Jess and Brian are playing the following game: Jess thinks of a fraction, and Brian flips a coin. If the coin turns up heads, Jess multiplies the number she's thinking of by $\frac{5}{6}$. If the coin turns up tails, she multiplies the number she's thinking of by $\frac{6}{5}$. Brian flips the coin ten times, and after each flip Jess multiplies the number in her head by either $\frac{5}{6}$ or $\frac{6}{5}$, depending on the coin flip. The ten coin flips turn out to be:\[ \text{THTTHTHTTT}, \]where H means 'heads' and T means 'tails.' What number is Jess thinking of at the end of the game if she starts out with the fraction $\frac{5}{9}$

Step-by-step explanation:

I have to assume the equations are

4x + y = 13

(1/2)y = -2x + 5

let's bring both of them into a "y = ..." form :

y = -4x + 13

y = -4x + 10

now we see that both equations are lines with the same slope but different y-intersect.

so, they are parallel but not identical.

therefore, there are 0 solutions. the lines will never intersect and have no point in common.

Answer: 4y (4y^2-2y-5)

Step-by-step explanation:

The total number of terms which are in the polynomial  expression  –2p³ – 3p² + 4p + 7 is 4 terms.

A polynomial expression is made up of multiple terms joined either by addition , subtraction or multiplication or division.

The given expression is

–2p³ – 3p² + 4p + 7

If we will break them down in simpler terms we will get ,

–2p³, – 3p², + 4p, + 7

Therefore, number of terms are found to be  4

The terms of an algebraic expression are referred to as the the components of that expression . An algebraic expression can have one or more terms.

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Answer:

1.Solve one of the equations for either variable.

2.Substitute the expression from Step 1 into the other equation.

3.Solve the resulting equation.

4.Substitute the solution in Step 3 into one of the original equations to find the other variable.

5.Write the solution as an ordered pair.

6.Check that the ordered pair is a solution to both original equations.

Step-by-step explanation:

The constant of variation for the given data is 1/4.

If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.

Given that the data in the table is,

x        f(x)

-8       -2

-4       -1

0        0

4         1

8        2

The constant of proportionality will be calculated as,

F(x) = kx

-2 = k x -8

k = -2 / -8

k = 1 / 4

Here, the proportionality constant will be 1/4.

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The beat three options are:  The slope of the line is 1/5, (2) The possible equation if the line is y=1/5x, (3) The slope and the y intercept are the same

Lope is the rate of change of y with respect to x.  slope is also the increase in y over increase in x vice versa

Slope is denoted by rise/run

The Possible solutions from the graph are:

Taking any two points on the graph : (4, 1) and -4, -1,)

We can find the slope as (1--1)/4--4

Therefore, the Slope = 2/3≡1/5

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Consequently, y-1 = 2 is the point-slope form linear equation for the line passing through (1, 3) and having a slope of 2. (x-3).

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.

Here,

Y = mx + c in this instance.

(y- y₁) = m(x - x₁)

where,

The coordinate for the x-axis is x and x1,

The coordinate for the y-axis is y and y1.

The slope of the line is m, and

The y-intercept can be represented by the letter c.

Replace the value of the slope and the point in the general equation to obtain the equation for the line passing through (1, 3) and having a slope of 2.

y-1 = 2(x-3) (x-3)

Consequently, y-1 = 2 is the point-slope form equation for the line passing through (1, 3) and having a slope of 2. (x-3).

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The correct answer is c. as the age of a student increases, the frequency of the student's ages increases.

A skewed right population means that the data is distributed in such a way that the majority of the values are on the right side of the data set. In the case of a population of college students, this would mean that there is a greater frequency of older students (those in their late twenties or older) than younger students. As the age of a student increases, the frequency of the student's ages increases.

Option a. there are a greater number of older students is also correct, but it is not complete.

