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To find Martin's average total income, we need to add his average weekly wage to his average weekly tips:

$240 (weekly wage) + $356 (weekly tips) = $596 (average total income)

Therefore, Martin's average total income is $596 per week.

Answer: 113.10 inches squared

Step-by-step explanation:

formula for area: A=(pi)r^2

the diameter is 2x the radius so the radius would be 12/2=6. plug 6 in for r and solve. The answer is 113.097 so when you round to the nearest hundredth it becomes 113.10

The probability that Alice has the disease given that she tested positive is only about  0.00563

To solve this problem, we can use Bayes' theorem, which relates the conditional probabilities of two events. Let's define the following events

A: Alice has the disease.

B: Alice tests positive.

We want to find P(A|B), the probability that Alice has the disease given that she tested positive. Bayes' theorem tells us that

P(A|B) = P(B|A)× P(A) / P(B)

where

P(B|A) is the probability of testing positive given that Alice has the disease, which is 1 - the false negative rate = 0.85.

P(A) is the frequency of the disease in the population, which is 0.1% or 0.001.

P(B) is the overall probability of testing positive, which can be calculated using the law of total probability

P(B) = P(B|A) × P(A) + P(B|not A) × P(not A)

where

P(B|not A) is the probability of testing positive given that Alice does not have the disease, which is the false positive rate = 0.15.

P(not A) is the complement of P(A), i.e., the probability that Alice does not have the disease, which is 1 - P(A) = 0.999.

Therefore,

P(B) = 0.85 × 0.001 + 0.15 × 0.999 = 0.15084

Now we can substitute these values into Bayes' theorem

P(A|B) = 0.85 × 0.001 / 0.15084 = 0.00563

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The answer of the given question based on the graph  transformations  is  option (c): (x-4, y+0), 90° counterclockwise rotation, reflection over the x-axis.

Reflection is a transformation that flips an object over a line, plane, or point. The line, plane, or point is called the "line of reflection", the "plane of reflection", or the "point of reflection", respectively. Reflection is a fundamental concept in geometry, and it has applications in various fields of mathematics, physics, and engineering. It is often used in symmetry analysis, transformation geometry, and computer graphics.

The series of transformations that would carry the rectangle onto itself is option (c): (x-4, y+0), 90° counterclockwise rotation, reflection over the x-axis.

To see why, we can analyze each transformation and its effect on the rectangle:

(x-4, y+0) translates the rectangle left by 4 units.

90° counterclockwise rotation preserves the right angles and parallel sides of the rectangle.

Reflection over the x-axis preserves the right angles of the rectangle and also preserves the orientation of its parallel sides.

Therefore, the final image after all three transformations would be congruent to the original rectangle, i.e., the rectangle would be carried onto itself.

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Answer:

a₅ = 11

Step-by-step explanation:

using the recursive rule [tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + 2 , with a₁ = 3 , then

a₂ = a₁ + 2 = 3 + 2 = 5

a₃ = a₂ + 2 = 5 + 2 = 7

a₄ = a₃ + 2 = 7 + 2 = 9

a₅ = a₄ + 2 = 9 + 2 = 11

We can conclude after answering the presented question that Use the equation data to discover potential for process changes that might result in a reduction in the time necessary to perform the activity.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or readings of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the calculation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

The procedures that a manufacturing organisation might take to undertake a time study analysis are as follows:

List the tasks performed by the workers and describe what constitutes a complete unit of labour.

Choose a representative sample of employees to observe. The sample size should be high enough to be statistically significant, but not so large that observing all workers becomes unfeasible.

Use the data to discover potential for process changes that might result in a reduction in the time necessary to perform the activity.

By doing a time study analysis, the manufacturing organisation may acquire useful insights into their workers' productivity and find chances for process changes that will help them fulfil the rising demand for their products.

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Answer:

After 16 years Mr. Jibril will be twice as old as his son.

Step-by-step explanation:

t - age Mr. Jibril

s - son age

t=4s (father is 4 times older than son)

t-4=7(s-4) (4 years ago they both have 4 year old less and father was 7 times older than son)

t=7s-28+4

t=7s-24

7s-24=4s

3s=24

s=8

t=32

x- years after Mr. Jibril will be twice as old as his son.

