Solve the inequality. 1/3+x+2/9>5/6

Answer:

32760

Step-by-step explanation:

There are 4 positions on the board.  There are 15 possible candidates for the first position.  That leaves 14 candidates for the second position.  Which leaves 13 for the third position, and 12 for the fourth position.

15 × 14 × 13 × 12 = 32760

Answer: There are 32,760 ways that research board can be chosen.

Step-by-step explanation:

Since we have given that

Number of research doctors participating in the study = 15

the research board requires to be established with offices of director, Assistant director, Quality control analyst, and Correspondent.

Since there are 15 choices for the Offices of director,

There are 14 choices for the Assistant director,

There are 13 choices for Quality control analyst,

There are 12 choices for Correspondent.

So, by applying "Fundamental theorem of counting", we get that

Number of ways that research board can be chosen is given by

[tex]15\times 14\times 13\times 12\\\\=32,760[/tex]

Hence, there are 32,760 ways that research board can be chosen.

Answer: Option C

[tex]a> 0[/tex]

Step-by-step explanation:

The graph shows a radical function of the form [tex]f(x)=a(x+k)^{\frac{1}{n}}+c[/tex]

Where n is a positive number.

For this type of function, if the coefficient [tex]a> 0[/tex] then then when x tends to [tex]\infty[/tex] f(x) tends to [tex]\infty[/tex] and when x tends to [tex]-\infty[/tex] then f(x) tends to [tex]-\infty[/tex].

Notice in the graph that as x increases then f(x) also increases and as x decreases f(x) also decreases.

This indicates that the coefficient [tex]a> 0[/tex]

Answer:

y=-2x+20 or y-4=-2(x-8)

Step-by-step explanation:

first we need to calculate the slope

y2-y1/x2-x1

-6+4/7-8

-2/1

The slope is -2

Nows lets find the y intercept using

y-y1=m(x-x1)

y-4=-2(x-8)

y-4=-2x+16

+4 +4

y=-2x+20

Y intercept is 20

Answer:

I didn't know what form you wanted the line in.

Slope-intercept form: y=2x-20

Standard form:  2x-y=20

Point-slope form: y+4=2(x-8) or y+6=2(x-7)

You gave the points (8,-4) and (7,-6).

That last point was (7,-6) right?  I seen (7-6) and just thought you probably meant (7,-6.

Step-by-step explanation:

Equation of a line in slope-intercept form is y=mx+b where m is the slope and b is the y-intercept.

To find the slope: I'm going to line up the points vertically and subtract them vertically, then put 2nd difference over 1st difference.

I feel like some people like this more than the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] or [tex]\frac{y_1-y_2}{x_1-x_2}[/tex]. It is the same thing just a different way to organize things.

So let's do the finding of the slope:

( 8  ,  -4)

-( 7  ,  -6)

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

 1        2

So the slope is 2/1=2.

So we have m=2.

Let's input into our equation y=2x+b.

We need to find the y-intercept.  We could do that by using a point on the line. We get to choose between (8,-4) or (7,-6).  It does not matter.

y=2x+b with (8,-4)

-4=2(8)+b

-4=16+b

Subtract 16 on both sides:

-4-16=b

-20=b

So the y-intercept is -20.

The equation is y=2x+-20 or y=2x-20 (your pick-same thing).

Now let's also put it in standard form which is ax+by=c where it is preferable to have a,b, and c as integers. (Integers are {...,-3,-2,-1,0,1,2,3,...}.)

y=2x-20

Subtract 2x on both sides:

-2x+y=-20

This is in ax+by=c form.

You could multiply both sides by -1:

2x-y=20.

This is still in standard form.

Let's also go for point-slope form which is y-y1=m(x-x1) where (x1,y1) is a given point on the line and m is the slope.

We already have the slope is 2.

We have two points to choose from.  Choose one and go with it. Let's choose (x1,y1)=(8,-4).

y-(-4)=2(x-8)

or

y+4=2(x-8)

Now if you did go with the other point (x1,y1)=(7,-6) it would be:

y-(-6)=2(x-7)

y+6=2(x-7)

You are probably wondering how those are the same lines.  Let's confirm.  Solve both of them for y.

y+4=2(x-8)

Distribute 2:

y+4=2x-16

Subtract 4 on both sides:

y=2x-16-4

Simplify:

y=2x-20

Now the other line:

y+6=2(x-7)

Distribute 2:

y+6=2x-14

Subtract 6 on both sides:

y=2x-14-6

y=2x-20

Answer:

Step-by-step explanation:

We have given:

-2x+y=4     ---------equation1

3x+4y=49 ---------equation 2

We will solve the 1st equation for y and substitute the value into the 2nd equation.

