Question down below about linear equations.

The required system of equations that can be used to determine the total number of ounces in the jug of water (x), and the total number of ounces in the bottles of juice (y) is

[tex]x - y = 192[/tex]

[tex]\frac{9}{64}x+\frac{3}{32}y=42[/tex]

To write an equation,

It is given that,

The difference between the jug of water and the bottle of juice that Kira is drinking is 192 ounces

Kira has consumed a total of 42 ounces, which is 3/32 of the bottle of juice and 9/64 of the jug of water.

Consider,

The total number of ounces in the jug of water = x

The total number of ounces in the bottle of juice = y

Applying these variables in the above sentences,

[tex]x-y=192[/tex]

[tex]\frac{9}{64}x+\frac{3}{32}y=42[/tex]

Therefore, these two equations are used to determine the total number of ounces in the jug of water and the bottle of juice.

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Jamie purchases 4 chocolate (3.57), 7 strawberry/vanilla, and 7 peanut butter cupcakes for an office party.

The steps involved are:

Given that,

Jamie is ordering cupcakes for an office party.

There are three flavors - Chocolate, Strawberry/vanilla, and peanut flavors.

Jamie purchased a total of 18 cupcakes for $55.75

The cost for a single cupcake of each flavor is as follows:

Chocolate - $3

Strawberry  - $2.75

Peanut - $3.50

Consider the number of cupcakes of each flavor as x, y, and z respectively.

So, the equations we can write from this data are,

x + y + z = 18 and

3x + 2.75y + 3. 50z = 55.75

But it is given that,

There are twice as many chocolate cupcakes purchased as peanut butter cupcakes.

So, z = 2x

Then the above two equations become,

3x + y = 18 and

10x + 2.75y = 55.75

By solving these two equations we get,

x = 3.57 ≅ 4

y = 7.28 ≅ 7

Since we know that z = 2x,

⇒ z = 2 × 3.57 = 7.14 ≅ 7

So,

There are 4 chocolate, 7 strawberry, and 7 peanut cupcakes.

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Chantelle can use the following equation,

n = (Number of stickers) / (Number of friends)

or n = 56/8

Given Information

Chantelle has 56 stickers

⇒ Number of stickers = 56

She will distribute all of the stickers to 8 friends

⇒ Number of friends = 8

The number of stickers each friend will get = n

We have to form an equation for n.

Forming the Equation

Equation for  the number of stickers to be given to each friend is as follows,

n = (Number of stickers) / (Number of friends)

n = 56/8

n = 7

Therefore, Chantelle needs to give 7 stickers to each of her 8 friends. And, the equation used to find this count, n is n = (Number of stickers) / (Number of friends) or n =56/8

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Answer: C

Step-by-step explanation:

Each term is half the previous term.

The probability that you pick a striped shirt AND a blue suit  is 1/4 AND a pink tie is 3/8.

According to the statement

Number of blue suit = 1

Number of black suit = 2

Number of brown suit = 1

Number of blue ties = 2

Number of red ties = 3

Number of pink ties = 3

Now we find the probability by its formula

Probability that picked suit is blue = blue suits/ total number of suits

Probability = 1/4

Now,

Probability that picked tie is pink = Pink tie / total number of ties

Probability = 3/8

So, The probability that you pick a striped shirt AND a blue suit  is 1/4 AND a pink tie is 3/8.

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The friend's probability of beating the next level on her first attempt are 22.5 percent.

Describe probability.

To forecast how likely occurrences are to occur, probability has been introduced in mathematics. This is the fundamental theory of probability, which is also applied to the probability distribution, and from which you will discover the likelihood of results for a random experiment.

This idea is used to discuss the probability or likelihood of an event happening.

The frequency of the number 8 is seven.

The frequency of the number 9 is 11.

The full list of frequencies is provided as

10 + 9 + 6+ 7 + 8 + 12 + 4 + 6 + 7 + 11 = 80

7 + 11 = 18

18/80 is the probability.

