What is the greatest common factor of 30, 21, and 56?

Answer:

1.2+2.56.7×3218°÷456.7820

Answer:

Step-by-step explanation:

First write the reciprocal of 5/9 which it is 9/5 then multiply by 5 which it equal to 36/5

Step-by-step explanation:

I just answered this with all explanations.

Answer: 5

Step-by-step explanation: To find the distance between 2 points, we should use this formula:

d=√((x_2-x_1)²+(y_2-y_1)²)

So, using that it would be written as:

[tex]\sqrt{9 + 16}[/tex] (after simplified)

Now, we need to find the square root of 25

The square root of 25= 5

So, that is how I got my answer.

Answer:

Rectangle

Step-by-step explanation:

Welcome to Brainly! :]

A rectangle uses A=lw to calculate area

Where l is length and w is width

Hope this helps,

:]

Answer: 7% at 6 years would best fit their payment option. They would then be paying $238.69 monthly and which is under $250, I hope this helps!

Answer: 720.0 cm³

Step-by-step explanation:

To convert the volume of the die from millimeters to centimeters, we need to divide the volume by the conversion factor that relates millimeters to centimeters. Since 10 millimeters is equal to 1 centimeter, the conversion factor is 10.

To convert the volume to centimeters, we can divide it by the conversion factor:

7200 mm³ / 10 = 720 cm³

This means that the volume of the die is 720 cm³. Rounded to the nearest tenth, the volume of the die is 720.0 cm³.

The number of possible wins if the ball lands on red is  4.86 games.

Let there be 100 successive spins,

Random Variable (winnings): $1, -$1

Associated probabilities:

P($1) = 18/38 =9/19

P(-1) = 20/38 = 10/19

Expected winnings is (9/19)*1 + (10/19)*-1

= -1/19 on one spin.

= -2/19 on two spins

= -2/19 on a single spin for $2

= -100/19 on 100 successive spins

since there are 100 spins,  n =100

18 out of 38 spots are red, thus p=18/37 =0.486

expected number of wins = np

= 100* 0.486

=4.86

Probability is synonymous with possibility. It is a mathematical branch that deals with the occurrence of a random event. The value ranges from zero to one. Probability has been introduced in mathematics to predict the likelihood of events occurring. Probability is defined as the degree to which something is likely to occur.

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If each large truck $70,000. Past experience shows that they need twice as many vans as small trucks. The number of each type of vehicle they can buy is; Small truck 80, Commercial van 160, Large van 80.

Since the company intends to purchase 320 vehicle, Let write this equation:

C + S + L = 320 (Eq. 1)

Total cost of the vehicles:

25C + 80S +70L = 16,000 (Eq. 2)  (Divided by 1000 to keep the numbers small)

Number of commercial vans is twice the number of small trucks,

C = 2S

Substituting 2S in place of C in Eq. 1 and Eq. 2

2S + S + L = 320

25(2S) +80S +70L = 16,000

130S + 70L = 16,000

Multiplying the first of those equations by 70

210S + 70L = 22,400

130S + 70L = 16,000

Subtracting the second equation from the first:

80S = 6400

Divide both  side by 80S

S = 6400/80

S = 80 (Small truck)

Then:

C = 2S

C= 2(80)

C= 160 (Commercial van)

So,

C + S + L = 320

160 + 80 + L = 320

L = 320 - 160 - 80

L =80 (Large van)

Therefore  the number of each type of vehicle they can buy is; Small truck 80, Commercial van 160, Large van 80.

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Answer:

(a) A(w) = w(950-2w) = 950w-2w^2

(b) w = 237.5

(c) A = 112812.5

Step-by-step explanation:

First of all the maximum area is always a square. You can get the answer first to check your work later.

950/4 = 237.5

One side is not needed so add that length to the non-parallel side.

237.5+237.5=475 feet is the length and 237.5 feet is the width(s)

A=475*237.5

A=112812.5 square feet

Doing the algebra...

