You’ve decided to give your best friend a bag of marbles for his birthday. Since you know that your friend likes green marbles better than red ones, the bag has twice as many green marbles as red. The label on the bag says it contains a total of 84 marbles.

How many green marbles are in the bag? Write an equation (or system of equations) for this problem. Then solve the problem using any method you choose. Be sure to check your answer when you are finished.

The coordinates of the midpoints of GH are M (4,3) and the coordinates of one endpoints are G (5,-6) the coordinates of the other endpoints are

The co - ordinates of another end point is

(x,y) = (3, 12)

mid point formula:-

Let [tex](x_{1}, y_{1}) and (x_{2}, y_{2})[/tex] be any two end points

Mid point of two given points are

[tex](\frac{x_{1}+ x_{2}}{2}, \frac{y_{1}+ y_{2}}{2} )[/tex]

let (x,y ) be the another end point

given one end point is (5,-6)

now by using mid-point formula , we get

 [tex](\frac{x+5}{2} ,\frac{y-6}{2})[/tex]  this is equating to given mid-point is M(4,3)

now [tex](\frac{x+5}{2}, \frac{y-6}{2}) = (4,3)[/tex]

simplify , we get

[tex]\frac{x+5}{2} = 4 and \frac{y-6}{2} = 3[/tex]

cross multiplication and simplify

x+5 = 8 and y-6 = 6

so x = 3 and y = 12

Hence the another point is (x,y) = (3,12)

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The solution to the compound inequality is 1 ≤ x < 21

Compound inequality are  type of inequality that has two or more parts.

In order to solve these simultaneous inequalities, we need to write them as two separate inequalities, and find the values of x that satisfy both of them

(-4x [tex]\leq[/tex]x-5 -------------------------------Equation  1

(x-5< 16) --------------------------------Equation  2

Move all the term to the left side

(-4x +(-x+5) ≤ (x-5) +(-x+5) ---------Equation 3

(x-5) +(-16) < 16+(-16)------------------Equation  4

We need to get rid of expression interval. If there is a negative sign in front of it, each term within the expression changes sign

(-4x -x +5 ≤x-5-x+5)-------------------Equation 5

( X-5 -16 < 16 -16) ----------------------Equation 6

Rearrange and Simplify equation (5 & 6)

(-5x+5 ≤ ) ---------------------------------Equation 7

(x -21 < 0)----------------------------------Equation 8

We need to get rid of expression interval and subtract 5 from equation (7) and add 21 to equation (8)

(-5x ≤ -5) ---------------Equation (9)

(x  <  21)------------------Equation (10)

Divide equation (9) by 5 on both sides and flip the sign because of the negative

5x/ 5 ≥ 5/ 5  

( x  ≥  1 )  

(x  <  21 )

Therefore the solution to the compound inequality is 1 ≤ x < 21

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Using the difference, the difference between the number of heads and half the number of tosses is 1.

In the given question,

The proportion of heads is 0.49 in 100 tosses.

We have to find the difference between the number of heads and half the number of tosses.

The proportion of heads=0.49

Total tosses =100

So the total number of heads

=0.49*100

=49

Since we have to find the difference between the total number of head and half the number of tosses.

So the half on the number of tosses=Total number of tosses/2

The half on the number of tosses=100/2

The half on the number of tosses=50

So, The difference=The half on the number of tosses−Total number of heads

The difference=50−49

The difference=1

Hence, the difference between the number of heads and half the number of tosses is 1.

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The average acceleration is -3.71m/s². Any procedure where the velocity varies is referred to as acceleration.

acceleration = change in velocity / Time taken

a = 0 - 15.6 / 4.2

= -15.6 / 4.2

=  -3.71

The average acceleration is -3.71m/s²

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After using the Simplification method we will get the value (x - 3) / (x + 5)

What is Simplification?

To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. We can —

By eliminating all common elements from the numerator and denominator and putting the fraction in its simplest/lowest form, fractions can be made simpler.

By combining and grouping like terms, mathematical expressions can be made simpler. This makes the phrase simple to comprehend and to solve.

