The ratio of yellow marbles to purple marbles was 13 to 4. If there were 102 marbles in the bag, how many were yellow marbles?

Answer: In this scenario, the length of the backpacking trip is the independent variable and the amount of trail mix Wesley will bring is the dependent variable.

The independent variable is the variable that is being changed or controlled in an experiment or study. In this case, the length of the backpacking trip is the independent variable because it is being determined by Wesley and is not influenced by any other factor.

The dependent variable is the variable that is being measured or observed in an experiment or study. In this case, the amount of trail mix Wesley will bring is the dependent variable because it depends on the length of the backpacking trip. Wesley's decision on how much trail mix to bring will be influenced by how long he plans to go backpacking.

By factor theorem (v+5) is not a factor of the given polynomial f(v).

What does factor theorem mean?

When thoroughly factoring the polynomials, mathematicians apply the factor theorem. The polynomial's zeros and factors are connected by this theorem.

                   The factor theorem states that if a is any real number and f(x) is a polynomial of degree n 1 then (x-a) is a factor of f(x) if f(a)=0.

The factor theorem states that

f(x) has a factor (x-k) if and only if f(k) = 0

We are given the following information.

F(v) = v 4 + 16v 3 + 8v 2 - 725

        We have to check whether (v+5) is a factor of given polynomial.

( v + 5 ) = ( v - ( - 5 )

 f( -5 ) = [tex]( -5 )^{4} + 16( -5)^{3} + 8( -5)^{2} - 725[/tex]

          = - 1900

 f(-5) ≠ 0

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Using mathematical operations, we know that 27/4 pounds of Ham are still left with M.D.

An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.

The operation's arity is determined by the number of operands.

Most people believe that addition, subtraction, multiplication, and division are the four basic operations in mathematics.

So, we know that:
M.D. bought 8½ pounds of Ham.

He gave 1¾ pounds to Mr. Chavir.

Remaining Ham with M.D.:

8½ - 1¾

16+1/2 - 4+3/4

17/2 - 7/4

34 - 7/4

27/4

Therefore, using mathematical operations, we know that 27/4 pounds of Ham are still left with M.D.

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Answer:

m = 40

Step-by-step explanation:

m% = 40%

135x40% = 54

The range of the given relation is:

R: {1, 2, 4, 5}

Thus the correct option is A.

A relation maps elements from one set, the set of the inputs called the domain, into elements from another set, the range.

A point in a relationship is written as (x, y), where y is on the range.

Here we have the relation given by the pairs:

(1, 2), (2, 4), (4, 5), (6, 1)

The range is the set given by the second values of each point, thus the range is:

R: {1, 2, 4, 5}

The the correct option is A.

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The equation of a line perpendicular to y=4/24x that pass through the point (-8, -4) is -6x-4y=16 where x-intercept is -6 and y-intercept is -4.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables.

The formula for a straight line is y=mx+c where c is the height at which the line intersects the y-axis, often known as the y-intercept, and m is the gradient.

Given line ;

y=1x/6

now comparing it with y=mx+c to find the value of m and we found;

m1=1/6

now if two lines are perpendicular then,

m1.m2=-1

m2=-6

now finding the equation of line passing through the point (-8, -4)

x1=-8

y1=-4

(y−y1)=m(x−x1)

Y+4=(-6)(x+4)

Y+4=(-6x/4)

Y=(-6x/4)-4

Y=(-6x-16)/4

4y=-6x-16

rearrange;

-6x-4y=16

this is our required value.

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The solution of the trigonometric equation is x = 26.57° or 153.43°

A trigonometric equation is an equation that contains the trigonometric ratios.

Given the trigonometric equation 2cos x - sin x = 3/(2cos x + sin x)

We solve for x in the equation. We proceed as follows.

Since 2cos x - sin x = 3/(2cos x + sin x)

Multiplying both sides by (2cos x + sin x), we have that

(2cos x - sin x)(2cos x + sin x) = 3

Now, we know that (a² - b² = (a + b)(a - b)

Applying this where a = 2cosx and b = sinx, we have that

(2cos x - sin x)(2cos x + sin x) = 3

(2cos x)² - (sin x)² = 3

4cos² x - sin² x = 3

Since sin²x = 1 - cos²x, substituting this into the equation, we have that

4cos² x - sin² x = 3

4cos² x - (1 - cos²x) = 3

4cos² x - 1 + cos²x = 3

4cos² x + cos²x  = 3 + 1

5cos²x  = 4

cos²x  = 4/5

Taking square root of both sides, we have that

cosx  = ±√(4/5)

cosx  = ±2/√5)

cosx  = ±2/√5 × √5/√5

cosx  = ±2√5/5

Taking inverse cosine of both sides, we have

x = cos⁻¹(±2√5/5)

x = cos⁻¹(±0.8944)

x = cos⁻¹(0.8944) or x = cos⁻¹(-0.8944)

x = 26.57° or (180 - 26.57)°

x = 26.57° or 153.43°

So, the solution is x = 26.57° or 153.43°

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In exchange for a $300 million fixed commitment line of credit, your firm had agreed to pay an up-front commitment fee of .130 percent of the amount of the line.

