A manufacturer makes ball bearings out of motel steel. it takes 5.24 cubic centimeters of molten steel to make ball bearings that each have a diameter of 1 centimeter

The mean of the distribution of sample proportions is 179.8 and the standard deviation is 0.019

The sample distribution of the proportions is used to measure the proportion with which success is achieved. The chance of an event taking place is the proportion computed by dividing the number of successes by the size of the sample.

Given that, You intend to draw a random sample of size n = 580 from a population whose parameter is p = 0.31, we are asked to find the mean of the distribution of sample proportions and standard deviation of the distribution of sample proportions.

Under the sampling distribution of the proportions, the mean and standard deviation are calculated by :

a) The mean is given as ;

μ = nP

Where, n is the sample size

P is the population proportion

Therefore,

μ = 580(0.31)

μ = 179.8

b) The standard deviation is given as follows :

δ = [tex]\sqrt{\frac{P(1-P)}{n} }[/tex]

δ = [tex]\sqrt{\frac{0.31(1-0.31)}{580} }[/tex]

δ = 0.019

Hence, the mean of the distribution of sample proportions is 179.8 and the standard deviation is 0.019

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The quotient is the number that is generated when we perform division operations on two numbers, and the result of the division is called the quotient.

There are four main terminologies used in the arithmetic division such as divisor, dividend, quotient, and remainder.

The number is divided by another number to get a different number as an output.

Dividend = Quotient × Divisor + Remainder

If the remainder is equal to 0, then;

Dividend = Quotient × Divisor

Therefore,

Quotient = Dividend ÷ Divisor

Dividend: The number which is required to be divided

Divisor: The number which divides the given dividend

Remainder: The number which is left after the division method. When a number is completely divided then the remainder is zero.

Consider an example 25/5=5-----quotient.

where 25 is the dividend

5 is the divisor.

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Answer:

75%

Step-by-step explanation:
part/whole(100)

360/489 = .75

.75(100) = 75%

The percent of [tex]\frac{480}{360}[/tex] equals to 75%

The value of the third side of the triangle, that is x is 24.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side. When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.

The given triangle is a right- angles triangle.

Use the Pythagorean theorem to find the third side of the triangle.

The Pythagorean theorem is given by the following formula:

a^2 + b^2 = c^2

10^2 + b^2 = 26 ^2

100 + b^2 = 676

b^2 = 676 - 100

b^2 = 576

b = 24

Hence, the value of the third side of the triangle, that is x is 24.

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Sarah will make 6 baskets in her next 6 shots.

If Sarah made a basket on one of her first shots in a basketball game, and she continues to make baskets at the same rate, we can use that information to predict the number of baskets she will make in her next 6 shots.

Since we know that Sarah made a basket on one of her first shots, we can assume that the probability of her making a basket on any given shot is 1/1 or 100%.

If the probability of Sarah making a basket on any given shot is 100%, then we can expect her to make a basket on all 6 of her next shots. Therefore, Sarah will make 6 baskets in her next 6 shots.

Therefore, Sarah will make 6 baskets in her next 6 shots.

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Answer: A. Use one-digit numbers 0-9; let 0 represent babies born with some kind of major birth defect, and 1-9 represent babies born without a major birth defect and skip 9.

This is the simplest way to assign random numbers to conduct a simulation based on the statistic that 2% of babies born in the world have some kind of major birth defect.

Using one-digit numbers 0-9 and designating 0 as babies born with a major birth defect and 1-9 as babies born without a major birth defect allows for a simple and easy-to-understand simulation, as only 2% of the numbers generated will be 0.

The other options are not the most simple way to conduct a simulation based on this statistic, as they would require more digits and more complex rules for assigning numbers to represent babies with and without major birth defects.

Step-by-step explanation:

The m ∠SPR of the rhombus with sides PQRS is 65, option C.

Only the opposite angles of a rhombus are equal. A rhombus's diagonal angle is 90 degrees.

