18 Which expression uses the greatest common factor and distributive property to write 18 + 24 as a product? Circle the letter of the correct answer.

The simplest expression of the ratio of circles to squares is 5:3.

Describe ratio.

A relationship between two quantities is called a ratio, and it is expressed as one quantity divided by the other.

There are 6 circles and 10 squares.

These steps can be used to determine the ratio of two quantities:

Finding the quantities of both scenarios for which we are calculating the ratio is the first step. There are 10 squares and 6 circles in this instance.

It should be expressed as a fraction, a/b. Thus, we represent it as 10/6.

If you can, make the fraction even simpler. The ultimate ratio will be shown by the simple fraction.

In this case, 10/6 can be reduced to 5/3.

As a result, the simplest expression of the ratio of circles to squares is 5:3.

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The value of x = 6cm.

What is surface area?

The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object refers to the space occupied by its outer surface.

From the given figure,

Surface area(A) = [tex]192cm^{2}[/tex]

Height = 8cm

a base side = 6 cm

b base side = 10 cm

c base side = x cm

Therefore,  TSA= 2B +Px = [tex]2 \times\frac{1}{2} \times8\times6 +(6+10+8)x[/tex]

                                          =48+24x

Thus, 60+24x=192

                     [tex]x=\frac{192-48}{24}[/tex]

                      x= 6cm

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Answer:

5cm. 8cm

Step-by-step explanation:

Label all the vertices then use Pythagorean theorem

c² = a² + b²

The slope and y-intercept of this function is

B. The slope is 5/6, The y-intercept is (0, -3

Linear function is a function of the form y = mx + c

m = slope

c = intercept

The slope is represented as m, The slope by definition is the ratio change of the output values to the input values

the slope, m calculated using the points (0, -3) and  (6, 2)

m = (y₀ - y₁) / (x₀ - x₁)

m = (2 - -3) / (6 - 0)

m = (5) / (6)

m = 5/6

c = y intercept, from the table

c = -3

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Answer:

For the first graph:

Domain: -∞ [tex]\leq[/tex] x [tex]\leq[/tex] ∞

Range: y [tex]\geq[/tex] 3

For the second graph:

Domain: 0 [tex]\leq[/tex] x [tex]\leq[/tex] 4

Range: y [tex]\leq[/tex] 64

Step-by-step explanation:

For the second graph, I'm assuming that that point are stopping at (0,0) and (4,0) that's why I wrote that for the domain. If it doesn't stop, then the domain would be the same and the first graph.

The linear correlation between the given two variables be,

4.5y + 5.2x = 168.34

Given, data for a classroom of students who measured each (approximately) in inches.

Femur Length 18.7 14.2 20.5 15.9 16.2 13.1 15.0 12.4 19.0 16.2 21.3

Tibia Length  15.8 21.0 16.2 14.3 12.1 15.8 13.0 18.8 14.3 18.7 13.8

we have to find a linear correlation between the two variables,

linear correlation be,

(y - 15.8)/(x - 18.7) = (15.8 - 21.0)/(18.7 - 14.2)

(y - 15.8)/(x - 18.7) = (- 5.2)/4.5

4.5y - 71.1 = -5.2x + 97.24

4.5y + 5.2x = 168.34

So, the linear correlation between the given two variables be,

4.5y + 5.2x = 168.34

Hence, the linear correlation between the given two variables be,

4.5y + 5.2x = 168.34

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Answer:

8+8-8×1

8+8-8

16-8

8 Ans.

The cost per ounce in both options is the same. Then the correct option is D.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The rate is the ratio of the amount of something to the unit.

Jorge wants to buy a drink.

Choice 1: 24-ounce cup for $1.92

Choice 2: 12-ounce cups for $0.96 each

The cost per ounce in choice 1 is calculated as,

⇒ $1.92 / 24

⇒ $0.08 per ounce

The cost per ounce in choice 2 is calculated as,

⇒ $0.96 / 12

⇒ $0.08 per ounce

The cost per ounce in both options is the same. Then the correct option is D.

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The vehicle can travel 12 miles per gallon of gasoline.

What is the Mixed fraction ?