P=l+2w

950=l+2w

950-2w=l

A=lw

A=(950-2w)w

A=950w-2w^2

Here is the frequency table based on the data:

1 - 200                7

201 - 400            1

401 - 600            2

601 - 800            3

801 - 1000           1

1001 - 1200          1

1201 - 1400

1401 - 1600          1

1601 - 1800         1

A  frequency table is a table that is used to compress a large dataset into a smaller format that can be easily interpreted. A  frequency table is usually made up of a class interval and frequency.

A class is the group of a numbers. The frequency of the class is the total number of times that numbers within the class appear in the dataset.  For example in the class 100 - 200, there are 7 numbers in the dataset that have a value between 100 and 200. This means that the frequency of 100-200 is 7.

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The value of x is 9 and the value of y is 4.

What is the congruent triangle?

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.

The HL Postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.

The system of equations is

x + 3 = 3y ....(i)

x = y + 5 .....(ii)

Putting x = y + 5 in equation (i):

y + 5 + 3 = 3y

y + 8 = 3y

3y = y + 8

3y - y = 8

2y = 8

y = 4

Putting y = 4 in equation (ii)

x = 4 + 5 = 9

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The equation of the total amount is A = 500 + 500 * 6% * 1 and the value is $530

From the question, we have the following parameters that can be used in our computation:

Principal, P = $500

Rate, r =6%

Time = 1 year

The amount is calculated as

A = P + PRT

Substitute the known values in the above equation, so, we have the following representation

A = 500 + 500 * 6% * 1

The above represents the equation

So, we have

A = 530

Hence, the amount is $530

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Step-by-step explanation:

be a function, there needs to be one unique

value of +y+ for every +x+

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

The 1st set has 5 different values of +y+

for +x+=+1+ and violates definition

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

The 2nd set is a function

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

The 3rd set has

( 1,2 ) & ( 1,1 )

( 2,3 ) & ( 2,2 )

( 3,4 ) & ( 3,3 )

Each of these pairs violates the definition

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

The 4th set has ( 2,-7 ) & ( 2,0 ) which

violate definition

The difference between the largest and the smallest fraction is 0.24.

A fraction is a component of a whole.

Mathematically, the number is expressed as a quotient, where the numerator and denominator are divided.

In a simple fraction, both are integers.

In a complex fraction, a fraction can be found in either the numerator or the denominator.

A suitable fraction has a numerator that is less than its denominator.

So, first, we will figure out the smallest and the greatest fraction:

We have: 3/5, 5/6, 2/3, 9/8, 7/9 and 3/4

LCM of denominators: 2*2*2*3*3*5 = 360

216/360, 300/360, 240/360, 405/360 (Improper), 280/360, 270/360

Smallest: 216/360

Largest: 300/360

Subtract smallest from largest:

300/360 - 216/360

84/360

7/30

0.2333

Round off: 0.24

Therefore, the difference between the largest and the smallest fraction is 0.24.

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The inverse of y=-x²+9 is [tex]x=\sqrt{9-y}[/tex]

What is Inverse of a Function?

A function takes in values, applies specific operations to them, and produces an output. The inverse function acts, agrees with the outcome, and returns to the initial function.

The output of a function is returned by the inverse function, which also returns the initial value.

If f and g are inverse functions, then f(g(x)) = g(f(x)) = x. The initial value is fetched via a function that is its inverse.

For instance, f(x) = 2x + 5 = y

Therefore, the inverse of f is g(y) = (y-5)/2 = x. (x).

The relationship that results from swapping out an independent variable with a variable that depends on a given equation; the inverse may or may not be a function.

A function is said to be an inverse function if its own inverse is represented by the symbol f-1.

[tex]x^2=9-y\\\\\x=(9-y)^\frac{1}{2}\\\\ x=\sqrt{9-y}[/tex]  is the inverse of y=-x²+9

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Answer:

$11.25

Step-by-step explanation:

If Stephen receives a 4.5% hourly pay increase each year, his hourly pay will be $10.30 + (4.5% * $10.30) = $10.30 + $0.465 = $10.765 after the first year.