-2x+y=4     ---------equation1

Move the values to the R.H.S except y

y = 2x+4

Now substitute the value of y in  2nd equation:

3x+4y=49

3x+4(2x+4)=49

3x+8x+16=49

Combine the like terms:

3x+8x=49-16

11x=33

Now divide both the sides by 11

11x/11 = 33/11

x= 3

Now substitute the value of x in any of the above equations: We will substitute the value in equation 1:

-2x+y=4

-2(3)+y=4

-6+y=4

Combine the constants:

y=4+6

y = 10

Thus the solution set of (x,y) is {(3,10)}....

Answer:

Option C (207.5 feet)

Step-by-step explanation:

The questions which involve calculating the angles and the sides of a triangle either require the sine rule or the cosine rule. In this question, the two sides that are given are adjacent to each other the given angle is the included angle. This means that the angle is formed by the intersection of the lines. Therefore, cosine rule will be used to calculate the length of b. The cosine rule is:

x^2 = y^2 + z^2 - 2*y*z*cos(X).

Let x be the distance covered by the outfielder's throw, let y be the distance between the pitcher's mound and the home plate, let z be the distance covered by the batter's shot, and let X be the mentioned angle.

The question specifies that y=60.5 feet, X=31°, and z=257 feet. Plugging in the values:

x^2 = 60.5^2 + 257^2 - 2(60.5)(257)*cos(31°).

Simplifying gives:

x^2 = 43053.9184501 feet.

Taking square root on the both sides gives x = 207.5 feet (rounded to the one decimal place).

This means that the Option C is the correct choice!!!

[tex]\bf \begin{array}{ccll} vinegar&oil\\ \cline{1-2} 2&5\\ 9&x \end{array}\implies \cfrac{2}{9}=\cfrac{5}{x}\implies 2x=45\implies x=\cfrac{45}{2}\implies x=22\frac{1}{2}[/tex]

22.5 ounces of oil should be mixed with 9 ounces of vinegar

An equation is an expression that shows the relationship between two or more variables and numbers.

Given that:

2 part vinegar 5 part oil.

Let y represent the amount of oil to be mixed with 9 ounces of vinegar.

y = (5/2) * 9 = 22.5 ounces

22.5 ounces of oil should be mixed with 9 ounces of vinegar

Find out more on Equation at: https://brainly.com/question/2972832

Answer:

Step-by-step explanation:

f(x) = 1/4 x²+bx+10

the derivate is : f'(x) = 1/2 x +b

you have : f'(6)=0

1/2 (6)+b=0

3+b =0

b = -3

so f(x) = 1/4 x²-3x+10.......f(6) =1/4(6)² -3(6)+10 =9-18+10 =1

f(x) = 1/4(x-6)²+1... the vertex form

Value of 'b' from the quadratic function will be (-3).

If the quadratic equation for the parabolic path has been given as,

Axis of symmetry of the parabola will be given by,

Axis of symmetry = [tex]-\frac{b}{2a}[/tex]

  Quadratic function given in the question → [tex]f(x)=\frac{1}{4}x^2+bx+10[/tex]

Compare this equation by [tex]f(x)=ax^2+bx+c[/tex]

[tex]a=\frac{1}{4},b=b,c=10[/tex]

Axis of symmetry of the parabola will be,

Axis of symmetry = [tex]-\frac{b}{2(0.25)}[/tex]

                             = [tex]-2b[/tex]

Axis of symmetry has been given as x = 6,

[tex]6=-2b[/tex]

[tex]b=-3[/tex]

    Therefore, value of b will be (-3).

Learn more about the quadratic function here,

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Answer:

3x^2-4x+20/x^2-5x .

Step-by-step explanation:

The given rational expression is:

3x/x-5 - 4/x

Hence to find the difference of the rational numbers we have to take the L.C.M of the denominators:

Thus the L.C.M of x-5 and x is (x-5)(x) and then solve for the numerator:

x(3x) - 4(x-5)/(x-5)(x)

Now solve the numerator and denominator:

3x^2-4x+20/x^2-5x

Thus the answer is 3x^2-4x+20/x^2-5x ....