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100). Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent.

Here,

Your company had agreed to pay an upfront commitment fee equal to.13% of the line's value in exchange for a $300 million fixed commitment line of credit.

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Answer: 251.20

Step-by-step explanation:

The unit rate is 2 servings per package

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

Packages Servings

3                 6

13.5             27

The unit rate is calculated as

The unit rate = Servings/Packages

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

The unit rate = 6/3

Evaluate

The unit rate = 2

Hence, the unit rate is 2

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Observing the cases provided with the formula of probability and implementing it with OR rule , The answer is 0.22.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

All potential results make up the sample space of a random experiment. A subset of the sample space is an event connected to a random experiment. Any outcome's probability is a value between 0 and 1. The sum of all the outcomes' probabilities is one.

Probability that dice rolled shows a 5 once =  1/36

Probability that dice rolled shows a 5 twice =  2/36

Probability that the sum is 8 = 5/36

Total probability = 1/36 + 2/36 + 5/36 = 0.22

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For the given equation y=x+1/5x, if the value of x is 40, y will be 48.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, the equation is

y=x+1/5x

We have to find the value of y when the value of x is 40.

Substitute the value of x in order to obtain the value of y as

y=40+40/5

y=40+8

y=48

Thus, for the given equation y=x+1/5x, if the value of x is 40, y will be 48

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Answer:

48

Step-by-step explanation:

y = x + 1/5 x

y = 40 + 1/5 × 40

y = 40 + 8

y = 48

Answer:

Step-by-step explanation:

y - 3 = x - 3

y = x

Answer:

Step-by-step explanation:

The slope of the given line is 40 mi/h.

How to find slope of the line in the graph?

The slope of a line is the ratio of rise to run. Hence, here are the steps to find slope from a graph.

Select any two random points on the graph of the line (preferably with integer coordinates).

Label them as A and B (in any order).

Calculate the "rise" from A to B. While going vertically from A to B, if we have to go

"up", then the rise is positive;

"down", then the rise is negative.

Calculate the "run" from A to B. While going horizontally from A to B, if we have to go

"right", then the run is positive;

"left", then the run is negative.

Now, use the formula: slope = rise/run.

According to the given question:

To calculate the slope of the line in given graph let point A be (5, 200) and point B (10, 400).

Run = 5

Rise = 200

Therefore, slope = rise/run = 200/5 = 40 mi/h

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The number of chickens that can be fed with 140 kg of corn is 2800.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x = 8 is an equation.

We have,

250 kg corn  = 5000 chicken

Multiply 140/250 on both sides.

140 kg of corn = 140/250 x 5000 chicken

140 kg of corn = 2800 chicken

Thus,

2800 chickens can be fed with 140 kg of corn.

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Answer: x[tex]\geq[/tex]1

Step-by-step explanation:

x is all the numbers equal to or less than 1. The closed dot means its less than or equal to and the dot is on 1. It cant be more than 1, because the arrow shows that all those numbers are greater than one and cant be x.

The equation use to determine the value of [tex]x[/tex] is [tex](2x+5)+3(2x+5)=92[/tex].

The measures of [tex]\angle A, \angle B[/tex] are [tex]23^\circ, 69^\circ.[/tex]

Let us assume the measures of [tex]\angle A, \angle B[/tex] are [tex]z, y[/tex].

Now according to the question, we can write the relation between [tex]\angle A, \angle B[/tex] is [tex]y=3z....(i)[/tex].

We know, the measure of [tex]\angle A[/tex] is [tex]2x+5[/tex] so [tex]2x+5=z....(ii)[/tex]. Now, we will substitute the value of [tex]z[/tex] from equation [tex](ii)[/tex] in equation [tex](i)[/tex].

[tex]y=3z\\= 3 \times (2x+5)\\=6x+15[/tex]

So, the final equation will be [tex](2x+5)+3(2x+5)=92[/tex]

⇒ [tex]6x+15+2x+5=92[/tex]

⇒ [tex]8x+20=92[/tex]

⇒ [tex]8x=72[/tex]

⇒ [tex]x=9[/tex]

[tex]\therefore[/tex] measure of [tex]\angle A[/tex] is [tex]2x+5=(2 \times 9)+1=25[/tex] and measure of [tex]\angle B[/tex] is [tex]2 \times 23 = 69[/tex].

