Kerry invited 23 friends to his pool party. They played a game where everyone had to separate into groups. Each group had the same number of children. The game could not be played with all 24 children in one group, and each group had to have more than 2 children.
Which of the following are ways that they could divide into groups?

Answer:

Irrational, Rational, and Complex Roots

Step-by-step explanation:

Irrational roots cannot be written as a fraction, for example, √2 is an irrational root because 2 is not a square number

Rational roots can be written as a fraction. For example, √4 is a rational root because it can be either -2 or 2 which are both rational.

Complex/imaginary roots take the form of [tex]a+bi[/tex] where "a" is the real part and "b" is the imaginary part. For example, √(-1) = i which is complex/imaginary.

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

Step-by-step explanation:

Two triangles will be better than one half times five times thirteen. We'll also have a single rectangular piece. It measures 12 by 10. 20 times 2 equals 40. 13 divided by 2 divided by 2 is equal to 4. I am capable of 44 times two times two. 13 is 52 One is equal to 10 x 2 x 1/2. 12 times 10 is 120, and 5 times 13 is 65. Consequently, the area is 297 square feet (40 plus 52 plus 20 plus 65 plus 120).

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Answer: 297 ft.2

Step-by-step explanation:

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:

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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Exponential form is a way of representing repeated multiplications of the same number by writing the number as a base with the number of repeats written as a small number to its upper right.

In the exponential form, the exponent indicates the number of times the base is used as a factor.

For example, in the case of 16 it can be written as 2 × 2 × 2 × 2  = [tex]2^{4}[/tex], where 2 is the “base” and 4 is the “exponent.

A product in which the factors are identical is called a power of that factor.  The number that is repeated is called the base, and the number of times it repeats is called the exponent, power or degree. And the power that is written on the right upper side are called exponents. when multiplying the numbers having same base and different exponents then the base is kept same and the exponents are added.

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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 equivalent expression is  -1.9b + 7.8.

There is a concept known as an analogous expression, which is an expression that has the same value as another expression but has a different appearance.

Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.

Combine similar phrases now:

The definition of like words is the terms that have the same variable raised to the same power. Only the numerical coefficients can change in algebra.

When we combine the term b's coefficient, we get

1.3b + 7.8–3.2b

= (1.3−3.2)⋅b + 7.8

By condensing the equation, we obtain

= (- 1.9) +b + 7.8

= −1.9b + 7.8

There is a condensed equivalent formula of -1.9b + 7.8.

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Answer:

Step-by-step explanation:

factors of 8

Answer:

F- of a 8* i think

Step-by-step explanation:

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:

x=24.8

Step-by-step explanation:

24.8/4 = 6.2 and 6.2 times 4 is 24.8

The Remainder Theorem states that if a polynomial P(x) is divided by (x - c), the remainder is P(c). To find the factor of a polynomial using the Remainder Theorem, you can use the following steps:

Example:

P(x) = x^3 + 3x^2 + 2x -6

Factor = (x-2)

P(2) = 8 + 12 + 4 - 6 = 0

So, the factor of P(x) is (x-2)

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The required dimensions of the dilated kitchen is 8.5 inch by 13.09.

The scale factor is defined as the ratio of modified change in length to original length.

Here,
Current dimension of the graph = 8.5 inch by 11 inch
Final dimension of the graph = 24 inch by 36 inch

Now,
Dilated dimension of the kitchen
Length = 24 / 8.5 × 3 = 8.5 inch

Width = 36/11 × 4 = 13.09

Thus, the required dimensions of the dilated kitchen is 8.5 inch by 13.09.

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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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A rental car company charge $50 per day to rent a car and $0. 15 for every mile driven, then the inequality for the number of days will be represented as x ≤ 2.21 days.

It is referred to as being unfair when two terms are joined by a sign like "not equal to," "more than," or "less than." The inequality illustrates the relationship between variables and numbers in terms of greater than and less than.

In mathematics, a relationship between two expressions or values that are not equal to each other is called 'inequality'. So, a lack of balance results in inequality.

Given that a rental car company charges $50 per day to rent a car and $0.15 for every mile driven.

The equation of inequality will be written as,

C ≥ [tex]0.15m + 50x[/tex]    

Here, C is the total cost, m is the number of miles, and x is the number of days.

C ≥ [tex]0.15m + 50x[/tex]    

C ≥ ( [tex]0.15*100[/tex] ) + [tex]50x[/tex]

130 ≥ 19.5 + [tex]50x[/tex]

130 - 19.5 ≥ [tex]50x[/tex]

[tex]50x[/tex] ≤ 110.5

x ≤ 110.5 / 50

x ≤ 2.21 days

Therefore,

A rental car company charge $50 per day to rent a car and $0. 15 for every mile driven, then the inequality for the number of days will be represented as x ≤ 2.21 days.

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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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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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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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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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Answer:

8

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Answer:y ≥ 15 − 5x

Step-by-step explanation:

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.

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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Answer:

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

Given system:

Solve by substitution:

Find y:

The matching choice is A.

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