Answer:

3x^2-4x+20

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

   x(x-5)

Step-by-step explanation:

Answer:

When studying a random sample of the population, you are studying one of many (generally the same) flying squirrels that live. This small selection represents the whole population, (because as said before, they are generally the same). In this way, you can assume that the small section that you picked is going to represent the entire flying squirrel population.

Answer:

Riding is independent variable and cost is dependent....

Step-by-step explanation:

According to the given statement Jewels has $6.75 to ride the ferry around Connecticut. It will cost her $0.45 every time she rides.

It means that if she rides a ferry, she pays

If she does not ride the ferry she won't pay

This shows that the paying depends on riding.

Thus riding is independent variable and cost is dependent....

Answer: the number of rides is the independent variable, and the total cost is the dependent variable.

Answer:

The answer is $0.32.

Step-by-step explanation:

You achieve this answer by taking the total price ($7.68) divided by the number of units for that price (24 cans).  Therefore:

[tex]\frac{7.68}{24} = 0.32[/tex]

Answer:

( 6x + 11 ) ( x - 5 )

Step-by-step explanation:

Let

6x2 - 19x - 55 = 0

6x2 - (30-11)x - 55 = 0

6x2 - 30x + 11x - 55 = 0

6x ( x - 5 ) + 11 ( x - 5 ) = 0

( 6x + 11 ) ( x - 5 ) = 0

Therefore, ( 6x + 11 ) ( x - 5 ) = 6x2 - 19x - 55

Final answer:

The length of line segment PR is the sum of the lengths of PQ and QR, which is 14 units.

Explanation:

The question asks us to determine the length of line segment PR given that point Q is on line segment PR, QR=11 units, and PQ=3 units. To find the length of PR, we simply add the lengths of PQ and QR together, since Q lies on line segment PR meaning PQ and QR are consecutive segments.

Therefore, the length of PR is PQ + QR = 3 + 11, which equals 14 units.

Answer:

r ≤ 29, r-5

The sale price can be compared with the regular price, r-5 ≤ 24

Step-by-step explanation:

Amount to spend = $24

Regular price = r

Sale = $5

Sale Price = r-5

The regular price will be $5, at the max, more than the amount Roopesh has to spend.

The sale price will be $24 or less than that for Roopesh to afford.

Inequality for regular price:

r-5 ≤ 24

r ≤ 29

So, the product Roopesh can afford is $29 or less than that.

What is the unknown? r ≤ 29

Following expression can represent the sale price:

Sale price = r-5  

The sale price can be compared with the regular price with the following:

Inequality representing the situation: r-5 ≤ 24

Answer:

the price is $160000

Step-by-step explanation:

0.22x = 35200

x=160000

Answer:

Step-by-step explanation:

[tex]f(x)=(x^2+6x+8)(x^2+6x+13)\\\\f(x)=0\iff(x^2+6x+8)(x^2+6x+13)=0\iff\\x^2+6x+8=0\vee x^2+6x+13=0\\\\x^2+6x+8=0\\x^2+4x+2x+8=0\\x(x+4)+2(x+4)=0\\(x+4)(x+2)=0\iff x+4=0\ \vee\ x+2=0\\x+4=0\qquad\text{subtract 4 from both sides}\\\boxed{x=-4}\\x+2=0\qquad\text{subtract 2 from both sides}\\\boxed{x=-2}\\\\x^2+6x+13=0\qquad\text{subtract 13 from both sides}\\x^2+6x=-13\\x^2+2(x)(3)=-13\qquad\text{add}\ 3^2=9\ \text{to both sides}\\x^2+2(x)(3)+3^2=-13+9\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\(x+3)^2=-4<0\qquad\bold{no\ solution}[/tex]

Answer:

c (–2, –4, –3 + 2i, –3 – 2i) on edg2021

Step-by-step explanation:

Answer:

241,389.613

Step-by-step explanation:

The first 1 is in the hundred millons place​.

Answer:

3

Step-by-step explanation:

Answer:

54, 72, and 90

To select a number between 49 and 95 that is a multiple of 6, 9, and 18, Salma can choose either 54 or 90.