= 0.225 x 100

22.5 percent

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Answer:

160 ft

Step-by-step explanation:

We have

2(length + width)= perimeter

than,

let, width =x

now,

2(x+60+x) = 520

or, 2x+60 = 260

or, 2x = 200

or, x = 100

so length is 100+60 = 160

Triangles ABC and DEF are similar. The scale factor for the pair is: 1/6.

The ratios of the corresponding sides of similar triangles are equal, because they are proportional.

If triangles ABC and DEF are similar triangles, then:

AB/DE = BC/EF = AC/DF

Plug in the given values

2/12 = 5/30 = 6/36 = 1/6

This means that the triangles are certianly similar. The scale factor for the pair is: 1/6.

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Answer:

Step-by-step explanation:

floating point

The interior angle of a regular octagon is 135 degrees.

An octagon is a polygon that has 8 sides. Therefore, a regular octagon is a octagon with all it sides and angles equal to each other.

Therefore, the sum of angles in an octagon is each interior angle multiply by the number of sides.

Therefore,

n = number of sides = 8

Hence,

interior angle = (n - 2)180 / n

interior angle = (8 - 2)180 / 8

interior angle = 6 × 180 / 8

interior angle = 1080 / 8 = 135°

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Answer:

x² - 5x + 17 = [tex](2x)^{3x}[/tex]

Step-by-step explanation:

using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]

given

[tex]log_{2x}[/tex] (x² - 5x + 17) = 3x , then

x² - 5x + 17 = [tex](2x)^{3x}[/tex]

The reference angle after rotating the unit circle anti-clockwise is;  π/3 Radians

To draw the angle θ = -120° in the unit circle, we will move clockwise 90°, and thereafter another angle of 30°.

This tells us that we pass the fourth quadrant and stop in the third quadrant.

The reference angle of an angle theta in the third quadrant, is; θ + 180°.

Thus, the reference angle of -120° is; -120° + 180° = 60°.

Converting 60° to radians gives; (60/360) * 2π Radians = π/3 Radians

Thus, the Reference angle is π/3 Radians

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Skew lines and parallel lines do not intersect

As a general rule, skew lines are lined that are not on the same plane; they are not parallel to each other and they do not intersect

Using the above definition as a guide, the skew lines in the figure are:

Parallel lines and skew lines are different in the following ways:

Parallel lines and skew lines are alike in the following way:

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Answer:

(x-4)=0 or (x+2)=0 is correct

Step-by-step explanation:

(x+1)(x-3)=5

x^2 -3x +x -3=5

x^2-2x-8=0

x^24x+2x-8=0

(x+2)(x-4)=0

so,

(x-4)=0 or (x+2)=0

The solutions to the expression are:

x - 4 = 0 or x + 2 = 0.

Option C is the correct answer.

We have,

To determine which of the following statements is true:

(x + 1) = 0 or (x - 3) = 0

(x + 1) = 5 or (x - 3) = 5

(x - 4) = 0 or (x + 2) = 0

We can solve the given equation (x + 1)(x - 3) = 5 by expanding the equation and setting it equal to 0:

(x + 1)(x - 3) - 5 = 0

Expanding the equation:

x² - 3x + x - 3 - 5 = 0

x² - 2x - 8 = 0

Now we can factor the quadratic equation:

(x - 4)(x + 2) = 0

From this factorization, we find two possible solutions:

x - 4 = 0 --> x = 4

x + 2 = 0 --> x = -2

Therefore,

The correct statement is:

(x - 4) = 0 or (x + 2) = 0

i.e

x - 4 = 0 or x + 2 = 0.

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If Eli ate  one third of a pie on friday ,one fourth proportion of the pie on saturday and 50 ounces of the pie on sunday then it is found that she ate 30 ounces of pie.

Given that Eli ate one third of a pie on friday, one fourth of the pie on saturday, and final 50 ounces of the pie on sunday which is left out.

