If Dr. I.M. smart mixes 30mL of acid into 50 ml of a 20% acid solution, what is the quantity and concentration of the final solution?
the final solution is ______ mL with ______ % concentration

thank you so much for the help!

Answer: The answer for 9 is 50 miles per hour and the one who drove farthest is is ben because at 5 hours he drove already 250 miles. And for number 9 according to the table she is driving 15 miles per hour because on the bottom it always adds up by 15 miles.

Step-by-step explanation: So first to figure out 9 I used y2-y1/x2-x1 to figure out the rate of change and got 50 miles per hour and the point I used were (5,100) and (5,250). Then According to Ben's graph it shows that he drove 250 miles at 5 hours while sally was at 100 miles for 5 hours. So Ben drove the farthest. Then finally for number 9 I concluded that sally is driving 15 miles per hour because distance always adds up by 15 miles.

Hope this Helps :D

Step-by-step explanation:

f(x) = x³ + 2x² - 3x - 6

f(-2) = (-2)³ + 2(-2)² - 3(-2) - 6

= -8 + 8 + 6 - 6

= 0

The scale factor of the graph image shown is 1.5, using the letters with prime as the original image

Scale factors are used to increase or decrease image. The situation of increment is usually called magnifying.

For the given graph the values with prime is assumed to be the the original shape while the the values without prime represent the factored image.

Taking a point of reference say s' and s. The coordinates of s' and the coordinates of s are ( 2, 4 ) ( 3, 6 ) respectively.

solving for the factor, assuming the factor is k

x axis

2k = 3

k = 3/2 = 1.5

y axis

4k = 6

k = 6/4 = 1.5

This factor works for other coordinates hence we say that the scale factor is 1.5

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Answer:

53.13

Step-by-step explanation:

[tex]\tan \alpha=\frac{8}{6} \\ \\ \alpha=\arctan(8/6) \\ \\ \approx 53.13^{\circ}[/tex]

Answer:

53.13

Step-by-step explanation:

correct

The Coordinates of the point D will be (-3, 3) and point E will be (0, 5) and point F will be (2, -2).

According to the statement

We have to find that the points of the coordinates.

So, For this purpose, we know that the

Coordinates are a set of values which helps to show the exact position of a point in the coordinate plane.

From the given information:

the coordinates of D, E, and F after a reflection over the y axis? Plot these points on the grid, and label them D′, E′ and F′.

Then

Coordinates of a point is given by (x,y)

And

Here, x represents the horizontal distance of the point from origin (0,0) and y represents the vertical distance of the point from origin.

Let's take an example of point D,

Horizontal distance of point D from origin x =-3 and vertical distance from origin y =3.

Then

Coordinates of the point D will be (-3, 3).

Coordinates of the point F will be (2, -2).

Coordinates of the point E will be (0, 5).

For more details please see the image below.

So, The Coordinates of the point D will be (-3, 3) and point E will be (0, 5) and point F will be (2, -2).

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The interest earned in next 90 days is  $390.6.

The amount of money earned, in compound interest, after t years, is given by:

A= P[tex]( 1+ r/n)^{(nt)}[/tex]

Given:

A = Amount

P = Principal = $28,214.35

r = rate = 0.055

n = number of periods=365

t = time in years=3/12= 1/4

Using compound interest formula

A= P[tex]( 1+ r/n)^{(nt)}[/tex]

A(90)=  28,604.95[tex]( 1 + 0.055/365)^{(365 * 1/4)}[/tex]

A(90)=28241.35 [tex](1.00015)^{(91.25)}[/tex]

A(90)=  $28,604.95

So, the interest earned in next 90 days is

=28,604.95 - 28,604.95

= $390.6

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Answer:

yes

Step-by-step explanation:

you can classify people into categories by name, state, and age. Hope this helps!

Step-by-step explanation:

and ... ? what do we need to do ?