To find a number between 49 and 95 that is a multiple of 6, 9, and 18, we need to find the common multiples of these numbers within the given range:

Therefore, Salma can choose either 54 or 90 as the numbers between 49 and 95 that are multiples of 6, 9, and 18.

Answer:

is there an option for no solution? because when I solved there were no possible rational solutions

Step-by-step explanation:

Answer:

This was the correct answer choice in my case.

Step-by-step explanation:

Hope this helps!

Answer:

( − ∞ , ∞ )  { x | x ∈ R }

Step-by-step explanation:

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Answer:

We have the following function:

x g(x)

−2 2

−1 −3

0 2

1 17

And the following statements:

(A)The function is increasing from x = −2 to x = −1.

(B)The function is increasing from x = 0 to x = 1.

(C)The function is decreasing from x = −1 to x = 0.

(D)The function is decreasing from x = 0 to x = 1.

Option A is false. Because from x=-2 to x=-1, the function is degresing given that for x=-2, g(x) = 2 and for x=-1 the value of g(x) decreases.

Option C is false. Because from x=-1 to x=0 the value of g(x) goes from -3 to 2. Therefore it increases.

Option D is false. from x=0 to x=1 the value of g(x) goes from 2 to 17. Therefore it increases.

The correct answer is OPTION B.

Answer:

12 children

Step-by-step explanation:

you would just find the GCF (greatest common factor) of these 2 numbers, which is 12

so each child would get 3 prizes and 2 balloons

Answer:

2 more hours

Step-by-step explanation:

6/75 = x/100

Answer:

12.5% is left which is 3 more hours

Step-by-step explanation:

Hope this helped out! :3

Answer:

I don't know what your choices are but they are alternate interior angles.  Alternate interior angles are congruent.

Step-by-step explanation:

Alternate interior angles are the angles at the different intersection along the transversal that are on opposite sides of the transversal and inside the parallel lines.

This is exactly what you have here, alternate interior angles are congruent when the the lines are parallel.

There are also alternate exterior.  These are at the different intersections along the trasversal that are opposite sides of the transversal but outside the parallel lines.

There is also corresponding angles.  I like to call these the copy and paste angles because when you copy one intersection and paste it over the other, the corresponding angles will be the ones that lay on top of each other.

There are also same-side interior angles. There are inside and on the same side of the transveral at the different intersections. These angles add up to be 180 degrees when the transversal cuts through parallel lines.

Answer:

The answer is ---> x = y

Step-by-step explanation:

Here are the answer choices.

I got it correct, so this was the answer

Answer:

279+1.80s

Step-by-step explanation:

If we add the material cost to the labor cost, this would give us the manufacturing cost.

M(s)+L(s)=(225+0.65s)+(54+1.15s)

We will not combine like terms.

(M+L)s=225+54+0.65s+1.15s

Simplify.

(M+L)s=279+1.80s

Final answer:

The manufacturing cost per scissors can be calculated by adding the material cost and the labor cost for producing a single scissors. The correct expression for the manufacturing cost per scissors is 279 + 1.80s.

Explanation:

The manufacturing cost per scissors can be calculated by adding the material cost and the labor cost for producing a single scissors.

The material cost is represented by the function M(S) + 225 + 0.65s, and the labor cost is represented by the function L(S) = 54 + 1.15s.

To calculate the manufacturing cost per scissors, we add the two functions together:

M(S) + 225 + 0.65s + L(S) = (M(S) + L(S)) + 225 + 0.65s = (225 + 54) + (0.65 + 1.15)s = 279 + 1.80s.

Therefore, the correct expression that represents the manufacturing cost per scissors is 279 + 1.80s.

Answer:

(Choice A)

-4(3e + 4)

Step-by-step explanation:

This is the only answer that makes sense:

-7 - 12e - 9 [Distribute the 3 amongst all the other terms in parentheses]

Then you combine like-terms:

-16 - 12e

Finally, you factor out the Greatest Common Factor [GCF]:

-4[4 + 3e]

12e is NOT an option, so you are left with (Choice A).

I am joyous to assist you anytime.

Answer:

C. Left-handed: 48, Right-handed: 504

D. Left-handed: 30, Right-handed: 315

Step-by-step explanation:

We are given that there are 58 left-handed students and 609 right-handed students at East Middle School and these numbers of students are proportional to the number of left and right handed students at East Middle School.

