There are 8 marbles in a bag, all of different colors. In how many orders can 4 marbles be chosen? In other words, what is the
number of permutations of picking 4 marbles from the bag?
A
1680
B
70
С
40320

So on solving the provided question, we can say that the mathematical expression will be as follows, z-12, 17xy, 4x+75.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the expression 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +. In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted.

x - 6 + z  = 9-6+5 = 8

5*(x+y) = 5*(9 + 10 ) = 95

2x + z = 2*9 + 5 = 23

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The Classification of each sample ( i.e., sampling technique ) are

1) Cluster sampling is a type of sampling in which the whole population is divided into separate groups (clusters). After which a simple random sample is selected from these clusters to conduct the analysis. To determine whether the students have less homework to do now as compared to the previous year, all teachers of two buildings in a large school districted are interviewed. In the provided scenario, the two buildings can be considered as two cluster. Since, all the teachers of these two strata are interviewed, the sampling method can be considered as cluster sampling.Hence, the sampling method can be considered as a cluster sampling.

2)Systematic sampling is a type of sampling in which every k member is included in the sample, after the selection of the first unit. According to the question, every seventh customer is asked about his/her favorite store. Since, every seventh customer is asked about his/her favorite store, the sampling method can be considered as a systematic sampling.

3) Simple random sampling is a type of sampling in which every unit of the population has an equal chance of being included in the sample.

In the provided scenario, nursing supervisors are selected using random numbers. That is, the nursing supervisors are selected randomly from the population. Hence, the sampling method can be considered as simple random sampling.

4) According to the question, every hundredth Hamburg manufactured is checked. Since, every hundredth Hamburg manufactured is selected for checking, the sampling method can be considered as a systematic sampling.

5) Stratified random sampling is one of type of sampling techniques, which is used for a heterogeneous population. In case of stratified sampling, the heterogeneous population is divided into strata before collecting the sample . According to the question, mail carriers are divided into four groups according to gender and the route use by them. Then 10 people are selected randomly from each group for interview. Therefore, the population is divided into four groups according to two different characteristics and then 10 people are selected randomly from each group. Hence, the sampling method can be considered as stratified sampling.

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Complete question :

Classify each sample as random, systematic, stratified, or cluster

1. In a large school district, all teachers from two buildings are interviewed to determine whether they believe the students have less homework to do now than in previous years.

2. Every seventh customer entering a shopping mall is asked to select his or her favorite store.

3. Nursing supervisors are selected using random numbers in order to determine annual salaries.

4. Every hundredth hamburger manufactured is checked to determine its fat content.

5. Mail carriers of a large city are divided into four groups according to gender (male or female) and according to whether they walk or ride on their routes. Then 10 are selected from each group and interviewed to determine whether they have been bitten by a dog in the last year.

Critical F value with 8 numerator and 29 denominator degree of freedom at α = 0.01 is 3.20

The critical F value with 8 numerator degrees of freedom (also known as the numerator degrees of freedom or the numerator df) and 29 denominator degrees of freedom (also known as the denominator degrees of freedom or the denominator df) at a significance level of 0.01 can be found using a table of F-distribution values or by using a calculator or a software that can compute the F-distribution function.

The critical F value with 8 numerator degrees of freedom (df1) and 29 denominator degrees of freedom (df2) at a significance level of 0.01 can be found using the following formula:

F_critical = F(1 - alpha, df1, df2)

where F(1 - alpha, df1, df2) is the inverse of the cumulative distribution function (CDF) of the F-distribution, alpha is the significance level (0.01 in this case), and df1 and df2 are the numerator and denominator degrees of freedom, respectively.

For this case, the critical F value can be found using the inverse cumulative distribution function with 1- alpha = 0.99, df1 = 8 and df2 = 29

F(0.99,8,29) = 3.17

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We can see here that the missing proof is option D: ΔBPQ ∼ ΔDRS Reason: SSA.