I guess finding the number of quarters and dimes.

x = number of quarters

y = number of dimes

x + y = 185

x = 185 - y

0.25×x + 0.1×y = 26.75

after all, a quarter has a value of $0.25, and a dime of $0.10.

let's use the identity of the first equation in the second equation :

0.25×(185 - y) + 0.1×y = 26.75

to make is simpler to see let's multiply the whole thing by 100 :

25×(185 - y) + 10y = 2675

4625 - 25y + 10y = 2675

4625 - 15y = 2675

1950 = 15y

y = 130

x = 185 - y = 185 - 130 = 55

there are 55 quarters and 130 dimes in the bag.

The equation of the line in standard form is 12x-2y=13.

Given that line that is the perpendicular bisector of the segment whose endpoints are R(-1, 6) and S(5, 5).

R≡(-1,6) and S≡(5,5)

The perpendicular bisector of the line segment joining R and S will pass through the midpoint M.

coordinate of M is =((-1+5)/2,(6+5)/2)

coordinate of M is=(2,11/2)

Slope of the line joining R and S is

m₁=(6-5)/(-1-5)

m₁=-1/6

We know that for two perpendicular lines having slope m₁ and m₂,

m₁m₂=-1

Here, m₁=-1/6

Let m₂ be the slope of the perpendicular bisector

(-1/6)m₂=-1

m₂=6

Equation of the perpendicular bisector will be,

(y-yₙ)/(x-xₙ)=m₂   [(xₙ,yₙ) is the coordinate of M]

(y-11/2)/(x-2)=6

(2y-11)/2=6(x-2)

2y-11=12x-24

12x-2y=13

Hence, the equation of the given line in standard form when ine that is perpendicular bisector of the segment whose endpoints are R(-1, 6) and S(5, 5) is 12x-2y=13.

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Answer: 1/6

Step-by-step explanation:

The value of g(4) is 7 when given function is g(x)= 4x-9 .

By considering the given function

g(x)= 4x-9

g(4)=4(4)-9

g(4)=16-9

g(4)=7

A function in mathematics that goes from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are referred to as the function's domain and codomain, respectively.

a mathematical expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). Functions are everywhere in mathematics, and they are essential for constructing physical relationships in the sciences.

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The solution to the given inequality -3(x - 2) ≤ 1/3 is x ≤ 17/9

-3(x - 2) ≤ 1/3

-3x + 6 ≤ 1/3

-3x ≤ 1/3 - 6

-3x ≤ (1-18) / 3

-3x ≤ -17/3

x ≤ -17 /3 ÷ -3

x ≤ -17/3 × 1/-3

x ≤ -17/-9

x ≤ 17/9

A verbal statement describing the solution to the inequality is x is less than equal to 17 over 9

Verifying the solution of the inequality:

-3(x - 2) ≤ 1/3

-3x + 6 ≤ 1/3

-3(17/9) + 6 ≤ 1/3

-51/9 + 6 ≤ 1/3

(-51+54) / 9 ≤ 1/3

3/9 ≤ 1/3

1/3 ≤ 1/3

Therefore, the -3(x - 2) ≤ 1/3 to the inequality -3(x - 2) ≤ 1/3 in verbal statement is x is less than equal to 17 over 9.

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Based on the given equation, the solution to x is -32.

The formula given is:

x / -2² = 4 (-2)

To solve for x, solve for the exponents:

x / -2² = 4 (-2)

x / 4 = 4 (-2)

Then solve the brackets:

x / 4 = 4 (-2)

x / 4 = -8

Then solve for x:

x / 4 = -8

x = -8 x 4

x = -32

In conclusion, based on the equation of x given, the value of x can be found to be -32.

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The expression y3¹⁰ - 10y³ is a binomial polynomial.

In the given situation y3¹⁰ - 10y³ is a binomial polynomial as there are two terms in the expression.

Therefore, the expression y3¹⁰ - 10y³ is a binomial polynomial.

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Answer:

a) 28

Step-by-step explanation:

Given information,

→ w = 5

→ x = 9

→ y = 2

The given expression is,

→ x + 20 - 1

Let's solve the expression,

→ x + 20 - 1

→ 9 + 20 - 1

→ 29 - 1

→ 28

Hence, the answer is 28.