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Answer: y = 1x + 5

Step-by-step explanation:

This is where the equation; y=mx+b comes in handy.

We are given m, 1.

And we are given a coordinate to plug in.

2=1(-3)+b

2=-3+b

b=5

y = 1x + 5

Answer:

Step-by-step explanation:

The standard form of a line is Ax+By=C.  To solve this problem, begin with the point-slope form [tex]y-y_1=m(x-x_1)[/tex].  For this problem, let

[tex](x_1,y_1)=(-3,2)\\m=1[/tex]

Input these values into the point-slope form equation and convert to slope-intercept form,

[tex]y-(2)=(1)[x-(-3)]\\y-2=x+3\\y-2+2=x+3+2\\y=x+5[/tex]

Next, convert slope-intercept form to standard form:

y=x+5

-x+y=5

For standard form, A must be positive.  So,

-(x-y)=5

x-y=-5

Answer:

a. 2664 Explanation: 543 + 534 + 453 + 435 + 354 + 345 = 2664

Step-by-step explanation:

Therefore, the solution to given problem is the density of metal block comes out to be 2717.4 kg/[tex]m^{3}[/tex]

The substance's density is defined as its mass per unit of volume. Although the Latin letter D can also be utilized, the most popular density symbol is. In mathematics, density is calculated as mass divided by volume:

Here,

Given : mass =5kg

volume = 1.84 x [tex]10^{-3}[/tex]

thus, density = mass/volume

we apply density formula , we get

density = 5/ 1.84 x [tex]10^{-3}[/tex]

density =2717.4 kg/[tex]m^{3}[/tex]

Therefore the density of metal block comes out to be 2717.4 kg/[tex]m^{3}[/tex]

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Answer:

15

Step-by-step explanation:

To find the total number of combinations you can make with these four coins, we have to do 2 to the power of the total amount of coins. This because each coin has two choices: to be included in the combination or not. There are 4 total coins, and 2^4 is 16. There are 16 total combinations. But since one of those possibilities are that none of the coins are included, we subtract 1 from the total, and get 15. There are 15 combinations with 1 or more coins, which each give us different amounts.

Billy suffers from a stutter, so he expresses himself in a manner in which he can be successful.

Doctor Spivey grants McMurphy's request for a pass to take a fishing trip with nine other patients, accompanied by two of his aunts.

Why is McMurphy tired after the fishing trip?

McMurphy adds Rub-a-Dub George, a neat-freak Swedish fisherman and sailor, to the group. Nurse Ratched says they can't go because there isn't enough capacity in one car for all the patients when Candy Starr arrives without her buddy to pick up the patients for their outing.

McMurphy has his own weakness, his self-centeredness. At first he is willing to sacrifice the patients for his own well-being

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Answer:

it is very easy for even a third grader 2x4=8

to get the slope of any straight line, we simply need two points off of it, let's use the ones in the picture below.

[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{12})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{24}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{24}-\stackrel{y1}{12}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{5}}} \implies \cfrac{ 12 }{ 2 } \implies \text{\LARGE 6}[/tex]

1/8, 1/4, 3/8, 2/3, 3/4

By simply dividing the fractions!

In 1/4, we can divide the numbers:

1 ÷ 4 = 0.25.

In 1/8:

1 ÷ 8 = 0.125

In 2/3:

2 ÷ 3 = 0.66

In 3/8:

3 ÷ 8 = 0.375

And in 3/4:

3 ÷ 4 = 0.75

0.125, 0.25, 0.375, 0.66, 0.75

Now, we have to put them into their original fractions, not decimals:

1/8, 1/4, 3/8, 2/3, 3/4

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

Answer: 8x + 2

Step-by-step explanation:

Answer:

8x+2

Step-by-step explanation:

x3+2x2+x+2

=3x+4x+x+2

=8x+2

Both a smaller and a bigger number are 25 and 68

The outcome or conclusion we get at when we add two or more integers is known as the SUM. example the total of the addends, 6, and 4, is 10. In other words, we may argue that 8 plus 5 equals 13 or that 8 plus 5 equals 13.

Here, we've been given two numbers, one smaller and one bigger, where the smaller number is X and the larger number is 18  more than twice the smaller number.

2X + 18 is the greater number.

Because the total is now 93, X + (2X+18) = 93

3X = 93 - 18 .

X = 25

larger number will be 2(25) + 18 = 68

Thus the numbers are smaller number is 25 and larger number is 68.

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i hope you understand cause i can write on a screen