Suppose that a and b are integers with a < b How many numbers are in the list a, a+1, a+2.... b?

So I thought about doing a-(a-1) to get the first number to one so the list becomes 1,2,3 but i soon realized that does not work

The number line with the points 3/6, 3/4, and 3/12 graphed on it is attached.

When fractions are represented on a number line, we can plot them on a number line just like we do with whole numbers and integers. Parts of a whole are represented by fractions. As a result, fractions on the number line are represented by splitting a whole into equal parts, ranging from 0 to 1, and the number of those equal parts would match the denominator of the fraction.

To graph the given fractions on the number line, we first convert them to like fractions.

3/6, 3/4, and 3/12

= 6/12, 9/12, and 3/12, which are like fractions.

Now we divide the number line with the minimum mark as 1/12, the least fraction, with 12 as denominator.

Now, we can mark the points 6/12, 9/12, and 3/12, as shown.

Thus, the number line with the points 3/6, 3/4, and 3/12 graphed on it is attached.

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Answer:

9060$ is the final amount because 7060 is the interest

The amount of money after 45 years will be $64,060.

Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

Investments increase exponentially by about 26% every 3 years.

If you made a $2,000 investment.

Then the equation will be

[tex]\rm A = 2000 \times \left (1.26 \right )^{\frac{t}{3}}[/tex]

Where t is the number of years.

Then the amount of money after 45 years will be

[tex]\rm A = 2000 \times \left (1.26 \right )^{\frac{45}{3}}[/tex]

Simplify the equation, then we have

A = 2000 × (1.26)¹⁵

A = 2000 × 32.03

A = $64,060

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Since the Dilating polygon WXYZ will alter the side lengths of the polygon. The correct option is option  (b) the slope of WX is 3/4, and the length of W'X' is 15.

The coordinates in the question were:

(3,2), and  (7,5).

Then the slope of WX is:

[tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

So m   = [tex]\frac{{5} - 2 }{7-3} }[/tex]

    =3/4

The length of WX is calculated by:

[tex]WX = \sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1}) ^ 2}[/tex]

[tex]\sqrt{(7-3)^2 + (5-2)^2} \\\\= \sqrt{25} \\\\= 5[/tex]

Since, The scale factor is  =  3.

Hence, WX = 3 x 5 = 15

Therefore, Since the Dilating polygon WXYZ will alter the side lengths of the polygon. The correct option is option  (b) the slope of WX is 3/4, and the length of W'X' is 15.

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Answer:    slope 3/4 and length 15

Step-by-step explanation: plato

The dy/dx of equation  [tex]x^{3} -3x^{2} y+2xy^{2} =12[/tex] is [tex](6xy-3x^{2} -2y^{2} )/(4xy-3x^{2})[/tex].

Given an equation [tex]x^{3} -3x^{2} y+2xy^{2} =12[/tex].

We are required to find dy/dx of the equation.

Equation is like a relationship between two or more variables that are expressed in equal to form. Equations of two variables look like ax+by=c.

Differentiation is basically finding the change in variables.

It may be linear equation, quadratic equation,cubic equation or many more depending on the power of the variable present in the equation.

Equation:[tex]x^{3} -3x^{2} y+2xy^{2} =12[/tex]

Differentiating with respect to x.

3[tex]x^{2}[/tex]-3([tex]x^{2}[/tex]*dy/dx+y*2x)+2(x*2y*dy/dx+[tex]y^{2}[/tex])=0

3[tex]x^{2} -3x^{2} dy/dx-6xy+4xy dy/dx+2y^{2}[/tex]=0

Taking dy/dx at one side and take the other part to other end.

[tex]-3x^{2} dy/dx+4xy dy/dx[/tex]=[tex]6xy-3x^{2} -2y^{2}[/tex]

dy/dx=[tex](6xy-3x^{2} -2y^{2})/(4xy-3x^{2} )[/tex]

Hence the dy/dx of equation  [tex]x^{3} -3x^{2} y+2xy^{2} =12[/tex] is [tex](6xy-3x^{2} -2y^{2} )/(4xy-3x^{2})[/tex].

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The simplification of the algebraic fraction equation given as 3a³ - 5b³ + (3/a) + b³ is; (3/a)(a⁴ + a) - 4b³

We want to solve the algebraic fraction equation given as;

3a³ - 5b³ + (3/a) + b³

Rearranging the algebra to get;

(3a³ + (3/a)) + b³ - 5b³

Factorizing out 3/a and simplifying gives;

(3/a)(a⁴ + a) - 4b³

This is the final part for the simplification of the given algebraic fraction. Thus, we can conclude that the simplification of the algebraic fraction equation given as 3a³ - 5b³ + (3/a) + b³ is; (3/a)(a⁴ + a) - 4b³

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The computation shows that the number of weeks that it take to repair this stretch of road will be 4 weeks.