A mixed fraction is one that is represented by both its remainder and quotient. Consequently, a mixed fraction is created by combining a whole number and a proper fraction.

What is the Rate ?

A rate is the comparison of two comparable amounts expressed in different units. If the ratio's denominator is written as a single unit of one of these quantities, and if it is assumed that this quantity can be modified systematically (i.e., is an independent variable), then the numerator of the ratio indicates the comparable rate of change in the other (dependent) variable.

The vehicle travels 13\frac{1}{2} by using 1\frac{1}{8} gallons of gasoline.

since the units are in mixed fraction, we can simplify it to simple fraction,

distance travelled= 13\frac{1}{2} = [(13 × 2) + 1] / 2 = 27/2 miles.

gasoline used= 1\frac{1}{8} = [(1×8)+1] /8 = 9/8 gallons.

∴ Miles per gallon of gasoline = distance travelled ÷ gasoline used

                                                  = 27/2 miles ÷ 9/8 gallons

                                                  = 12 miles per gallon of gasoline.

Hence, The rate of miles per gallon of gasoline is 12 miles/gallon of gasoline.

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The solution for x in the inequality expression is x < -8

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

-4x+5>37

Subtract 5 from both sides of the inequality

So, we have

-4x + 5 - 5 >37 - 5

Evaluate the like terms

This gives

-4x > 32

Divide both sides by -4

x < -8

Hence, the solution is x < -8

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The probability that the number 6 will appear between 150 and 200 times inclusively is 0.926.

In the given question, one thousand independent rolls of a fair die will be made.

We have to compute an approximation to the probability that the number 6 will appear between 150 and 200 times inclusively.

Let n=1000 are independent trails.

The probability of success is constant, p=1/6

The probability of success is not constant,

q=1-1/6 = 5/6

let X be the number of times the die shows a 6.

μ = np

μ = 1000*1/6

μ = 166.7

σ=√npq

σ=√1000*1/6*5/6

σ=√5000/36

σ=11.785

Now we used the correlation continuity for finding the probability that number 6 will appear between 150 and 200 times is

P(150≤X≤200)=P(X≤200)-P(X<150)

P(150≤X≤200)=P(Z≤(200+0.5-166.7)/11.785)-P(Z≤(150-0.5-166.7)/11.785)

P(150≤X≤200)=P(Z≤2.87)-P(Z≤-1.46)

P(150≤X≤200)=0.998-0.072

P(150≤X≤200)=0.926

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The values are;

⇒ F ∩ H = Ф

⇒ F ∪ H = (- ∞, 7]

What is Coordinates?

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Given that;

F and H are defined as;

F = {v | v < 4 }

H = {v | v ≥ 7 }

Now,

Since, F and H are defined as;

F = {v | v < 4 }

H = {v | v ≥ 7 }

Hence, The values are;

F ∩ H = {v | v < 4 } ∩  {v | v ≥ 7 }

         = Ф

And, F ∪ H = {v | v < 4 } ∪  {v | v ≥ 7 }

                 = (- ∞, 7]

Thus, The values are;

⇒ F ∩ H = Ф

⇒ F ∪ H = (- ∞, 7]

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If mean of 11 numbers is 7 one of the numbers, 13, is deleted then the mean of remaining 10 numbers is 6.4

The mean of 7 numbers = 11

We know,

Mean = Sum of the terms / Number of terms

Substitute the values in the equation

11 = Sum of the terms / 7

The sum of the terms = 11 × 7

= 77

Number 13 is deleted

Sum of the terms = 77 - 13

= 64

Number of terms = 11 - 1

= 10

The mean = Sum of the terms / Number of terms

Substitute the values in the equation

= 64 / 10

= 6.4

Hence, the mean of the remaining 10 numbers is 6.4

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A comparison of multiple treatments and the use of the double-blind method are two fundamental components of all statistically designed experiments. (6) Compare various treatments; assign patients to treatments at random.

What is double-blind method?

A kind of clinical experiment in which neither the participants nor the researcher is aware of the treatment or intervention that each participant is receiving until the trial is complete.

                      This reduces the likelihood of skewed study outcomes.

What is a sample of a double-blind study?

Imagine, for instance, that researchers are looking into the effects of a novel medication.