32+x=2(8+x)

32+x=16+2x

16=x

x=16

The unknown angle in the triangle is as follows;

m∠S = 38 degrees

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.

In the triangle QRS,

m∠Q = 4m∠R

m∠R = 3 / 4 m∠S

Therefore, let's find the angle m∠S in the triangle as follows:

Therefore,

m∠Q + m∠R + m∠S = 180°

let

m∠R = x

4x + x + 4 / 3 x = 180

5x + 4 / 3 x  = 180

15x + 4x / 3 = 180

19x / 3 = 180

19x = 180 × 3

19x = 540

x = 540 / 19

x = 28.42

Therefore,

m∠S = 4 / 3 (28.42)

m∠S = 37.8947368421

m∠S = 38 degrees

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Answer:

Step-by-step explanation:

To write the ratio of baking soda to salt, we need to compare the amount of baking soda to the amount of salt in the recipe.

The recipe uses 3/4 teaspoon of baking soda and 3 teaspoons of salt, so the ratio of baking soda to salt is:

3/4 : 3

To simplify this ratio, we can divide both numbers by the greatest common factor (GCF) of 3 and 4, which is 1.

3/4 divided by 1 = 3/4

3 divided by 1 = 3

So the simplified ratio of baking soda to salt is:

3/4 : 3 = 3: 12

To find the value of the ratio, we can divide both the numerator and denominator by 3:

3/3 : 12/3 = 1: 4

Therefore, the value of the ratio of baking soda to salt is 1:4.

Answer:

Circumfrance= 21.991

area= 38.48

Step-by-step explanation:

2piR

R=3.5

:)

Answer: c

Step-by-step explanation:

The rate at which the volume of water in the tank is changing is 58π(dr/dt).

To find the rate at which the volume of water in the tank is changing if the rate at which the height is decreasing is 8 centimeters per minute when the height is 4 meters, we need to use the formula for the volume of a cylinder, which is given by:

V = πr²hwhere V is the volume of the cylinder, r is the radius, and h is the height.

We also need to differentiate the formula for the volume of a cylinder with respect to time to get an equation for the rate of change of the volume of the cylinder. Differentiating the formula for the volume of a cylinder with respect to time, we get:

dV/dt = πr²dh/dt + 2πrhdr/dt

where dV/dt is the rate of change of the volume of the cylinder, dh/dt is the rate of change of the height of the cylinder, and dr/dt is the rate of change of the radius of the cylinder.

Substituting the given values into the formula and simplifying, we get:

dV/dt = π(5²)(-8/100) + 2π(5)(6)(dr/dt) = -2π + 60π(dr/dt) = 58π(dr/dt)

Therefore, the changes in water volume in the tank is 58π(dr/dt).

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Answer: x = -5, y = 1

Step-by-step explanation:

These are simultaneous equations

I will use the substitution method

BTW [1] means the top equation, and [2] the bottom equation

Rearrange [2] for x

-x = -4 + 9y

x = 4 - 9y

Substitute 4 - 9y into [1]

3(4 - 9y) - 2y = -17

Expand the bracket

12 - 27y - 2y = -17

Simplify

12 - 29y = -17

Rarrange for y

12 = 29y - 17

29y = 12 + 17 = 29

Now substitute y into either equation to solve for x

I will use [2] as it looks easier

-x - 9(1) = -4

Expand the bracket

-x -9 = -4

-x = 5

Now lets substitute x and y into [1] to check our answer

3(-5) - 2(1) = -17

-15 - 2 = -17

The standard deviation of the sampling distribution of  30 seconds songs then the total number of songs are 36.

The mean and the standard deviation of the sampling distribution of x:

The mean and the standard deviation of the sampling distribution of x are defined according to the Central Limit Theorem, which states that:

The mean is the same as the population mean. The standard deviation is the division of the population standard deviation by the square root of the sample size. The central limit theorem states that as long as the sample size is large enough, the sampling distribution of the mean will always be normally distributed. The sampling distribution for the mean will be normal whether the population is normally distributed, Poisson, binomial, or any other distribution.