We have to find the amount of pie that she ate one saturday.

We are given fraction and we know that sum of all fractions of something is equal to 1.

Let the proportion that she ate on sunday be x.

1/3+1/4+x=1

Taking LCM.

(4+3+12x)/12=1

7+12x=12

12x=12-7

12x=5

x=5/12

So the left out out portion that she ate on sunday is 5/12 of the pie.

We are given that she ate 50 ounces on sunday so the total pie will be 12/5*50=120 ounces.

Portion eaten by Eli on saturday =1/4

Pie that she ate on saturday=1/4*120

=30 ounces.

Hence Eli ate 30 ounces of pie on saturday.

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In the graph, the constant of proportionality is 40

From the question, we are to determine the constant of proportionality

The constant of proportionality = [tex]\frac{y}{x}[/tex]

From the graph, a point on the line is (1, 40)

That is,

When x = 1 and y = 40

Thus,

The constant of proportionality = [tex]\frac{40}{1}[/tex]

Constant of proportionality = 40

Hence, the constant of proportionality is 40

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Answer:

40

Step-by-step explanation:

The constant of proportionality is 40/1 which equals 40.

By definition of a binomial random variable,  the probability that the machine will be working is 0.82045.

First of all, you should know that the Probability is the greater or lesser possibility that a certain event will occur.

In other words, the probability establishes a relationship between the number of favorable events and the total number of possible events.

On the other hand, a random variable is a function that associates a real number, perfectly defined, to each sample point.

A random variable is discrete if the numbers it gives rise to are integers.

Finally, a binomial distribution is a discrete probability distribution that describes the number of successes in performing n independent experiments on a random variable.

The expression to calculate the binomial distribution is:

P(X=x)=([tex]n\\ x[/tex]) pˣ qⁿ⁻ˣ

Where:

Remember that:

([tex]n\\ x[/tex])=[tex]\frac{n!}{x!(n-x)!}[/tex]

where the exclamation mark represents the factorial symbol, that is, the product of all positive integers from 1 to n.

A machine has 28 identical components which function independently. The probability that a component will fail is 0.19.

The following random variable is defined:

x= the number of components will stop working.

Being n the total number of pieces (in this case, 12 pieces) and p the probability of success (the piece fails, in this case 0.19), the expression to be used is expressed as:

P(X=x)=([tex]12\\ x[/tex]) 0.19ˣ (1-0.19)¹²⁻ˣ

P(X=x)=[tex]\frac{12!}{x!(12-x)!}[/tex] 0.19ˣ (0.81)¹²⁻ˣ

Since the machine will stop working if more than three components fail, you need to know the probability that the machine will be working if 3 or less than 3 components fail. In other words, it may be that 0, 1, 2 or 3 pieces are broken and the machine continues to work:

P(X≤3)= P(X=0) + P(X=1) + P(X=2) + P(X=3)

Then:

P(X≤3)= [tex]\frac{12!}{0!(12-0)!}[/tex] 0.19⁰ (0.81)¹²⁻⁰ + [tex]\frac{12!}{1!(12-1)!}[/tex] 0.19¹ (0.81)¹²⁻¹ + [tex]\frac{12!}{2!(12-2)!}[/tex] 0.19² (0.81)¹²⁻² + [tex]\frac{12!}{3!(12-3)!}[/tex] 0.19³ (0.81)¹²⁻³

Solving:

P(X≤3)= [tex]\frac{12!}{0!12!}[/tex] ×1×(0.81)¹² + [tex]\frac{12!}{1!11!}[/tex] 0.19×(0.81)¹¹ + [tex]\frac{12!}{2!10!}[/tex] 0.19²×(0.81)¹⁰ + [tex]\frac{12!}{3!9!}[/tex] 0.19³×(0.81)⁹

P(X≤3)= 1×1×(0.81)¹² + 12×0.19×(0.81)¹¹ + 66×0.19²×(0.81)¹⁰ + 220×0.19³×(0.81)⁹

P(X≤3)= (0.81)¹² + 2.28×(0.81)¹¹ + 2.3826×(0.81)¹⁰ + 1.50898×(0.81)⁹

P(X≤3)= 0.82045

Finally, the probability that the machine will be working is 0.82045.