Given,

(x^2-x-6) / (x^2+7x+10)

This equation can be separated into two parts, the top and the bottom, which we can simplify further.

Simplifying the top part

x² - x - 6

This can be factored into the following:

x² + 2x - 3x - 6

x(x + 2) - 3(x + 2)

(x + 2)(x - 3)

Now, Simplifying the bottom part

x²+7x+10

x² + 2x + 5x + 10

x(x + 2) + 5(x + 2)

(x + 2)(x + 5)

Now, we can write the new numerator and denominator

(x + 2)(x - 3) / (x + 2)(x + 5)

(x - 3) / (x + 5)

Hence, (x - 3) / (x + 5) is the answer when simplifying

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The number of small rooms reserved is 13 and the number of large rooms reserved is 12.

Given, Nolan is blocking off rooms for the guests. We will solve the problem using the linear equation. The number of small rooms is x and number of large rooms is y.

There are total of 25 rooms, which can be written as,

x+y=25 ------(1)

Small room can accommodate 3 people and large room 5 people, which can be written as follows,

3x+5y=99 --------(2)

Multiplying the equation 1 by 3, we get

3x+3y=75

Substracting equation 1 and 2, we get

3x+5y=99

3x+3y=75

-    -       -

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

0x+2y=24

2y=24

y=12

x+12=25

x=25-12

x=13

Therefore, the number of small rooms is 13 and large rooms is 12.

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We can see that the p-value for above test is less than α=0.05 and it indicates that we have very strong evidence against H(0) to reject it and we can conclude that there is highly significant relationship between money spent on advertising and sales.

In the given question we have to find is there a statistically significant relationship between money spent on advertising and sales.

Here we have Sales(in $1000) as dependent variable (y) and spend on Advertising (in $1000) as independent variable (x).

The significance of relationship between x and y is given by the significance of regression coefficient of regression of y of x.

So we have to test

H(0): β1=0

H(1): β1≠0

From the table that is given below, we have;

b(1)=3.778221987

se(b(1)) =0.563520732

The test statistic to test the above hypothesis is

t=b(1)/se(b(1))

From the given output, we already have

t=6.704672556

p-value=0.0000146

We can see that the p-value for above test is less than α=0.05 and it indicates that we have very strong evidence against H(0) to reject it, so we reject the H(0) and we can conclude that there is highly significant relationship between money spent on advertising and sales.

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0.21 inches of rain for one hour for ratio of 5 inches of rain in 24 hours

A division is a process of splitting a specific amount into equal parts.

Given,

5 inches of rain in 24 hours

We need to find the unit rate.

For this we need to use the division.

Divide five by twenty four

5/24

Zero point two zero eight

0.208

Zero point two one

0.21

Hence 0.21 inches of rain for one hour for ratio of 5 inches of rain in 24 hours

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Answer:

[tex]y=\frac{\pi}{6}[/tex]

Step-by-step explanation:

Given that:

[tex]\sin(\frac{2\pi}{3})=\cos y[/tex]

Substitute the value [tex]\frac{2\pi}{3}=\frac{\pi}{2}+\frac{\pi}{6}[/tex].

[tex]\sin(\frac{\pi}{2}+\frac{\pi}{6})=\cos(y)[/tex]

(Using the formula: [tex]\sin(\alpha+\beta)=\sin\alpha\cos\beta+\cos\alpha\sin\beta[/tex])

[tex]\sin\frac{\pi}{2}\cos\frac{\pi}{6}+\cos\frac{\pi}{2}\sin\frac{\pi}{6}=\cos y[/tex]

Using [tex]\sin\frac{\pi}{2}=1, \cos\frac{\pi}{2}=0[/tex], we obtain:

[tex]1\times\cos\frac{\pi}{6}+0\times \sin\frac{\pi}{6}=\cos y[/tex]

This is equivalent to:

[tex]\cos\frac{\pi}{6}=\cos y[/tex]

Applying cos inverse on both sides, we get:

[tex]y=\frac{\pi}{6}[/tex]

The evaluation of the quadratic equations are as follows;