A proof is a logical argument that demonstrates the truth of a statement or theorem. In mathematics, a proof is a sequence of logical steps that shows that a statement is true by using a combination of logical reasoning, definitions, established facts, and accepted rules of inference.

In other fields, such as computer science, a proof may refer to a demonstration that a program or algorithm is correct or that a system has a certain property.

We see here that the option selected above is actually the missing step in the proof.

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It's worth noting that to solve for T2 you need to have the values of other variables such as K1, K2, Ea, R and T1

What is the Arrhenius Equation?

The Arrhenius equation is a mathematical equation that describes the relationship between the rate constant (K) of a chemical reaction and the temperature (T) of the reaction. The equation was first proposed by Svante Arrhenius in 1889 and it states that the rate constant of a chemical reaction is directly proportional to the exponential of the negative activation energy (Ea) of the reaction, divided by the gas constant (R) and the absolute temperature (T). The equation can be written as:

K = A * e^(-Ea / (R*T))

The Arrhenius Equation Two-point form is a mathematical equation that describes the relationship between the rate constant (K) of a chemical reaction, the activation energy (Ea) of the reaction, the universal gas constant (R), and the temperature (T) of the reaction.

Given the equation K2/K1 = Ea / R (1/T1 - 1/T2)

a. To solve for K2, we can multiply both sides of the equation by

K1: K2 = K1 * Ea / R (1/T1 - 1/T2)

b. To solve for K1, we can divide both sides of the equation by

Ea / R (1/T1 - 1/T2): K1 = K2 / Ea / R (1/T1 - 1/T2)

c. To solve for Ea, we can multiply both sides of the equation by

R (1/T1 - 1/T2): Ea = K2/K1 * R (1/T1 - 1/T2)

d. To solve for T2, we can use the equation 1/T2= 1/T1 - Ea/R * K1/K2

It's worth noting that to solve for T2 you need to have the values of other variables such as K1, K2, Ea, R and T1.

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The inequality that can be used to find the number of windows is d + r ≤ 235 and 250r + 220d ≥ 55000

An equation is an expression that shows how two or more numbers and variables are related to each other. Types of equations can either be linear, quadratic or cubic

Inequalities are used to show the nonequal comparison of two or more numbers and variables

Let r represent the regular price and let d represent the discounted price.

Gerald company has an inventory of 235 windows, hence:

d + r ≤ 235   (1)

Also, the regular price is $250 and the discounted price is $220. The sales goal is $55000, hence:

250r + 220d ≥ 55000   (2)

The inequality is d + r ≤ 235 and 250r + 220d ≥ 55000

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Answer:

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

Use the coordinates to determine the function.

Point (0, 2):

The function becomes:

It has a multiplier of 0.8, so b = 0.8, so the function is:

Use the first point:

Use the second point:

The function is:

Answer:

[tex]\textsf{a)} \quad y=2(0.8)^x[/tex]

[tex]\text{b)} \quad y=3.5(3)^x[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]

Given:

Substitute the values of a and b into the exponential function formula:

[tex]\implies y=2(0.8)^x[/tex]

The y-intercept is when x = 0.  Therefore, given the function passes through point (0, 3.5), the y-intercept is 0.35 ⇒ a = 3.5.

Substitute the found value of a and given point (2, 31.5) into the exponential function formula and solve for b:

[tex]\implies 31.5=3.5b^2[/tex]

[tex]\implies b^2=9[/tex]

[tex]\implies b=3[/tex]

Substitute the values of a and b into the exponential function formula:

[tex]\implies y=3.5(3)^x[/tex]

The solution to the system of equations is

The number of ducks D = 8 ducks

The number of cows C = 6 cows

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of ducks be D

Let the number of cows be C

Now , the total number of animals = 14

So , D + C = 14   be equation (1)

And , the total number of legs = 40

Number of legs for ducks = 2 legs

Number of legs for cows = 4 legs

And , the total number of legs = 2D + 4C = 40

So , 2D + 4C = 40   be equation (2)

On simplifying the equations , we get

Multiply equation (1) by 2 , we get

2D + 2C = 28   be equation (3)

Subtracting equation (3) from equation (2) , we get

2C = 40 - 28

2C = 12

Divide by 12 on both sides of the equation , we get

C = 6 cows

Substituting the value of C in equation (1) , we get

D = 14 - 6

D = 8 ducks

Therefore , the value of C and D is 6 and 8 respectively

Hence , the number of cows is 6 and number of ducks is 8

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there is no question!

