Solve the inequality. Graph the solution.

−8≤2/5(k−2)




















Solve the inequality. Graph the solution.

−8≤2/5(k−2)

In linear equation, 275 hamburgers were sold on Wednesday​ .

What in mathematics is a linear equation?

Let x = the number of hamburgers sold

Let x - 67 = the number of cheeseburgers sold

x + x - 67 = 483

2x = 483 + 67

2x = 550

x = 275

x = 275 hamburgers

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The solution to these are in form of equation as follows.

What is equation?

In arithmetic, an equation may be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.

Main body:

x= number of HD headphones           y= number of basic headphones

z = price of HD headphones.             w = price of basic headphones

a)

110 (70) + y*w = 10,000

7,700+ y*w = 10,000

y*w = 2,300

y = 2,300/w

b)

x*z+ 55(20) = 2000

x*z = 2000 -1100

x*z = 900

z = 900/x

c)

x*z+y*w = 800

x*z+8(80) = 800

x*z+640=800

X*z=160

Hence the values to the equation are as follows.

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Answer: The probability of 60% or less scared speechless out of a group of 50 customers (i.e. 30 customers) is 0.0932% or 0.000932.

Step-by-step explanation: Given problem meets all criteria for application of a binomial distribution with the probability of success; p=0.8 or 80% (which makes probability of failure; q=0.2 or 20%) and the total number of trials; n=50.

Let probability of 30 or less people scared (30 is 60% of 50 people) be P(x≤30), where x≤30 encapsulates all possibilities from 0 to 30 people scared speechless.

Then, by binomial distribution,

P(x≤30) =r=030nCr*pr*q(n-r)

Now we can substitute given values and find the desired probability,

P(x≤30) =r=03050!(50-r)!r!*(0.8)r*(0.2)(50-r)

P(x≤30) =r=03050!(50-r)!r!*(0.8)r*(0.2)-r*(0.2)50

P(x≤30) =(0.2)50*r=03050!(50-r)!r!*(0.8)r*(0.2)-r

P(x≤30) =(0.2)50*r=03050!(50-r)!r!*4r

The first value on the right hand side of equation is a very small number while the summation factor on second is a relatively larger number.

P(x≤30) = 0.000932

Thus, there is a 0.09% chance of 30 or less people scared speechless out of a group of 50.

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Answer:

The coefficient is 7 and the term that has it.

The amount of money the social worker can spend is $146.59 ≤ m ≤ $293.17

An equation shows the relationship between two or more numbers and variables.

Let m represent the amount of money the social worker can spend.

A social worker earns an average bi-weekly net pay of $1,465.87. Hence:

Monthly revenue = 2 * $1465.87 = $2931.74

For a debt of 5%:

m = 5% of $2931.74 = 0.05 * $2931.74 = $146.59

For a debt of 10%:

m = 10% of $2931.74 = 0.1 * $2931.74 = $293.17

$146.59 ≤ m ≤ $293.17

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Answer:

$158.80 ≤ m ≤ $317.61

Step-by-step explanation:

Hello,

So first step is we would use the bi-weekly net pay of $1465.87 then times it by 26 so it would look like this

1465.87 × 26 = 38112.62

Then we would divide 38112.62 by 12

38112.62 ÷ 12 = 3176.0516

Then, we would determine how much the social worker can spend if the monthly budget for debt is between 5% and 10%.

3176.0516 × 5% = 158.80

3176.0516 × 10% = 317.61

So, therefore the answer is $158.80 ≤ m ≤ $317.61.

the solution for the  given equation is  x= 1/2

an equation could be a formula that communicates the balance of two expressions, by interfacing them with the equals sign. Understanding an equation containing factors comprises deciding which values of the factors make the equality true. The factors for which the equation must be fathomed are moreover called unknowns, and the values of the unknowns that fulfill the balance are called solutions of the condition. There are two sorts of equations such as conditional and identities equations. An identity is genuine for all values of the factors. A conditional equation is as it were genuine for specific values of the factors

since the  given expression is :

`(2-4)=2(-5+1)x²

so solving for the simple  arithmetic expression on both sides  :

=>-2 =2(-4)x²

=> -2 = -8x²

=>2/8=x²

=>1/4= x²

=>x= 1/2

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Answer:

L=12, W=6

Step-by-step explanation:

L=2W

(L+2L)=36

3L=36

2L=12

L=6

She should use (b) x + 1 to represent her second number

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

As a general rule

Consecutive numbers are number that have a difference of 1 i.e both numbers are next to each other

Take for instance:

2 and 3, 5 and 6, 10 and 11 are all instances of consecutive numbers

Recall that she uses x to represent her first number

This means that the next number is

Next number = First number + 1

Substitute the known values in the above equation, so, we have the following representation

Next number = x + 1

Hence, the second number is (b) x + 1

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If Adira has 3 more than 50 percent of the number of cards that kip has. Kip has 18 cards. The expression for the total number of cards the groups has is:  1/3 ⋅9+(3+0.5⋅18)+18.

