A regular softball has a 1.5 in radius. What is its exact volume?

Answer: 512/9 and 6,144/81

Step-by-step explanation:

The sequence is:

18, 24, 32, 128/3, ...

Now, is easy to see that it is not an arithmetic sequence, so we can jump to see if this is a geometric sequence.

To see this, we must see at the quotient of two consecutive numbers in the sequence, and that quotient must be the same for any pair of consecutive elements.

24/18 = 1.33...

32/24 = 1.33...

(128/3)/32 = 1.33....

The quotient is constant, then this is a geometric sequence.

Then we can write the n-th term as:

Aₙ = Aₙ₋₁*1.33...

And we first should write 1.33 in a way that is easier to use:

1.33... = 1 + 0.33...

The left side can be writen as:

0.33... = 0.33...*(10/10) = (3.3.../10)

Now we can subtract the initial number:

(3.33..../10) - 0.33... = 3/10 = 0.33...*(9/10)

0.33... = (3*10)/(9*10) = 30/90 = 3/9

then we have:

1.33... = (1 + 3/9) = (9/9 + 3/9) = (12/9)

Then the two next terms are:

(128/3)*(12/9) = 128*4/9 = (512/9)

And the next term is:

(512/9)*(12/9) = (6,144/81)

Then the first six terms are:

18, 24, 32, 128/3, 512/9, 6,144/81

Answer:

SU = 32 and <SVT = 32

Step-by-step explanation:

math, i am pretty sure about the angle and positive on the diagonal

Answer:weeks 1 and 3

Step-by-step explanation:

13 / 50 to percentage is 26%. I took the test

The team sell the same amount of candy bars in the first and the third week. Therefore, option B is the correct answer.

Given that, a school sports team sold candy bars to raise money for new uniforms.

In the first week they sold 26%, in the second week they sold 3/11 and in the third week, they sold 13/50.

The percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Now, in the second week, they sold 3/11=3/11 ×100=27.27%

In the third week, they sold 13/50= 13/50 ×100=26%.

In the first week and the third week, they sold the same quantity of candies.

Therefore, option B is the correct answer.

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Solution:

Similar shapes are enlargements of each other using a scale factor.

Given that the two rectangular frames are similar, where one frame is 3 feet wide and 6 feet long.

This implies that

Thus, we have the dimension of the other frame to be:

The correct option is C

2.1.1. An IRP5 is the employee's tax certificate, detailing all the employee-related incomes, deductions, and related taxes.  The IRP5 assists the employee in making his tax returns for the subsequent year.

2.1.2. Mr. Johnson's taxable income for the year is R490,414,56.

2.1.3 Mr. Johnson's medical credit for the financial year is R33,600.

2.1.4 The annual tax payable by Mr. Johnson for the financial year from 1 March 2021 to 28 February 2022 is R118,988,24.

2.1.5 Calculate Mr. Johnson's monthly taxes are R9,915,69.

Gross Pay = R47,400,00

Pension fund contributions = 7.5% (R3,555,00)

WVF contribution = 1% (R177,12)

Medical aid contributions = R2,800

Annual medical credit = R33,600 (R2,800 x 12)

Total deductions = R6,532,12 (R3,555,00 + R177,12 + R2,800)

Taxable income = R40,867,88 (R47,400 - R6,532,12)

Annual taxable income = R490,414,56 (R40,867,88 x 12)

Annual tax liability = R110 739 + 36% of taxable income above R467 500

= R110,739 + 36% of R22,914,56 (R490,414,56 - R467,500)

= R110,739 + R8,249,24

= R118,988,24

Monthly Tax = R9,915,69 (R118,988,24/12)

Thus, the taxable income (gross pay minus deductions)  forms the basis for determining the tax payable by Mr. Johnson during the tax year.

