payments is the term of the mortgage multiplied by 12. In this case, it's 20 years * 12 months, which equals 240 months.

Now, we can substitute the values into the formula:

M = 270,000 * (0.5833% * (1 + 0.5833%)^240) / ((1 + 0.5833%)^240 - 1).

Calculating this equation will give us the monthly mortgage payment for Abigail and Curtis Siebert.

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Answer:

m = 25 + 6n

Step-by-step explanation:

To write a function for the amount of money Makayla spent going to the movies during the club, you need to consider two things: the annual registration fee and the discounted ticket price. The annual registration fee is a fixed amount that does not depend on the number of movie tickets Makayla purchases. The discounted ticket price is a variable amount that depends on the number of movie tickets Makayla purchases. You can use a letter, such as n, to represent the number of movie tickets Makayla purchases. Then, you can write an expression for the amount of money Makayla spent on movie tickets, which is 6 times n, or 6n. To find the total amount of money Makayla spent going to the movies during the club, you need to add the annual registration fee and the amount of money spent on movie tickets. This gives you the expression 25 + 6n. You can use another letter, such as m, to represent the total amount of money Makayla spent going to the movies during the club. Then, you can write an equation that relates m and n, which is m = 25 + 6n. This equation is a function that models the amount of money Makayla spent going to the movies during the club as a function of the number of movie tickets she purchased.