                            The participants in a double-blind study would not be aware of who was receiving the real medication and who was receiving a placebo, and neither would the researchers who interact with them.

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The complete question is -

Two essential features of all statistically designed experiments are (2 Points) O use enough subjects; always have a control groups O always have a placebo group; use the double - blind method O use a block design; use chance to assign subjects to treatments O compare several treatments; use the double - blind method O compare several treatments; use chance to assign subjects to treatments.

By using the concept of maxima, it can be calculated that

Volume is maximum if the radius of the cone is 40 cm

What is maxima of a function?

Maxima of a function gives the maximum value of the function on a certain interval or on the whole domain.

Let the height of the cylinder be h and radius be r

Sum of height and circumference = h + 2πr

By the problem,

h + 2πr = 60

h = 60 -2πr

Volume(V) = π[tex]r^2[/tex] h

             = π[tex]r^2[/tex](60 - r)

             = 60π[tex]r^2[/tex] - π[tex]r^3[/tex]

[tex]\frac{dV}{dr} = 120\pi r - 3 \pi r^2[/tex]

For maximum volume

[tex]\frac{dV}{dr} = 0[/tex]

[tex]120\pi r - 3 \pi r^2 = 0\\[/tex]

[tex]3 r^2 = 120 r\\3r = 120 [r \neq 0]\\r = \frac{120}{3}\\r = 40 \ cm[/tex]

[tex]\frac{d^2V}{dr^2} = 120 \pi - 6 \pi r\\[/tex]

Putting r = 40

[tex]\frac{d^2V}{dr^2} = 120 \pi - 6 \pi \times 40\\\frac{d^2V}{dr^2} =120\pi - 240 \pi\\\frac{d^2V}{dr^2} = -120\pi < 0[/tex]

Hence Volume is maximum

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c=1/2  which makes fx|y (x, y) a valid conditional probability mass function.

What is conditional probability?

The possibility of an event or outcome occurring based on the existence of a prior event or outcome is known as conditional probability. It is determined by multiplying the likelihood of the earlier event by the increased likelihood of the later, or conditional, event.

Given that;

p(x) = [tex]c (\frac{2}{3} )^n[/tex]   where x = 1,2,3,........

for getting value of c we are using the expression :

[tex]\sum_{n=1}^{\infty} c(\frac{2}{3})^n = 1[/tex]

[tex]c\sum_{n=1}^{\infty} (\frac{2}{3})^n = 1[/tex]

Since we want p(x) to be a Probability Mass Function, your approach is correct, since for any such function

fX:A→[0,1],X:S→A⊆R, it is :

[tex]\sum _{x\in A} \ fX(x)=1[/tex]

As long as you've correctly understood that condition, you can proceed with your specific exercise as follows:

[tex]\sum_{n=1}^{\infty} c(\frac{2}{3})^n = 1[/tex]

⇔ [tex]c\sum_{n=1}^{\infty} (\frac{2}{3})^n = 1[/tex]

⇔2c = 1

⇔c = 1/2

Hence c =  1/2 is the valid conditional probability mass function.

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The value of h ( 12 ) is 26

What is an Equation?

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 equation be A

Now , the value of equation A is

h ( x ) = 4x - 22   be equation (1)

Now , to find the value of h ( 12 ) , substitute the value of x = 12 in the equation , we get

h ( x ) = 4x - 22  

h ( 12 ) = 4 x 12 - 22

On simplifying the equation , we get

h ( 12 ) = 48 - 26

           = 22

Therefore , the value of h ( x ) when x = 12 is 22

Hence , The value of h ( 12 ) is 26

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Answer:

Slope-intercept form: y = 3x + 5

Slope: 3

y-intercept: 5

Step-by-step explanation:

When the equation of a line is written in the slope-intercept form, we can easily identify the slope from the coefficient of x and the y-intercept from the constant.

The slope-intercept form is expressed as y = mx + c, where m is the slope and c is the y-intercept. Note that other textbooks might use y = mx + b instead, but both have the same meaning as both m and b or c will be replaced by a certain value.

To rewrite an equation in the slope-intercept form, isolate the y term on the right-hand side of the equation and divide the whole equation by the coefficient of y.