From the information given, we are told that a thirteen kilometers stretch of road needs repairs and that the workers can repair three and half kilometers of road per week.

The question is simply for us to calculate the number or weeks that it will take to be able to repair the stretch of road.

Therefore, based on the information given, it should be noted that to get the number of weeks that will be used to repair the road, we simply have to divide the total distance or the road by the distance that is repaired every week.

Therefore, the number of weeks that it will take to be able to repair this stretch of road will be:

= 13/3.5

= 3.7

= 4 weeks approximately

Therefore, based on the information given, the number of weeks that's required is 4 weeks.

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Based on the information, it is expected Fareed can be assigned to live on any of the floors.

The only condition that limits the floor Fareed can be assigned to is that he cannot be immediately below Damaris. This means that as long as Damaris is not immediately above him, he can be assigned to all floors. Here are two possible arrangements:

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By Euler's method the numerical approximate solution of the definite integral is 4.189 648.

In this problem we must make use of Euler's method to estimate the upper bound of a definite integral. Euler's method is a multi-step method, related to Runge-Kutta methods, used to estimate integral values numerically. By integral theorems of calculus we know that definite integrals are defined as follows:

∫ f(x) dx = F(b) - F(a)     (1)

The steps of Euler's method are summarized below:

The table for x, f(xₙ, yₙ) and y is shown in the image attached below. By direct subtraction we find that the numerical approximation of the definite integral is:

y(4) ≈ 4.189 648 - 0

y(4) ≈ 4.189 648

By Euler's method the numerical approximate solution of the definite integral is 4.189 648.

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Answer:

7×10³+3×10²+4×10¹+2×10 or 7.342×10³

Answer: x = 9

Step-by-Step Solution:

Hypotenuse = 15 units

Base = 12 units

Altitude = x units

Using Pythagoras Theorem,

=> Hypotenuse^2 = Base^2 + Altitude^2

(15)^2 = (12)^2 + x^2

225 = 144 + x^2

225 - 144 = x^2

81 = x^2

x^2 = 81

x = √81

=> x = 9

Therefore, Altitude = 9 units

Using the probability concept, we have that:

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there are 35 people, out of which 17 are female and 5 are male that prefer mint chocolate chip, hence:

p = (17 + 5)/35 = 22/35 = 0.6286.

There is a 0.6286 = 62.86% probability that a randomly selected person is female or prefers mint chocolate chip.

Out of the same 35 people, 11 people prefer cookie and cream and 2 people prefer vanilla, hence:

p = (11 + 2)/35 = 13/35 = 0.3714

There is a 0.3714 = 37.14% probability that a randomly selected person prefers cookie and cream or vanilla.

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Answer:

w = 15 cm

Step-by-step explanation:

We want to find the width, as the area of a rectangle is length (l) * width (w).

Since we know the area and the length, we have 480 = 32w

Isolating w by dividing both sides by 32 gives us w = 15 cm

the inequality gives the 'y' value as -4

An inequality is a mathematical tool that compares two values, expressing when one is less than, greater than, or not equal to the other value.

For instance,

a ≠ b says that a is not equal to b

a < b says that a is less than b

a > b says that a is greater than b

From the information given, that 3y+1 is less than -11 . It can be expressed as;

3y + 1 ∠ -11

Let's collect like terms

3y ∠ -11 - 1

add like terms

3y ∠ -12

make 'y' the subject of formula

y ∠ -12/3

y ∠ -4

The inequality gives the 'y' value as -4

Thus, the inequality gives the 'y' value as -4

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Answer:

1.46m or 14600cm are left over

Step-by-step explanation:

Assuming you mean that there were 4m of string and 254cm were used/removed.

Applying the initial conditions, the specific solution is:

[tex]y = e^{-2x}(-3\sin{3x} + 4\cos{3x})[/tex]

The general solution is given by:

[tex]y = e^{-2x}(C_1\sin{3x} + C_2\cos{3x})[/tex]

We apply the initial conditions to find the specific solution.