1) The equation is true for n = $12.30

2) 24 fluid ounces is equivalent to 3 cups.

Here we want to see for which values of n is the equation:

3n = $36.90

true.

To get that,we need to isolate the variable n. To do so, we can divide both sides by 3.

n = $36.90/3

n = $12.30

That is the value of n.

We want to write 24 fluid ounces as cups, we know the relation:

1 fluid ounce = 0.125cups.

Then we can just do the change of units as follows:

24 fluid ounces = 24*(0.125 cups.) = 3 cups.

So there are 3 cups on 24 fluid ounces.

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Answer:

[tex]x > 11[/tex]

Step-by-step explanation:

Greetings!!

Given equation

[tex]x + 2 > 13[/tex]

subtract 2 from both sides

[tex]x + 2 - 2 > 13 - 2[/tex]

simplify

[tex]x > 11[/tex]

[tex]solution \: \: x > 11 \\ interval \: notation \: (11, \infty )[/tex]

Hope it helps!!

The probability that the student finishes the inquiry in less than 1.5 hours is 0.45.

Mean= 4/3 and standard deviation= √(11/90)

a) To find the probability that the student finishes the inquiry in less than 1.5 hours, we need to find the area under the probability density function (PDF) of f(x) between the lower limit of 1 and the upper limit of 1.5.

This is given by the definite integral of f(x) from 1 to 1.5:

∫f(x)dx from 1 to 1.5

= ∫(2/5(x + 1))dx from 1 to 1.5

= (2/5)∫(x + 1)dx from 1 to 1.5

= (2/5)[x^2/2 + x] from 1 to 1.5

= (2/5)[(1.5)^2/2 + 1.5 - (1)^2/2 - 1]

= (2/5)[2.25/2 + 1.5 - 1/2 - 1]

=(2/5)[2.25/2]

=0.45

b) To find the mean, we need to use the formula:

Mean = ∫x*f(x)dx from a to b

In this case:

Mean = ∫x*(2/5(x + 1))dx from 1 to 2

= (2/5)∫x(x + 1)dx from 1 to 2

= (2/5)[x^3/3 + x^2/2] from 1 to 2

=(2/5)[(2)^3/3 + (2)^2/2 - (1)^3/3 - (1)^2/2]

= (2/5)[8/3 + 4/2 - 1/3 - 1/2]

=(2/5)[7/3 + 3/2]

=(2/5)[(20)/6]

=4/3

=1.333

To find the standard deviation, we need to use the formula:

Standard deviation^2 =(∫(x-μ)^2*f(x)dx) from a to b

Where μ is the mean

In this case,

Standard Deviation ^2= ∫(x-μ)^2(2/5)(x+1) dx from 1 to 2

=(2/5)∫(x-μ)^2(x+1) dx from 1 to 2

Simplifying, we get,

(x-μ)^3*(3x+μ+4)/30 from 1 to 2

=[(2-μ)^3*(6+μ+4)-(1-μ)^3*(3+μ+4)]/30

=[(2-μ)^3*(10+μ)-(1-μ)^3*(7+μ)]/30

Substituting the value of μ,

=[(2-4/3)^3*(10+4/3)-(1-4/3)^3*(7+4/3)]/30

=11/90

Therefore, Standard Deviation= √(11/90)

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The solution for the system of linear equations is (1,-3)

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here: -4x+5y=-19

                     -x-2y=5

Solving for x we get y equal to -3

Thus putting y=-3 in equation 1 we get x=1

Hence, The solution for the system of linear equations is (1,-3)

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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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The diagram that shows the C intercept D would be = diagram B. That is option B.