Given data:

Number of trading cards = 1/3

Adira number of cards = 23 more than 50%

Kip number of cards = 18 cards

Now let formulate an expression and then make use of the formulated expression to find the number of cards

Hence,

Number of cards =  1/3 ⋅9+(3+0.5⋅18)+18

Number of cards  =  1/3 ⋅9+(3+9)+18

Number of cards  =  1/3 ⋅9+(12)+18

Number of cards  =3 + 12+18

Number of cards = 33 cards

Therefore the expression is :  1/3 ⋅9+(3+0.5⋅18)+18.

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The equation is y = 4x. And the value of the function at x = 6 will be 24.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

If y varies directly to x. Then the relationship between them is written as,

y ∝ x

y = kx

When y = 8 and x = 2, then the value of the constant k is given as,

8 = k (2)

k = 8 / 2

k = 4

Then the equation is written as,

y = 4x

Then the value of the function at x = 6 will be given as,

y = 4 (6)

y = 24

The equation is y = 4x. And the value of the function at x = 6 will be 24.

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The length of the line segment BD is 3 centimeters.

Herein we find two triangles proportional to each other. According to Thales's theorem, two triangles are proportional when both have congruent angles. The geometric system is represented by the following expression:

AB / AD = BC / DE = AC / AE

By direct inspection we notice that the two triangles are proportional as they have congruent angles. If we know that DE = 10 cm, BC = 8 cm and AB = 12 cm, then the side AD has the following measure:

12 cm / AD = 8 cm / 10 cm

AD = (10 cm / 8 cm) × 12 cm

AD = 15 cm

And the length of the line segment BD is:

BD = AD - AB

BD = 15 cm - 12 cm

BD = 3 cm

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Using distributive property, the simplified form of (5x - 7)(4x + 1) is 20x^2- 23x - 7.

In the given question we have to solve the given expression.

The given expression is (5x - 7)(4x + 1).

To simplify the given expression we use the distributive property.

According to property; a(b+c) = ab+bc

Now simplifying the expression;

(5x - 7)(4x + 1)=5x(4x + 1) - 7(4x + 1)

(5x - 7)(4x + 1)=(5x*4x + 5x*1) - (7*4x + 7*1)

(5x - 7)(4x + 1)=(20x^2 + 5x) - (28x + 7)

Simplifying

(5x - 7)(4x + 1)=20x^2+5x -28x - 7

(5x - 7)(4x + 1)=20x^2- 23x - 7

The simplified form of (5x - 7)(4x + 1) is 20x^2- 23x - 7.

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As per the given percentage, Sherry want to invest $2,000 amount in mutual fund and $13,200 amount in bonds.

Percentage:

Percentage means the number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".

Given,

Sherry has 15,200 dollars to invest in mutual funds and in bonds. Sherry has selected a mutual fund that earns 1% a year and a bond that earns 4% a year.

Here we need to find if she wants to earn 548 at the end of the first year, how much does she need to invest in each type of account.

It is given that the total amount is 15200.

So, let us consider x be the amount invested in mutual funds then 15200 - x be the amount invested in bonds.

Therefore, it can be written in the following matrix,

[tex]\begin{bmatrix}x & 15200-x\end{bmatrix}[/tex]

Now, we have know that the total interest amount after 1 year is 548,

So, it can be written like the following expression

amount invested x percentage = final amount

Therefore,

[tex]\begin{bmatrix}x & 15200-x\end{bmatrix}\times\begin{bmatrix}\frac{1}{100} \\\frac{4}{100}\end{bmatrix}=548[/tex]

It can be simplified as,

[tex]\begin{bmatrix}x\times(\frac{1}{100})+(15200-x)\times(\frac{4}{100}) \end{bmatrix}=[548][/tex]

=> x/100 + 60800-4x/100 = 548

=> x + 60800 - 4x = 54800

=> -3x = 54800 - 60800

=> -3x = -6000

=> x = 2000

=> 15200 - 2000 = 13200

Therefore, she invests $2,000 in mutual funds and $13, 200 in bonds.

