You have 16 yellow beads, 20 red beads, and 24 orange beads to make identical bracelets. What is the greatest number of bracelets that you can make using all of the beads?

We can model this problem by an exponential growth:

where A is the amount accumulated, P is the principal, r is the interest rate, n is the number of times per year and t is the time. By substituting our given data, we get

therefore, the model is

Now, by substituting t=10 years, we have

then, the amount will be

Expression 2x²-(-1) - [7x-8] is equal to 2x² - 7x +9

Expression is combination of math operations , numbers and unknown variables.

Math operation can be subtraction , addition , multiplication or division.

There are two types of expression : numerical expression and algebraic expression . Expression consists of only numbers are numerical where expression containing numbers and variables are algebraic expression.

Subtract 7x-8 from 2x²-(-1)

2x²-(-1) - [7x-8]

product of two minus is plus

2x²+1 -[7x-8]

open the bracket and change the minus sign

2x²+1 - 7x + 8

there is no x² and x term so,

2x² - 7x +1+8

2x² - 7x +9 is our required expression

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Given equation is

[tex] \sqrt[3]{x {}^{2} - 7 } = \sqrt[3]{2x + 1} [/tex]

to solve this equation we first need to cube both the sides . As this would remove the cube root on both the sides ,

[tex]\longrightarrow (\sqrt[3]{x^2-7})^3 = (\sqrt[3]{2x+1})^3[/tex]

This would become ,

[tex]\longrightarrow x^2-7=2x+1 \\[/tex]

[tex]\longrightarrow x^2-2x-7-1=0\\[/tex]

[tex]\longrightarrow x^2-2x-8=0\\[/tex]

[tex]\longrightarrow x^2 -4x +2x -8=0\\[/tex]

[tex]\longrightarrow x(x-4)+2(x-4)=0\\ [/tex]

[tex]\longrightarrow (x+2)(x-4)=0\\[/tex]

[tex]\longrightarrow \underline{\underline{ x = 4,-2}} [/tex]

And we are done!

Answer:

[tex]\textsf{To solve the given equation, $\boxed{\sf cube}$ both sides}.[/tex]

Step-by-step explanation:

Given equation:

[tex]\sqrt[3]{x^2-7} =\sqrt[3]{2x+1}[/tex]

[tex]\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]

[tex]\implies (x^2-7)^{\frac{1}{3}}=(2x+1)^{\frac{1}{3}}[/tex]

Cube both sides of the equation:

[tex]\implies \left( (x^2-7)^{\frac{1}{3}}\right)^3= \left((2x+1)^{\frac{1}{3}}\right)^3[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies (x^2-7)^{\frac{3}{3}}=(2x+1)^{\frac{3}{3}}[/tex]

[tex]\implies (x^2-7)^{1}=(2x+1)^{1}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^1=a:[/tex]

[tex]\implies x^2-7=2x+1[/tex]

Subtract 2x from both sides:

[tex]\implies x^2-2x-7=1[/tex]

Subtract 1 from both sides:

[tex]\implies x^2-2x-8=0[/tex]

Rewrite -2x as (-4x + 2x):

[tex]\implies x^2-4x+2x-8=0[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies x(x-4)+2(x-4)=0[/tex]

Therefore:

[tex]\implies (x+2)(x-4)=0[/tex]

Apply the zero-product property:

[tex]x+2=0 \implies x=-2[/tex]

[tex]x-4=0 \implies x=4[/tex]

Approximately 95% of the data fall within 2 standard deviations of the mean. That is, 2 standard deviations below and 2 standard deviations above the mean as in the following picture:

Given

The system of equations,

To find the solution using substitution technique.

Explanation:

It is given that,

That implies,

And,

Substitute 3y=1.2+2x in the above equation.

That implies,

And, substitute x=-0.6 in (1).

That implies,

Hence, the solution is (-0.6,0).

Answer:

Step-by-step explanation:

Let the cost of T-shirt is x.

The cost of pair of shoes is $49.95 and the total should be no more than $60.

This can be modeled as:

The matching choice is C.

The volume of a sphere is given by

Since a hemisphere is half sphere, its volume is given by

where r is the radius.

Case a.

In this part r=3 ft, then by substituting this values into our last formula we get

which gives

Case b.