A universal set is defined as the set that contains all the values that makes up a data.

The universal set contains the following:

A = ( yellow corn)

B = ( yellow corn with variety kernel)

C = ( white corn)

D= ( white corn with variety butter and sugar).

The C intercept means the contents that are in C that can be found in D. The diagram that represents this form is diagram B.

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Running made Ava’s heart beat faster.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

While playing basketball, Ava’s heartbeat is 80 times in 30 seconds.

And, While running, her heartbeat was 60 times in 20 seconds.

Clearly, Ava's heartbeat is faster when he was running.

So, Running made Ava’s heart beat faster.

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Answer:

Step-by-step explanation:

[tex]\cfrac{s}{31}=24[/tex]

Multiply both sides by 31.

[tex]\cfrac{31s}{31}=24\times\:31[/tex]

[tex]\boxed{s=744}[/tex]

-Hope this helps!

Answer:

s = 744

Step-by-step explanation:

Now we have to,

→ find the required value of s.

The equation is,

→ s/31 = 24

Then the value of s will be,

→ s/31 = 24

→ s = 24 × 31

→ [ s = 744 ]

Hence, the value of s is 744.

The numerical length of TU is TU = 26.

What is the numerical length?

The formula states that the base-numerical length of a number is the number of digits in the base-numeral for where is the floor function. An -digit's length is another name for its multiplicative persistence.

Given:

ST=4x-4,   TU=4x-10,   and SU =5x+1

We have to find the numerical length of TU.

Here,

SU = ST + TU

5x + 1 = 4x - 4 + 4x - 10

Simplifying,

5x + 1 = 8x - 14

Subtract 1 on both sides,

5x + 1 - 1 = 8x - 14 - 1

        5x = 8x - 15

Subtract 5x on both sides,

5x - 5x = 8x - 15 - 5x

        0 = 3x - 15

      3x = 15

        x = 5

⇒ TU = 5(5) + 1 = 25 + 1 = 26

Hence, the numerical length of TU is TU = 26.

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Answer:

A (x,y) becomes A'(y,-x)

Step-by-step explanation:

this means we switch x and y to make x a negative

The requried equation model for the age of Jenna and her sister is given as y = x + 4.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

here,

A variable can be used in an expression that represents a real-world situation where one value is unknown, not stated or can change.
Let the age of the Jenna sister be x,
According to the question,
Jenna[y] is four years older than her sister,
So,
y = x + 4

Form above expression
When her sister is of 4 years,
Jenna age,

y = 4 + 4
y = 8 years

Thus, the requried equation model for the age of Jenna and her sister is given as y = x + 4.

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The  correct option is  the root of auxiliary equation are 0 and6

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The rate of change for the interval between –6 and –3 on the x-axis is; 2

To find the rate of change  for the interval between –6 and –3 on the x-axis, the first step is to locate the ordered pairs at those two points. Locating the two ordered pairs from the graph is seen to be (3, -2) and (6, 4).

Applying the slope formula with those two points, we can find the rate of change as;

slope; m = (y₂ - y₁)/(x₂ - x₁)

m = (4 + 2)/(6 - 3)

m = 6/3

m = 2

This value of m represents the rate of change

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To solve the equation 6x - 7y = 18 for y, you can start by isolating y on one side of the equation. To do this, you can add 7y to both sides of the equation:

6x - 7y + 7y = 18 + 7y

6x = 18 + 7y

Next, divide both sides of the equation by 7:

6x/7 = 18/7 + 7y/7

x = 3 + y

So the solution is y = 3 - x

This is the final solution for y in the equation 6x - 7y = 18

The cost per pint of juice $0.63875.

What is division?

Division, or the process by which two or more numbers are joined together to generate a new number, is one of the four basic arithmetic operations. Addition, subtraction, and multiplication make up the remaining operations.