There are two ways to find the angle SPR of the rhombus, PQRS;

If ∠PQR = 50°  then, ∠PQR = ∠PSR (opposite sides)

∠OSR = 1/2 x 50° = 25° where SQ bisects ∠PSR

∠ORS + ∠ROS + ∠OSR = 180°

∠ORS + 25° + 90°  = 180°

∠ORS = 180° - 115°

∠ORS = 65°

Also, it can be calculated thus:

Because rhombus adjacent sides are supplementary, it can be written as; ∠QRS + ∠PQR = 180°

∠QRS = 180° - ∠PQR

∠QRS = 180° - 50°

∠QRS = 130°

Even though a rhombus' diagonal is an angular bisector, the ∠PRS is half of the ∠QRS.

Therefore ∠SPR = ∠QRS/2

∠SPR = 130°/2

∠SPR = 65°

The value of ∠SPR is half the angle because the opposite angles are equal therefore each side has 65°.

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Answer:

--------------------------

Given system:

Solve by substitution:

Find y:

The matching choice is A.

Answer:

3

Step-by-step explanation:

Dilating a shape will proportionately affect its side lengths.

To find the scale factor between the given triangles, take one side on the larger triangle and divide it by the corresponding side on the smaller triangle. I will divide the triangles' top sides (24 and 8).

[tex]\textrm{scale factor} = \dfrac{24}{8} = 3[/tex]

So, the scale factor used was 3.

Remainder Theorem is a method for polynomial division using Euclidean geometry.

Algebraic expressions called polynomials include constants and indeterminates.

Polynomials can be thought of as a type of mathematics.

Nearly all branches of mathematics employ them to express numbers, and calculus is one of those branches where they play a crucial role.

A specific kind of expression is a polynomial.

A mathematical statement without the equals symbol (=) is called an expression. Let's examine the definition and usage of polynomials as they are described below.

An algebraic expression known as a polynomial requires that all of its exponents be whole numbers.

Any polynomial must have variable exponents that are non-negative integers. Although a polynomial contains variables and constants, we are unable to divide a polynomial by a variable.

Hence, Remainder Theorem is a method for polynomial division using Euclidean geometry.

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Using equations, the number of small boxes shipped is 15 while the number of large boxes shipped is 7.

An equation is described as a mathematical statement of the equality of two or more mathematical expressions.

Equations use the equation sign (=) to show that the expressions are equivalent or equal.

The volume of each small box = 7 ft³

The volume of each large box = 20 ft³

The number of small boxes = x + 8

The number of large boxes = x

The total volume of all the boxes = 245 ft³

The total volume of the 8 additional small boxes = 56 ft³ (8 x 7 ft³)

The remaining volume of the boxes after subtracting the volume of the 8 additional small boxes = 189 ft³ (245 - 56)

7x + 56 + 20x = 245

7x + 20x = 189

27x = 189

x = 7 (189/27)

The number of small boxes shipped, x + 8 = 7 + 8 = 15 boxes

The number of large boxes shipped, x = 7 boxes

Check:

Small boxes = 15 x 7 ft³ = 105 ft³

Large boxes = 7 x 20 ft³ = 140 ft³

Total               22              245 ft³

Thus, the paper company shipped 15 small boxes with 7 large boxes.

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Answer:

Step-by-step explanation:

factors of 8

Answer:

F- of a 8* i think

Step-by-step explanation:

Answer:

x=24.8

Step-by-step explanation:

24.8/4 = 6.2 and 6.2 times 4 is 24.8

5.33 trays must be sold to cover all costs including labor.

Cost means a price that must be paid for something or a sacrifice.

Given that,

Profit on each tray sold excluding labor cost = $35-$14 = $21

Thus, the Total labor cost for making a party tray for a day = Total labor hours * wages per hour* No. of labors = $7 * $8*2 = $112

The number of trays that must be sold to cover the cost will be = Total labor cost for making party tray for a day/ Profit on each tray sold excluding labor cost = $112/$21 = 5.33

Therefore, 5.33 trays must be sold to cover all costs including labor.

Complete question: Party trays which cost $14.00 to make not including labor are sold for $35.00. if two people work 8-hour shifts making the trays at $7.00 per hour, how many trays must be sold to cover all costs including labor?