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Answer: 150*40/100=60

60+150=210.

Step-by-step explanation:

Answer:

  1300.2 µL

Step-by-step explanation:

You want to know the volume of a nautilus chamber in 8 years if it is 880 µL in year 0 and increases at 5% per year.

The growth factor is ...

  growth factor = 1 + growth rate

  growth factor = 1 + 0.05 = 1.05

Since the problem statement is about volume, we assume the growth factor applies to the chamber volume. If it applies to the linear dimension of the chamber, then the growth factor for volume will be 1.05³.

The function describing the chamber volume can be written as ...

  volume = (initial volume)(growth factor)^years

In 8 years, the chamber volume will be ...

  volume = (880µL)(1.05^8) ≈ 1300.2 µL

The chamber created in 8 years is expected to be 1300.2 µL.

__

Additional comment

If the 5% growth rate is the rate of growth of the linear dimensions of a chamber, then its volume will grow at the rate of 1.05³ per year. In 8 years, the volume will be about 2838.1 µL.

(The wording "5% larger" is ambiguous here.)

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Yes, as the asymptotic chi-squared distribution would emerge from normal approximating the binomial distribution and then squaring it.

Given statement;

Suppose that we use a hypothesis test to evaluate a claim about the proportion of narwhals with tusks longer than 3 meters. If we use a chi-squared test, would the value of our test statistic be the square of the standardized value of the statistic that we would have used if we had chosen a binomial test instead.

→ Yes, since by normal approximation of the binomial distribution and then squaring it would give us the resulting asymptotic chi-squared distribution.

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The length, breadth and height will be 78 cm, 78cm, 78cm each.

let consider the length = l

breadth = b

height = h

we are provided that

l + b + h = 234cm .......(1)

Also we have to maximize the volume , provided length is equal to breadth

∴ eqn (1) becomes

2b + h = 234

h = 234 - 2b

also ,

volume(v) = lbh

v = b²(234 - 2b)

v = b²234 - 2b³

now to maximize the volume we take the first derivative of the volume wrt 'b' and place it equal to zero. ( lagrange method )

i.e. d( v)/db = 0

∴  468b - 6b² = 0

 6b² - 468b = 0

6b( b - 78 ) = 0

∴  b = 78 cm

now as length = breadth

l = b = 78 cm

also putting this value in eqn (1)

h = 234 - 2b

h =  78 cm

So , the dimensions will be equal and will be 78cm , 78cm, 78cm each .

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Answer: A. [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

To find the slope we must find the change in y over the change in x. Δ

Or rise over run.  [tex]\frac{rise}{run}[/tex]

In the graph, we have two "good" points. (0, -6) and (4,0)

So for Δy 0 to -6 = -6

So -6 goes on top  [tex]\frac{-6}{x}[/tex]

Now Δx goes from 4 to 0 so the change would be -4.

So now it becomes [tex]\frac{-6}{-4}[/tex]

Since there are two negatives it becomes a positive. [tex]\frac{6}{4}[/tex] Or simply put, [tex]\frac{3}{2}[/tex]

The no. of ways to select the 2 blue balls and 2 orange balls from the urn is 0.4545

No. of Blue balls in the urn = 6

No. of Orange balls in the urn = 6

Total no. of balls in the urn = No. of blue balls + No. of orange balls

                                            = 6 + 6

                                           = 12 balls

No. of blue balls to be selected = 2

No. of orange balls to be selected = 2

No. of balls to be selected = 4

The total. no of ways 4 balls can be selected =[tex]^{12}C_{4}[/tex]

The No. of ways 2 blue balls can be selected = [tex]^{6}C_{2}[/tex]

The No. of ways 2 orange balls can be selected =    [tex]^{6}C_{2}[/tex]

Therefore, No. of ways to select 2 blue balls and 2 orange balls from the urn

                      =  [tex]^{6}C_{2} \times ^{6}C_{2} /^{12}C_{4}[/tex]

Probability = No. of ways to select blue balls x No. of ways to select orange balls / Total no. of ways to select balls

                         P = (15×15)/495

                             = 225 / 495

                          P = 0.4545

Therefore,  the no. of ways to select blue and orange balls is 0.4545

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Answer:

23.29 ft

Step-by-step explanation:

The given scenario can be modelled as a right triangle, where the angle between the ground and the ladder is 76°, the side opposite the angle is the height the ladder reaches up the wall, and the hypotenuse is the ladder.