Now,

The parameters for this problem are given as follows:

Population mean of 225 seconds.

Population standard deviation of 60 seconds.

Sample size of 10 seconds.

Hence the standard deviation for the sampling distribution of x is given as follows:

s = 60/√(10) = 19 seconds.

if the sampling distribution of the songs is 30second tehn the tottal number of songs are 36

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The old age dependency ratio as a decimal is 0.190.

The old age dependency ratio is a measure of the number of people who are considered "dependent" on those who are of working age.

Specifically, it is the ratio of the number of people aged 65 years and over to the number of people aged 15 to 64 years old.

Old Age Dependency Ratio = (Number of people over 65) / (Number of people aged 15-64)

Old Age Dependency Ratio = 40,809 / 214,965 = 0.1895

Therefore, Rounding this to the thousandths place the Old Age Dependency Ratio as a decimal is 0.190.

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Answer:If (2t+1)is a factor then t=2−1 must be one of the zeroes of the given polynomial. Substituting in the given equation.

q((2−1))=4(2−1)3+4(2−1)2−(2−1)−1=4(8−1)+4(41)+(21)−1=(2−1)+1+(21)−1=0

Hence(2t+1) is a common factor of q(t)

Step-by-step explanation:

The center of the hyperbola is the midpoint between the vertices, which is (-2,6).

The distance between the center and each vertex is 3, so the distance between the center and each focus is c = 7.

The distance between each vertex and focus is a = 4.

The equation of the hyperbola with center (h,k) is:

(x - h)^2 / a^2 - (y - k)^2 / b^2 = 1

where b^2 = c^2 - a^2.

Plugging in the values we have:

- Center: (h,k) = (-2,6)

- a = 4

- c = 7

- b^2 = c^2 - a^2 = 49 - 16 = 33

So the equation of the hyperbola is:

(x + 2)^2 / 16 - (y - 6)^2 / 33 = 1

Answer:

1047

Step-by-step explanation:

a_n = a_1 + (n - 1)d

a_19 = 243

a_11 = 147

243 = a_1 + (19 - 1)d

147 = a_1 + (11 - 1)d

243 = a_1 + 18d

147 = a_1 + 10d

a_1 = 243 - 18d

a_1 = 147 - 10d

243 - 18d = 147 - 10d

-8d = -96

d = 12

a_1 = 147 - 10d

a_1 = 147 - 10(12)

a_1 = 27

The first term is 27. The common difference is 12.

a_86 = a_1 + (n - 1)d

a_86 = 27 + 85(12)

a_86 = 1047

Answer:

1 and 19

Step-by-step explanation:

3(x-10)^2 = 3(x^2-20x+100) = 3x^2 - 60x + 300

If 3x^2 - 60x + 300 = 243, 3x^2 - 60x + 57 = 0

Divide by 3 to get x^2 - 20x + 19 = 0

use the quadratic equation (-b±√(b²-4ac))/(2a) to get

(20±√324)/2 = (20±18)/2 = 1 and 19

Answer:

3

Step-by-step explanation:

do the brackets first

(5+3) = 8

24÷8=3

so the answer is 3

Answer:

The correct numerical expression using PEDMAS for "subtract the sum of 2 and 9 from the product of 4 and 3" is:

4 x 3 - (2 + 9)

Using the order of operations, first, we perform the addition inside the parentheses, then we multiply 4 and 3, and finally, we subtract the result of the sum from the product:

= 4 x 3 - 11

= 12 - 11

= 1

Therefore, the correct numerical expression is (4 x 3) - (2 + 9) = 1.

Step-by-step explanation:

This is the simplified ratio of lengths DE:EF as (2/√(29))√(34) : 1.

A ratio is a relationship between two or more quantities that indicates how many times one quantity is contained in another. It is a way of comparing quantities of the same kind, such as lengths, areas, volumes, or numbers. A ratio is usually expressed as a fraction or a colon (:). Ratios can be simplified by dividing both terms of the ratio by their greatest common factor (GCF). Ratios are used in many fields such as mathematics, finance, science, engineering, and statistics, among others. They are used to compare different quantities, to express proportions or rates, and to solve various mathematical problems.