Option b. the modal age is greater than the median age is not correct, as the modal age is the most common age in the population and the median age is the middle value of the population, and there is no relationship between them.

Option d. there are more younger students within the population is not correct as a skewed right population indicates the opposite.

Option e. not enough information is not correct as the question is providing enough information to make a conclusion.

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Answer:

Step-by-step explanation:

WX≅VY

VY = 7

CD≅BE

BE = 13

The formula for an isosceles triangle is A = (1/2) * b * h, where b is the base, h is the height, and A is the area.

The formula for an isosceles triangle is A = (1/2) * b * h. This formula is used to calculate the area of an isosceles triangle. To use the formula, you need to know the base, b, and the height, h, of the triangle. The base is the length of any one of the two equal sides of the isosceles triangle, and the height is the distance from the base to the opposite vertex. Once you have these measurements, you can plug them into the formula to calculate the area of the triangle. The formula multiplies the base, b, by the height, h, and then divides the product by two. This will give you the area of the triangle, A.

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In the equation [tex]3x-6y=-13[/tex] , the coefficient of equation are , coefficient  of  [tex]x[/tex] is [tex]3[/tex] and the coefficient of [tex]y[/tex] is [tex]-6[/tex] .

What are Coefficients ?

The Coefficients are defined as a number that is placed with a variable. It is a integer that is multiplied by the variable and written next to it.

In simpler words, we can say that ; a coefficient is a multiplicative factor in the terms of a polynomial, a series, or any expression.

The variables that do not have a number written with them are assumed to have 1 as their coefficient.

For example, in the expression [tex]3x[/tex] , the coefficient of [tex]x[/tex] is [tex]3[/tex] ,  but in the expression [tex]x^{2} +3[/tex], [tex]1[/tex] is the coefficient of [tex]x^{2}[/tex].

The equation to find the coefficient is given as [tex]3x-6y=-13[/tex] ,

we see that , the numerical part with [tex]x[/tex] is [tex]3[/tex] and with [tex]y[/tex] is [tex]-6[/tex] ;

Therefore , the coefficient of [tex]x[/tex] is [tex]3[/tex] and [tex]y[/tex] is [tex]-6[/tex] .

The given question is incomplete , the complete question is

What are the coefficients of the equation 3x -6y = - 13 ?

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by splanation, in be clearly what he taking about. the hamburger, usually. is 1/4 p.1/2 p. in triple hamburger on 4 by 4

The number of used hamburgers that is 80% lean is = 500

and the number of used hamburgers that is 88% lean is = 300.

Let the number of hamburger that is 80% lean be = x.

So the number of hamburger that is 88% lean is = 800 - x

According to question after the mixing all these the total percentage of lean in 800 ponds of burgers is 83%.

So, the suitable mathematical equation is,

80% of x + 88% of (800 - x) = 83% of 800

(80/100) x + (88/100) * (800 - x) = (83/100) * 800

80x + 88 (800 - x) = 83 * 800 [Multiplying 1000 with both sides]

80x + 88 * 800 - 88x = 83 * 800

88x - 80x = 88 * 800 - 83 * 800 = 800 (88 - 83) = 5 * 800

8x = 800 * 5

x = (800 * 5)/8 = 100 * 5 = 500

Hence the number of hamburger with 80% lean is 500 and the number of hamburger with 88% lean is = (800 - 500) = 300.

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Answer:

x) = 1 + 2(0.94)*

The y-intercept = (0, [?])

For x ≥ 0, the horizontal as

A situation where there might be a causal relationship could be the amount of fertilizer utilized in proportion to the kilograms of pumpkins harvested on the farm.

A scatter plot with a trendline along which the data points are situated can be used to demonstrate the relationship between correlated variables.

Indicating a positive correlation is when the trendline slopes higher from left to right, while the opposite is true.

Part A:

The correlation coefficient of r = 0.51 is valid based on the provided scatter plot.