Given the above information, we are are to determine which two options could be the the numbers of left-handed and right-handed students at West Junior High.

Ratio of right handed to left handed students at East Middle School = [tex]\frac{609}{58} = 10.5[/tex]

Checking for ratios of the given options:

A. [tex]\frac{483}{42} =11.5[/tex]

B. [tex]\frac{378}{28} =13.5[/tex]

C. [tex]\frac{504}{48} =10.5[/tex]

D. [tex]\frac{560}{56} =10[/tex]

E. [tex]\frac{315}{30} =10.5[/tex]

Therefore, the possible numbers of left-handed and right-handed students at West Junior High could be C. Left-handed: 48, Right-handed: 504 and D. Left-handed: 30, Right-handed: 315.

Answer:

OPTION C.

OPTION E.

Step-by-step explanation:

A relationship is proportional if the ratio between the variables is always the same.

In this case we know that the numbers of left- and right-handed students at West Junior High are proportional to the numbers at East Middle School and there are 58 left-handed students and 609 right-handed students at  East Middle School. Therefore, the ratio is:

[tex]ratio=\frac{58}{609}=\frac{2}{21}[/tex]

So, we can check the ratio in each option to know which has ratio [tex]\frac{2}{21}[/tex]:

OPTION A:

[tex]\frac{42}{483}=\frac{2}{23}[/tex]

OPTION B:

[tex]\frac{28}{378}=\frac{2}{27}[/tex]

OPTION C:

[tex]\frac{48}{504}=\frac{2}{21}[/tex]

OPTION D:

[tex]\frac{56}{560}=\frac{1}{10}[/tex]

OPTION E:

[tex]\frac{30}{315}=\frac{2}{21}[/tex]

Therefore, you can observe that the numbers of left-handed and right-handed students at West Junior High could be:

[tex]Left-handed: 48\\Right-handed: 504\\\\\\Left-handed: 30\\Right-handed: 315[/tex]

2 because everything is multiplied by 2 so the scale factor is two

Answer:

It shifts left two units, and up seven units.

Step-by-step explanation:

In your translation, it says X-2, this represents the shift to the left two times, next it says Y+7, this represents the upwards shift seven units. Basically, you're taking your beginning X and Y values, and changing them according to the right of the arrow.

Answer:

Translation of 2 units to the left and 7 units up.

Step-by-step explanation:

The general rule of translation is

[tex](x,y)\rightarrow (x+a,y+b)[/tex]              .... (1)

If a>0, then figure translate a units right and if a<0, then figure translate a units left.

If b>0, then figure translate b units up and if b<0, then figure translate b units down

The given rule of translation is

[tex](x,y)\rightarrow (x-2,y+7)[/tex]             .... (2)

On comparing (1) and (2), we get

a = -2 < 0, so figure translate 2 units left.

b = 7 > 0, so figure translate 7 units up.

Therefore, the given rule describes the translation of 2 units to the left and 7 units up.

Answer:

[tex]y = - \frac{1}{3}x[/tex]

Step-by-step explanation:

The equation of a direct variation is generally written as:

[tex]y = mx[/tex]

Where m is the slope of the equation of the direct variation line.

We want a direct variation equation that contains (6,-2).

We substitute the x=6 and y=-2 to find m.

[tex] - 2 = 6m[/tex]

Divide both sides by 6.

[tex] \frac{ - 2}{ 6} = \frac{6m}{ 6} [/tex]

[tex] - \frac{1}{3} = m[/tex]

The required equation is

[tex]y = - \frac{1}{3}x[/tex]

The equation of the direct variation that includes the point (6,-2) is y = -1/3x, calculated by substituting the point into the formula y = kx and solving for the constant of variation k.

The subject of this question is mathematical, focusing on direct variation - a specific type of relationship between two variables where one variable is a constant multiple of the other. In this case, the student is given the point (6,-2) on the graph of this relationship. With direct variation, the formula is typically written as y = kx, where k is the constant of variation.

For this particular question, we use the point (6,-2) and substitute x = 6 and y = -2 into the formula to find the constant of variation, i.e. -2 = k * 6. Solving for k, we get k = -2/6 = -1/3. Plugging this k back into y = kx gives us our equation of the direct variation: y = -1/3x.

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