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Answer:

y=-2x+5

Step-by-step explanation:

For every increase in x, y decreases by 2

so the slope is -2

You can solve for the y-intercept by going backward, 1-1=0, 3+2=5

the y-intercept is (0,5)

Using the slope intercept equation format, the answer is y-2x+5

Answer:

Step-by-step explanation:

Comment

The radius is 33 feet. The height is really a radius. The diameter consists of 2*r

r = diameter / 2

diameter = 66 feet

r = 66 /2 = 33

So you have 2 ways of finding the radius.

Solution

Area of a full circle = pi r^2

Area of a full circle = pi * 33^2

Area of a full circle = 1089 pi    

Area of a semicircle = area of a full circle / 2

Area of a semicircle = 1089 * pi /2

Area of a semicircle = 544.5 * pi

Answer

Exact answer in terms of pi is 544.5 * pi

Approximate answer using 3.14 for pi = 3.14*544.5 = 1709.73

Answer:

Area=

πr2

2

Step-by-step explanation:

3.14159⋅(33)2

2

=1710.5958

The first table is a quadratic function while the second table is a linear function.

1) For the first table, we have;

x y

0 5

1 0

2 -3

3 -4

4 -3

x = 2  and x = 4 have same value of y = -3  and as such it will be a Quadratic Function.

y = x²  - 6x + 5

2) For the second table, we have;

x y

2 5

5 14

6 17

8 23

10 29

This table is a Linear function because  slope is same and equal to 3 all through. Thus, the equation is y = 3x - 1  

3) For the third table, we have;

x y

-3 8

-2 4

-1 2

0 1

1 0.5

This is an exponential function because equation can be modelled by;

y = 2⁻ˣ

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1/3 portion of the mixture, costing $\$6$ contains chocolate.

Assume that, in a mixture:

chocolate = x pound

nuts = y pound

mixture= x+y

The desired value is found by dividing the weight of the chocolate by the overall weight, or x/(x+y).

From the given data,

cost of x pound chocolate at $\$10$per pound = 10x

cost of y pound nuts at $\$4$ per pound = 4y

cost of x+y pound mixture at $\$6$ = 6(x+y)

As per condition,

⇒10x + 4y = 6(x+y)

⇒10x + 4y = 6x+ 6y

⇒4x = 2y

⇒y = 2x

The fraction of the chocolate in the mixture is

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

Therefore, chocolate makes  1/3 of the mixture's weight.

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Answer:

1/3

Step-by-step explanation:

The mean calculated shows that the Chemistry score will be 87.

From the information given, the total scores will be:

= 84 × 4

= 336

The addition of the scores given will be:

= 72 + 85 + 92

= 249

The Chemistry score will be:

= 336 - 249

= 87

Complete question:

If the mean of the data set is 84 points, find Harukas final exam score in Chemistry.

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The number of gallons of the 35% acid solution eli should add is; 0.125 gallons

From the given table, since Eli wants to combine 0.5 gallon of a 10% acid solution with some 35% acid solution to make a 15% acid solution, then we can say that;

(0.10)(0.5) + 0.35g = 0.15(g + 0.5)

where g is number of gallons

Now,  for us to determine how many gallons of the 35% acid solution eli should add, we will solve the word problem earlier to get;

(0.10)(0.5) + 0.35g = 0.15(g + 0.5)

⇒ 0.05 + 0.35g = 0.15g + 0.075

⇒ 0.35g - 0.15g = 0.075 - 0.005

⇒ 0.2g = 0.025

g = 0.025/0.2

g = 0.125 g

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For the eradication of malignancies like the aggressive type of human brain tumour known as glioblastoma multiforme (GBM), 3D platforms are crucial for tracking tumour growth and assessing treatment candidates.

