A line is drawn to model the relation ship between the number of weeks and the change in price. Is the slope of this line positive or negative? Explain.

Answer:

a.) x=6 b.) y=-7 c.) a=0.25

Step-by-step explanation:

a.) 2(3x+2)=2x+28

6x+4=2x+28

subtract 4 on both sides

6x=2x+24

subtract 2x on both sides

4x=24

divide both sides by 4

x=6

b.) 5y+13=-43-3y

add 43 on both sides

5y+56=3y

subtract 5y on both sides

56=-8y

divide both sides by 8

-7=y or y=-7

c.) 4(2a+2)=8(2-3a)

8a+8=16-24a

add 24a on both sides

32a+8=16

subtract 8 on both sides

32a=8

divide both sides by 32

a=0.25

(hope you understood how I solved for each equation..)

Answer: 1/3

Step-by-step explanation:

The algebraic expression of the phrase Two-tenths of a number is 2x/10. The simplest form of the expression is x/5.

What is a phrase?

A mathematical expression is an expression that contains numbers, variables, and/or operations on those numbers and variables. A mathematical phrase is a verbal phrase that contains words and/or figures that can be turned into a mathematical expression.

Given phrase is Two-tenths of a number.

The value of two tenths is 2/10.

Assume that x be the number.

Two-tenths of x is 2/10 × x = 2x/10

Divide the denominator and numerator by 2:

= x/5

The expression is x/5.

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Answer:

This would not form a triangle

Step-by-step explanation:

due to the triangle inequality theorem, in order to find out if three numbers can form a triangle, you have to have each pair of numbers add up to more than the remaining number. The first combination added is 5+10 which is 15, and that is not greater than 17, so the answer is no, this is not a triangle.

hope this helps! :3

From the given ratio, there is a total of 100,000 vending machines in Osaka.

What is the ratio?

By comparing two amounts of the same units, the ratio can be used to calculate how much of one item is included in the other. There are two different categories for ratios. The first is a part-to-part ratio, whereas the second is a part-to-whole ratio.

Given, the ratio of vending machines to people is 1 to 24

That means, for every vending machine, there are 24 people.

In the city of Osaka, there are about 2,400,000 people.

So, the number of  vending machines = 2400000/24 = 100000

Hence, there is a total of 100,000 vending machines in Osaka.

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Answer:

top right

Step-by-step explanation:

6x3=18

0.954 represents population of the town increases by 0.954 each year.

Two or more expressions with an Equal sign is called as Equation.

Given,

The population of a heard of buffalo after t

years is represented by the function

[tex]f(x)=2186(0.954)^{t}[/tex]

We need to find the what does the value 0.954 represent in this

situation.

In the given function 2186 represent the initial population.

t represents the time in years

and 0.954 represents population of the town increases by 0.954 each year.

Hence, 0.954 represents population of the town increases by 0.954 each year.

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The total Volume of tank = 35 liters

In three dimensions, everything takes up some space. What is being measured here is the area's volume. The volume of an object is the area occupied inside its three-dimensional boundaries. Sometimes it is referred to as the

According to the Given information

Volume of each marble = 0.04 liters

Number of marbles to be put in the water tank = 50 marbles

Volume of 50 marbles = 0.04 × 50 = 2 liters

Volume of water added to the tank = 33 liters

Total Volume of tank = 2 liters + 33 liters

                                    =     35 liters

SO,

The total Volume of tank = 35 liters

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The p-value of the given hypothesis is; 0.9999

The formula for the z-score of proportions is;

z = (p^ - p)/√(p(1 - p)/n)

where;

p^ is sample proportion

p is population proportion

n is sample size

We are given;

p^ = 15% = 0.15

p = 20% = 0.2

n = 5000

Thus;

z = (0.15 - 0.2)/√(0.2(1 - 0.2)/5000)

z = -8.8388

From p-value from z-score calculator, we have;

P(Z < -8.8388) = 1 - 0.0001 = 0.9999

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The question is based on the calculus and the derivative for given equation [tex]t^{4} - 24t^{2} \\ \\[/tex] is t = 0.

Calculus is a discipline of mathematics that focuses on rates of change, to put it simply. For instance, you could wish to determine how quickly an automobile will slow down when it approaches a stop sign. Calculus can assist you in calculating that change. Calculus introduces movement into math, that's correct!