The table of the function y = (1/2)x + 3 is when (x = 4, y = 5), (x = 6, y = 6),

( x = 9, y = 15/2), ( x = 11, y = 17/3).

An expression represents that two different forms of numerical and variables are the same.

Given an expression y = (1/2)x + 3 we have to determine the range of this function corresponding to the domain { 4, 6, 9, 11 }.

For x = 4,

y = (1/2).4 + 3.

y = 2 + 3.

y = 5.

For x = 6,

y = (1/2).6 + 3.

y = 3 + 3.

y = 6.

For x = 9,

y = (1/2).9 + 3.

y = 9/2 + 3.

y = 15/2.

For x = 11,

y = (1/2).11 + 3.

y = 11/2 + 3.

y = 17/3.

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Strategy 2 will generate higher expected profit and the company should invest k 8000 for market research to determine with certainty whether demand will be strong or weak.

                                       →Strong demand (P= 0.6) k12000 outflow

                                   →|

                                       →Weak demand (P=0.4) k30000 outflow

New product launch   ║

                                       →Strong demand (P= 0.6) k80000 outflow

                                    →|

                                       →Weak demand (P=0.4) k20000 outflow

Expected market value in strategy 1 is

= - 120000 x 0.6 + (-30000) x 0.4

= -k 84000

Expected market value in strategy 2 is

= - 80000 x 0.6 + 20000) x 0.4

= k 56000

Therefore strategy 2 will generate higher expected profit

In strategy 2

Expected value in strong demand is 80000 x 0.6 = k 48000

Expected value of weak demand is 20000 x 0.4 = k 8000

Thus the company should invest k 8000 for market research to determine with certainty whether demand will be strong or weak

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The net pay of the individual after having deducted total deductions is $166.54

How do we determine the amount of each deduction?

The amount of each deduction is based on the gross pay of $351.00, as a result, we simply multiply the percentage of deduction by the gross pay to determine the dollar amount of each deduction.

the gross pay=$351

federal tax (assuming 20% of gross earnings)=$351*20%=$70.20

state tax (assuming 6% of gross earnings)=$351*6%=$21.06

social security deductions (assuming 7.05% of gross earnings)=$351*7.05%=$24.75

group health insurance (assuming 13% of gross earnings)=$351*13%=$45.63

pension deduction (assuming 6.5% of gross earnings)=$351*6.5%=$22.82

total deductions=$70.20+$21.06+$24.75+$45.63+$22.82

total deductions=$184.46

net pay=$351-$184.46

net pay=$166.54

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The Three solutions for the linear equation are: (0, -0.333), (1,1) and (3, 3.667).

According to the statement

We have to find that the solution of the linear equation.

So, For this purpose, we know that the

A linear equation is defined as an equation that is written in the form of Ax+By=C.

From the given information:

The three solutions for the linear equation 4x-3y = 1.

Then

The given equation is :

4x-3y = 1

Slope intercept form is

y = 4/3x - 1/3.

Then

For x = 0, we have that

y = 4/3x - 1/3.

y = 4/3(0) - 1/3.

y =  - 1/3.

y = -0.334

Then

For x = 1, we have that

y = 4/3x - 1/3.

y = 4/3(1) - 1/3.

y =  3/3.

y = 1.

Then

For x = 3, we have that

y = 4/3x - 1/3.

y = 4/3(3) - 1/3.

y =  11/3.

y = 3.67.

So, The Three solutions for the linear equation are: (0, -0.333), (1,1) and (3, 3.667).

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Work Shown:

[tex](x_1,y_1) = (7,-6) \text{ and } (x_2,y_2) = (6,-6)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-6 - (-6)}{6 - 7}\\\\m = \frac{-6 + 6}{6 - 7}\\\\m = \frac{0}{-1}\\\\m = 0\\\\[/tex]

Lines with slope of 0 are always horizontal. The y coordinates are the same value.