Glioblastoma (GBM), commonly known as a grade IV astrocytoma, is an aggressive brain tumour that grows quickly. The local brain tissue gets invaded, but it typically does not spread to distant organs. GBMs can develop from lower-grade astrocytomas or develop from new brain tumours.

Some characteristics of GBM are-

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The slant height of the hexagonal pyramid is: B. 14 inches.

Area of a regular hexagon = 3√3/2(s²)

First, find the area of the regular hexagon:

Area = 3√3/2(s²) = 3√3/2(10²) = 150√3 in.².

Surface area is given as 420 + 150√3 in.².

Area of the 6 triangles = surface area - area of hexagonal base = 420 + 150√3 - 150√3

Area of the 6 triangles = 420 in.²

Area of 1 triangle = 420/6 = 70 in.²

Use the area of a triangle to find the slant height (h):

70 = 1/2(10)(h)

2(70) = 10(h)

140/20 = h

h = 14 in.

The answer is B. 14 inches.

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The functions f(x) = -4x + 11 and f(x) = 2/3x - 8 are having the range of {y ∈ R | -∞ < y < ∞}.

Step 1: Finding the range for the function f(x) = -(x + 1)² - 4

The given function is quadratic in the form of a(x - h)² + k,

So, the range of the function is y ≤ k if a < 0 or y ≥ k if a > 0

For the given function, a = -1 so, a < 0. thus, the range of the given function is y ≤ k, where k = -4

∴ Range of f(x) = -(x + 1)² - 4 is: (-∞ -4], {y | y ≤ -4}

Step 2: Finding the range for the function f(x) = -4x + 11

This is a linear function. So, the range is R.

∴ Range of f(x) = -4x + 11: (-∞, ∞), { y | y ∈ R}

Step 3: Finding the range for the function f(x) = 2/3x - 8

This is also a linear function. So, the range is R.

∴ Range of f(x) = 2/3x - 8: (-∞, ∞), { y | y ∈ R}

Step 4: Finding the range for the function f(x) = 2^x + 3

This is an exponential function. So, the range is y > k

Here k = 3.

∴ Range of f(x) = 2^x+3: (3, ∞), {y | y > 3}

Step 5: Finding the range for the function f(x) = x² + 7x - 9

This is a quadratic function.

we can write it as,

f(x) = x² + 2 × x × (7/2) + (7/2)² - (7/2)² - 9

     = (x + 7/2)² - 85/4

This is in the form of a(x - h)² - k. where a = 1 > 0 and k = -85/4

Since a > 0, the range of the function is y ≥ -85/4

∴ Range of f(x) = x² + 7x - 9: [-85/4, ∞), {y | y ≥ -85/4}

Therefore, the functions f(x) = -4x + 11 and f(x) = 2/3x - 8 are having the given range {y ∈ R, -∞ < y < ∞}

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Decreasing the pressure in the reaction vessel will keep this reaction from shifting to form more of the produce(ammonia).

This is defined as the force per unit area of a body and the S. I unit is in Pascal.

Ammonia production involves reaction between hydrogen and nitrogen gas in which pressure has an effect on the reaction rate unlike in solids and liquids. An increase in pressure will result in more products being formed and vice versa.

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Answer:

875

Step-by-step explanation:

1-0.32=0.68 so its 0.68 of its original price.

x*0.68=595 x is the original price

x=595/0.68

x=875

Considering it's asymptotes, the rational function shown in the graph is:

C. [tex]F(x) = \frac{1}{(x + 2)(x - 1)}[/tex]

In this graph, there are vertical asymptotes at x = -2 and x = 1, hence the denominator of the function is:

(x + 2)(x - 1).

The horizontal asymptote is of y = 0, hence the function can be given by:

C. [tex]F(x) = \frac{1}{(x + 2)(x - 1)}[/tex]

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