Calculus is a tool used by engineers to calculate things like rates of change and areas; in fact, calculus is the mathematical "backbone" for dealing with problems where variables change with time or some other reference variable. Calculus is concerned with two basic operations: differentiation and integration.

We are given

x(t) = [tex]t^{4} - 24t^{2} \\ \\[/tex]

we need to find its derivative only then we can comment on its increasing decreasing nature

x'(t) = [tex]4t^3 -48t\\\\[/tex]

we will check where derivative is zero

[tex]4t^3 - 48t = 0\\\\4t^2(t-4) = 0\\\\\\t = 0 \\\\t = 4\\[/tex]

hence increasing for all x E R except interval (0,4)

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Answer:  [tex]f^{-1}(\text{x}) = \frac{2-\text{x}}{3}\\\\[/tex]

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

Work Shown:

[tex]f(\text{x}) = 2-3\text{x}\\\\\text{y} = 2 - 3\text{x}\\\\\text{x} = 2 - 3\text{y}\\\\\text{x} + 3\text{y} = 2\\\\3\text{y} = 2-\text{x}\\\\\text{y} = \frac{2-\text{x}}{3}\\\\f^{-1}(\text{x}) = \frac{2-\text{x}}{3}\\\\[/tex]

-----------------

Explanation:

The process to find the inverse involves this outline.

This process is followed in the "work shown" portion above.

To confirm the answer, let g(x) be the inverse of f(x).

If they were inverses of each other, then these two properties would hold true:

Here's the verification for the first part.

[tex]f(\text{x}) = 2-3\text{x}\\\\f(g(\text{x})) = 2-3*g(\text{x})\\\\f(g(\text{x})) = 2-3*\frac{2-\text{x}}{3}\\\\f(g(\text{x})) = 2-(2-\text{x})\\\\f(g(\text{x})) = 2-2+\text{x}\\\\f(g(\text{x})) = \text{x}\\\\[/tex]

I'll let you do the other confirmation.

$150 is the least amount of money you can spend if you want to increase the computer performance by 25%, assuming that you can improve one or all the components in the computer.

RAM is a type of volatile memory, which means that data is only stored there while the chip is powered and is completely erased when the computer is turned off. In gigabytes, RAM memory is measured (GB).

Random access memory is referred to as RAM. Because the data may be swiftly read and updated in any sequence, it is termed random access. Compared to previous storage devices like CD-RWs, which access data in a slower, predetermined order, this is faster.

There are much more methods through which we can improve computer performance but by spending the least amount of money we can do it by upgrading  your RAM. We can upgrade the RAM of the system to 8 GB and 16 GB. If we want to upgrade the RAM to 8 GB then it can be done for around $75 and If we want to upgrade the RAM to 16 GB then it can be done for around $150.

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The complete question is as follows:

What is the least amount of money you can spend if you want to increase the computer performance by 25%, assuming that you can improve one or all the components in the computer?

Part a: y = -6x + 5 is : Not proportional.

Part b: y = 7/8x proportional:  proportionality constant = 7/8.

For the stated question;

Part a: y = -6x + 5

To check the proportional relation, put value of 'x' and find the corresponding value of 'y'.

The ratio = y/x must be same.

For x = 1, y = -1

y/x = -1

And, for x = 2, y = 7

y/x = 7/2

Thus, ratio is not equal, Not proportional.

Part b:  y = 7/8x

For x = 1, y = 7/8

y/x = 7/8

Now, For x = 2, y = 14/8

y/x = 7/8, both ratios are equal.

Thus,  y = 7/8x proportional:  proportionality constant = 7/8.

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The cost of the pyramid shape sign is $240.

A pyramid is a 3D figure that has a base made of a polygon and faces that are all triangular and connected. The conventional shape of a pyramid is created by joining each vertex of the base to a single common tip or apex. In this section, let's study more about pyramids.

We know the volume of a pyramid is (1/3)×length of the bese×width of the base×height.

∴ The volume of the pyramid with base length of 6feet, base width of 3feet and height 5 feet is,

= (1/3)×6×3×5 cubic feet.

= 30 cubic feet.

Given, The aluminum costs $8 per cubic foot.

∴ The total cost of the pyramid is = (30×8) = $240.

