Select the correct answer from each drop-down menu.

A researcher is examining the claims made by a water softener salt manufacturer. He performs an experiment using water from a variety of sources. For each water source, he has a sample with no treatment and a sample treated with the recommended amount of the water softener salt.

He then tests each sample to measure the softness and compares the results, determining that the claims made by the manufacturer are true.

The conclusion drawn from the study is _____ because the sample is _____. In this instance, an ______study was performed.

Answer:

Step-by-step explanation:

The attached graph shows the graph opens downward, so the vertex at (-2, 6) is a maximum. The y-intercept is the constant, +2.

The range is the vertical extent of the function. Its upper limit is the maximum value of the function (6), and its lower limit is negative infinity.

  The range is {y l y ≤ 6}.

The graph opens downward, so it is increasing to the left of its maximum value, and decreasing to the right of its maximum. The x-coordinate of the maximum (-2) defines the upper limit of the increasing interval.

  The function is increasing over the interval (-∞, -2).

The y-intercept of the graph is where it crosses the y-axis. The value of x is zero there, so the value of the function is the value of its constant, +2.

  The function has a positive y-intercept.

The two factors multiplied together to make a trinomial is (x-1)(3x-2).

Given equation is 3x²-5x+2.

An algebraic equation which of the second degree in x is known as quadratic equation. The quadratic equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

In the given equation,

Multiply the first coefficient 3 with the last coefficient 2  so we get 2×3=6

Use any two numbers which on multiply give 6 and on adding or subtracting give -5.

Such two numbers are -2 and -3

On multiplying, (-3)×(-2)=6

On Adding, -3-2=-5

So, break -5x into -3x and -2x and we get

3x²-3x-2x+2

Taking out 3x common from the first two terms and -2 from the last two terms as

3x(x-1)-2(x-1)

Taking out the common term (x-1) as common and get

(x-1)(3x-2)

Hence, the two factors of the equation 3x²-5x+2 that can be multiplied together to make this trinomial is (x-1)(3x-2).

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Answer:

2.75 is the median

Answer:

1.25 is the median

Step-by-step explanation:

it is the middle of the number sequence.

to find the median, place the numbers in value order and find the middle

since there is an even amount of numbers, add 2.5 and 0 (the two middle numbers) and divide them by two

Emil starts the day with 16 liters of lemonade if he is left with 4 liters by the end of the day. Computed using the fractional values given.

Let the initial quantity of lemonade with Emil be x liters.

Quantity sold by Emil in the morning = Half of his lemonade = (1/2)x liters, that is half fraction of x.

Quantity left with Emil = x - x/2 = x/2 liters, that is half fraction of x.

Quantity sold by Emil at lunchtime = Quarter of what was left = (1/4)(x/2) liters = x/8 liters, that is the one-eight fraction of x.

Quantity left with Emil = x/2 - x/8 = 3x/8 liters, that is the three-eight fraction of x.

Quantity sold by Emil in the afternoon = One-third of what was left = (1/3)(3x/8) liters = x/8 liters, that is the one-eight fraction of x.

Quantity left with Emil = 3x/8 - x/8 = x/4 liters, that is the quarter fraction of x.

Now, we are said that Emil closes for the day with 4 liters remaining.

Therefore, x/4 = 4, or, x = 4*4 = 16 liters.

Therefore, Emil started the day with 16 liters of lemonade.

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Answer:

Original Salary: [tex]5,957.14[/tex]

Increase in 3%: [tex]6,135.85[/tex]

Step-by-step explanation:

So when something increases by x%, the new value is (100+x)% the original value. So 6255, is 105% the original value. This means to find the original value, we have to find the number that has 6255 as 105% of it's value. Whenever you try to find x% of a number, you multiply it by the decimal value of the percentage, which is found by dividing by 100. So to find x%, you do: [tex]o*\frac{x}{100}[/tex] where o = original value, x=percent. In this case the percent is 105%, which when divided by 100 is 1.05. So this gives us the equation: [tex]o*1.05=6255 \implies o = \frac{6255}{1.05} = 5,957.14[/tex]. This is his original salary. You need to do this process, do not make the mistake of subtracting 5% from 6255. This is because 5% of 6255 does not equal the 5% of the original value. 5% of 6255 should be greater than 5% of the original value, since the new value is an increase of 5%. So since we have his original salary, we can calculate the salary increase had it been 3%. to do this we multiply by 1.03 (103% divided by 100). This gives us the equation: [tex]5,957.14*1.03=6,135.85[/tex]

Answer:

factors are (x-1),(x+2),(x+4),(x+3)

Answer:

N=15

Step-by-step explanation:

Answer:

what is the price of an article costing rs 2000 after levying 13 value added tax find it

Answer:

4

Step-by-step explanation:

i dont cap

The solution of the expression [tex]\dfrac{60-48}{6\times 7}[/tex] is [tex]\dfrac{2}{7}[/tex].