Part B:

The amount of fertilizer applied in connection to the kilograms of pumpkins harvested on the farm can be a scenario where a causal relationship exists.

Hence, A situation where there might be a causal relationship could be the amount of fertilizer utilized in proportion to the kilograms of pumpkins harvested on the farm.

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Answer:

slope = 2

Step-by-step explanation:

calculate the slope m using the slope formula

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

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (1, 4) ← 2 points on the line

m = [tex]\frac{4-0}{1-(-1)}[/tex] = [tex]\frac{4}{1+1}[/tex] = [tex]\frac{4}{2}[/tex] = 2

Answer: The slope is 2.

Step-by-step explanation: To find the slope of a line, we first need to pick two points on a line. To solve this, I picked points (-2, -2) and (1, 4). The slope is rise over run, so you need to find the rise and run and divide.

We need to go 6 spaces up from (-2, -2) to get to (1, 4). This is our rise. Then, we go 3 spaces to the right. That is our run. 6 / 3 is 2, so that's your slope. Notice that if you cannot divide the rise and run into a whole number, keep it as a fraction instead.

Let me know if this is right! :)

The length of the hypotenuse will be 5√2 = 7.07

The triangle specified in the question is right-angled, one angle is mentioned to be 90°. It is also an isosceles triangle since both other angles are equal. if both angles are equal, both sides will also be equal.

So the length of both equal sides = 5 cm

Pythagoras' theorem tells us about the relationship between the three sides of a right-angled triangle. It states that the square of the hypotenuse of the right-angled triangle will be equal to the sum of squares of the other two sides. If a, b, and c are the sides

 c² = a²+ b²

  c = √(a²+b²)

According to Pythagoras' theorem, Hypotenuse = √base²+ alt²

                                                          Hypotenuse = √5²+5²

                                                                                = 5√2

                                                                               = 7.07 cm

So the length of the hypotenuse is 5√2 = 7.07 cm.

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Answer:

Blue:  y = x²

Red:  y = -x² + 18

Step-by-step explanation:

The blue parabola opens upwards, therefore the term in x² is positive.

The red parabola opens downwards, therefore the term in x² is negative.

The x-value of the vertices of both parabolas is x = 0.

Therefore, the equations of both parabolas will not have a term in x.

The y-intercept of the blue parabola is also the y-value its vertex: y = 0.

The y-intercept of the red parabola is also the y-value its vertex: y = 18.

Therefore, the equation for each parabola is:

To check, substitute x = ±3 into both equations:

Blue

[tex]x=3 \implies y=(3)^2=9[/tex]

[tex]x=-3 \implies y=(-3)^2=9[/tex]

Red

[tex]x=3 \implies y=-(3)^2+18=9[/tex]

[tex]x=-3 \implies y=-(-3)^2+18=9[/tex]

Answer:

y = x2

y = –x2 +18

Step-by-step explanation:

I got it right on the test.

(a) The distance traveled by motorcycle is 1548 ft.

(b) The distance traveled by motorcycle is 1512 ft.

(c) (b) is a lower estimate and (a) is an upper estimate since v is a decreasing function of t.

What is velocity?

The primary indicator of an object's position and speed is its velocity. It is the distance that an object travels in one unit of time. The displacement of the item in one unit of time is the definition of velocity.

Given table is:

t (s)        0       12      24     36     48      60

v (ft/s)   30      28     25     21      25      27

The distance traveled by motorcycle during this time period using the velocities at the beginning of the time intervals is:

12(30 + 28 + 25 + 21 + 25)

=12 × 129

= 1548 ft

The distance traveled by motorcycle during this time period using the velocities at the end of the time intervals is:

12(28 + 25 + 21 + 25 + 27)

=12 × 126

= 1512 ft

The distance traveled by motorcycle at the end of the time intervals is greater than the distance traveled by motorcycle at the beginning of the time intervals.