Working

[tex]y - ( - 7) = 3(x - ( - 4))[/tex]

Expand:

[tex]y + 7 = 3(x + 4)[/tex]

[tex]y + 7 = 3x + 12[/tex]

Subtract both sides by 7:

[tex]y = 3x + 12 - 7[/tex]

[tex]\bf{y = 3x + 5}[/tex]

Since the coefficient of y is already 1, we have arrived at our final answer.

When the equation is in the slope-intercept form, the slope can be identified from the coefficient of x. This refers to the number that comes before x which is multiplied to x.

Thus, the slope is 3.

The y-intercept is the value of the constant in the slope-intercept form. This refers to the number that is not attached to any variables.

Hence, the y-intercept is 5.

Note that the y-intercept can also be found by substituting x = 0 into the equation.

The x-intercept occurs at y = 0. Since we have the equation of the line, we can substitute y = 0 into the equation to find the value of x when y = 0.

Working

y = 3x + 5

When y = 0,

0 = 3x + 5

3x = -5

Divide both sides by 3:

[tex]x = - \frac{5}{3} [/tex]

I have attached the graph as an image. If only a sketch is required, there are 3 pieces of information that needs to be labelled on the graph:

Additional resources:

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A) 3x+9y-1 = 3(x+3y) -1, here distributive property is used the 3 is multiplied with each term inside the bracket.

What is algebraic operations?
Any of the common arithmetic operations, such as addi - tion, subtraction, multiplication, division, raising to a complete number power, and taking roots, are considered basic algebraic operations in mathematics (fractional power). These operations could be applied to numerical data, in which case people are frequently referred to as arithmetic operations. Similar operations can be carried out on factors, algebraic expressions, and, more generally, on components of algebraic structures like groups and fields. Another way to describe an algebraic operation is as a function from the Cartesian power of the a set to the same set. The dot product is an example of an operation that can be described by compounding simple algebraic operations, and is referred to as an algebraic operation.

b) 7x+5y-5y = 7x

Here the Additive inverse of 5y is used which is -5y .

c) (x-4)(x+3) = 0

here distributive property of addition over multiplication is used.

d) 4x+5x = 5x+4x

here commutative property is used.

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The expression  -3/10 X (-8/15) is positive

Expression

Expression in mathematics has two or more variables, terms and constants. Also, arithmetic expression contains only numbers and mathematical operators and algebraic expression

The expression has negative sign and from mathematical calculation we already know the following relation:

+ x + = +

positive multiply by positive equals Positive

- x - = +

Negative multiply by Negative equals Positive

+ x - = -

Positive multiply by Negative equal Negative

hence,   - [tex]\frac{3}{10}[/tex] x - [tex]\frac{8}{15}[/tex]

The negative sign multiply by  -3/10 X (-8/15) sign will give positive.

Therefore, the expression  -3/10 X (-8/15) is positive.

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Answer:

18k +37

Step-by-step explanation:

13k + 7 + 5(k + 6)

13k + 7 + 5k + 30

13k + 5k + 7 + 30

18k +37

The statemet 2, the variable K represent carrying capacity and the variable N represent population size, is correct.

In the given question we have to review the video to determine whether each statement about the following equation is true or false.

The given equation is:

[tex]\frac{dN}{dt}=rN(\frac{K-N}{K})[/tex]

The given equation is used to find the annual growth of population.

In which, dN/dt = the annual increase for the population,

r = the annual growth rate,

N = the population size, and

K = the carrying capacity.

So the statemet two, the variable K represent carrying capacity and the variable N represent population size, is correct.

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ΔXYZ will also be an equilateral triangle.

What is equilateral triangle?

An equilateral triangle in geometry is a triangle with equal-length sides on all three sides. In the well-known Euclidean space, an equilateral triangle also is equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others. It's also referred to it as a regular triangle because it is a regular polygon.

As X,Y,Z are the midpoints of sides of equilateral triangle so when we will join the X,Y,Z we will find that distances XY=YZ=XZ are three are equal because this is proved by similarity of triangles which in itself is a detailed and vast topic

Hence XYZ will also be an equilateral triangle

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The amount of money that Margret needs to deposit to reach this amount is $8.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

Since Margret has $32.00 in a savings account. Margret wants to have a balance of $40.00 in the account, the amount needed will be:

= $40 - $32

= $8

She'll need $8 more.