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

The expression is solved as,

[tex]\dfrac{60-48}{6\times 7}= \dfrac{12}{42}[/tex]

Solve the fraction [tex]\dfrac{12}{42}[/tex].

[tex]\dfrac{60-48}{6\times 7}= \dfrac{2}{7}[/tex]

Therefore, the solution of the expression [tex]\dfrac{60-48}{6\times 7}[/tex] is [tex]\dfrac{2}{7}[/tex].

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Answer:

B

Step-by-step explanation:

subtract 1/3 from both sides

m< -2 7/12

Answer:

  22

Step-by-step explanation:

The segment addition theorem tells us the whole is the sum of the parts. We can use this to write an equation relating the expressions for segment length.

  OQ = OP +PQ . . . . . segment addition theorem

  4x +2 = (3x -3) +(4x -10) . . . . substitute given expressions

  15 = 3x . . . . . . add 13 -4x to both sides

  5 = x . . . . . . . divide by 3

  OQ = 4x +2 = 4(5) +2 = 22

The length of OQ is 22 units.

Answer:

x = 25, y = 10

Step-by-step explanation:

I'll add a drawing of my own so that it's easier for me to explain, and for you to understand.  

Since line BC and line DE are parallel and line AE is being shared, angle ACB and angle CED will be the same. So the square will also be 3y.

Since line AB and line CD are parallel and line AE is being shared, angle CAB and angle ECD will be the same. So the heart will be 2x.

Now that we figured out two unknown angles, we can see that the two triangles share two angles with the same value. Since angles in a triangle add up to 180 (Added angles in every triangle are the same), the triangle shape (I drew) will be 4x.

We have a few clues to find the value of x and y.

1) 2x + 4x + 3y = 180 (all angles in a triangle add up to 180)

2) 3y + 2x = 180 - 100 (If you look near point C, we can see that 3y + 100 + 2x equals a flat line. A flat line equals 180)

We can use substitution. 3y + 2x can be replaced with 80.

So our new equation will be: 4x = 100

x = 25.

Now we can replace x with 25 in our second clue.

3y + 2(25) = 80

3y + 50 = 80

3y = 30

y = 10.

We can conclude that x = 25, and y = 10

Answer:

x = 25 and y = 10

Step-by-step explanation:

The arrows on the line segments mean the lines are parallel.

Therefore, the diagram shows two similar triangles, which means their interior angles are the same size.  (Refer to the attached diagram).

Interior angles of a triangle sum to 180°:

⇒ 2x + 4x + 3y = 180

⇒ 6x + 3y = 180

⇒ 3(2x + y) = 180

⇒ 2x + y = 60

⇒ 2x = 60 - y

Angles on a straight line sum to 180°:

⇒ 3y + 100 + 2x = 180

⇒ 2x + 3y = 80

⇒ 2x = 80 - 3y

Substitute the first equation into the second equation, and solve for y:

⇒ 60 - y = 80 - 3y

⇒ 60 + 2y = 80

⇒ 2y = 20

⇒ y = 10

Substitute the found value of y into one of the equations and solve for x:

⇒ 2x = 60 - 10

⇒ 2x = 50

⇒ x = 25

Therefore, x = 25 and y = 10.

Answer: W = 113/20

What we know:

Set up equation                                                W + 3/5 = 6 1/4

Expand                                                              W + 3/5 = 6*4+1 /4

Simplify                                                              W + 3/5 = 25/4

Common denominator                                     W + 3*4/5*4 = 25*5 / 4*5

Simplify                                                              W + 12/20 = 125/20

Subtract                                                                   -12/20    -12 /20

Solve                                                                  W = 113/20

Check:

By converting our answers into decimals, we can see if the sides are equal:

113/20 = 5.65

3/5 = 0.6

5.65 + 0.6 = 6.25

Does 6.25 = 6 1/4?

1/4 = 0.25

6 + 0.25 = 6.25

6.25 = 6.25

Therefore, W = 113/20 is the correct answer.

The complete inequality is y < x and y< -x

The expressions are given as:

y[ ]x and y[ ]-x

From the graph, we can see that:

Only the lower regions are shaded

This represents the less than inequality sign

Hence, the complete inequality is y < x and y< -x

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The calculation of 129 ÷ 3.332 rounded to the appropriate number of significant digits is 39.

Given that;

129 ÷ 3.332

First we convert 3.332 to fraction

3.332 = 3.332/1

3.332 = 3.332/1 × 1000/1000 = 3332/1000

3.332 = 833/250

Hence we have;

129 ÷ 833/250

This can be written as

= 129 × 250/833

= 32250/833

= 38.71549 ≈ 39

Therefore, the calculation of 129 ÷ 3.332 rounded to the appropriate number of significant digits is 39.