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Appendix A (Tax Rates)

Taxable Income              Rate of tax (R)

R1 – R216 200                18% of taxable income

R216 201 – R337 800    R38 916 + 26% of taxable income above R216 200

R337 801 – R467 500   R70 532 + 31% of taxable income above R337 800

R467 501 – R613 600   R110 739 + 36% of taxable income above R467 500

Answer:

12

Step-by-step explanation:

Based on the information given, there are a total of 118 solutions.

This is a problem of solving a Diophantine equation subject to some conditions. Let's introduce a new variable y4 = 20 - (x1 + x2 + x3 + x4). Then the problem can be restated as finding the number of solutions to:

x1 + x2 + x3 + y4 = 20

Subject to the following conditions:

0 ≤ x1 < 3

0 ≤ x2 < 4

0 ≤ x3 < 5

0 ≤ y4 < 6

We can solve this problem using the technique of generating functions. The generating function for each variable is:

(1 + x + x^2) for x1

(1 + x + x^2 + x^3) for x2

(1 + x + x^2 + x^3 + x^4) for x3

(1 + x + x^2 + x^3 + x^4 + x^5) for y4

The generating function for the equation is the product of the generating functions for each variable:

(1 + x + x^2)^3 (1 + x + x^2 + x^3 + x^4 + x^5)

We need to find the coefficient of x^20 in this generating function. We can use a computer algebra system or a spreadsheet program to expand the product and extract the coefficient. The result is: 1118

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Answer: This problem involves finding the number of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints. We can use the stars and bars method to solve this problem.

Suppose we have 20 stars representing the sum x₁ + x₂ + x3 + x₁. To separate these stars into four groups corresponding to x₁, x₂, x₃, and x₄, we need to place three bars. For example, if we have 20 stars and 3 bars arranged as follows:

**|**||

then the corresponding values of x₁, x₂, x₃, and x₄ are 2, 4, 6, and 8, respectively. Notice that the position of the bars determines the values of x₁, x₂, x₃, and x₄.

In general, the number of ways to place k identical objects (stars) into n distinct groups (corresponding to x₁, x₂, ..., xₙ-₁) using n-1 separators (bars) is given by the binomial coefficient (k+n-1) choose (n-1), which is denoted by C(k+n-1, n-1).

Thus, the number of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints is:

C(20+4-1, 4-1) = C(23, 3) = 1771

However, this count includes solutions that violate the upper bounds on x₁, x₂, x₃, and x₄. To eliminate these solutions, we need to use the principle of inclusion-exclusion.

Let Aᵢ be the set of non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20 subject to the given constraints, where xᵢ ≥ mᵢ for some integer mᵢ. Then, we want to find the cardinality of the set:

A = A₀ ∩ A₁ ∩ A₂ ∩ A₃

where A₀ is the set of all non-negative integer solutions to the equation x₁ + x₂ + x3 + x₁ = 20, and Aᵢ is the set of solutions that violate the upper bound on xᵢ.

To find the cardinality of A₀, we use the formula above and obtain:

C(20+4-1, 4-1) = 1771

To find the cardinality of Aᵢ, we subtract the number of solutions that violate the upper bound on xᵢ from the total count. For example, to find the cardinality of A₁, we subtract the number of solutions where x₂ ≥ 4 from the total count. To count the number of solutions where x₂ ≥ 4, we fix x₂ = 4 and then count the number of solutions to the equation x₁ + 4 + x₃ + x₄ = 20 subject to the constraints 0 ≤ x₁ < 3, 0 ≤ x₃ < 5, and 0 ≤ x₄ < 6. This count is given by:

C(20-4+3-1, 3-1) = C(18, 2) = 153

Similarly, we can find the cardinalities of A₂ and A₃ by fixing x₃ = 5 and x₄ = 6, respectively. Using the principle of inclusion-exclusion, we obtain:

|A| = |A₀| - |A

Step-by-step explanation:

Answer:

81 degrees

This is an acute angle since it’s less then 90 degrees

Step-by-step explanation:

All three angles of a triangle always equal 180 degrees

180-(78+31)

180-109

81 degrees

Hopes this helps please mark brainliest

Answer:

D. x ≥ -10

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

10 - 4x ≤ 50

Step 2: Solve for x

Here we see that any value x greater than or equal to -10 would be a solution to the inequality.