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The height of the kite assuming that there is no slack in the string is 86.6 m.

We have given that,

the string of a kite is 100 meters long and it makes an angle of 60°.

and we have to find the height of the kite.

So therefore we know the formula for right angled triangle,

i.e. sinθ = Opposite side/ Hypotenuse

Here θ = 60°

Opposite side = height of the kite = h (say)

Hypotenuse = length of string = 100 m

⇒ sin60° = [tex]\frac{h}{100}[/tex]

           h = 100sin60°

              = 100 × [tex]\frac{\sqrt{3} }{2}[/tex]

              = 50 × 1.732

           h = 86.6 m

Hence the height of the kite is 86.6 m.

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Answer: it would be 18 candies that are left

Step-by-step explanation:  

I did the math

An equation is formed when two equal expressions. The time the same pump will take to empty a tank containing 108,000 gallons of water is 4.5 hours.

When two equal expressions are added together with the aid of the equal sign "=," an equation is created.

Given that the time it takes a water pump to empty a tank directly correlates with the tank's capacity. Consequently, the relationship can be expressed as,

V ∝ T

V = kT

Substituting the volume and time in the equation,

60,000 gallons = 2.5 hours × k

Solving the equation for k,

k = 60,000 gallons / 2.5 hours

k = 24,000 gallons per hour

Now, the equation for the relationship can be written as,

V = 24,000 gallons per hour × T

Now, the time the same pump will take to empty a tank containing 108,000 gallons of water is,

V = 24,000 gallons per hour × T

108,000 gallons = 24,000 gallons per hour × T

108,000 gallons / 24,000 gallons per hour = T

T = 4.5 hours

Hence, the time the same pump will take to empty a tank containing 108,000 gallons of water is 4.5 hours.

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The exact value of sin(u + v), obtained using trigonometric identities is for sine and cosine is 16/65

Trigonometric identities are equations that involve trigonometric functions that are valid for all values of the input variable.

The possible value of sin(u) obtained from a similar question posted online is; sin(u) = 5/13

Both u and v are in quadrant II

The trigonometric identity of the addition formula for the sine of the sum of two angles, indicates;

sin(u + v) = sin(u)·cos(v) + sin(v)·cos(u)

sin(u) = 5/13

cos(v) = -4/5

sin(v) = √(1 - (cos(v))²)

Therefore;

sin(v) = √(1 - (-4/5)²) = 3/5

cos(u) = √(1 - (sin(v))²)

Therefore;

cos(u) = √(1 - (5/13)²) = 12/13

Therefore;

sin(u + v) = (5/13) × (-4/5) + (3/5) × (12/13) = 16/65

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To maximize the profit 29.6 units must be produced.

What is the maxima or minima?

The maxima and minima of a function collectively referred to as extrema in mathematical analysis, are the highest and lowest values of the function, either on the whole domain or within a specific range.

We have given,

The revenue function is,

R(x)=3x

Cost function,

C(x)=0.05x^2+0.04x+10,

Where

x = number of units produced.

Thus, profit = revenue - cost

P(x) = 3x - (0.05x^2+0.04x+10)

= -0.05x^2 + 2.96x - 10

Differentiating with respect to x,

P'(x) = -0.1x + 2.96

Again differentiating with respect to x,

P''(x) = -0.1

For maxima or minima,

P'(x) = 0,

0 = -0.1x + 2.96

-0.1x = -2.96

x = 2.96/0.1

For x = 29.6,

P''(x) = negative,

Hence, to maximize the profit 29.6 units must be produced.

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The time that Diana spent looking at the exhibits is given as follows:

1.582 hours.

As stated in the problem, the total time that Diana spent at the museum is given as follows:

3 hours.

The total time that Diana spent at the museum was divided into two activities, presented as follows:

The times of each activity are given as follows:

Then the time that Diana spent looking at exhibits is obtained as follows:

x + 1.418 = 3

The time is obtained by the subtraction of 3 by 1.418 as follows:

x = 3 - 1.418

x = 1.582 hours.

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