In this part r=(13/2) cm, then by substituting this values into our last formula we get

which gives

Answer:

1. 1

2. 24

3. 1

4. 1 [ab]

5. 3

6. 1

Step-by-step explanation:

Every variable or alphabet's coefficient is the number on the left of it.

e. g coefficient of x is 1.

or coefficient of 83x is 83

We need to first find the intersection between Q and R, which is the common elements between both groups. We have:

Now we need to determine the union between them:

we ahve

110.4 ÷4

so

110.4/4

Multiply by 10/10 the expression

1104/40

simplify

1104/40=552/20=276/10=27.6

the answer is 27.6

Answer:

18 ft.

Step-by-step explanation:

To complete the tables, we multiply the given numbers:

First table:

Second table:

Now, to determine which option is less expensive we compute the total annual expenses for each case:

1.-Rental:

2.- Homeowner:

From the above calculations, we can conclude that the cheaper option based on the given annual expenses is to rent.

Renting is less expensive.

I hope this helps! Good luck! Lmk if you need more help dude.

Step-by-step explanation:

A. Slope formula: y2-y1/x2-x1

(0,1) and (1,3)

3-1/1-0=2

The slope is 2.

B. I think the slope means there are 2 pages for every 1 short story written.

C. y=2x+1

2 is the slope, we see the line crosses through at (0,1) so it is our y-intercept.

A. The slope of the linear equation is 2.

B. The slope indicates that the number of pages written increases by a constant rate of 2 pages.

C. The y-intercept means that the initial number of page is 1.

D. The equation of the line in slope-intercept form is y = 2x + 1.

Part A. First of all, we would determine the slope of the line represented by this graph;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (7 - 3)/(3 - 1)

Slope (m) = 4/2 = 2.

Part B.

The meaning of the slope is that the number of pages written by this writer increases by 2 every year. Therefore, there are two number of pages for every (1) short story that is written by the writer.

Part C.

The y-intercept is located at point (0, 1) and in the context of the situation, it indicates that there is a page when the number of short story is equal to zero (0) or when there are no short stories written.

Part D.

In Mathematics and Geometry, the slope-intercept form of a straight line can be calculated by using the following mathematical equation:

y = mx + b

Where:

By substitution, a linear equation for the line is given by:

y = mx + b

y = 2x + 1

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Cost price = $44

mark up percent = 80% = 80/100 = 0.8

selling price = ?

The markup formula:

The answer is C, the square root of 65 (8.062).

The value of x is 120.

70/100 shows 70% as a ratio. The ratio x : 84 compares 84 to the whole, x. Write an equation so that the first ratio is multiplied by the second ratio. Solve for x : x = 120.

Given, that 84 is 70% of the whole.

Let the whole be x,

According to the question,

(70/100) × x = 84

On multiplying both the sides by 100/70, we get

x = 84×100/70

Now, on solving the expression, we get

x = 120

Hence, 70/100 shows 70% as a ratio. The ratio x : 84 compares 84 to the whole, x. Write an equation so that the first ratio is multiplied by the second ratio. Solve for x : x = 120.

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Consider the experiment of picking one digit first from the initial set (digits from 1 t) 6, and then pgrabbing a second digit without eplace,ment.

As for the first part of the experiment, there are 6 digits to choose from; however, during the second round, there are only 5 digits available. Therefore, according to the counting principle, the sample space has

30 elements. he answer is 30 elements in the sampele space.

Answer:

The degree of the polynomial is the greatest of its various terms' exponents (powers). This is a seconds degree polynomial.

Step-by-step explanation:

2x^2 - 3x^5 + 5x^6.

We observe that the above polynomial has three terms. Here the first term is 2x^2, the second term is -3x^5 and the third term is 5x^6.

Now we will determine the exponent of each term.

(i) the exponent of the first term 2x^2 = 2

(ii) the exponent of the second term 3x^5 = 5

(iii) the exponent of the third term 5x^6 = 6

Since the greatest exponent is 6, the degree of 2x^2 - 3x^5 + 5x^6 is also 6.

Therefore, the degree of the polynomial 2x^2 - 3x^5 + 5x^6 = 6.

Easy peasy, hope you understand now.

Image of point O(-2,-1) after two reflections , first across the line y=5 and then across the line x = 2 is (6,11) .

What do you mean by reflection in coordinate plane?

A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another. The reflected picture should have the same size and shape as the original, but it faces the opposite way. Changes in position during contemplation may also result in translation. Pre-image and image are terms used to refer to the same thing in this context.