In the second year, his hourly pay will be $10.765 + (4.5% * $10.765) = $10.765 + $0.486 = $11.251.

Therefore, in two years, Stephen's hourly pay will be $11.251. This is closest to the answer choice of $11.25, so it is the correct answer.

In a two-way ANOVA, the two independent variables are known as factors. Two variables, or factors, are supposed to influence the dependent variable.

First, let's understand what is 2-way ANOVA using 2 factors.

To determine how the values of two categorical factors affect the mean of a quantitative variable, a two-way ANOVA is utilized. When you wish to determine how two independent factors interact with one another to effect a dependent variable, use a two-way ANOVA.

To evaluate if there is a statistically significant difference between the means of three or more independent groups that have been divided on two factors, a two-way ANOVA is utilized.

Given is that the first factor has 4 levels and the second factor has 9 levels.

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Therefore, by using mean and standard deviation the required probability is P( 38 ≤ x ≤ 90) = P(-1<x<3) = 0.83999

The mean (also known as the arithmetic mean, as opposed to the geometric mean) of a dataset is the sum of all values divided by the total number of values. It's the most commonly used measure of central tendency and is often referred to as the "average.

A standard deviation (or) is a measure of how dispersed the data is in relation to the mean. A low standard deviation indicates that data are clustered around the mean, whereas a high standard deviation indicates that data are more spread out.

Given:

mean = μ = 51

Standard deviation = σ = 13

as per the question, the probability that X is between 38 and 90 will be

P( 38 ≤ x ≤ 90)

By using the 0.68 - 0.95 - 0.997 rule

P( 38 ≤ x ≤ 90) = P((x-μ)/σ≤z≤(x-μ)/σ)

P( 38 ≤ x ≤ 90) =P((38-51)/13≤z≤(90-51)/13)

from z standard normal table  

P(x<-1) = 0.15866

P(x>3) = 0.0013499

Therefore, by using mean and standard deviation the required probability is

P( 38 ≤ x ≤ 90) = P(-1<x<3) = 0.83999

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The numbers, square root of 26 and twenty eight sixths can be compared using the known values of the square root of a number near to 26, such as 25, and inequality symbols, which indicates;

An inequality is a comparison between values that have different measures or magnitude, such that one values may be less than, <, greater than, >, or not equal to, ≠, the other value in the comparison.

The square root of 26 is √(26)

Twenty eight sixths is [tex]\dfrac{28}{6}[/tex]

26 is a larger number than 25, therefore;

√(26) > √(25) = 5

The square root of 26, is larger than 5; √(26) > 5

Expressing the fraction of twenty eight sixths as a proper fraction, indicates

[tex]\dfrac{28}{6} = 4\frac{4}{6} =4\frac{2}{3}[/tex]

Twenty eight sixths is four and two thirds, therefore;

Four and two thirds is less than 5, therefore;

[tex]4\frac{2}{3} < 5[/tex]

Substituting twenty eight sixths with four and two thirds, indicates;

[tex]\dfrac{28}{6} = 4\frac{2}{3} < \sqrt{26} > 5[/tex]

[tex]\dfrac{28}{6} = 4\frac{2}{3} < 5 < \sqrt{26}[/tex]

[tex]\dfrac{28}{6} < \sqrt{26}[/tex]

The correct option is therefore;

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Using the cross-multiplication method, we know that the actual height of the building is 91 m.

One might cross-multiply an equation between two fractions or rational expressions in mathematics, more specifically in elementary arithmetic and elementary algebra, to make the equation simpler or to find the value of a variable.

To cross-multiply two fractions, multiply the first fraction's numerator by the second denominator and the second fraction's numerator by the first fraction's denominator.

So, we know that:

The height of the building scale is 14 cm.

The scale is 2 cm and the actual height is 13 m.

Now, the actual height of the building will be:

14/x = 2/13

Use cross-multiplication method as follows:

14/x = 2/13

2x = 14 * 13

2x = 182

x = 182/2

x = 91 m

Therefore, using the cross-multiplication method, we know that the actual height of the building is 91 m.