Question 5

Question 6

Question 7

Sometimes; Factoring

Always; Quadratic formula

Always; Completing the square

Sometimes; Square root method

Sometimes; Factoring by group

Question 8

The numerator are;

(a) 8

4

(b) The denominator value;

4

(c) The roots are;

2

1

A quadratic equation is an equation of the form; a·x² + b·x + c = 0

Question 5

The quadratic equation, x² + 6·x + 10 = 0

The discriminant is 6² - 4×1×10 = -4

The discriminant < 0, therefore, the equation does not have solution

Question 7

Factoring;

Method of solving equations work more when the coefficient of x and the constant can be expressed as a + b and a·b

Where;

a·b = The constant

a + b = The coefficient of x

Therefore, factoring works sometimes

Sometimes; Factoring

Quadratic formula

The quadratic formula is an equation that involves the use of the constant and the coefficients of x

The quadratic formula therefore works all the time

Always; Quadratic formula

Complete the square

The completing the square method works by rearranging the equation in the form;

a·x² + b·x + c ⇒ a·(x + m)² + n

Where;

m = b/(2·a),

n = c - (b²/(4·a))

The method therefore works all the time

Always; Completing the square

Square root method

The square root method involves placing the square term of the equation on one side of the equation and the constant term on the other side

The square root method  works for equations that can be expressed in the form x² = b

The method  works sometimes

Sometimes; Square root method

Factoring by group

The method involves finding the common factors and grouping based on the common factors

The method only works when there are common factors

Sometimes; Factoring by group

Question 8

The  equation is 2·x² - 5·x = x - 4,

Writing the equation so that we have;

2·x² - 5·x - x + 4 = 0

2·x² - 6·x  + 4  = 0

x = (6 ± √((6² - 4× 2 × 4))/(2×2) =

Therefore;

x = 8/(2×2)  or x =  4/(2×2)

The numerators are 8 and 4

8

4

(b) The denominator is (2 × 2) = 4

(c) The two roots of the quadratic equation are;

x = 8/4 = 2 and x = 4/4 = 1

2

1

Question 6

The equation, x² - 16·x + 64 = 4

The left side of the equation can be factored as follows;

x² - 16·x + 64 = 4

x² - 8·x - 8·x + 64 = 4

(x² - 8·x) + (64 - 8·x) = 4

x·(x - 8) - 8·(x - 8) = 4

(x - 8)·(x - 8) = (x - 8)² = 4

Yes; (x - 8)² = 4

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Answer:

534,000

Step-by-step explanation:

12 days pass from may 10 to may 22 so we replace x with 12

190,000(1.09)^12
190,000(2.81266)

534406.309

But rounded to the nearest thousands

534,000

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The constant of proportionality that relates the cost in 72 dollars as y, to the number of gallons of unleaded gasoline in 22.5 gallons of unleaded gasoline as x is $3.20 per gallon of unleaded gasoline.

The constant of proportionality is the ratio of the so-called proportional relationship that relates two given values ​​to each other.

Other names for the constant of proportionality are constant ratio, constant rate, unit rate, variable constant, and even rate of change.

The relationship between two variables, X and Y, is directly proportional if it can be expressed in terms of Y/X = k or Y = Xk.

y/x = k

k is the constant of proportionality.

Given that:

y = $72 and x = 22.5 gallons.

So, the value of the constant of proportionality (k) = 72/22.5

=> k = 720/225

Dividing both by the numerator and denominator by 45. We get,

=> k = 16/5

The value of the constant of proportionality (k) = $3.20 per gallon of unleaded gasoline.

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Part A: The length (number of hours) of each CD is 0.875 hours.

Part B: The Hernandez family can listen each for 0.875 hours

Given that,

The Hernandez family is on a road trip. They have been driving for 3 1/2 hours. They have listened to 4 CDs of equal length.

What is an equation?

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Part A

Let the length (number of hours) of each CD be x.

Now, x = 7/2 = 3.5/4 = 0.875

= 0.875 hours

Part B

If the family has 1 hour of their drive left, still they can listen 4 CDs.

Therefore, the Hernandez family can listen each for 0.875 hours.

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The sphere with the volume 1436.03 m³ has 7m long radius.