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Answer:

x^2=ab

Step-by-step explanation:

Please mark as brainlist

Answer:

.

Step-by-step explanation:

Step-by-step explanation:

1. Right angled triangle , scalene triangle

2. isosceles triangle, obtuse angled triangle

3. equilateral triangle

4. right angled triangle, isosceles triangle

5. scalene triangle, obtuse angled triangle

6. scalene triangle, acute angled triangle

Answer:

Step-by-step explanation:

Isabella’s error is  Isabella should have divided the product of 12π and 9 by 3 to get V = 12π(9)/3 option fourth is correct.

It is defined as a three-dimensional shape in which the base is a circular shape and the diameter of the circle decreases as we move from the circular base to the vertex.

[tex]\rm V=\pi r^2\dfrac{h}{3}[/tex]

Isabella equation:

[tex]\rm V = \dfrac{1}{3}(12)^2(9)\pi[/tex]

The area of the base = 12π square cm

[tex]\rm V = \dfrac{12\pi (9 )}{3}[/tex]

Thus, Isabella’s error is  Isabella should have divided the product of 12π and 9 by 3 to get V = 12π(9)/3 option fourth is correct.

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The point J connote that the mixture has more than the expected volume and has the optimal butterfat percentage.

Note that in the question, it was supplied that  Otto intended to make a mixture of 12% butter fat.

Since:

Milk = 2% butter fat

Whipping cream = 30% butter fat.

This implies that  the milk contains the smallest of butter fat and it also implies that Otto would require  a lot more milk than cream, to be able to attain the 12% mixture.

This is known to be when point J is said to meet, and by using that data from point J, Otto require more of milk than the cream to get what he wants.

Therefore, The point J connote that the mixture has more than the expected volume and has the optimal butterfat percentage.

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Answer:

-1

Step-by-step explanation:

Simply plug in (-1) to both equations and add.

Equation 1:

2(-1)^2 = 2

3(-1) = -3

2 + -3 - 1 = -2

Equation 2:

-( - 1) = 1

Add both together:

-2 + 1 = -1

Answer:

The equation is 2x² + 3x - 1 and here f(x) is -1

Putting f(x) = -1.

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

[tex]f(x) = 2 (1) - 3 - 1[/tex]

[tex]f(x) = 2 - 3 - 1[/tex]

[tex]f(x) = - 1 - 1[/tex]

[tex]f(x) = - 2[/tex]

For g(x) put as -1

[tex]g(x) = - ( - 1)[/tex]

[tex]g(x) = 1[/tex]

Last step,

-2 + 1 = -1

So, option ( a) is correct

The probability that the next person chosen will be in the 40-49 or 50-59 age groups is 0.32

The frequency table is added as an attachment

From the attached image, we have:

40 - 49 or 50 - 59 = 6869 + 6323

40 - 49 or 50 - 59 = 13192

The probability that the next person chosen will be in the 40-49 or 50-59 age groups is then calculated as:

P = 13192/41557

Evaluate

P = 0.32

Hence, the probability that the next person chosen will be in the 40-49 or 50-59 age groups is 0.32

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Answer:

DC= 32.3 units

Step-by-step explanation:

Use Pythag theorem to find BC   first

15 ^2 +  BC ^2 = 22^2      then BC = sqrt 259

Then use the Pythagorean Theorem again to find DC

DC^2 = 28^2 + sqrt(259)^2

       DC=32.3

Answer:

$5750

Step-by-step explanation:

For simple interest,

I = prt

115 = p × 0.03 × 8/12

p = 5750

Answer:

f-(g/h) is an algebraic expression of the difference of f and the quotient of g and h.

Step-by-step explanation:

[tex]f - ( \frac{g}{h} )[/tex]

I hope it was helpful for you..m

The requried algebraic expression of English phrase is given as f - g/h.

The algebraic expression consists of constants and variables. eg x, y, z, etc.

the equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

here,
The difference between f and the quotient of g and h.
The difference represents the subtraction of values, and the quotient can be obtained by division of g by h.
So,
Required algebraic expression,
= f - g/h

Thus, the required expression is given as f - g/h.

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Answer:

Step-by-step explanation:

The multiples of 5 and 6 based on the information have been illustrated below.

It should be noted that a multiple is a number that can be divided by another number without a remainder.

Here, the multiples of 5 will be:

5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60.

6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ...

In this case, the multiples of the numbers have been illustrated.

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The answers to the statements that have been made here are:

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Answer:

[tex]C-\frac{1}{3(lnx- \pi)^3}.[/tex]

Step-by-step explanation:

[tex]\int\ {\frac{1}{x(lnx- \pi)^4} } \, dx=\int\ {\frac{d(lnx- \pi)}{(lnx- \pi)^4}} \, dx=-\frac{1}{3(lnx- \pi)^3} +C.[/tex]