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1. d. 8/52 (Ace ∪ 5)

2. h. 0 (Ace ∩ 5)

3. b. 20/52 (Even')

4. c. 36/52 (Even ∪ black)

5. a. 3/52 (Face ∩ Diamond)

What is probability?

Probability means the quality or state of being the outcome; the extent to which something is likely to happen or take place. Probability means the possibility of any outcome which can take place in any event.

Solution:

1. Probability of Ace ∪ 5 = (No. of Aces + no. of cards with face value 5)/52 = 8/52

2. Probability of Ace ∩ 5 = (Intersection of Ace and face value of card 5)/52 = 0

∵ Intersection of ace and 5 is 0 as there is no intersection in between the 2 subevents.

3. Probability of Even complement = No. of cards with odd values/52                    

 {A,3,5,7,9,A,3,5,7,9,A,3,5,7,9,A,3,5,7,9}/52      =20/52

4. Probability of Even ∪ black = {(2,4,6,8, 10)×4 types of cards odd black spades + odd black clubs = 20+16/52

                                          = 36/52

5.  Probability of Face ∩ Diamond = No. of face cards in diamonds/52

                                                        = {Jack, Queen, King}/52

                                                        = 3/52

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Answer:

960.00

Step-by-step explanation:

Interest = principle x rate x time

interest = 6000 x .04 x 4

960.00

Answer:

I = $ 960.00

Step-by-step explanation:

I = Prt

Since we are figuring out how much money was earned in interest, we will need to convert our R (which is the interest rate) into decimals, which will be, r = R/100 = 4%/100 = 0.04 per year.

Step 1. Divide R by 100, in this case, R is 4, so it will be 0.04.

Step 2. Times 6000 (the money that was deposited) by 0.04, then times it with 4 (the years) and you will get 960.

I = 6000 × 0.04 × 4 = 960

I = $ 960.00

I hope this helps you!

7,701 divided by 36 is 213.91

The division is the process of sharing a collection of items into equal parts and is one of the basic arithmetic operations in mathematics. For example, we can divide a group of 20 members into 4 groups of 5 members

The number 7701 is called the numerator or dividend, and the number 36 is called the denominator or divisor.

The quotient of 7701 and 36, the ratio of 7701 and 36, as well as the fraction of 7701 and 36 all mean (almost) the same:

7701 divided by 36, often written as 7701/36

Therefore, 7701 divided 36 is 213.91

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The inequality and statement about the possible amount of money in the other piggy bank is 0 ≤ PB₂ ≤ 2.69.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, Teddy has two piggy banks. The difference in the amount of money between the two banks is no more than $10.

∴ PB₁ + PB₂ ≤ 10.

One piggy bank has $7.31 in it.

∴ 7.31 + PB₂ ≤ 10.

PB₂ ≤ 2.69.

So, The amount in PB₂ can be  0 ≤ PB₂ ≤ 2.69.

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5b+3.79 has two terms, 5b and 3.79.

The variable b seems to represent the cost of one bagel.  Since we know Gaspar bought 5 bagels, 5b would represent the cost of 5 bagels.

In 5b, 5 is the coefficient and b is the variable.

Since 5b represents the cost of the bagels, then 3.79 would appear to be the cost of the cream cheese.

Answer:

The variable "b" represents the cost of one bagel (in dollars).

The coefficient "5" represents the number of bagels purchased.

The constant "3.79" represents the cost of one container of cream cheese (in dollars).

Step-by-step explanation:

Given algebraic expression:

If the given algebraic expression represents the total cost, in dollars, of buying 5 bagels and a container of cream cheese, then:

Answer:

5

Step-by-step explanation:

In an isosceles triangle two of the angles are equal and the corresponding sides are also equal

Here ∠A = ∠B

AC = BC

3x + 4 = 10

3x = 6

x = 2

Side AB = x + 3 = 2 + 3 = 5

****