To find how high up the wall the ladder reaches, use the sine trigonometric ratio:

[tex]\sin(\theta)=\sf \dfrac{O}{H}[/tex]

where:

The angle of elevation is 76°, so θ = 76°.

Let x be the height the ladder reaches up the wall, so O = x.

H is the length of the ladder, so H = 24.

Substitute the given values into the sine ratio and round the answer to the nearest hundredth:

[tex]\sin(\theta)=\sf \dfrac{O}{H}[/tex]

[tex]\sin(76^{\circ})= \dfrac{x}{24}[/tex]

[tex]\sin(76^{\circ})\cdot 24= \dfrac{x}{24}\cdot 24[/tex]

[tex]24 \sin(76^{\circ})= x[/tex]

[tex]x=24 \sin(76^{\circ})[/tex]

[tex]x=23.28709743...[/tex]

[tex]x=23.29\; \sf ft\;(nearest\;hundredth)[/tex]

Therefore, the ladder reaches 23.29 ft up the wall, rounded to the nearest hundredth.

Answer: $2100

Step-by-step explanation:

Since 12.5 percent of 2400 is 300, Just subtract 300 from 2400 to get the selling price with no sales tax. And the final answer is $2100.

The inequality represented by the graph is y ≥ -x + 2

A graph is a pictorial representation of data and the graph presented represents inequality data

The graph shows a linear function written in the form

y = mx +c

where slope, m calculated as

c = intercept

x = input variables

y = output variables

calculation of slope

The points used for the slope is gotten from the graph as (0. 2)  (1, 1)

m = (y₂ -y₁) / (x₂ - x₁)

substituting the values

= ( 2 - 1 ) / ( 0 - 1 )

= 1 / -1

= -1

y intercept, c this is a point where the graph cuts the y axis

c = 2

The two points result greater than or equal to written with the symbol ≥

hence the equation is

y ≥ -x + 2

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The equations represent functions where x is the input and y is the output are y = 2x and x+y = 2

The 1st equation is x =2

Since there is no component of y and the value of x is fixed. So this is not the desired option.

The 2nd equation is y = 2

Since there is no component of x, and the value of y is fixed. So this is not the desired option.

The 3rd equation is y = 2x

In this equation, x is the input and y is the output. For different values of x, we will have different values of y.

Thus, this is the desired option.

The 4th equation is x =2y

In this equation, y is the input and x is the output. For different values of y, we will have different values of x.

The 5th equation is x+y = 2

So, x + y = 2

y = 2 - x

In this equation, x is the input and y is the output. For different values of x, we will have different values of y.

Thus, this is the desired option.

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Answer: A. 9

Step-by-step explanation:

Answer:

5√3

Step-by-step explanation:

There are two triangles shown in the image.

First one is a 45°-45°-90° right triangle with side lengths represented with a-a-a√2 respectively to the angle measures.

The second triangle is 30°-60°-90° special right triangle with side lengths represented with b-b√3-2b respectively to the angle measures.

In first triangle hypotenuse (the side length represented with a√2) is given as 10√2 so a = 10.

This is also the measure of hypotenuse for the second triangle which is represented with 2b, so b = 5 in this case.

x is the side length that sees angle measure 60° which we said is represented with b√3, we said b = 5 so the value of x = 5√3 the answer is the first option.

The value of the given expression will be 4 / 3.

An equation using the logarithm of an expression containing a variable is referred to as a logarithmic equation. Check to verify if you can write both sides of the equation as powers of the same number before attempting to solve an exponential equation.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given logarithmic expression is log₂(∛16). The expression will be solved as below,

[tex]E = log_2\sqrt[3]{16}\\E = log_2(2^{\frac{4}{3})\\E = \dfrac{4}{3}log_22\\E = \dfrac{4}{3}[/tex]

Therefore, the solution of the expression will be equal to 4 / 3.

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Y=5p+3

Y equals the total amount of tape rolls

P is for the number of packages there are.

Hope this helped!

:)

Answer:

Y=5p+4

Y equals the total amount of tape rolls

P is for the amount of packages there are

Step-by-step explanation:

Answer: 4

Step-by-step explanation: in average, they drink 12/3 = 4 milk jugs per day.