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Function has one y for one x. if you pass line through x = 7 it cuts graph on different values of y

it is not function

Answer: (x-5)(x)(x+9)(x+2)

Step-by-step explanation:

A rational expression that excludes the values 2 and -2 would be (any polynomial)/(x² - 4).

A rational expression is simply a fraction with polynomials as the numerator and denominator. When the denominator of a rational expression equals 0 (because division by 0 is undefined), you get excluded values.

The numerator can be any number. It could be 1, 10000x + x² or anything that comes to mind. Any polynomial in the numerator will not produce an excluded value. We get ( x - ( - 2 ) ) and ( x - 2 ) by excluding -2 and 2. We multiply them together: ( x + 2 ) ( x - 2 ) = x² - 4.

= (any polynomial)/(x² - 4)

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First add 15 to 93 which equals 108.
-9h=108

/-9     /-9     divide both sides by -9

h=-12

[tex]-9h-15=93[/tex]

Add 15 to both sides:
[tex]-9h-15+15=93+15[/tex]

[tex]-9h=108[/tex]

Divide both sides by -9:

[tex]\dfrac{-9h}{-9} =\dfrac{108}{-9}[/tex]

[tex]\fbox{h = -12}[/tex]

The function represented by the table can be written as:

y = -4x + 3

Here we have a function represented by a table. Notice that for each increase of one unit in the x-value, the y-value decreases by 4.

Then we have a linear function, which can be written in a general form as:

y = a*x +b

Where a isthe slope and b is the y-intercept.

Because of the first pair on the table, (0, 3), we conclude that the y-intercept is 3, then we can rewrite:

y = a*x + 3

Now we can use the second point (1, - 1) and replace the values on the equation above.

-1 = a*1 + 3

-1 = a + 3

-1 - 3 = a

-4 = a

The linear function is:

y = -4x + 3

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The volume of air in the spherical ball is [tex]\frac{4}{3}\cdot \pi\cdot 3^3\cdot 10^6[/tex]. So the option A is correct.

In the given question, we have to find the volume of air in the spherical ball.

A sphere's capacity is measured by its volume. It is the area the sphere calls home. Cubic units are used to express the volume of a sphere. The sphere has a three-dimensional, rounded shape. Its shape is defined by its three axes, which are the x, y, and z axes.

Since the cross-section of the sphere is a circle, the volume in this situation is dependent on the radius's diameter. A sphere's surface area is the area or region of its outside. The following formula can be used to determine the volume of a sphere whose radius is "r":

V = [tex]\frac{4}{3}\pi r^{3}[/tex]

As given r = 3·10^2. So,

V = [tex]\frac{4}{3}\pi (3\cdot 10^2)^{3}[/tex]

V = [tex]\frac{4}{3}\cdot \pi\cdot 3^3\cdot 10^6[/tex]

V = [tex]4\cdot \pi\cdot 3^2\cdot 10^6[/tex] cm^3

Hence, the option A is correct.

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The complete question is given below:

The pair in the solution of the equation 2x-3y = 7 is (5,1).

The set of all values that, when substituted for unknowns, make an equation true is known as the solution.

A specific location on the graph is the solution of a linear equation in two variables, where ax+by = c, meaning that when the x-coordinate is multiplied by a and the y-coordinate is multiplied by b, the sum of these two values equals c. There are essentially an endless number of solutions to a linear equation with two variables.

Now in the question,

To find the pair of solutions of equation 2x - 3y = 7, we satisfy all the pairs one by one in the given equation

1. Putting the value of (x, y) as (0,2) in the equation we get-

2*0 - 3*2 = 7 ⇒ -6 =7

Therefore LHS ≠ RHS

Hence it is not the solution to the equation.

2. Putting the value of (x, y) as (2,-3) in the equation we get-

2*2 - 3*-3 = 7 ⇒ 13 =7

Therefore LHS ≠ RHS

Hence it is not the solution to the equation.

3. Putting the value of (x, y) as (5,1) in the equation we get-

2*5 - 3*1 = 7 ⇒ 7 = 7

Therefore LHS = RHS

Hence it is the solution to the equation.