The volume of a cuboid or box is the multiplication of length, width, and height by that expression the width of the given cuboid box is 10 inches.

Volume is the scalar quantity of any object that specified occupied space in 3D.

For example, the space in our room is referred to as volume.

The volume of cuboid = length × height × width.

Given that,

Height (H) = 9 inches.

The length is three inches more than the width.

So,

L = 3 + W

Now,

Volume of box = 1170 inches³

Now,

The volume of the cuboid is given as

V = L×W×H

1170 = (3 + W) × W×9

W² + 3W - 130 = 0

W² + 13W - 10W - 130 = 0

W(W + 13) - 10(W + 13) = 0

(W + 13)(W - 10) = 0

W = 10,-13 since the length can never be negative so 10 inches will be right.

Hence "The width of the given cuboid box is 10 inches".

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Answer:

12, 24, 36, 48, 60, 72, 84, 96

Step-by-step explanation:

The smallest natural number that is a common multiple of 3 and 4 is 12. The answer is all multiples of 12 less than 100.

Answer: 12, 24, 36, 48, 60, 72, 84, 96

The relation can be written as a set of ordered pairs as: a. {(–3, 3), (0, 0), (2, –2)}.

A relation, in maths, is defined as a relationship between two variables, x and y, which are linked to each other.

The x-value and the y-value of each set of points in a relation is written as (x, y).

Thus, in the given relation that is represented by the graph below, we have the following set of ordered pairs representing each point on the graph: (–3, 3), (0, 0), and (2, –2).

Therefore, the relation can be written as a set of ordered pairs as: a. {(–3, 3), (0, 0), (2, –2)}.

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According to this formula, the time when the world population reach 8 billion is D. 2026.

From the information given, the capita growth rate of the world population continues to be what it was in the year 2016, the world population t years after July 1, 2016, will be 7.4 ✕ 1.011t billion.

Therefore, the year when the world population reach 8 billion will be:

80 billion = 7.4 × 1.011t billion

1.011t = 80/7.4

1.011t = 10.8

t = 10.8/1.011

t = 10

Therefore, the number of years will be added. This will be:

= 2016 + 10

= 2026

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Answer:

Step-by-step explanation:

Background: f(x) is the same thing as y but represents the value of x in parentheses.

Ej: f(2)=3x+2, this solution would be "8" because the value in the parentheses represents the value of x. (if the parentheses have an "x" then the value of x is unknown.

1.

f(x)=5x+8   g(x)=(x-8)/5

f(g(x))=?, 5((x-8)/5)+8

f(g(x))=x-8+8

f(g(x))=x

g(f(x))=5x+8-8/5

g(f(x))=5x/5

g(f(x))=x

g(f(x))=f(g(x)) because they both equal x proving they are inverses

Sorry, I don't have time to answer the rest of the steps (I will give the answers to check the work).

All of them are x=x because they are all inverse functions.

The measurement of the angle X is 60 degrees.

Angles L and X are the highest angles according to the diagram. They line up to have an angle of L = X = 60 degrees.

However, because the figures in a diagram could be oddly arranged, you shouldn't rely exclusively on it. A more effective strategy is to consider the letter combinations JKLMN and VWXYZ.

Observe how the third letters of JKLMN and VWXYZ, respectively, are L and X. This indicates that the letters are congruent angles and couple up (since the polygons are similar). Thus, this is a non-visual method of understanding how angle L = angle X = 60.

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Step-by-step explanation:

0.25(x+10) = 2+0.5(x-1)

0.25 * x + 0.25 * 10 = 2.05 * x - 2.05 * 1

0.25x + 2.5 = 2.05x - 2.05

0.25x - 2.05x = -2.05 - 2.5

-1.8x = - 4.55

x = -4.55/-1.8

x = 2.53777777778

Answer:

x= 8

Step-by-step explanation:

Sum of the two angles = 90

12x - 30 + 3x = 90

15x -30 = 90

15x = 90 + 30

15x = 120

x = 120/15 = 8

Answer:

Rectangular Cross Section Surface