First, we have that y(0) = 4, then:

[tex]4 = e^{-2(0)}(C_1\sin{3(0)} + C_2\cos{3(0)})[/tex]

Since cos(0) = 1, we have that:

[tex]C_2 = 4[/tex]

Then:

[tex]y = e^{-2x}(C_1\sin{3x} + 4\cos{3x})[/tex]

The derivative is:

[tex]y^\prime(x) = -2e^{-2x}(C_1\sin{3x} + 4\cos{3x}) + e^{-2x}(3C_1\cos{3x} - 4\sin{3x})[/tex]

Since y'(0) = -17, then:

[tex]-17 = -8 + 3C_1[/tex]

[tex]3C_1 = -9[/tex]

[tex]C_1 = -3[/tex]

Then the specific solution is:

[tex]y = e^{-2x}(-3\sin{3x} + 4\cos{3x})[/tex]

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By using the linear function which models the data in the given table, the cost of a textbook with 402 pages is equal to $47.4478.

A scatter plot can be defined as a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.

A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.

By critically observing the graph (see attachment) which models the data in the given table, we can infer and logically deduce that the linear function is given by:

y = 0.1057x + 4.9564

If x = 402, then y is given by:

y = 0.1057(402) + 4.9564

y = 42.4914 + 4.9564

y = $47.4478.

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Answer:

ummm the answer is very simple

The answer is 0/6

Step-by-step explanation:

[tex] \frac{1}{2 \times 3} - \frac{1}{6} [/tex]

[tex] \frac{1}{6} - \frac{1}{6} [/tex]

[tex]1 - 1 = \frac{0}{6} [/tex]

Answer:15

Step-by-step explanation: 20 divided by 8=2.5 x 6=15

By the 30 - 60 - 90 theorem the right options of the multiple choice question is:

A. The hypotenuse is twice as long as the shorter leg.

D. The longer leg is √3 times as long as the shorter leg.

In this problem we must look for the right choices in a multiple choice question. According to the Euclidean geometry, 30 - 60 - 90 have the following properties:

Thus, the right options of the multiple choice question is:

A. The hypotenuse is twice as long as the shorter leg.

D. The longer leg is √3 times as long as the shorter leg.

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Answer:

plane HNA, HMB, ANG ...

Step-by-step explanation:

Any combination of three points on plane K will work unless all three are on the same line.

The probability of 11 voters out of 15 voting candidate A is 0.9770

According to the statement

we have given that the percentage of voters is 81% and poll conducts are 15 and we have to find the probability that 11 of the 15 voters will prefer Candidate

So, For this purpose,  

the question in based on binomial probability which means the probability of exactly x successes on n repeated trials in an experiment which has two possible outcomes p and q and p+q=1

let probability of choosing candidate A be p

and probability of choosing candidate B be q

In question p=0.81 and q=0.16

n be total number of voters=15

x be number of successes

then P(x=x)= [tex]\frac{n}{x} p^{x} q^{n-x}[/tex]

P(x=11)= [tex]\frac{11}{15} 0.81^{11} 0.16^{4}[/tex]

= 0.9770

So, the probability of 11 voters out of 15 voting candidate A is 0.9770

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Answer:

y = 1/3x - 3

Step-by-step explanation:

We can find the equation of the line, by finding the slope and combine with our y-intercept (-3).

We need to use the slope formula to find the slope.

Thus, we have (-3 - (-2)) / 0 - 3 = -1/-3 = 1/3

So our equation is y = -1/3x - 3

sin^4x as a product of two squared terms is sin^2(x) * sin^2(x)

The sine expression is given as

sin^4x

The above means

sin x raised to the power of 4

This in other words, the expression is represented as

(sin(x))^4

Express 4 as 2 + 2

(sin(x))^(2 + 2)

Apply the law of indices

(sin(x))^2 * (sin(x))^2

This gives

sin^2(x) * sin^2(x)

Hence, sin^4x as a product of two squared terms is sin^2(x) * sin^2(x)

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Step-by-step explanation:

x =130.......................

Answer:

[tex]12.3 - 33.9 = 21.6 \div 10 = 2.16[/tex]

The critical values corresponding to a 0.01 significance level used to test the null hypothesis of ρs = 0 is (a) -0.881 and 0.881

The scatter plot of the election is added as an attachment

From the scatter plot, we have the following highlights

Start by calculating the degrees of freedom (df) using

df =n - 2

Substitute the known values in the above equation

df = 8 - 2

Evaluate the difference

df = 6

Using the critical value table;

At a degree of freedom of 6 and significance level of 0.01, the critical value is

z = 0.834

From the list of given options, 0.834 is between  -0.881 and 0.881

Hence, the critical values corresponding to a 0.01 significance level used to test the null hypothesis of ρs = 0 is (a) -0.881 and 0.881

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