To find out the approximate length of its radius by using the formula to calculate volume of sphere is:

V= 4πr³/3

The value of π is 22/7 or 3.14.

So, V = 4 × 3.14 × r³ / 3

Volume of the sphere is given which is 1436.03 m³.

Thus, r³ = 1436.03×3 / 4×3.14

r = ³√ 4308.09/12.56 = ³√343 = 7 m.

Hence, the radius of the given sphere is 7 m.

The cube root of a number is the factor that we multiply by itself three times to get that number.

For example, the cube root of 27 is 3.

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Answer:

The answer is [tex]\frac{4}{13}[/tex].

Step-by-step explanation:

Additive rule:

According to this rule, the probability that events A or B will occur is given by the formula,

[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]

Here,

We know that there are 13 spades and 4 queens in a deck of 52 cards. Also, there is only one queen of a spade.

Then,

[tex]\begin{aligned}P(S)&=\frac{13}{52}\\P(Q)&=\frac{4}{52}\\P(S\cap Q)&=\frac{1}{52}\end{aligned}[/tex]

Therefore, the probability that the card you select is a spade or queen is given by,

[tex]\begin{aligned}P(S\cup Q)&=P(S)+P(Q) -P(S\cap Q)\\&=\frac{13}{52}+\frac{4}{52}-\frac{1}{52}\\&=\frac{16}{52}\\&=\frac{4}{13}\end{aligned}[/tex]

Therefore, the answer is [tex]\frac{4}{13}[/tex].

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Caspian Sea is elevated at 92 feet (or 28 meters) below sea level. (globally preferred unit is meters)

On the scale of sea levels, a certain height has been assigned zero elevation. This acts as a reference point for rest of the measurements and is called Mean Sea Level (MSL). It is also known as still water level.

Caspian Sea at 92 feet below sea level means it is 92 feet below MSL. Thus, its elevation is considered 92 feet below sea level.

Global MSL is calculated using the spatial average of the complete ocean's level.

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Answer:

How I got the answer:

93 doesn't have an exact square root. So, we need to try numbers that fit with the equation.

x will be less than the square root of 93. Since the square root of 93 is between 9 and 10. The largest perfect square that we can try is 9. Let us see if that number works.

x + x² + √x = 93

9 + 9² + √9 = 93

9 + 81 + 3 = 93

93 = 93 ✔

It does work.

So the number is 9.

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The number in scientific notation is 2.1×10⁵.

Adjusting a number's digits so that it produces an approximation of a result is known as rounding.

The given number is 2.085×10⁵.

Round the number 2.085 to the nearest tenth:

2.085 ≈ 2.1

Therefore, the number in scientific notation is 2.1×10⁵.

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Answer: 55 rounded to the nearest tenth is 60.

Step-by-step explanation: Hope this helps!!!

Answer: 60

Step-by-step explanation

James bond should come ashore 3.464 miles from point A to reach B in least time.

Calculus  is defined as a branch of mathematics concerned with the calculation of instantaneous rates of change (differential calculus) and the summation of infinitely many small factors to determine some whole (integral calculus).

Let's say the James bond travels x miles from point A.

We are aware that time = distance / speed

Total time taken by James bond to reach B is

t(x) = √(x^2+36)/6 + (10-x)/12

dt/dx = x/(6√(x^2+36)) - 1/12

for critical point dt/dx =0

= x/(6√(x^2+36)) - 1/12 = 0

√(x^2+36) = 2x

Squaring on both sides we get

X2 + 36 = 4x2

X2 = 12

X2 = 2√3

T(0) = √(0^2+36)/6 + (10-0)/12 = 41/6

= 6.833 hours

T(2√3) = √(12+36)/6 + (10-2√3)/12 = (5+3√3)/6

= 1.699 hours

T(0) = √(10^2+36)/6 + (10-10)/12 = √34/3

= 1.94 hours

Therefore James bond should come ashore 3.464 miles from point A to reach B in least time

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The value of the sum of the arithmetic sequence from a₃ to a₆ is 38

An arithmetic sequence is a sequence in which the difference between two consecutive terms is a constant.