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Answer: i need your help, XD

Step-by-step explanation:

Solutions refers to the answer to the problem, The example of real solution can be the solution for the value of 'x' in a equation.

In mathematics, a solution refers to a value or set of values that satisfies a given equation, system of equations, or problem. For example, if the equation is x + 2 = 4, then the solution is x = 2, because substituting 2 for x in the equation makes it true. In the case of systems of equations or more complex problems, a solution may be a set of values that satisfies all the equations or conditions of the problem. In such case, the solution may be represented graphically or as coordinates of a point.

In mathematics, an ideal solution refers to a solution that meets all the desired criteria or requirements without any constraints. It is the "best case" scenario. A real solution, on the other hand, refers to a solution that takes into account all the limitations and constraints of a problem. It is a more practical and realistic solution.

example:

x+2=0

x=-2

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================================================

Explanation:

The x and y are placeholders for numbers.

Think of them as boxes so to speak, and we fill each box with a number.

In this case we will plug in x = 6 and y = 2.

The steps are shown below.

[tex]\frac{3\text{x}+4}{\text{y}}\\\\\frac{3*6+4}{2}\\\\\frac{18+4}{2}\\\\\frac{22}{2}\\\\11\\\\[/tex]

The final answer is choice B

-----------

This means,

[tex]\frac{3\text{x}+4}{\text{y}} = 11 \ \text{when} \ \text{x} = 6 \ \text{and y} = 2 \\\\[/tex]

Put another way

[tex](\text{x},\text{y}) = (6,2) \ \text{ is a solution to } \frac{3\text{x}+4}{\text{y}} = 11[/tex]

In a visual sense, the point (6,2) is on the equation of [tex]\frac{3\text{x}+4}{\text{y}} = 11[/tex]

well, what's 230% of $480?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{230\% of 480}}{\left( \cfrac{230}{100} \right)480}\implies \text{\LARGE 1104}[/tex]

The  set of equations correctly representing x are as follows:

(x + 1/2) and (x = 7/2).

A set or group of equations that you solve all at once is referred to as a "system" of equations. The simplest linear system is one that has two equations as well as two variables. Linear equations (those that graph as straight lines) are easier to understand than non-linear ones.

Systems of equations in mathematics are a collection of relationships between different unknown variables that can be stated in terms of algebraic expressions. They are also known as simultaneous equations. Graphing, substitution, as well as elimination by addition, are methods that can be used to find the solutions to a basic system of equations.

Sum means addition (+).

Given that sum of a number, x and 1/2 is 4.

This means the adding  two numbers

x+1/2=4

Now make x the subject of formula,

x=4-1/2

Finding the L.C.M  = 8-1/2

                        x=7/2

                     ∴ x=3 1/2

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The total number of cookies baker sold in all are 350 cookies.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, sugar cookies make up 38% of all sales for a local baker's cookie sales.

Let the total number of cookies be x.

Now, 38% of x=133

38/100 ×x=133

x=13300/38

x=350

Therefore, the total number of cookies baker sold in all are 350 cookies.

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Choose the range of values for the x-axis and the y-axis , Plot the points on the graph, using the logarithmic formula , Connect the points with a smooth curve and Label the axes and add any other details you want to include.

1. Choose the range of values for the x-axis and the y-axis. Select the minimum and maximum values for both the x-axis and the y-axis.

2. Plot the points on the graph, using the logarithmic formula. Use the formula log(x) = y to calculate the points that should be plotted on the graph. For example, if the x-axis range is from 1 to 10, and the y-axis range is from 0 to 10, then the first point would be (1,0).

3. Connect the points with a smooth curve. Once all the points have been plotted, use a ruler or a graphing calculator to connect them with a smooth curve.

4. Label the axes and add any other details you want to include. Use a ruler or a graphing calculator to label the axes and add any other details you want to include, such as a title, a legend, or a grid.

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Submarine must descend 17 feet in the 5th minute.

What is the average of the data?