Given point is O(-2,-1)

It is given that point O has reflected twice,

Firstly point O has reflected across the line y= 5

So, it become ,

(-2,11)

Secondly, it is reflected across the line x = 2

So, it become,

(6,11)

Hence, image of point O(-2,-1) after two reflections , first across the line y=5 and then across the line x = 2 is (6,11) .

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Answer:

13

Step-by-step explanation:

.

Answer:

Alex is 14 years old.

Step-by-step explanation:

You can take William's age and divide it by 3, because William is 3 times the age of Alex:

31 divided by 3 = 10.33.

So, we will just say 10 for now.

Now, we add 4 to the 10 because WIlliam is 4 years older than three times his age.

So, in conclusion, Alex is 14 years old.

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The function is  f(x) = x² +3,then f (x + h)  = [tex]x^2+2xh +h^2+3[/tex].

Given,

In the question:

The function is given as:

f(x) = x² +3

To find the f (x + h) = ?

Now, According to the question:

Substitute x = x + h into f(x) = x² +3

f(x + h) =  (x+ h)² +3

Expand the expression using:

[tex](a +b)^2 = a^2 +2ab+b^2[/tex]

f(x + h) = [tex]x^2+2xh +h^2+3[/tex]

Hence, The function is  f(x) = x² +3,then f (x + h)  = [tex]x^2+2xh +h^2+3[/tex].

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We are given an experiment, and we are asked about the probability that either event happens. Therefore, we use the addition rule of probability, which states that if A and B are two events in a probability experiment the probability that either one of the events to happen is:

Therefore, in our specific case, we have that the probability of A is 1/2, since we have 2 odd numbers out of possible 4 outcomes. The probability of B is 1/4, since we have a number 4 out of 4 possible outcomes. The probability of A and B is 0, because obtaining a 4 and an odd number are two mutually exclusive events. Therefore we have that our probability simply is the sum of our two probabilities:

Therefore, our answer is 3/4

Recall that the order of the operations PEMDAS

1. Parenthesis

2. Exponents.

3. Multiplication.

4. Division.

5. Addition.

6. Subtraction.

1. Given expression is

Multiply 3 and 5, we get

Divide 6 by 2, we get

Subtract 3 from 8, we get

Add 5 and 15, we get

The answer is

2.Given expression is

Multiply 7 and 3, we get

Divide 15 by 5, we get

Subtract 3 from 21, we get

The answer is

3. Given expression is

First, we need to solve inside the parenthesis, divide 12 by 2, we get

Add 1 and 6, we get

Solve exponent.

Multiply 2 and 49, we get

Add 8 and 98, we get

The answer is

The unit rate per yard is 0.03yards per unit

The length of fence B is 0.3yards

A rate is a ratio that is used for comparing two different kinds of quantities which have different units. On the other hand, the unit rate illustrates how many units of quantity correspond to the single unit of another quantity. We say that when the denominator in rate is 1, it is called unit rate. In fact, unit rate is said to be the amount of something in each unit or per unit.

Fence A which is 1 1/2yards but 1 4/5inches on blueprint. 1 inch = 0.0278 yards

blueorint reading = 9/5×0.0278=0.05=5/100yards

therefore the scale is 3/2 : 5/100 = 3/2÷5/100

= 3/2×100/5= 1:30 = 0.03 :1

therefore the unit rate / yard = 0.03yardperunit

if a fence B is 10yards then on the blueprint it will be 10×0.03= 0.3yards

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Step 1

Given; The equations in the elimination method are written in the standard form as ____

Step 2

Simultaneous linear equations can be solved using the elimination method. First of all, make sure that the equations are written in the standard form either Ax+By=C or Ax+By+C=0. In this method, we multiply both the equations with a non-zero number to make the coefficients of any one variable equal.

Thus the answer is; The equations are written in standard form as seen below

Ava has 70 stickers.

Given that the ratio of the number of stickers Ava has to the number of stickers Cole has = 5:3 = 10:6

Also, the ratio of the number of stickers Cole has to the number of stickers Zane has = 2:3 = 6:9

Thus, the compounded ratio of the number of stickers Ava, Cole and Zane has is = 10:6:9

Let the numbers of stickers of Ava has be = 10x

The number of stickers of Cole has, is = 6x

The number of stickers of Zane has, is = 9x

According to question, the total number of stickers they have is 175. So,

10x+6x+9x = 175

25x = 175

x = 175/25

x = 7

Hence Ava has = 10x = 10*7 = 70 stickers.

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The formula for the area (A) of the sector is,

Given

Therefore,

Solve for θ

Hence, the answer is