4. Putting the value of (x, y) as (1,5) in the equation we get-

2*1 - 3*5 = 7 ⇒ -13 =7

Therefore LHS ≠ RHS

Hence it is not the solution to the equation.

Thus (5,1) is the solution of the equation.

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The amount of yogurt that Karolina used when making 800 ml of salad is 300 ml.

Ratio is  used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another quantity. In a ratio, two quantities are compared using division. Here the dividend is called the 'antecedent' and the divisor is called the 'consequent'.

A salad dressing is made by mixing yoghurt and mayonnaise in the ratio

3:5.

For 800 ml of salad dressing:

Amount of yoghurt = (3 / (3 + 5)) * 800 ml

Amount of yoghurt = 300 ml

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The answer is 300 ml!!!

The sum of the first six terms of the given series is 31.99.

A list of elements or objects that have been arranged sequentially is referred to as a sequence.

The total of all the terms in a sequence can be used to very broadly define a series. All of the terms in the sequence must, however, clearly relate to one another.

The given sequence is 4, 10, 2.5, 0.625, . . .

Every successive term in given series is divided by 4, and the so the first six terms of the series are:

[tex]\frac{40}{4} = 10\\ \\ \frac{10}{4} = 2.5 \\\\\frac{2.5}{4}= 0.625\\ \\\frac{0.625}{4} = 0.156\\\\\frac{0.156}{4}= 0.039\\\\\frac{0.039}{4}= 0.0097[/tex]

Also, every even term in the series is subtracted from the previous term.

Adding all the given terms we have:

[tex]40-10+2.5-0.625+0.156-0.039 = 31.99[/tex]

Hence the sum of the first six terms of the series is 31.99.

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Answer:y ≥ 15 − 5x

Step-by-step explanation:

Jamine will earn $193.75.To give us an accurate amount, we round the answer up to the hundredth place, which gives us our final amount of $193.75.

To give us an accurate amount, we round the answer up to the hundredth place, which gives us our final amount of $193.75.

1. Take the hourly rate of $15.50 and multiply it by the number of hours worked, 12.5, to get the total amount earned.

2. $15.50 x 12.5 = $193.75

3. Round the answer up to the hundredth place for a total of $193.75

Jamine charges $15.50 per hour to baby-sit. In one weekend, he baby-sat for 12.5 hours. To calculate how much money he will earn, we take the hourly rate of $15.50 and multiply it by the number of hours worked, 12.5. This gives us a total of $193.75. To give us an accurate amount, we round the answer up to the hundredth place, which gives us our final amount of $193.75.

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Step 1: Group the first two terms together, followed by the last two terms. Step 2: Extract a GCF from each binomial separately. Step 3: Remove the common binomial. It's worth noting that if we multiply our answer by itself, we get the original polynomial.

A polynomial is an expression in mathematics that consists of variables (also known as indeterminates) and coefficients and includes only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Step 1: Combine the first two terms, then the last two terms. Step 2: Separately extract a GCF from each binomial. Step 3: Get rid of the common binomial. It's worth noticing that dividing our solution by itself yields the original polynomial. A polynomial is an equation made up of variables, constants, and exponents that are mixed using mathematical operations including addition, subtraction, multiplication, and division (No division operation by a variable).

Here,

Step 1: Combine the first two terms, then the last two terms. Step 2: Separately extract a GCF from each binomial. Step 3: Get rid of the common binomial. It's worth noticing that dividing our solution by itself yields the original polynomial.

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Answer:

8

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

So on solving the provided question we cans say that factors of  4y^2=81 are - y = +9/4 and - 9/4

Any natural number other than 1 with just itself and the number 1 as its divisors is considered a prime factor. Actually, 2, 3, 5, 7, 11, and so on are some of the first prime numbers. an amount that has been multiplied to produce another amount. By dividing 15 by 3 and 5, for instance, we get 3 5 = 15. main elements: Prime factors include all factors that are prime but are not composite. A few prime factors of 30 are 2, 3, and 5. Only 2 and 3 are prime factors of 12, so listing 2 twice as 2 2 3 (or 22 3) is necessary to factorize 12. The sum of 2 + 3 is not 12.

factors of  4y^2=81

are -

y = +9/4 and - 9/4

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