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The slope of the given function is 0.25. The function that has  the same slope is y = 0.25x + 5. Option B is the correct option.

What is a function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Given table is

x         0          1            2             3

y      -0.5       -0.25      0           0.25

The slope of a function that passes through the points (x₁, y₁) and (x₂, y₂) is m = (y₂ - y₁)/(x₂ - x₁)

Assume that x₁ = 0, y₁ = -0.5, x₂ = 1, y₂ = -0.25

The slope of the function is [-0.25 - (-0.50)]/(1 - 0) = 0.25

Now compare the equation y = -0.25x - 2 with y = mx + c

m =  -0.25

The slope of the function is -0.25.

Now compare the equation y = 0.25x + 5 with y = mx + c

m =  0.25

The slope of the function is 0.25.

Now compare the equation y = 4x - 5 with y = mx + c

m =  4

The slope of the function is 4.

Now compare the equation y = -4x + 34 with y = mx + c

m =  -4

The slope of the function is -4.

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The probability she makes at least 65 is 0.0139.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

[tex]\begin{aligned}P(x \geq 65) & =1-P(x < 65) \\& =1-P\left(\frac{x-\mu}{n} < \frac{65-56}{4.0988}\right) \\& =1-P(z < 2.1958) \\& =1-0.9861 \\& =0.0139\end{aligned}[/tex]

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Answer: 300000000000000000

Step-by-step explanation:

50000x6000000000000 can be written as 3 times 10^17

So the answer is 300000000000000000

Hence, the coordinates of the new triangle are [tex]A(2,0),B(7,-2),C(2,-2)[/tex].

What is the coordinates?

A pair of numbers that describe the position of a point on a coordinate plane by using the horizontal and vertical distances from the two reference axes. Usually represented by [tex](x,y)[/tex] the x-value and y-value.

Here given coordinates are

[tex](-2,3),(3,1),(-2,1)\\\\(-2,0),(3,-2),(-2,-2)\\\\( - 2 , 0 ) , ( 3 , - 2 ) , ( - 2 , -2 )[/tex]

Suppose [tex]a[/tex] units on the horizontal and [tex]b[/tex] units on the vertical. Then, the new coordinate become

[tex]A(x,y)=A(x+a,y+b)[/tex]

As per the question triangle [tex]ABC[/tex] is translated [tex]4[/tex] units to the right and [tex]-3[/tex]units down.

So, [tex]a=4,b=-3[/tex] and the coordinates are

[tex]A(-2,3),B(3,1),C(-2,1)\\\\[/tex]

Then,

[tex]A(-2+a,3+b)=A(-2+4,3-3)=A(2,0)\\\\B(3+a,1+b)=B(3+4,1-3)=B(7,-2)\\\\C(-2+a,1+b)=C(-2+4,1-3)=C(2,-2)[/tex]

Hence, the coordinates of the new triangle are [tex]A(2,0),B(7,-2),C(2,-2)[/tex].

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If cos x= 2/3 and x is in quadrant I, then the exact value of sin(2x) is (4/3)sin x.

A branch of mathematics called trigonometry examines the connections between triangles' angles and sides. It is predicated on the idea of right triangles, where one angle is 90 degrees and two sides are perpendicular to one another. The six fundamental functions of trigonometry—sine, cosine, tangent, cotangent, secant,  cosecant. These values of functions can be used to address real-world angle and length issues, such as determining the height of a structure or the distance between two locations. Calculus, geometry, and other areas of mathematics are all strongly connected to trigonometry.Modeling actual phenomena like item motion, wave behaviour, and light dispersion is possible with these functions. Physics, engineering, and astronomy are just a few of the disciplines that use trigonometry extensively.

How to solve?

In quadrant I, cos x = 2/3 and sin x > 0.

sin(2x) = 2sin x cos x

sin(2x) = 2 * 2/3 * (sin x)

sin(2x) = (4/3)sin x

If sin x > 0, then sin(2x) = (4/3)sin x > 0.

The exact value of sin(2x) is (4/3)sin x

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Applying reciprocal property the equation 36 / 5 = 8 / a is solved to find the value of a as 10/9

The definition of reciprocal in mathematics is the inverse of a value or a number.

If n is a real number, then 1/n will be n's reciprocal.