Answer:

0.8413

Step-by-step explanation:

p = 0.10

σ = √(pq/n) = 0.01

z = (x − μ) / σ

z = (0.11 − 0.10) / 0.01

z = 1

P(Z < 1) = 0.8413

The probability that the proportion of books checked out in a sample of 899 books would be less than 11% is approximately 0.5425.

We have,

We can use the normal approximation to the binomial distribution to find the probability that the proportion of books checked out in a sample of 899 books would be less than 11%.

First, we need to calculate the mean and standard deviation of the binomial distribution:

Mean:

np = 899 × 0.1 = 89.9

Standard deviation:

√(np(1-p)) = √(899 × 0.1 × 0.9) = 9.427

Next, we need to standardize the sample proportion of 11% using the formula:

z = (x - μ) / σ

where x is the sample proportion, μ is the mean of the distribution, and σ is the standard deviation of the distribution.

Substituting the values we have, we get:

z = (0.11 - 0.1) / 0.9427 = 0.1059

Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score less than 0.1059 is 0.5425.

Therefore,

The probability that the proportion of books checked out in a sample of 899 books would be less than 11% is approximately 0.5425.

Rounded to four decimal places, the answer is 0.5425.

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Answer:

8=8 so it is true

Step-by-step explanation:

Answer:

Sorry for being late it is Fewer than 14.05 Hope this helps :D

Step-by-step explanation:

Answer:

The answer is "Fewer than 14.05"

Step-by-step explanation:

Based on Pythagorean's theorem, the lengths of the sides of △OPR are:

x = 35 units.

y = 55 units.

z = 30 units.

In Mathematics and Geometry, a perpendicular bisector is a line that bisects or divides a line segment exactly into two (2) equal halves and forms an angle that has a magnitude of 90 degrees at the point of intersection.

Since line segment OS bisects line segment PQ, we have the following:

x = QR = 35 units.

y = z + 25

By applying Pythagorean's theorem, we have the following:

x² + z² = y²

(z + 25)² = 35² + z²

z² + 50z + 625 = 1,225 + z²

50z = 1,225 - 625

50z = 600

z = 600/50

z = 30 units.

y = z + 25

y = 30 + 25

y = 55 units.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Complete Question:

O is the centre of the circle. x, y, and z indicate the lengths of the sides of △OPR. Find with reasons the values of the following:

1.1.1   x

1.1.2  z

1.1.3  y

Answer:

2) B). Minimize 7S + 9C

3) D) . 3S + 4C ≤ 500

4) B). S + C ≥ 150

5) C) $1150

Step-by-step explanation:

The company makes two types of balls, the balls and their costs are written below:

Soccer ball, S = $7

Cork ball, C = $9

Production time of each ball:

Soccer ball = 3 hours

Cork balls = 4 hours

2) To find the objective function.

Since the cost of each soccer ball is $7 and S balls are produced, the total cost of soccer balls is 7S.

Similarly, the cost of each cork ball is $9 and C balls are produced, total cost is 9C.

The objective function maximize profits and minimizes losses. Here, the objective for this linear programming model is to fulfil the given production requirements at a minimum cost.

Therefore the objective function here is: Minimize 7S+9C

3)The constraint equation for the production hours.

To produce one soccer ball, 3 hours are needed, i.e 3S, to produce one Cork ball 4 hours are needed, i.e 4C.

Since we are given a maximum productin time of 500 hours, the constraint equation for the production hours would be:

3S + 4C ≤ 500

4) Since we are told the combined production quantity for these two balls must be at least 150 units, the constraint equation for the combined production quantity is:

S + C ≥ 150

5)Since each soccer ball costs $7, 100 soccer balls would cost:

7*100 = $700

Similarly, since each Cork ball costs $9, 50 cork balls would cost:

9*50 = $450

Therefore the total cost of production would be:

$700 + $450 = $1,150

Note: Question number 1 isn't a question, it's an expression.