Only numerical variables, whether continuous or discrete, can be used to calculate the mean. It is calculated by merely dividing the total number of values in a data set by the sum of all the values in the data set. A frequency table of data or raw data can both be used for the calculation.

Let the distance descended by submarine in 5th minute = x feet

Average distance descended by the submarine

= (Total distance distended/ Duration or time)

= (6 + 8 + 14 + 15 + x) / 5

= (43 + x) / 5

Statement given in the question → "Submarine must descend at an average rate of at least 12 feet per minute"

So the inequality for the statement will be,

(43 + x) / 5 ≥ 12

43 + x ≥ 60

x ≥ 17

Therefore, submarine must descend 17 feet in the 5th minute.

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Answer:

Step-by-step explanation:

because HA⊥HR, HR⊥DR, so HA ║ DR, then we know ∠DHR=∠ARH,

we konw, AR=HD, They have a common segment HR, as well as the same angle，so HRA≅RHD

The probability that the mean thickness in these 16 measurements x is farther than 3 units away from the target value is 0.15 + 0.15 = 0.30 which corresponds to the answer B) 0.32.

What is the Central Limit Theorem?

The central limit theorem states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed.

We can use the Central Limit Theorem to determine that the sampling distribution of the mean thickness of a random sample of size 17 from a population with a mean of 200 units and a standard deviation of 12 units will be approximately normal with a mean of 200 units and a standard deviation of (12 units)/√17 = 2.8 units.

Given that the mean thickness in these 17 measurements x is farther than 3 units away from the target value, we can use the standard normal table to find the probability.

Let's call X = mean thickness,

if X > 203, we have P(X>203) = P(Z> (203-200)/2.8) = P(Z>1.071) = 0.15

if X < 197, we have P(X<197) = P(Z< (197-200)/2.8) = P(Z<-1.071) = 0.15

Hence, the probability that the mean thickness in these 16 measurements x is farther than 3 units away from the target value is 0.15 + 0.15 = 0.30 which corresponds to the answer B) 0.32.

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Answer:

7

Step-by-step explanation:

The density of the wood is between 0.35 g/cm^3

The density of a substance can be calculated using the formula:

density = mass / volume

To calculate the volume of the cuboid, we can use the formula:

volume = length x width x height

So, using the measurements provided:

volume = 13.2 cm x 16.0 cm x 21.7 cm = 5541.44 cm^3

To calculate the density of the wood, we divide the mass by the volume:

density = 1970 g / 5541.44 cm^3

We can convert cm^3 to g/cm^3 by converting the volume to g

1cm^3 = 1g/cm^3

density = 1970 g / 5541.44 g/cm^3

density = 0.3555 g/cm^3

However, as the measurements provided have a degree of uncertainty, we should consider bounds to find the range of possible densities.

The lower bound for the length is 13.2 cm - 0.1 cm = 13.1 cm

The upper bound for the length is 13.2 cm + 0.1 cm = 13.3 cm

The lower bound for the width is 16.0 cm - 0.1 cm = 15.9 cm

The upper bound for the width is 16.0 cm + 0.1 cm = 16.1 cm

The lower bound for the height is 21.7 cm - 0.1 cm = 21.6 cm

The upper bound for the height is 21.7 cm + 0.1 cm = 21.8 cm

The lower bound for the mass is 1970 g - 5 g = 1965 g

The upper bound for the mass is 1970 g + 5 g = 1975 g

We can now use these bounds to calculate the range of possible densities:

Density lower bound = 1965 g / (13.3 cm x 16.1 cm x 21.8 cm) = 0.350 g/cm^3

Density upper bound = 1975 g / (13.1 cm x 15.9 cm x 21.6 cm) = 0.360 g/cm^3

So the density of the wood is between 0.35 and 0.36 g/cm^3 to one decimal place.

So the density is 0.35 g/cm^3 with an uncertainty of 0.01 g/cm^3

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