The first term of the sequence is 20, the common difference is 17 - 20 = 14 - 17 = 11 - 14 = 8 - 11 = 5 - 8 = 2 - 5 = -3

The sum from n = 3 to n = 6 of aₙ is found as follows;

The sequence is an arithmetic progression of the form aₙ = a + (n - 1)·d

Where;

aₙ is the value of the nth term

a = The first term

d = The common difference

From the sequence, we have;

a = 20, d = -3, from which we have;

aₙ = 20 + (n - 1) × (-3) = 20 - 3·(n - 1)

aₙ = 20 - 3·(n - 1)

From which we have;

a₃ = 20 - 3×(3 - 1) = 14

a₄ = 20 - 3×(4 - 1) = 11

a₅ = 20 - 3×(5 - 1) = 8

a₆ = 20 - 3×(6 - 1) = 5

a₃ + a₄ + a₅ + a₆ = 5 + 8 + 11 + 14 = 38

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When the function g(x) = 4 - x and fog (x) = 11 - 2x then the function f(x) is

When a function is expressed in terms of another function it can be called a composite function

if g(x) = 4 - x and fog (x) = 11 - 2x

let f(x) = ax + b

fog = f(g(x))

11 - 2x = f((4 - x) + b)

11 - 2x = a(4 - x) + b

11 - 2x = 4a - ax + b

grouping by coefficients

11 - 2x = (4a + b) - ax

equating the coefficients

11 = 4a + b

-2x = -ax

a = 2

plugging a = 2 into 11 = 4a + b

11 = 4 * 2 + b

11 = 8 + b

b = 3

if a = 2  and b = 3 then f(x) = 2x + 3

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The equation to represent the area of the.large office is 3.5l = 42.

An equation is simply used to illustrate the relationship between the variables given.

In this case, the large office desk has an area of 42ft² anz the width is 3.5 feet. It should be noted that the area is calculated as:

= Length × Width

Therefore, l × w = 42

where w = 3.5

l × 3.5 = 42

3.5l = 42

Therefore, the equation is 3.5l = 42

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As per the statement the function which is best suited for this calculation is averageif.

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A total of 676 different three-letter initials combinations end with the letter Z using the uppercase characters in English alphabets.

We have three letters which have to be filled in.

English alphabets consist of 26 letters (A-Z). Let's suppose A1, A2 & A3 are the three initials.

For A1, we have 26 alphabets to choose from i.e. A-Z

For A2, we again have 26 alphabets to choose from i.e. A-Z

For A3, we have only one option i.e. Z

Thus, total different three-letter initials combinations for "**Z" pairings are:

26 x 26 x 1 = 676

Please note that combinations allow repetition of values. If one wants to avoid repetition, permutation needs to be calculated.

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You could use

2x((2x5)+5+2)+1

Answer:√(9) is a rational number.

Step-by-step explanation:

Answer:This is a rational numer because it can be expressed in the form of p/q

Step-by-step explanation:If a number can be expressed int he form of p/q then its rational.

The possible length of the rectangular garden is L ≥ 6225ft which has a perimeter of 540 feet,

The interior angles of a four-sided polygon are all 90 degrees. At each corner or vertex, the two sides meet at a right angle. The rectangle varies from the square in that its two opposite sides are of equal length.

Let L represent the garden's length.

Let W represent the garden's width.

The perimeter is 540 feet.

The rectangle's perimeter is equal to 2(L + W) = 540

L + W = 270      ....(i)

W = 270 - L      ....(ii)

The rectangle's area is equal to its length times its width, which is given  12000 square feet.

L × W ≤ 12000  ....(iiI)

Substitute the value of equation (ii) into (iii)

(270 - L)(L)   ≤   12000

270l  -  L²  ≤   12000

0   ≤  L²  -  270l +  12000

L²  -  270l  +  1200  ≥  0

Solving the quadratic inequality above, and we get

L ≥  6225

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Answer:

they all are odd numbers

Step-by-step explanation:

trick question they all are odd numbers, unless you can divide or subtract  the numbers

Answer:3716

Step-by-step explanation: any number landing in an even number is even