Weight of juice for a classroom party is 5 gallons.

Total price is $25.55.

We know that 1 US liquid pint = 0.125 US liquid Gallon

=> 0.125 US liquid Gallon = 1 US liquid pint

Therefore, 5  US liquid Gallon = 5/0.125 US liquid pint

=> 5  US liquid Gallon = 8*5 US liquid pint

=> 5  US liquid Gallon = 40 US liquid pint

Now, the required price is 25.55/40 = $0.63875

Hence, the cost per pint of juice $0.63875.

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The statement which is not true for the given number line is |a| > b, option(a).

What is a number line?

A number line is a representation of a graduated straight line that is used to represent real numbers visually. It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.

For the given question,

Point a is to the left of 0, so it is a negative number.

So taking the modulus of a, we get the positive value of a.

But since a is closer to 0 than b, if the positive value of a is less than b.

For example if a = -4 and b is 6

|a| = |-4| = 4 < b

So |a| < b

Therefore the incorrect statement is option(a), |a| > b.

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Answer:

-8m+24-32n

Step-by-step explanation:

Distribute the -8 to each term inside the parentheses.

(m−3+4n)⋅(−8)=

-8 *m -3 * -8 + 4n * -8

-8m+24-32n

Answer:

[tex] \sf \: -8m - 32n + 24 [/tex]

Step-by-step explanation:

Given expression,

→ (m - 3 + 4n)(-8)

Let's simplify the expression,

→ (m - 3 + 4n)(-8)

→ (-8 × m) + (-8 × -3) + (-8 × 4n)

→ -8(m) - 8(-3) -8(4n)

→ -8m - (-24) - 32n

→ -8m + 24 - 32n

→ -8m - 32n + 24

Thus, answer is -8m - 32n + 24.

The total amount of wood to build the shelves will be;

⇒ 17[tex]\frac{1}{4}[/tex] feet

A fraction is a piece of a whole number and a technique to divide a number into pieces that are each the same.

Or, a fraction is a number that is stated as a quotient.

It can be written as the form of p : q, which is equivalent to p / q.

Given that;

To build the bookshelf, Tim want the three horizontal length of each length 3[tex]\frac{2}{3}[/tex] feet and two vertical length with each length 2[tex]\frac{5}{8}[/tex] feet.

Now, Find the total lengths for the amount of wood as;

The length of each horizontal = 3[tex]\frac{2}{3}[/tex] feet

And, The vertical length = 2[tex]\frac{5}{8}[/tex] feet

So, Total horizontal length = 3 × 3[tex]\frac{2}{3}[/tex]

                                        = 3 x 11/3

                                       = 11 feet.

And, Vertical length = 2 × 2[tex]\frac{5}{8}[/tex] feet.

                                  = 2 × 21/8

                                  = 5[tex]\frac{1}{4}[/tex] feet

Thus, Total length of wood = 11 + 21/4 feet

                                        = ( 44 + 21 ) / 4

                                        = 69 / 4 feet

                                       = 17[tex]\frac{1}{4}[/tex] feet

Therefore,

The total amount of wood to build the shelves will be;

⇒ 17[tex]\frac{1}{4}[/tex] feet

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Answer:

10

Step-by-step explanation:

180-140=20

20÷2=10

×=10

y=10

The y-coordinate rises as the x-coordinate rises when a line's slope is positive, indicating that the line "slopes upward."

You may quickly determine whether the graph of a quadratic function expands upward or downward by looking at the leading coefficient: if it is larger than zero, the parabola opens upward; if it is less than zero, the parabola opens downward.

An upward-sloping line has a positive slope when the y-coordinate rises while the x-coordinate falls. In the case of a line with a negative slope, the y-coordinate falls as the x-coordinate rises, causing the line to "slide downward.

With a positive slope, two variables are positively correlated, meaning that as x rises, y rises as well, and as x falls, y falls as well. A line on a line graph with a positive slope goes from left to right while maintaining its visual slope.

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