Therefore, we must change the number to its upside-down form. For instance, 1 divided by 9 is the reciprocal of 9, or 1/9.

The result of multiplying a number by its reciprocal now equals one. multiplicative Inverse is another name for it.

Similarly,  36 / 5 = 8 / a

the reciprocal is 5 / 36 = a / 8

cross multiplying

5 * 8 = 36 * a

36a = 40

a = 40 / 36

a = 10/9

The value of a is 10/9

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The maximum number of spheres that can be made through ice will be 135.

To convert any unit into another is called a unit conversion.

In order to convert units, we need to care about their dimensions their dimension should not be changed.

As per the given,

Number of ice portions = 40

Weight of one ice portion = 3 ounce

Since, 1 lb = 16 ounce

3 ounce = 3/16 lb

Weight of 40 portion = 120/16 lb

The weight of one sphere of ice = 18 lb

Number of possible spheres = (120/16)/18

⇒ 120/16 x 18

⇒ 135 sphere

Hence "135 spheres are the most that can be produced by ice".

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Answer:

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

[tex] slope=\frac{8-1}{7-1} [/tex]

[tex] slope=\frac{7}{6} [/tex]

slope = 7/6

Answer:

a. 88

b. I disagree with Kris

Step-by-step explanation:

88 is by far the biggest outlier here being 11 numbers away from the second highest being 77. This means there is one kid that is much higher than the rest of the group.

Answer:

Step-by-step explanation:

1. Increase of 10% in price of shirt.
2. Decrease of 10% in price of shirt.
Hence- both amounts cancel out, therefore there is 0% change in price of shirt as both percentages cancelled out, or we can say nullified each other. Because they added the same amount to the item and then subtracted the same percent leading to no change.

Answer:

Step-by-step explanation:

1. Lin, Tyler, and Jada's information is missing.

2. 9 1/8 = 73/8

1 2/8 = 10/8

73/8 - 10/8 = 63/8.

His shoe length was 63/8 inches.

Answer:

Parallel: Y= -7/3x - 37/3

Perpendicular: Y=3/7x + 7

Step-by-step explanation:

Use the formula: Y - Y1 = M(X - X1) Plug in -7 as X1 and 4 as Y1 and your M value is your slope. (-7, 4) where it passes from.

Remember when the slope is parallel it's always the same slope in this case -7/3

When perpendicular flip it and change the sign 3/7

The correct statement regarding the exponential functions g(x) and h(x) is given as follows:

B g( x) ≥ h( x) on the interval –2 ≤ x ≤ 2.

The standard definition of an exponential function is given as follows:

y = ab^x.

In which the coefficients of the function are described as follows:

Function h(x) is defined as follows:

h(x) = 3^x - 2.

For the graphed function g(x), when x = 0, y = 4, hence the intercept of the function is given as follows:

a = 4.

When x = 1, y = 5, hence the rate of change of the function is obtained as follows:

b = 5/4.

b = 1.25.

Then function g(x) is given as follows:

g(x) = 4(1.25)^x.

Due to the higher intercept, g(x) ≥ h( x) at x = 0. This will change when they intersect, which from the image given at the end of the answer is at x = 1.906, which is approximately 2, hence statement B is correct.

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The number will be decreased by a percentage of 32%.

If a number N is increased by a percentage X, then the new value is:

N' = N*(1 + X/100%)

If instead the number is decreased, then the new value is:

N' = N*(1 - X/100%)

So if we apply a decrease by 60% followed by an increase of 80%, we will have:

N' = N*(1 - 60%/100%)*(1 + 80%/100%)

N' = N*(1 - 0.6)*(1 + 0.8)

N' = N*(0.4)*(1.8)

N' = N*0.72

We can rewrite that as:

N' = N*(1 - 0.32)

0.32 = 32%/100%

So that is equivalent to a decrease by 32%

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A researcher obtains a negative value for the chi square test.1 is the value is negative .

What is chi-square value?

The difference between the frequencies of results of a collection of events or variables that were observed and those that were expected is measured by the chi-square (2) statistic.

                   Such variations in categorical variables can be examined using chi-square, particularly when they are nominal in nature.

We know that the chi-square is the sum of square of difference between observed and expected frequencies divided by the expected frequency. So, it is clear that the chi-square value can never be negative because sum of squares is always positive.

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