Here,

We can use the distance formula to find the lengths DE and EF, and then calculate their ratio:

Length DE = √[(xE - xD)² + (yE - yD)²]

= √[(10 - 4)² + (15 - 4)²]

= √(6² + 11²)

= √(136)

= 2√(34)

Length EF = √[(xF - xE)² + (yF - yE)²]

= √[(12 - 10)² + (20 - 15)²]

= √(2² + 5²)

= √(29)

Therefore, the ratio of lengths DE:EF is:

DE:EF = (2√(34)) : (√(29))

We can simplify this ratio by dividing both sides by √(29):

DE:EF = (2√(34))/√(29) : (√(29))/√(29)

= (2/√(29))√(34) : 1

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Note that the transformation for the above vertices are given as follows.

From the given graph, we can determine the transformations as follows:

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Full Question:

Although part of your question is missing, you might be referring to this full question: See attached image.

The volume of the pyramid is 4480ft³

A pyramid is a three-dimensional shape. A pyramid has a polygonal base and flat triangular faces, which join at a common point called the apex.

The volume of a pyramid is expressed as:

V = 1/3 b × h

b = base area

h = height

Here, base are = 17.5 × 32

= 560ft²

Height = 24ft

V = 1/3 × 560 × 24

V = 560 × 8

V = 4480 ft³

Therefore the volume of the pyramid is 4480ft³

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Answer:

x1 ≈ 0,84; x2 ≈ 4,16

Step-by-step explanation:

Find the discriminant and then both values of x according to the formulas (I added a photo of my solution)

The arithmetic equation that correctly describes the following real-world situation is (s x 10) ÷ 5 = 225.

What is arithmetic?

Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots.

Here, we have

Given: 10 pieces of candy are given to s students from a bag of candy containing 225 pieces. There are 5 pieces left over.

We have to find the equation that correctly describes the following real-world situation.

(s x 10) ÷ 5 = 225

2s = 225

s = 112.5

Hence, the value of s is 112.5

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Answer: ( s x 10 ) `-. = 225

Step-by-step explanation:

Thus, each book has an 8-inch height.

What are some math examples of volume?

The quantity of space taken up by a three-dimensional object can also be used to describe volume. By determining the number of units cubes it contains, the volume of such a solid like such a cube or cuboid can be determined.

Get the volume of a single book in cubic centimeters to get things started. We can accomplish this by multiplying a book's length, width, and height:

Volume of one book = 6 inches x 3/4 inches x height

Volume of one book = 4.5 cubic inches x height

Since the 12 books are all the same size, their combined volume is:

Total volume of books = 12 books x Volume of one book

Total volume of books = 12 books x 4.5 cubic inches x height

Total volume of books = 54 cubic inches x height

Since we are aware that the case has a total volume of 432 cubic inches, we can construct the following equation:

Total volume of case = Total volume of books

432 cubic inches = 54 cubic inches x height

When we solve for height, we obtain:

height = 432 cubic inches / 54 cubic inches

height = 8 inches

Thus, each book has a height of 8 inches.

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Therefore, the scale factor of triangle ABC to triangle UVW is  5 and option C is the correct choice.

Two triangles are shown to us in the photograph. We must determine the ABC to UVW scale factor.

To find the scale factor of our given triangles, we will divide one side of triangle UVW by its corresponding side of triangle ABC.

Original side  ×scale factor = new side

5 × scale factor =25

By multiplying both sides of the equation by 5, we obtain:

5/5×scale factor/5 =25/5

scale factor = 5

What exactly is scale factor?

A scale factor is a figure that, when multiplied by a certain amount, creates a smaller or bigger replica of the original figure. It is the ratio of a blueprint, map, model, or actual thing to the distance or object1. Every inch on a home layout, for instance, would correspond to 4 inches in real life if the scale factor was 1/41.

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Answer: ANSWER IS 5

Step-by-step explanation:

Answer:

18 sides

Step-by-step explanation:

We know the relation between exterior angle, interior angle. Given that each interior angle is 8 times the exterior. So, there are 18 sides for such a polygon given in question.