Answer:

D.

Step-by-step explanation:

The mean is 11,000

Answer:

FV= $160.68

Step-by-step explanation:

Giving the following information:

Initial investment= $150

Interest rate= 3.5% compounded annually

Number of periods= 2

To calculate the future value, we need to use the following formula:

FV= PV*(1+i)^n

PV= present value

i= interest rate

n= number of periods

FV= 150*(1.035^2)

FV= $160.68

Answer:

3.002 * 10⁵

Step-by-step explanation:

3 * 10⁵ = 3 * 10³ * 10² = 3000 *10²

3 * 10⁵ + 2* 10² = 3000 * 10² + 2*10²

                        = (3000 + 2) * 10²

                       = 3002 * 10²

                       = 3.002 * 10³ * 10²

                      = 3.002 * 10⁵

Answer:

S = 2π(3^2) + 2π(3)(8.2) = 67.2π = 211 cm^3

8/21 of the lawn still needs to be mowed.

To compare fractions, we need a common denominator. The least common multiple of 7 and 3 is 21.

Miss Lianto's fraction: (2/7) x (3/3) = 6/21

Son's fraction: (1/3) x (7/7) = 7/21

To calculate how much of the lawn still needs to be mowed, we can subtract the combined fractions mowed from the total:

Combined fractions mowed: 6/21 + 7/21 = 13/21

So, Remaining fraction: 1 - 13/21 = 8/21

Therefore, 8/21 of the lawn still needs to be mowed.

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The distance between the base of the second ladder and the wall is 1.6 meters.

So we know that the two ladders are parallel, then the triangles that we are forming (between the ladder, the floor, and the wall) are two similar triangles.

We know that the length of the first ladder is 4.2m

The length of the second ladder is 5.6 m

Then the scale between these sides is:

4.2m*k = 5.6m

k = 5.6m/4.2m =  4/3

Then the distances of the bases are related by tha same scale, the distance between the base and the wall of the second base is:

(4/3)*1.2 m= 1.6m

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If Ibuprofen is given for fever to children 6 months of age up to 2 years.The amount of  much medicine that would be usual dose for a 18 month old weighing 22 pounds is 50kg.

1 pound = 0.45 kg    

Hence,

22 pounds = 22×0.45 Kg

22 pounds = 9.9Kg

Now let find the the amount of medicine that would be the usual dose  

Medicine dose = 5mg × 9.9kg

Medicine dose =49.5 kg

Medicine dose = 50 kg

Therefore the medicine dose is 50kg.

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Answer:

y = sec(x-2) - 1

Step-by-step explanation:

We can determine the graph is of a secant by the repeating parabolas. From there, graph sec(x) and add the transformations necessary to replicate the graph.

Answer:

21x-114

Step-by-step explanation:

\(\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=15\pi \end{cases}\implies 15\pi =2\pi r\implies \cfrac{15\pi }{2\pi }=r\implies \cfrac{15}{2}=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2 \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=\frac{15}{2} \end{cases}\implies A=\pi \left( \cfrac{15}{2} \right)^2\implies A=\cfrac{225\pi }{4}\implies A=56.25\pi\)

Answer: 808

Step-by-step explanation:

Answer: The solution  is \((-2,\frac{5}{3} )\)

Step-by-step explanation:

it already gives you the solution for x so just plot it into the equation to solve for y.

y= \(\frac{2}{3} *\frac{-2}{1}+3\)  

y= \(\frac{-4}{3}+\frac{3}{1}\)

y= \(\frac{5}{3}\)

Answer: -2 5/3

Step-by-step explanation:

y= 2/3*-2/1+3

y= -4+3/1

-2 5/3

Answer: is A

Step-by-step explanation:

Answer: 30%

Step-by-step explanation: 21/70 = 21 divide 70 = 0.3 = 30%

Answer:

79

Step-by-step explanation:

add this you have easily find answer